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cp2k/tools/maple2f90/pbe.mw
Ole Schütt 792121551a Add directory tools/maple2f90 
svn-origin-rev: 14256
2014-09-08 09:02:21 +00:00

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<Worksheet><Version major="6" minor="1"/><View-Properties><Zoom percentage="100"/></View-Properties><Styles><Layout alignment="left" bullet="none" name="Warning"/><Layout alignment="left" bullet="none" linespacing="0.0" name="Heading 3" spaceabove="0.0" spacebelow="0.0"/><Layout alignment="left" bullet="none" name="Error"/><Layout alignment="left" bullet="none" name="Heading 2" spaceabove="8.0" spacebelow="2.0"/><Layout alignment="left" bullet="none" name="Heading 1" spaceabove="8.0" spacebelow="4.0"/><Layout alignment="left" bullet="none" firstindent="0.0" leftmargin="0.0" linebreak="space" name="Normal" rightmargin="0.0" spaceabove="0.0" spacebelow="0.0"/><Layout alignment="centred" bullet="none" name="Maple Plot"/><Layout alignment="centred" bullet="none" linespacing="0.5" name="Maple Output"/><Font background="[0,0,0]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" name="Maple Input" opaque="false" size="12"/><Font background="[0,0,0]" bold="false" family="Times New Roman" foreground="[0,0,0]" italic="false" name="Text" opaque="false" size="12" underline="false"/><Font background="[0,0,0]" family="Monospaced" foreground="[0,0,255]" name="Warning" opaque="false" readonly="true" size="12"/><Font background="[0,0,0]" family="Monospaced" foreground="[0,0,255]" name="Line Printed Output" opaque="false" readonly="true" size="12"/><Font background="[0,0,0]" bold="true" family="Serif" italic="true" name="Heading 3" opaque="false" size="14"/><Font background="[0,0,0]" bold="true" family="Serif" name="Heading 2" opaque="false" size="16"/><Font background="[0,0,0]" bold="true" family="Serif" name="Heading 1" opaque="false" size="18"/><Font background="[0,0,0]" family="Monospaced" foreground="[255,0,255]" name="Error" opaque="false" readonly="true" size="12"/><Font background="[0,0,0]" family="Times New Roman" foreground="[0,0,255]" name="2D Output" opaque="false" readonly="true" size="12"/></Styles><Group><Input><Text-field layout="Normal" style="Text">The present worksheet contains the formulaes necessary to calculate the PBE functional, and to generate code that calculate it efficently in different languages (fortran for example).</Text-field><Text-field layout="Normal" style="Text">They are distributed under GPL v2 (http://www.gnu.org/copyleft/gpl.html) as part of the CP2K Project.</Text-field><Text-field layout="Normal" style="Text"/><Text-field layout="Normal" style="Text">Fawzi Mohamed</Text-field></Input></Group><Section><Title><Text-field layout="Heading 1" style="Heading 1"> PBE</Text-field></Title><Group><Input><Text-field layout="Normal" style="Text">Reference: John P. Perdew, Kieron Burke, Matthias Ernzerhof, Phys. Rev. Letter, vol. 77, n 18, pp. 3865-3868, 28. oct. (1996)</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sost:=eqs -&gt; subs(seq(eqs[nops(eqs)-i],i=1..(nops(eqs)-1)),rhs(eqs[nops(eqs)])):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">unk:=eqs -&gt; indets(sost(eqs),symbol):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc:=eqs -&gt; indets(eqs,symbol) minus unk(eqs):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc2:=eqs -&gt; indets(map(lhs,eqs),symbol):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">e:='e': m:='m': h_bar:='h_bar': a_0:='a_0':myIF:='myIF':</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">e:=1: m:=1: h_bar:=1: a_0:=h_bar^2 /(m*e^2):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">indice:=proc(el,l) local i,ii,elAtt,el_s;
i:=-1; ii:=0; el_s:=convert(el,string);
for elAtt in l do
ii:=ii+1;
if evalb(el_s=convert(elAtt,string)) then
i:=ii;
end if;
end do;
i;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">indiceDef:=proc(el,l) local i,ii,elAtt;
i:=-1; ii:=0;
for elAtt in l do
ii:=ii+1;
if evalb(el=lhs(elAtt)) then
i:=ii;
end if;
end do;
i;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">definizioni:= eqs -&gt; map(eq -&gt; if type(eq,equation) then lhs(eq); else 0; end if ,eqs):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sameNameSameDef:=proc(eqs1,eqs2) local commonDef,res,d;
commonDef:=convert(definizioni(eqs1),set)intersect convert(definizioni(eqs2),set);
res:=true;
for d in commonDef do
if not evalb(subs(eqs1,d)=subs(eqs2,d)) then;
print("def different for "||d);
res:=false;
end if;
end do;
res;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"># check same name -&gt; same def apart from eqs at the indexes returned by the function eqs_to_rm
checkCompatible:=proc (eqss,eqs_to_rm) local i,j,im_indx,eqd1,eqd2,res,ii,attComp;
res:=true;
for i from 1 to nops(eqss)-1 do
im_indx:=eqs_to_rm(eqss[i]);
#print("removed",map(lhs,[eqss[i][im_indx[ii]]$ii=1..nops(im_indx)]));
eqd1:=subsop('im_indx[ii]=NULL'$ii=1..nops(im_indx),eqss[i]):
for j from i+1 to nops(eqss) do
#print("doing (",i,j,")");
im_indx:=eqs_to_rm(eqss[j]);
#print("removed",map(lhs,[eqss[j][im_indx[ii]]$ii=1..nops(im_indx)]));
eqd2:=subsop('im_indx[ii]=NULL'$ii=1..nops(im_indx),eqss[j]):
attComp:=sameNameSameDef(eqd1,eqd2);
res:=attComp and res;
if not attComp then
print("incompatibility between",i,j);
end if;
end do;
end do;
res;
end proc: </Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">getDef:=proc(symb,eqs) local eq;
for eq in eqs do
if(lhs(eq)=symb) then
return eq;
end if;
end do;
0;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqUses:=(eq1,eq2)-&gt;evalb(lhs(eq2) in indets(rhs(eq1),symbol)):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">enforceDependencies:=proc(eqs) local dep,eq1,eq2,i,j,ii,eqns;
dep:=true;
eqns:=eqs;
ii:=0;
i:=1;
while (i&lt;=(nops(eqs)-1) and ii&lt;100000) do
dep:=false;
j:=i+1;
while (j&lt;=nops(eqs) and ii&lt;100000) do
if eqUses(eqns[i],eqns[j]) then
ii:=ii+1;
eqns:=subsop(i=NULL,j=(eqns[j],eqns[i]),eqns);
dep:=true;
else
j:=j+1;
end if;
end do;
if not dep then i:=i+1; end if;
end do;
eqns;
end proc: </Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">combineEqs:=proc(ord) local def,defs,allDefs,allEq;
allDefs:=[]:
allEq:=[]:
for defs in ord do
for def in defs do
if not lhs(def) in allDefs then
allDefs:=[op(allDefs),lhs(def)];
allEq:=[op(allEq),def];
end if;
end do;
end do;
allEq;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">combineDefs:=proc(ord) local def,defs,allDefs;
allDefs:=[]:
for defs in ord do
for def in defs do
if not def in allDefs then
allDefs:=[op(allDefs),def];
end if;
end do;
end do;
allDefs;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sostConst:=proc(eqs) local sAtt,sToDo,result;
sToDo:=[];
result:=[];
for sAtt in eqs do
sAtt:=subs(op(sToDo),sAtt);
if type(rhs(sAtt),numeric) then sToDo:=[op(sToDo),sAtt]; end if;
if rhs(sAtt)&lt;&gt;0 then result:=[op(result),sAtt]; end if;
end do;
result;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">calcDerivs:=proc(eqs,arg_names) local cs,r,d,eq,eq2,eq3,i;
cs:=CompSeq(locals=loc(eqs),globals=convert(unk(eqs),set)minus convert(arg_names,set),
params=arg_names,eqs);
r:=convert(cs,procedure);
d:=[seq(D[i](r),i=1..nops(arg_names))];
eq:=map(f-&gt;op(-1,convert(f,CompSeq)),d);
# ensure that the variables are bound in the global namespace
eq2:=map(f-&gt;evalindets(f,symbol,g-&gt;convert(convert(g,string),symbol)),eq);
eq3:=[seq(subs(result=convert(cat(lhs(eqs[nops(eqs)]),"_",arg_names[i]),symbol),eq2[i]),i=1..nops(arg_names))];
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">fCostanti:=proc(costanti,eqs) local cs,pr, pEq;
pEq:=map(x-&gt;getDef(x,eqs),costanti);
print(pEq);
cs:=CompSeq(globals=costanti,pEq);
pr:=convert(cs,procedure);
Fortran(pr);
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">rmDefs:=proc(lNames,eqs) local my_eqs,nm;
my_eqs:=eqs;
for nm in lNames do
my_eqs:=subsop(indiceDef(nm,my_eqs)=NULL,my_eqs);
end do;
my_eqs;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">with(CodeGeneration);</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the protected name Matlab has been redefined and unprotected</Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM3LEkiQ0c2IkkoRm9ydHJhbkdGJUkxSW50ZXJtZWRpYXRlQ29kZUdGJUklSmF2YUdGJUkzTGFuZ3VhZ2VEZWZpbml0aW9uR0YlSSdNYXRsYWJHNiRJKnByb3RlY3RlZEdGLEkoX3N5c2xpYkdGJUkmTmFtZXNHRiVJJVNhdmVHRiVJKlRyYW5zbGF0ZUdGJUksVmlzdWFsQmFzaWNHRiU=</Equation></Text-field></Output></Group><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">exchange</Text-field></Title><Group><Input><Text-field layout="Normal" style="Text">exhange energy (LDA)</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqx1:=ex_lda=rho*ex_unif*Fx;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcXgxRzYiL0knZXhfbGRhR0YlKihJJHJob0dGJSIiIkkoZXhfdW5pZkdGJUYqSSNGeEdGJUYq</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text">Uniform gas exchange:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqx2:=kf=(3*Pi^2*rho)^(1/3);
eqx3:=ex_unif=-3/(4*Pi)*kf;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcXgyRzYiL0kja2ZHRiUqJiIiJCMiIiJGKSomSSNQaUdJKnByb3RlY3RlZEdGLiIiI0kkcmhvR0YlRitGKg==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcXgzRzYiL0koZXhfdW5pZkdGJSwkKiZJI1BpR0kqcHJvdGVjdGVkR0YrISIiSSNrZkdGJSIiIiMhIiQiIiU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text">The enhancement factor Fx is function of just p an z;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqx4:=p=norm_drho^2/(4*(3*Pi^2)^(2/3)*rho^(8/3));
eqx5:=s=norm_drho/(2*kf*rho);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcXg0RzYiL0kicEdGJSwkKipJKm5vcm1fZHJob0dGJSIiIyIiJCMiIiJGLCokSSNQaUdJKnByb3RlY3RlZEdGMUYrIyEiI0YsSSRyaG9HRiUjISIpRiwjRi4iIzc=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcXg1RzYiL0kic0dGJSwkKihJKm5vcm1fZHJob0dGJSIiIkkja2ZHRiUhIiJJJHJob0dGJUYtI0YrIiIj</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalb(simplify(subs(eqx4,eqx5,eqx2,s^2=p),symbolic));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text">Fx can be written as</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqx6:=Fx=1+kappa-kappa/(1+mu*s^2/kappa);
eqk1:=kappa=0.804;
eqpbe8:=beta=0.066725;
eqk2:=mu=beta*(Pi^2/3);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcXg2RzYiL0kjRnhHRiUsKCIiIkYpSSZrYXBwYUdGJUYpKiZGKkYpLCZGKUYpKihJI211R0YlRilJInNHRiUiIiNGKiEiIkYpRjFGMQ==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcWsxRzYiL0kma2FwcGFHRiUkIiQvKSEiJA==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXBiZThHNiIvSSViZXRhR0YlJCImRG4nISIn</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcWsyRzYiL0kjbXVHRiUsJComSSViZXRhR0YlIiIiSSNQaUdJKnByb3RlY3RlZEdGLSIiIyNGKyIiJA==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_ex_lda := [eqk1,eqpbe8,eqk2,eqx2,eqx3,eqx5, eqx6, eqx1];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SStlcXNfZXhfbGRhRzYiNyovSSZrYXBwYUdGJSQiJC8pISIkL0klYmV0YUdGJSQiJkRuJyEiJy9JI211R0YlLCQqJkYtIiIiSSNQaUdJKnByb3RlY3RlZEdGNyIiIyNGNSIiJC9JI2tmR0YlKiZGOkY5KiZGNkY4SSRyaG9HRiVGNUY5L0koZXhfdW5pZkdGJSwkKiZGNiEiIkY8RjUjRisiIiUvSSJzR0YlLCQqKEkqbm9ybV9kcmhvR0YlRjVGPEZERj9GRCNGNUY4L0kjRnhHRiUsKEY1RjVGKEY1KiZGKEY1LCZGNUY1KihGMkY1RkhGOEYoRkRGNUZERkQvSSdleF9sZGFHRiUqKEY/RjVGQUY1Rk5GNQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">unk(eqs_ex_lda);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJJHJob0c2Ikkqbm9ybV9kcmhvR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc(eqs_ex_lda);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8Kkkic0c2Ikkma2FwcGFHRiVJI0Z4R0YlSSNrZkdGJUknZXhfbGRhR0YlSShleF91bmlmR0YlSSNtdUdGJUklYmV0YUdGJQ==</Equation></Text-field></Output></Group></Section><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">correlation</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqc1:=ec=rho*epsilon_cGGA;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcWMxRzYiL0kjZWNHRiUqJkkkcmhvR0YlIiIiSS1lcHNpbG9uX2NHR0FHRiVGKg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqc3:=chi=(rhoa-rhob)/rho;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcWMzRzYiL0kkY2hpR0YlKiYsJkklcmhvYUdGJSIiIkklcmhvYkdGJSEiIkYrSSRyaG9HRiVGLQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqc7:=rs=(3/(4*Pi*rho))^(1/3);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVlcWM3RzYiL0kjcnNHRiUsJCooIiIkIyIiIkYqIiIlIyIiI0YqKiZJI1BpR0kqcHJvdGVjdGVkR0YyISIiSSRyaG9HRiVGM0YrI0YsRi0=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text">PBE (alias epsilon_cGGA) from Perdew, Burke, Ernzehof, PRL, vol 77, p 3865 (1996) It has some corrections and discussions.</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqpbe1:=t=norm_drho/(2*phi*k_s*rho);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXBiZTFHNiIvSSJ0R0YlLCQqKkkqbm9ybV9kcmhvR0YlIiIiSSRwaGlHRiUhIiJJJGtfc0dGJUYtSSRyaG9HRiVGLSNGKyIiIw==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqpbe2:=phi=((1+chi)^(2/3)+(1-chi)^(2/3))/2;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXBiZTJHNiIvSSRwaGlHRiUsJiokLCYiIiJGK0kkY2hpR0YlRisjIiIjIiIkI0YrRi4qJCwmRitGK0YsISIiRi1GMA==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqpbe3:=k_s=sqrt(4*k_f/(Pi*a_0));
#eqpbe4:=a_0=h_bar^2 /(m*e^2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXBiZTNHNiIvSSRrX3NHRiUsJCokKiZJJGtfZkdGJSIiIkkjUGlHSSpwcm90ZWN0ZWRHRi4hIiIjRiwiIiNGMQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqpbe5:=H=(e^2/a_0)*gamma_var*phi^3*ln(1+beta/gamma_var*t^2*(1+A*t^2)/(1+A*t^2+A^2*t^4));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXBiZTVHNiIvSSJIR0YlKihJKmdhbW1hX3ZhckdGJSIiIkkkcGhpR0YlIiIkLUkjbG5HNiRJKnByb3RlY3RlZEdGMEkoX3N5c2xpYkdGJTYjLCZGKkYqKixJJWJldGFHRiVGKkYpISIiSSJ0R0YlIiIjLCZGKkYqKiZJIkFHRiVGKkY3RjhGKkYqLChGKkYqRjpGKiomRjtGOEY3IiIlRipGNkYqRio=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqpbe6:=A=beta/gamma_var*(exp(-epsilon_c_unif/(gamma_var*phi^3*e^2/a_0))-1)^(-1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXBiZTZHNiIvSSJBR0YlKihJJWJldGFHRiUiIiJJKmdhbW1hX3ZhckdGJSEiIiwmLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRjFJKF9zeXNsaWJHRiU2IywkKihJL2Vwc2lsb25fY191bmlmR0YlRipGK0YsSSRwaGlHRiUhIiRGLEYqRixGKkYs</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqpbe7:=epsilon_cGGA=epsilon_c_unif+H;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXBiZTdHNiIvSS1lcHNpbG9uX2NHR0FHRiUsJkkvZXBzaWxvbl9jX3VuaWZHRiUiIiJJIkhHRiVGKg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqpbe9:=gamma_var=(1-ln(2))/Pi^2;evalf(rhs(eqpbe9));
</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXBiZTlHNiIvSSpnYW1tYV92YXJHRiUqJiwmIiIiRiotSSNsbkc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YlNiMiIiMhIiJGKkkjUGlHRi4hIiM=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiMkIisnM3AhNEohIzY=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqpbe10:=k_f=(3*Pi^2*rho)^(1/3);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SShlcXBiZTEwRzYiL0kka19mR0YlKiYiIiQjIiIiRikqJkkjUGlHSSpwcm90ZWN0ZWRHRi4iIiNJJHJob0dGJUYrRio=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_pbec1 := [eqpbe8,eqpbe9,eqc3, eqpbe2, eqpbe10, eqpbe3, eqpbe1, eqpbe6, eqpbe5,eqpbe7,eqc1];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">unk(eqs_pbec1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8KEklcmhvYkc2IkklcmhvYUdGJUkvZXBzaWxvbl9jX3VuaWZHRiVJI1BpR0kqcHJvdGVjdGVkR0YpSSRyaG9HRiVJKm5vcm1fZHJob0dGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text">Uniform gas correlation from Perdew,Wang; PRB vol 45, p 13244, 1992</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">equc1:=epsilon_c_unif=e_c_u_0+alpha_c*f/f_ii_0*(1-chi^4)+(e_c_u_1-e_c_u_0)*f*chi^4;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjMUc2Ii9JL2Vwc2lsb25fY191bmlmR0YlLChJKGVfY191XzBHRiUiIiIqKkkoYWxwaGFfY0dGJUYqSSJmR0YlRipJJ2ZfaWlfMEdGJSEiIiwmRipGKiokSSRjaGlHRiUiIiVGL0YqRioqKCwmSShlX2NfdV8xR0YlRipGKUYvRipGLUYqRjJGM0Yq</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">equc2:=f=((1+chi)^(4/3)+(1-chi)^(4/3)-2)/(2^(4/3)-2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjMkc2Ii9JImZHRiUqJiwoKiQsJiIiIkYsSSRjaGlHRiVGLCMiIiUiIiRGLCokLCZGLEYsRi0hIiJGLkYsISIjRixGLCwmKiQiIiMjRixGMEY3RjRGLEYz</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">equc3:=f_ii_0=subs(chi=0,diff(subs(equc2,f),chi,chi));
evalf(rhs(equc3));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjM0c2Ii9JJ2ZfaWlfMEdGJSwkKiQsJiokIiIjIyIiIiIiJEYsISIjRi4hIiIjIiIpIiIq</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiMkIitMNCMqNDwhIio=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">G_uc:=-2*A*(1+alpha_1*rs)*ln(1+1/(2*A*(beta_1*rs^(1/2)+beta_2*rs+beta_3*rs^(3/2)+beta_4*rs^(p+1))));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSVHX3VjRzYiLCQqKEkiQUdGJSIiIiwmRilGKSomSShhbHBoYV8xR0YlRilJI3JzR0YlRilGKUYpLUkjbG5HNiRJKnByb3RlY3RlZEdGMUkoX3N5c2xpYkdGJTYjLCZGKUYpKiZGKCEiIiwqKiZJJ2JldGFfMUdGJUYpRi0jRikiIiNGKSomSSdiZXRhXzJHRiVGKUYtRilGKSomSSdiZXRhXzNHRiVGKUYtIyIiJEY7RikqJkknYmV0YV80R0YlRikpRi0sJkkicEdGJUYpRilGKUYpRilGNkY6RikhIiM=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">equc4c:=[p_1=1.0,A_1=0.031091,alpha_1_1=0.21370,beta_1_1=7.5957,beta_2_1=3.5876,beta_3_1=1.6382,
beta_4_1=0.49294];
equc4:={p=p_1,A=A_1,alpha_1=alpha_1_1,beta_1=beta_1_1,beta_2=beta_2_1,beta_3=beta_3_1,
beta_4=beta_4_1};
equc5:=e_c_u_0=subs(equc4,G_uc);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXVjNGNHNiI3KS9JJHBfMUdGJSQiIzUhIiIvSSRBXzFHRiUkIiYiNEohIicvSSphbHBoYV8xXzFHRiUkIiZxOCMhIiYvSSliZXRhXzFfMUdGJSQiJmRmKCEiJS9JKWJldGFfMl8xR0YlJCImd2UkRjovSSliZXRhXzNfMUdGJSQiJiNRO0Y6L0kpYmV0YV80XzFHRiUkIiYlSFxGNQ==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjNEc2IjwpL0knYmV0YV80R0YlSSliZXRhXzRfMUdGJS9JIkFHRiVJJEFfMUdGJS9JKGFscGhhXzFHRiVJKmFscGhhXzFfMUdGJS9JJ2JldGFfMkdGJUkpYmV0YV8yXzFHRiUvSSdiZXRhXzNHRiVJKWJldGFfM18xR0YlL0knYmV0YV8xR0YlSSliZXRhXzFfMUdGJS9JInBHRiVJJHBfMUdGJQ==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjNUc2Ii9JKGVfY191XzBHRiUsJCooSSRBXzFHRiUiIiIsJkYrRisqJkkqYWxwaGFfMV8xR0YlRitJI3JzR0YlRitGK0YrLUkjbG5HNiRJKnByb3RlY3RlZEdGM0koX3N5c2xpYkdGJTYjLCZGK0YrKiZGKiEiIiwqKiZJKWJldGFfMV8xR0YlRitGLyNGKyIiI0YrKiZJKWJldGFfMl8xR0YlRitGL0YrRisqJkkpYmV0YV8zXzFHRiVGK0YvIyIiJEY9RisqJkkpYmV0YV80XzFHRiVGKylGLywmSSRwXzFHRiVGK0YrRitGK0YrRjhGPEYrISIj</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">equc6c:=[p_2=1.0,A_2=0.015545,alpha_1_2=0.20548,beta_1_2=14.1189,beta_2_2=6.1977,beta_3_2=3.3662,
beta_4_2=0.62517];
equc6:={p=p_2,A=A_2,alpha_1=alpha_1_2,beta_1=beta_1_2,beta_2=beta_2_2,beta_3=beta_3_2,
beta_4=beta_4_2};
equc7:=e_c_u_1=subs(equc6,G_uc);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXVjNmNHNiI3KS9JJHBfMkdGJSQiIzUhIiIvSSRBXzJHRiUkIiZYYiIhIicvSSphbHBoYV8xXzJHRiUkIiZbMCMhIiYvSSliZXRhXzFfMkdGJSQiJyo9VCIhIiUvSSliZXRhXzJfMkdGJSQiJng+J0Y6L0kpYmV0YV8zXzJHRiUkIiZpTyRGOi9JKWJldGFfNF8yR0YlJCImPEQnRjU=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjNkc2IjwpL0kiQUdGJUkkQV8yR0YlL0knYmV0YV8xR0YlSSliZXRhXzFfMkdGJS9JKGFscGhhXzFHRiVJKmFscGhhXzFfMkdGJS9JInBHRiVJJHBfMkdGJS9JJ2JldGFfMkdGJUkpYmV0YV8yXzJHRiUvSSdiZXRhXzRHRiVJKWJldGFfNF8yR0YlL0knYmV0YV8zR0YlSSliZXRhXzNfMkdGJQ==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjN0c2Ii9JKGVfY191XzFHRiUsJCooSSRBXzJHRiUiIiIsJkYrRisqJkkqYWxwaGFfMV8yR0YlRitJI3JzR0YlRitGK0YrLUkjbG5HNiRJKnByb3RlY3RlZEdGM0koX3N5c2xpYkdGJTYjLCZGK0YrKiZGKiEiIiwqKiZJKWJldGFfMV8yR0YlRitGLyNGKyIiI0YrKiZJKWJldGFfMl8yR0YlRitGL0YrRisqJkkpYmV0YV8zXzJHRiVGK0YvIyIiJEY9RisqJkkpYmV0YV80XzJHRiVGKylGLywmSSRwXzJHRiVGK0YrRitGK0YrRjhGPEYrISIj</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">equc8c:=[p_3=1.0,A_3=0.016887,alpha_1_3=0.11125,beta_1_3=10.357,beta_2_3=3.6231,beta_3_3=0.88026,
beta_4_3=0.49671];
equc8:={p=p_3,A=A_3,alpha_1=alpha_1_3,beta_1=beta_1_3,beta_2=beta_2_3,beta_3=beta_3_3,
beta_4=beta_4_3};
equc9:=alpha_c=-subs(equc8,G_uc);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSdlcXVjOGNHNiI3KS9JJHBfM0dGJSQiIzUhIiIvSSRBXzNHRiUkIiYoKW8iISInL0kqYWxwaGFfMV8zR0YlJCImRDYiISImL0kpYmV0YV8xXzNHRiUkIiZkLiIhIiQvSSliZXRhXzJfM0dGJSQiJkppJCEiJS9JKWJldGFfM18zR0YlJCImRSEpKUY1L0kpYmV0YV80XzNHRiUkIiZyJ1xGNQ==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjOEc2IjwpL0kicEdGJUkkcF8zR0YlL0kiQUdGJUkkQV8zR0YlL0knYmV0YV8xR0YlSSliZXRhXzFfM0dGJS9JJ2JldGFfMkdGJUkpYmV0YV8yXzNHRiUvSSdiZXRhXzNHRiVJKWJldGFfM18zR0YlL0knYmV0YV80R0YlSSliZXRhXzRfM0dGJS9JKGFscGhhXzFHRiVJKmFscGhhXzFfM0dGJQ==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSZlcXVjOUc2Ii9JKGFscGhhX2NHRiUsJCooSSRBXzNHRiUiIiIsJkYrRisqJkkqYWxwaGFfMV8zR0YlRitJI3JzR0YlRitGK0YrLUkjbG5HNiRJKnByb3RlY3RlZEdGM0koX3N5c2xpYkdGJTYjLCZGK0YrKiZGKiEiIiwqKiZJKWJldGFfMV8zR0YlRitGLyNGKyIiI0YrKiZJKWJldGFfMl8zR0YlRitGL0YrRisqJkkpYmV0YV8zXzNHRiVGK0YvIyIiJEY9RisqJkkpYmV0YV80XzNHRiVGKylGLywmSSRwXzNHRiVGK0YrRitGK0YrRjhGPEYrRj0=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_e_c_unif:=[op(equc4c),op(equc6c),op(equc8c),eqc3,eqc7,equc5,equc7,equc9,equc3,equc2,equc1];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">unk(eqs_e_c_unif);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8JkklcmhvYkc2IkklcmhvYUdGJUkjUGlHSSpwcm90ZWN0ZWRHRihJJHJob0dGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc(eqs_e_c_unif)intersect loc(eqs_pbec1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8I0kkY2hpRzYi</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_pbec1_ind:=subsop(3=NULL,eqs_pbec1):
loc(eqs_e_c_unif)intersect loc(eqs_pbec1_ind);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8Ig==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_pbec2:=[eqs_e_c_unif[i]$i=1..nops(eqs_e_c_unif),eqs_pbec1_ind[i]$i=1..nops(eqs_pbec1_ind)];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">unk(eqs_pbec2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8J0klcmhvYkc2IkklcmhvYUdGJUkjUGlHSSpwcm90ZWN0ZWRHRihJJHJob0dGJUkqbm9ybV9kcmhvR0Yl</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc(eqs_pbec2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8SUkqZ2FtbWFfdmFyRzYiSSJmR0YlSSJIR0YlSSRBXzJHRiVJJHBfM0dGJUkkQV8zR0YlSS1lcHNpbG9uX2NHR0FHRiVJJEFfMUdGJUkkcF8yR0YlSSliZXRhXzRfM0dGJUkpYmV0YV8zXzNHRiVJL2Vwc2lsb25fY191bmlmR0YlSSNlY0dGJUkkY2hpR0YlSSphbHBoYV8xXzNHRiVJKWJldGFfMV8zR0YlSSliZXRhXzJfM0dGJUkjcnNHRiVJJHBoaUdGJUkpYmV0YV8zXzFHRiVJKmFscGhhXzFfMkdGJUkpYmV0YV8xXzJHRiVJKWJldGFfMl8yR0YlSSliZXRhXzRfMkdGJUkpYmV0YV8zXzJHRiVJKWJldGFfMl8xR0YlSSliZXRhXzRfMUdGJUkka19zR0YlSSRrX2ZHRiVJInRHRiVJJWJldGFHRiVJKWJldGFfMV8xR0YlSShlX2NfdV8wR0YlSShhbHBoYV9jR0YlSSdmX2lpXzBHRiVJKGVfY191XzFHRiVJIkFHRiVJJHBfMUdGJUkqYWxwaGFfMV8xR0Yl</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 2" style="Heading 2">costanti</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">costanti:=[kappa, beta,mu,gamma_var,
p_1,A_1,alpha_1_1,beta_1_1,beta_2_1,beta_3_1,beta_4_1,
p_2,A_2,alpha_1_2,beta_1_2,beta_2_2,beta_3_2,beta_4_2,
p_3,A_3,alpha_1_3,beta_1_3,beta_2_3,beta_3_3,beta_4_3,scale_ec,scale_ex]:</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSljb3N0YW50aUc2Ijc9SSZrYXBwYUdGJUklYmV0YUdGJUkjbXVHRiVJKmdhbW1hX3ZhckdGJUkkcF8xR0YlSSRBXzFHRiVJKmFscGhhXzFfMUdGJUkpYmV0YV8xXzFHRiVJKWJldGFfMl8xR0YlSSliZXRhXzNfMUdGJUkpYmV0YV80XzFHRiVJJHBfMkdGJUkkQV8yR0YlSSphbHBoYV8xXzJHRiVJKWJldGFfMV8yR0YlSSliZXRhXzJfMkdGJUkpYmV0YV8zXzJHRiVJKWJldGFfNF8yR0YlSSRwXzNHRiVJJEFfM0dGJUkqYWxwaGFfMV8zR0YlSSliZXRhXzFfM0dGJUkpYmV0YV8yXzNHRiVJKWJldGFfM18zR0YlSSliZXRhXzRfM0dGJUkpc2NhbGVfZWNHRiVJKXNjYWxlX2V4R0Yl</Equation></Text-field></Output></Group><Section><Title><Text-field layout="Heading 3" style="Heading 3">Fortran</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">fCostanti(costanti,eqs_lsd);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">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</Equation></Text-field></Output><Output><Text-field layout="Normal" style="Line Printed Output"> doubleprecision function pr ()
doubleprecision kappa
doubleprecision beta
doubleprecision mu
doubleprecision gamma_var
doubleprecision p_1
doubleprecision A_1
doubleprecision alpha_1_1
doubleprecision beta_1_1
doubleprecision beta_2_1
doubleprecision beta_3_1
doubleprecision beta_4_1
doubleprecision p_2
doubleprecision A_2
doubleprecision alpha_1_2
doubleprecision beta_1_2
doubleprecision beta_2_2
doubleprecision beta_3_2
doubleprecision beta_4_2
doubleprecision p_3
doubleprecision A_3
doubleprecision alpha_1_3
doubleprecision beta_1_3
doubleprecision beta_2_3
doubleprecision beta_3_3
doubleprecision beta_4_3
doubleprecision scale_ec
doubleprecision scale_ex
common kappa, beta, mu, gamma_var, p_1, A_1, alpha_1_1, beta_1_1
#, beta_2_1, beta_3_1, beta_4_1, p_2, A_2, alpha_1_2, beta_1_2, bet
#a_2_2, beta_3_2, beta_4_2, p_3, A_3, alpha_1_3, beta_1_3, beta_2_3
#, beta_3_3, beta_4_3, scale_ec, scale_ex
kappa = 0.804D0
beta = 0.66725D-1
mu = beta * 0.3141592654D1 ** 2 / 0.3D1
gamma_var = (0.1D1 - log(0.2D1)) / 0.3141592654D1 ** 2
p_1 = 0.10D1
A_1 = 0.31091D-1
alpha_1_1 = 0.21370D0
beta_1_1 = 0.75957D1
beta_2_1 = 0.35876D1
beta_3_1 = 0.16382D1
beta_4_1 = 0.49294D0
p_2 = 0.10D1
A_2 = 0.15545D-1
alpha_1_2 = 0.20548D0
beta_1_2 = 0.141189D2
beta_2_2 = 0.61977D1
beta_3_2 = 0.33662D1
beta_4_2 = 0.62517D0
p_3 = 0.10D1
A_3 = 0.16887D-1
alpha_1_3 = 0.11125D0
beta_1_3 = 0.10357D2
beta_2_3 = 0.36231D1
beta_3_3 = 0.88026D0
beta_4_3 = 0.49671D0
scale_ec = 0.1D1
scale_ex = 0.1D1
pr = scale_ex
return
end</Text-field></Output></Group></Section><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group></Section><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Tests</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc(eqs_pbec2)intersect loc(eqs_ex_lda);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8I0klYmV0YUc2Ig==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sameNameSameDef(eqs_pbec2,eqs_ex_lda);</Text-field></Input><Output><Text-field layout="Error" style="Error">Error, (in sameNameSameDef) invalid input: subs received [{alpha_1_1 = .21370, beta_1_1 = 7.5957, beta_2_1 = 3.5876, p_1 = 1.0, A_1 = 0.31091e-1, beta_3_1 = 1.6382, beta_4_1 = .49294}, {p_2 = 1.0, A_2 = 0.15545e-1, alpha_1_2 = .20548, beta_1_2 = 14.1189, beta_3_2 = 3.3662, beta_4_2 = .62517, beta_2_2 = 6.1977}, {beta_2_3 = 3.6231, beta_3_3 = .88026, A_3 = 0.16887e-1, p_3 = 1.0, beta_4_3 = .49671, alpha_1_3 = .11125, beta_1_3 = 10.357}, chi = (rhoa-rhob)/rho, rs = 1/4*3^(1/3)*4^(2/3)*(1/(Pi*rho))^(1/3), e_c_u_0 = -2*A_1*(1+alpha_1_1*rs)*ln(1+1/2/(A_1*(beta_1_1*rs^(1/2)+beta_2_1*rs+beta_3_1*rs^(3/2)+beta_4_1*rs^(p_1+1)))), e_c_u_1 = -2*A_2*(1+alpha_1_2*rs)*ln(1+1/2/(A_2*(beta_1_2*rs^(1/2)+beta_2_2*rs+beta_3_2*rs^(3/2)+beta_4_2*rs^(p_2+1)))), alpha_c = 2*A_3*(1+alpha_1_3*rs)*ln(1+1/2/(A_3*(beta_1_3*rs^(1/2)+beta_2_3*rs+beta_3_3*rs^(3/2)+beta_4_3*rs^(p_3+1)))), f_ii_0 = 8/9/(2*2^(1/3)-2), f = ((1+chi)^(4/3)+(1-chi)^(4/3)-2)/(2*2^(1/3)-2), epsilon_c_unif = e_c_u_0+alpha_c*f*(1-chi^4)/f_ii_0+(e_c_u_1-e_c_u_0)*f*chi^4, beta = 0.66725e-1, gamma_var = (1-ln(2))/Pi^2, phi = 1/2*(1+chi)^(2/3)+1/2*(1-chi)^(2/3), k_f = 3^(1/3)*(Pi^2*rho)^(1/3), k_s = 2*(k_f/Pi)^(1/2), t = 1/2*norm_drho/(phi*k_s*rho), A = beta/(gamma_var*(exp(-epsilon_c_unif/(gamma_var*phi^3))-1)), H = gamma_var*phi^3*ln(1+beta*t^2*(1+A*t^2)/(gamma_var*(1+A*t^2+A^2*t^4))), epsilon_cGGA = epsilon_c_unif+H, ec = rho*epsilon_cGGA], which is not valid for its 1st argument</Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_fxc:=combineEqs([eqs_pbec2,eqs_ex_lda,[Fxc=Fx+epsilon_cGGA/ex_unif]]):
unk(eqs_fxc);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8J0kjUGlHSSpwcm90ZWN0ZWRHRiVJJHJob0c2IkklcmhvYUdGJ0klcmhvYkdGJ0kqbm9ybV9kcmhvR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_fxc1:=subsop(indiceDef(s,eqs_fxc)=NULL,indiceDef(chi,eqs_fxc)=NULL,indiceDef(rs,eqs_fxc)=NULL,eqs_fxc):
unk(eqs_fxc1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8KEkjUGlHSSpwcm90ZWN0ZWRHRiVJInNHNiJJJHJob0dGJ0kqbm9ybV9kcmhvR0YnSSRjaGlHRidJI3JzR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">v_rho:=solve(getDef(rs,eqs_fxc),rho);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZ2X3Job0c2IiwkKiZJI3JzR0YlISIkSSNQaUdJKnByb3RlY3RlZEdGKyEiIiMiIiQiIiU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">getDef(chi,eqs_fxc);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRjaGlHNiIqJiwmSSVyaG9hR0YlIiIiSSVyaG9iR0YlISIiRilJJHJob0dGJUYr</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">v_ndrho:=solve(subs(getDef(kf,eqs_fxc),getDef(s,eqs_fxc)),norm_drho);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSh2X25kcmhvRzYiLCQqKkkic0dGJSIiIiomSSNQaUdJKnByb3RlY3RlZEdGLCIiI0kkcmhvR0YlRikjRikiIiRGLkYpRjBGL0Yt</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_fxc2:=[rho=v_rho,norm_drho=v_ndrho,chi=0,op(eqs_fxc1)]:
unk(eqs_fxc2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJInNHNiJJI3JzR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cs_eqs_fxc:=CompSeq(locals=loc(eqs_fxc2),
globals=[Pi],params=[rs,s],eqs_fxc2):
r_eqs_fxc:=convert(cs_eqs_fxc,procedure):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">plot([r_eqs_fxc(0.,s),r_eqs_fxc(2.,s),r_eqs_fxc(10.,s),r_eqs_fxc(1.0e4,s),r_eqs_fxc(1.0e3,s)],s=0..3,y=1..2);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" type="two-dimensional" width="400">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</Plot></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_fxc_p:=combineEqs([eqs_pbec2,subs(rho=2*rho,norm_drho=2*norm_drho,eqs_ex_lda),
[Fxc=Fx*2^(1/3)+2^(1/3)*epsilon_cGGA/ex_unif]]):
unk(eqs_fxc_p);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8J0kjUGlHSSpwcm90ZWN0ZWRHRiVJJHJob0c2IkklcmhvYUdGJ0klcmhvYkdGJ0kqbm9ybV9kcmhvR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_fxc1_p:=subsop(indiceDef(s,eqs_fxc_p)=NULL,indiceDef(chi,eqs_fxc_p)=NULL,indiceDef(rs,eqs_fxc_p)=NULL,eqs_fxc_p):
unk(eqs_fxc1_p);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8KEkjUGlHSSpwcm90ZWN0ZWRHRiVJInNHNiJJJHJob0dGJ0kqbm9ybV9kcmhvR0YnSSRjaGlHRidJI3JzR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">v_rho_p:=solve(getDef(rs,eqs_fxc_p),rho);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSh2X3Job19wRzYiLCQqJkkjcnNHRiUhIiRJI1BpR0kqcHJvdGVjdGVkR0YrISIiIyIiJCIiJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">getDef(chi,eqs_fxc_p);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRjaGlHNiIqJiwmSSVyaG9hR0YlIiIiSSVyaG9iR0YlISIiRilJJHJob0dGJUYr</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">v_ndrho_p:=solve(subs(getDef(kf,eqs_fxc_p),getDef(s,eqs_fxc_p)),norm_drho);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSp2X25kcmhvX3BHNiIsJCosSSJzR0YlIiIiKiZJI1BpR0kqcHJvdGVjdGVkR0YsIiIjSSRyaG9HRiVGKSNGKSIiJEYuRilGMEYvRi1GL0Yt</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_fxc2_p:=[rho=v_rho_p,norm_drho=v_ndrho_p,chi=1,op(eqs_fxc1_p)]:
unk(eqs_fxc2_p);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJInNHNiJJI3JzR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cs_eqs_fxc_p:=CompSeq(locals=loc(eqs_fxc2_p),
globals=[Pi],params=[rs,s],eqs_fxc2_p):
r_eqs_fxc_p:=convert(cs_eqs_fxc_p,procedure):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">plot([r_eqs_fxc_p(0.,s),r_eqs_fxc_p(2.,s),r_eqs_fxc_p(10.,s),r_eqs_fxc_p(10000.,s),r_eqs_fxc_p(200000.,s)],
s=0..3,y=1..2);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" type="two-dimensional" width="400">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</Plot></Text-field></Output></Group><Section><Title><Text-field layout="Heading 3" style="Heading 3">Compare with old QS PBE</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqsPbex:=[kappa = 0.804,cx_vwn_e=-3/4*(3/Pi)^(1/3)
,f13=1/3
,r2kf = 1/2*(3*Pi^2)^(-f13)
,mu = 0.2195149727645171
,rho13 = rho^f13
,rho43 = rho13*rho
,s = r2kf*drho/rho43
,p = 1/(1 + mu*s*s/kappa)
,fx = 1 + kappa*(1 - p)
,dfx = 2*mu*s*p*p
,ex = cx_vwn_e*rho43*fx
,vx = cx_vwn_v*rho13*(fx - s*dfx)
,vxg = cx_vwn_e*r2kf*dfx/drho,energy=ex];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">unk(eqsPbex);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJJWRyaG9HNiJJJHJob0dGJw==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cs_eqsPbex:=CompSeq(locals=convert(loc(eqsPbex),list),
globals=[Pi],params=[rho,drho],eqsPbex):
r_eqsPbex:=convert(cs_eqsPbex,procedure):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_ex_lda;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM3Ki9JJmthcHBhRzYiJCIkLykhIiQvSSViZXRhR0YmJCImRG4nISInL0kjbXVHRiYsJComRisiIiJJI1BpR0kqcHJvdGVjdGVkR0Y1IiIjI0YzIiIkL0kja2ZHRiYqJkY4RjcqJkY0RjZJJHJob0dGJkYzRjcvSShleF91bmlmR0YmLCQqJkY0ISIiRjpGMyNGKSIiJS9JInNHRiYsJCooSSpub3JtX2RyaG9HRiZGM0Y6RkJGPUZCI0YzRjYvSSNGeEdGJiwoRjNGM0YlRjMqJkYlRjMsJkYzRjMqKEYwRjNGRkY2RiVGQkYzRkJGQi9JJ2V4X2xkYUdGJiooRj1GM0Y/RjNGTEYz</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cs_eqsPbex2:=CompSeq(locals=convert(loc(eqs_ex_lda),list),
globals=[Pi],params=[rho,norm_drho],eqs_ex_lda):
r_eqsPbex2:=convert(cs_eqsPbex2,procedure):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">contourplot3d(r_eqsPbex-r_eqsPbex2,0.1..1,-1..1);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" type="three-dimensional" width="400">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</Plot></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">mu=sost([op(eqs_ex_lda),my_m=mu]),mu2=sost([op(eqsPbex),my_m=mu]);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiQvSSNtdUc2IiwkKiRJI1BpR0kqcHJvdGVjdGVkR0YpIiIjJCIrbm07Q0EhIzYvSSRtdTJHRiUkIjFyXmtGKFxePiMhIzs=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalf(rhs(%[1])-rhs(%[2])),evalf((rhs(%[1])-rhs(%[2]))/rhs(%[1]));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiQkIiYmeTkhIzUkIisqSGVfdCchIzo=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text">This uses VWN correlation instead of the (correct) PW92</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqsPbec:=[f43=4/3
,f13=1/3
,f76=7/6
,r2ks=1/4*(3/Pi)^(-1/6)
,ap = 0.0621814
,bp = 3.72744
,cp = 12.9352
,xp = -0.10498
,beta_pbe=0.66725e-1
,gamma_pbe=(1-log(2))/Pi^2
,rsfac = (f43*Pi)^(-f13)
,x2 = rsfac*rho^(-f13)
,x = sqrt(x2)
,xp2 = xp*xp
,xmxp = x - xp
,xmxp2 = xmxp*xmxp
,pp = x*x + bp*x + cp
,qp = sqrt(4*cp - bp*bp)
, ecp = 1/2*ap*(log(x2/xmxp2) - ((xp2 + cp)*log(pp/xmxp2) + 2*bp*(xp2 - cp)*arctan(qp/(2*x + bp))/qp)/ (xp2 + bp*xp + cp))
,decp = 1/2*f13*ap*((1 + bp/xmxp)*x2/pp - 1)
,ec = ecp*rho
,vc = ecp + decp
,e_var = ec/rho
,rhom76 = rho^(-f76)
,t = r2ks*drho*rhom76
,t2 = t*t
,expe = exp(-e_var/gamma_pbe)
,bog = beta_pbe/gamma_pbe
,a = bog/(expe - 1)
,at2 = a*t2
,q = 1/(1 + at2 + at2*at2)
,q2 = q*q
,p = 1 + bog*t2*(1 + at2)*q
,h = gamma_pbe*log(p)
,dpdt = 2*bog*t*(1 + 2*at2)*q2
,dtdr = -f76*t/rho
,dpda = -bog*at2*t2*t2*(2 + at2)*q2
,dade = a*a*expe/beta_pbe
,dedr = (vc - e_var)/rho
,dpdr = dpdt*dtdr + dpda*dade*dedr
,dhdr = gamma_pbe*dpdr/p
,dtddr = t/drho^2
,dhddr = gamma_pbe*dpdt*dtddr/p
,ec = ec + rho*h
,vc = vc + h + rho*dhdr
,vcg = rho*dhddr,energy=ec];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cs_eqsPbec:=CompSeq(locals=convert(loc(eqsPbec),list),
globals=[Pi],params=[rho,drho],eqsPbec):
r_eqsPbec:=convert(cs_eqsPbec,procedure):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">unk(eqs_pbec2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8J0kjUGlHSSpwcm90ZWN0ZWRHRiVJKm5vcm1fZHJob0c2IkklcmhvYUdGJ0klcmhvYkdGJ0kkcmhvR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_pbec2_lda:=[rhoa=rho/2,rhob=rho/2,op(eqs_pbec2)];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cs_eqsPbec2:=CompSeq(locals=convert(loc(eqs_pbec2_lda),list),
gobals=[Pi],params=[rho,norm_drho],eqs_pbec2_lda):
r_eqsPbec2:=convert(cs_eqsPbec2,procedure):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">with(plots);</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the name changecoords has been redefined</Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">convert(proc(r) local t; global Pi; t:=Pi*r^2; end proc,CompSeq);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMtSShDb21wU2VxRzYiNiYvSSdsb2NhbHNHRiU3I0kidEdGJS9JKGdsb2JhbHNHRiU3I0kjUGlHSSpwcm90ZWN0ZWRHRi8vSSdwYXJhbXNHRiU3I0kickdGJTcjL0YqKiZGLiIiIkYzIiIj</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">convert(CompSeq(locals=[t],params=[r],[t=r^2]),procedure);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiNmKjYjSSJyRzYiNiNJInRHRiZGJkYmPjgkKiQ5JCIiI0YmRiZGJg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">contourplot3d(r_eqsPbec-r_eqsPbec2,0.1..1,-1..1);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" type="three-dimensional" width="400">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layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group></Section></Section></Section><Text-field/><Section collapsed="true"><Title><Text-field layout="Heading 1" style="Heading 1">LDA</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc(eqs_ex_lda)intersect loc(eqs_pbec2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8I0klYmV0YUc2Ig==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sameNameSameDef(eqs_pbec2,eqs_ex_lda);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_lda:=combineEqs([subs(rhoa=rho/2,rhob=rho/2,eqs_pbec2),eqs_ex_lda,[exc=ex_lda+ec]]):
unk(eqs_lda);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM8JUkjUGlHSSpwcm90ZWN0ZWRHRiVJKm5vcm1fZHJob0c2IkkkcmhvR0Yn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">arg_lda_names:=[rho,norm_drho]; </Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SS5hcmdfbGRhX25hbWVzRzYiNyRJJHJob0dGJUkqbm9ybV9kcmhvR0Yl</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">deriv_lda1:=calcDerivs(eqs_lda,arg_lda_names):
deriv_lda2:=[seq(op(calcDerivs(deriv_lda1[i],[rho])),i=1..2),op(calcDerivs(deriv_lda1[2],[norm_drho]))]:
deriv_lda3:=[seq(op(calcDerivs(deriv_lda2[i],[rho])),i=1..3),op(calcDerivs(deriv_lda2[3],[norm_drho]))]:
</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_lda2:=sostConst(eqs_lda):
sameNameSameDef(eqs_lda2,deriv_lda1[i])$i=1..2;
sameNameSameDef(eqs_lda2,deriv_lda2[i])$i=1..3;
sameNameSameDef(eqs_lda2,deriv_lda3[i])$i=1..4;
seq(sameNameSameDef(deriv_lda1[i],deriv_lda2[j])$i=1..2,j=1..3);
seq(sameNameSameDef(deriv_lda1[i],deriv_lda3[j])$i=1..2,j=1..4);
seq(sameNameSameDef(deriv_lda2[i],deriv_lda3[j])$i=1..3,j=1..4);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJJXRydWVHSSpwcm90ZWN0ZWRHRiRGIw==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiVJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0Yj</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiZJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiM=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NihJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGI0Yj</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NipJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGI0YjRiNGIw==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">Ni5JJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGI0YjRiNGI0YjRiNGI0Yj</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_lda3:=combineEqs([eqs_lda2,op(deriv_lda1),op(deriv_lda2),op(deriv_lda3)]):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_lda4:=enforceDependencies([my_rho=rho,my_norm_drho=norm_drho,
op(subs(rho=my_rho,norm_drho=my_norm_drho,eqs_lda3))]):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">res_eqs_lda:={exc,exc_rho,exc_norm_drho,exc_rho_rho,exc_norm_drho_rho,exc_norm_drho_norm_drho,
exc_rho_rho_rho,exc_norm_drho_rho_rho,exc_norm_drho_norm_drho_rho,
exc_norm_drho_norm_drho_norm_drho};
for my_symb in res_eqs_lda do
print(my_symb,unk([op(eqs_lda4),result=my_symb]));
end do;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSxyZXNfZXFzX2xkYUc2IjwsSS5leGNfbm9ybV9kcmhvR0YlSTZleGNfbm9ybV9kcmhvX3Job19yaG9HRiVJPGV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX3Job0dGJUkoZXhjX3Job0dGJUkkZXhjR0YlSThleGNfbm9ybV9kcmhvX25vcm1fZHJob0dGJUkwZXhjX3Job19yaG9fcmhvR0YlSTJleGNfbm9ybV9kcmhvX3Job0dGJUksZXhjX3Job19yaG9HRiVJQmV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX25vcm1fZHJob0dGJQ==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJLmV4Y19ub3JtX2RyaG9HNiI8JUkjUGlHSSpwcm90ZWN0ZWRHRidJKm5vcm1fZHJob0dGJEkkcmhvR0Yk</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJNmV4Y19ub3JtX2RyaG9fcmhvX3Job0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJPGV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX3Job0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJKGV4Y19yaG9HNiI8JUkjUGlHSSpwcm90ZWN0ZWRHRidJKm5vcm1fZHJob0dGJEkkcmhvR0Yk</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJJGV4Y0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJOGV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvRzYiPCVJI1BpR0kqcHJvdGVjdGVkR0YnSSpub3JtX2RyaG9HRiRJJHJob0dGJA==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJMGV4Y19yaG9fcmhvX3Job0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJMmV4Y19ub3JtX2RyaG9fcmhvRzYiPCVJI1BpR0kqcHJvdGVjdGVkR0YnSSpub3JtX2RyaG9HRiRJJHJob0dGJA==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJLGV4Y19yaG9fcmhvRzYiPCVJI1BpR0kqcHJvdGVjdGVkR0YnSSpub3JtX2RyaG9HRiRJJHJob0dGJA==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRJQmV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX25vcm1fZHJob0c2IjwlSSNQaUdJKnByb3RlY3RlZEdGJ0kqbm9ybV9kcmhvR0YkSSRyaG9HRiQ=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">glob_eqs_lda4:={my_rho,my_norm_drho}union res_eqs_lda;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SS5nbG9iX2Vxc19sZGE0RzYiPC5JLmV4Y19ub3JtX2RyaG9HRiVJNmV4Y19ub3JtX2RyaG9fcmhvX3Job0dGJUknbXlfcmhvR0YlSTxleGNfbm9ybV9kcmhvX25vcm1fZHJob19yaG9HRiVJKGV4Y19yaG9HRiVJJGV4Y0dGJUk4ZXhjX25vcm1fZHJob19ub3JtX2RyaG9HRiVJMGV4Y19yaG9fcmhvX3Job0dGJUkyZXhjX25vcm1fZHJob19yaG9HRiVJLW15X25vcm1fZHJob0dGJUksZXhjX3Job19yaG9HRiVJQmV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvX25vcm1fZHJob0dGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cs_eqs_lda4:=CompSeq(locals=loc(eqs_lda4)minus glob_eqs_lda4,
globals=glob_eqs_lda4,params=[rho,norm_drho,tau],eqs_lda4):
r_eqs_lda4:=convert(cs_eqs_lda4,procedure):</Text-field></Input></Group><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Fortran code</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Fortran(r_eqs_lda4,defaulttype=float,optimize);</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, The following variable name replacements were made: ["cg", "cg0", "cg1", "cg10", "cg11", "cg12", "cg13", "cg14", "cg15", "cg16", "cg17", "cg18", "cg19", "cg2", "cg20", "cg21", "cg22", "cg23", "cg24", "cg25", "cg26", "cg27", "cg28", "cg29", "cg3", "cg30", "cg31", "cg32", "cg33", "cg34", "cg35", "cg36", "cg37", "cg38", "cg39", "cg4", "cg40", "cg41", "cg42", "cg43", "cg44", "cg45", "cg46", "cg47", "cg48", "cg49", "cg5", "cg50", "cg51", "cg52", "cg53", "cg54", "cg55", "cg56", "cg57", "cg58", "cg59", "cg6", "cg60", "cg61", "cg62", "cg63", "cg64", "cg65", "cg66", "cg7", "cg8", "cg9"] = ["norm_drho", "k_s1rho", "k_f", "epsilon_cGGArhorho", "epsilon_cGGArho", "ex_unifrho", "snorm_drho", "k_frhorho", "trhorho", "ex_unif", "srho1rho", "tnorm_drhorho", "Hnorm_drhorho", "Hnorm_drho", "k_srhorho", "Arhorho", "e_c_u_0", "trho1rho", "ex_unif1rho", "Fxrhorho", "Fxnorm_drho1rho", "e_c_u_02rho", "Fxnorm_drhonorm_drho", "Fxrho1rho", "epsilon_cGGA", "Fx1rhorho", "snorm_drho1rho", "kfrhorho", "tnorm_drho", "A1rhorho", "Arho1rho", "kfrhorhorho", "e_c_u_0rho1rho", "tnorm_drhorhorho", "s1rhorho", "e_c_u_0rho", "k_s", "trhorhorho", "rsrhorhorho", "t1rhorho", "k_f2rho", "k_s2rho", "k_srho1rho", "snorm_drhorho", "Fxnorm_drhorho", "ex_unif2rho", "k_srho", "ex_unifrho1rho", "ex_unif1rhorho", "ex_ldarhorhorho", "tnorm_drho1rho", "k_s1rhorho", "e_c_u_01rho", "Arhorhorho", "srhorho", "Fxnorm_drho", "gamma_var", "e_c_u_0rhorho", "rsrhorho", "ex_unifrhorho", "k_frho", "t2norm_drho", "e_c_u_01rhorho", "k_frhorhorho", "r_eqs_lda4", "e_c_u_0rhorhorho", "s2norm_drho", "Hnorm_drhonorm_drho"]
</Text-field></Output><Output><Text-field layout="Normal" style="Line Printed Output"> doubleprecision function cg66 (rho, cg, tau)
doubleprecision exc_norm_drho_rho_rho
doubleprecision exc_norm_drho
doubleprecision exc_rho
doubleprecision exc_rho_rho
doubleprecision exc
doubleprecision exc_norm_drho_norm_drho_rho
doubleprecision exc_norm_drho_norm_drho
doubleprecision exc_norm_drho_rho
doubleprecision exc_rho_rho_rho
doubleprecision exc_norm_drho_norm_drho_norm_drho
doubleprecision my_rho
doubleprecision my_norm_drho
common exc_norm_drho_rho_rho, exc_norm_drho, exc_rho, exc_rho_rh
#o, exc, exc_norm_drho_norm_drho_rho, exc_norm_drho_norm_drho, exc_
#norm_drho_rho, exc_rho_rho_rho, exc_norm_drho_norm_drho_norm_drho,
# my_rho, my_norm_drho
doubleprecision rho
doubleprecision cg
doubleprecision tau
doubleprecision rs2rho
doubleprecision t1021
doubleprecision t325
doubleprecision cg0
doubleprecision t738
doubleprecision t603
doubleprecision t281
doubleprecision t339
doubleprecision t133
doubleprecision t1076
doubleprecision t1885
doubleprecision t234
doubleprecision rs
doubleprecision cg1
doubleprecision t525
doubleprecision cg2
doubleprecision rsrho
doubleprecision cg3
doubleprecision t652
doubleprecision Arho
doubleprecision s
doubleprecision t1167
doubleprecision t915
doubleprecision t927
doubleprecision t573
doubleprecision cg4
doubleprecision t1720
doubleprecision cg5
doubleprecision t1865
doubleprecision t1871
doubleprecision cg6
doubleprecision t1627
doubleprecision t905
doubleprecision cg7
doubleprecision t407
doubleprecision cg8
doubleprecision t1932
doubleprecision t131
doubleprecision t132
doubleprecision t134
doubleprecision t136
doubleprecision t77
doubleprecision t79
doubleprecision t80
doubleprecision t81
doubleprecision t1079
doubleprecision t1019
doubleprecision t1501
doubleprecision t898
doubleprecision t1480
doubleprecision t962
doubleprecision t903
doubleprecision t349
doubleprecision t1286
doubleprecision cg9
doubleprecision t1074
doubleprecision cg10
doubleprecision cg11
doubleprecision cg12
doubleprecision cg13
doubleprecision cg14
doubleprecision Fx
doubleprecision t1237
doubleprecision cg15
doubleprecision t658
doubleprecision t1648
doubleprecision t1584
doubleprecision t432
doubleprecision t1080
doubleprecision t1081
doubleprecision t460
doubleprecision t462
doubleprecision t464
doubleprecision t467
doubleprecision t470
doubleprecision t471
doubleprecision t1702
doubleprecision Fxrho
doubleprecision cg16
doubleprecision t1433
doubleprecision t1443
doubleprecision t291
doubleprecision t294
doubleprecision cg17
doubleprecision t423
doubleprecision t145
doubleprecision t146
doubleprecision t149
doubleprecision t150
doubleprecision t152
doubleprecision cg18
doubleprecision cg19
doubleprecision cg20
doubleprecision t210
doubleprecision t211
doubleprecision t951
doubleprecision t664
doubleprecision t384
doubleprecision t1083
doubleprecision t1747
doubleprecision t1497
doubleprecision t586
doubleprecision t429
doubleprecision t63
doubleprecision t1636
doubleprecision t921
doubleprecision t1rho
doubleprecision t1330
doubleprecision t1333
doubleprecision cg21
doubleprecision t380
doubleprecision t383
doubleprecision t389
doubleprecision t392
doubleprecision t1086
doubleprecision t741
doubleprecision kf2rho
doubleprecision s2rho
doubleprecision t900
doubleprecision t1842
doubleprecision t960
doubleprecision t906
doubleprecision t229
doubleprecision t230
doubleprecision cg22
doubleprecision cg23
doubleprecision t282
doubleprecision t285
doubleprecision t287
doubleprecision t288
doubleprecision t418
doubleprecision t22
doubleprecision t1089
doubleprecision t992
doubleprecision t852
doubleprecision t618
doubleprecision t97
doubleprecision t964
doubleprecision t217
doubleprecision t218
doubleprecision t219
doubleprecision t1852
doubleprecision t1837
doubleprecision t1327
doubleprecision t1329
doubleprecision t574
doubleprecision t
doubleprecision t64
doubleprecision t494
doubleprecision t1891
doubleprecision t1068
doubleprecision t1090
doubleprecision t1091
doubleprecision t100
doubleprecision t101
doubleprecision t102
doubleprecision t1686
doubleprecision t1071
doubleprecision t433
doubleprecision t436
doubleprecision t437
doubleprecision t438
doubleprecision t442
doubleprecision t1236
integer t1
integer t2
doubleprecision cg24
doubleprecision t1786
doubleprecision t750
doubleprecision t1004
doubleprecision t1571
doubleprecision t94
doubleprecision cg25
doubleprecision t74
doubleprecision t75
doubleprecision t1094
doubleprecision cg26
doubleprecision t980
doubleprecision cg27
doubleprecision t1910
doubleprecision t545
doubleprecision t1477
doubleprecision t1328
doubleprecision mu
doubleprecision t194
doubleprecision t197
doubleprecision t206
doubleprecision t1484
doubleprecision t1050
doubleprecision t1451
doubleprecision t1794
doubleprecision t184
doubleprecision t1458
doubleprecision t1459
doubleprecision t1455
doubleprecision t943
doubleprecision t760
doubleprecision t890
doubleprecision t824
doubleprecision t1533
doubleprecision A1rho
doubleprecision cg28
doubleprecision t1096
doubleprecision t269
doubleprecision t273
doubleprecision t274
doubleprecision t279
doubleprecision cg29
doubleprecision t1913
doubleprecision t1273
doubleprecision t1098
doubleprecision kfrho
doubleprecision t1324
doubleprecision cg30
doubleprecision t908
doubleprecision t1054
doubleprecision t358
doubleprecision t84
doubleprecision t85
doubleprecision cg31
doubleprecision kf
doubleprecision t806
doubleprecision cg32
doubleprecision cg33
doubleprecision t293
doubleprecision t754
doubleprecision t1133
doubleprecision t984
doubleprecision t891
doubleprecision t1049
doubleprecision t1058
doubleprecision t553
integer t3
integer t4
doubleprecision t5
doubleprecision t1759
doubleprecision t1159
doubleprecision t311
doubleprecision t911
doubleprecision cg34
doubleprecision t2rho
doubleprecision t1924
doubleprecision t807
doubleprecision t6
doubleprecision t7
doubleprecision t8
doubleprecision t260
doubleprecision t1588
doubleprecision t1811
doubleprecision t1815
doubleprecision t108
doubleprecision t109
doubleprecision t110
doubleprecision t111
doubleprecision t112
doubleprecision t76
doubleprecision cg35
doubleprecision t57
doubleprecision t58
doubleprecision t59
doubleprecision t60
doubleprecision t559
doubleprecision t566
doubleprecision t571
doubleprecision cg36
doubleprecision t1102
doubleprecision cg37
doubleprecision t930
doubleprecision t190
doubleprecision t235
doubleprecision t236
doubleprecision t237
doubleprecision t240
doubleprecision t241
doubleprecision t242
doubleprecision t244
doubleprecision t245
doubleprecision t1514
doubleprecision t11
doubleprecision t160
doubleprecision t163
doubleprecision t164
doubleprecision t167
doubleprecision t168
doubleprecision t171
doubleprecision t172
doubleprecision t173
doubleprecision t909
doubleprecision t66
doubleprecision t1883
doubleprecision Fx2rho
doubleprecision t1517
doubleprecision t1520
doubleprecision t996
doubleprecision cg38
doubleprecision t224
doubleprecision t1425
doubleprecision t1943
doubleprecision t117
doubleprecision t120
doubleprecision t121
doubleprecision t122
doubleprecision t125
doubleprecision t129
doubleprecision t357
doubleprecision t416
doubleprecision srho
doubleprecision t318
doubleprecision t321
doubleprecision t323
doubleprecision t326
doubleprecision t329
doubleprecision t330
doubleprecision t1105
doubleprecision cg39
doubleprecision t68
doubleprecision t69
doubleprecision t12
doubleprecision t1166
doubleprecision t1552
doubleprecision t1240
doubleprecision cg40
doubleprecision t1578
doubleprecision cg41
doubleprecision t72
doubleprecision t73
doubleprecision t1111
doubleprecision A
doubleprecision t15
doubleprecision t1438
doubleprecision t882
doubleprecision t808
doubleprecision t1406
doubleprecision trho
doubleprecision t1087
doubleprecision cg42
doubleprecision t1053
doubleprecision cg43
doubleprecision t61
doubleprecision t62
doubleprecision Fx1rho
doubleprecision t153
doubleprecision t154
doubleprecision t157
doubleprecision t158
doubleprecision t159
doubleprecision t1806
doubleprecision t246
doubleprecision t17
doubleprecision t19
doubleprecision cg44
doubleprecision cg45
doubleprecision A2rho
doubleprecision cg46
doubleprecision cg47
doubleprecision cg48
doubleprecision t23
doubleprecision t324
doubleprecision t1446
doubleprecision t1951
doubleprecision t1956
doubleprecision t972
doubleprecision t250
doubleprecision t253
doubleprecision t254
doubleprecision t255
doubleprecision t258
doubleprecision t259
doubleprecision t261
doubleprecision t262
doubleprecision t263
doubleprecision t1684
doubleprecision t88
doubleprecision t89
doubleprecision cg49
doubleprecision t1176
doubleprecision t528
doubleprecision t532
doubleprecision t536
doubleprecision cg50
doubleprecision cg51
doubleprecision cg52
doubleprecision cg53
doubleprecision t576
doubleprecision t1112
doubleprecision t1172
doubleprecision t348
doubleprecision t351
doubleprecision t352
doubleprecision t354
doubleprecision t356
doubleprecision cg54
doubleprecision s1rho
doubleprecision t361
doubleprecision t365
doubleprecision t366
doubleprecision t369
doubleprecision t373
doubleprecision t375
doubleprecision t376
doubleprecision t377
doubleprecision cg55
doubleprecision t1207
doubleprecision t1208
doubleprecision t1848
doubleprecision t1006
doubleprecision cg56
doubleprecision t1766
doubleprecision t415
doubleprecision t177
doubleprecision t178
doubleprecision t179
doubleprecision t180
doubleprecision t182
doubleprecision t186
doubleprecision t98
doubleprecision t1683
doubleprecision cg57
doubleprecision t1439
doubleprecision t393
doubleprecision t398
doubleprecision t402
doubleprecision t403
doubleprecision t405
doubleprecision t406
doubleprecision cg58
doubleprecision cg59
doubleprecision t956
doubleprecision cg60
doubleprecision t546
doubleprecision t549
doubleprecision t730
doubleprecision t1180
doubleprecision t612
doubleprecision t506
doubleprecision t797
doubleprecision t513
doubleprecision t518
doubleprecision t523
doubleprecision t493
doubleprecision t874
doubleprecision t500
doubleprecision t501
doubleprecision t335
doubleprecision t336
doubleprecision t342
doubleprecision t345
doubleprecision t346
doubleprecision cg61
doubleprecision cg62
doubleprecision t36
doubleprecision t1506
doubleprecision t1563
doubleprecision t1564
doubleprecision cg63
doubleprecision t686
doubleprecision t522
doubleprecision t91
doubleprecision t1061
doubleprecision t913
doubleprecision t453
doubleprecision t457
doubleprecision t967
doubleprecision cg64
doubleprecision cg65
doubleprecision t1187
doubleprecision t611
doubleprecision t1829
doubleprecision t1833
doubleprecision t49
doubleprecision t424
doubleprecision t425
doubleprecision t426
doubleprecision t428
doubleprecision t430
doubleprecision t958
doubleprecision t295
doubleprecision t299
doubleprecision t301
doubleprecision t302
doubleprecision t303
doubleprecision t304
doubleprecision t55
integer t51
doubleprecision t474
doubleprecision t477
doubleprecision t478
doubleprecision t479
doubleprecision t482
doubleprecision t486
doubleprecision t490
doubleprecision t1442
doubleprecision t914
doubleprecision t876
doubleprecision t878
doubleprecision t879
doubleprecision t877
doubleprecision t1100
doubleprecision t1876
doubleprecision t628
doubleprecision t629
doubleprecision t634
doubleprecision t138
doubleprecision t140
doubleprecision t141
doubleprecision t142
doubleprecision t1130
doubleprecision t1194
my_rho = rho
my_norm_drho = cg
t1 = 3 ** (0.1D1 / 0.3D1)
t2 = 4 ** (0.1D1 / 0.3D1)
t3 = t2 ** 2
t4 = t1 * t3
t5 = 0.1D1 / 0.3141592654D1
t6 = 0.1D1 / rho
t7 = t5 * t6
t8 = t7 ** (0.1D1 / 0.3D1)
rs = dble(t4) * t8 / 0.4D1
t11 = 0.1D1 + 0.21370D0 * rs
t12 = sqrt(rs)
t15 = t12 * rs
t17 = rs ** 0.20D1
t19 = 0.75957D1 * t12 + 0.35876D1 * rs + 0.16382D1 * t15 + 0.492
#94D0 * t17
t22 = 0.1D1 + 0.1608182432D2 / t19
t23 = log(t22)
cg22 = -0.62182D-1 * t11 * t23
t36 = log(0.1D1 + 0.3216468318D2 / (0.141189D2 * t12 + 0.61977D1
# * rs + 0.33662D1 * t15 + 0.62517D0 * t17))
t49 = log(0.1D1 + 0.2960857464D1 / (0.10357D2 * t12 + 0.36231D1
#* rs + 0.88026D0 * t15 + 0.49671D0 * t17))
t51 = 2 ** (0.1D1 / 0.3D1)
t55 = log(0.2D1)
t57 = 0.3141592654D1 ** 2
t58 = 0.1D1 / t57
cg59 = (0.1D1 - t55) * t58
t59 = t57 * rho
t60 = t59 ** (0.1D1 / 0.3D1)
cg1 = dble(t1) * t60
t61 = cg1 * t5
t62 = sqrt(t61)
cg40 = 0.2D1 * t62
t63 = 0.1D1 / cg40
t64 = cg * t63
t = t64 * t6 / 0.2D1
t66 = 0.1D1 / cg59
t68 = exp(-cg22 * t66)
t69 = -0.1D1 + t68
A = 0.66725D-1 * t66 / t69
t72 = t ** 2
t73 = t66 * t72
t74 = A * t72
t75 = 0.1D1 + t74
t76 = A ** 2
t77 = t72 ** 2
t79 = 0.1D1 + t74 + t76 * t77
t80 = 0.1D1 / t79
t81 = t75 * t80
t84 = 0.1D1 + 0.66725D-1 * t73 * t81
t85 = log(t84)
cg3 = cg22 + cg59 * t85
mu = 0.2224166667D-1 * t57
kf = cg1
cg16 = -0.3D1 / 0.4D1 * t5 * kf
t88 = 0.1D1 / kf
t89 = cg * t88
s = t89 * t6 / 0.2D1
t91 = s ** 2
t94 = 0.1D1 + 0.1243781095D1 * mu * t91
Fx = 0.1804D1 - 0.804D0 / t94
t97 = rho * cg16
exc = t97 * Fx + rho * cg3
t98 = t8 ** 2
t100 = 0.1D1 / t98 * t5
t101 = rho ** 2
t102 = 0.1D1 / t101
rsrho = -dble(t4) * t100 * t102 / 0.12D2
t108 = t19 ** 2
t109 = 0.1D1 / t108
t110 = t11 * t109
t111 = 0.1D1 / t12
t112 = t111 * rsrho
t117 = rs ** 0.10D1
t120 = 0.3797850000D1 * t112 + 0.35876D1 * rsrho + 0.2457300000D
#1 * t12 * rsrho + 0.985880D0 * t117 * rsrho
t121 = 0.1D1 / t22
t122 = t120 * t121
cg4 = -0.1328829340D-1 * rsrho * t23 + 0.9999999999D0 * t110 * t
#122
t125 = t60 ** 2
cg62 = dble(t1) / t125 * t57 / 0.3D1
t129 = 0.1D1 / t62
cg5 = t129 * cg62 * t5
t131 = cg40 ** 2
t132 = 0.1D1 / t131
t133 = cg * t132
t134 = t6 * cg5
t136 = t64 * t102
trho = -t133 * t134 / 0.2D1 - t136 / 0.2D1
t138 = cg59 ** 2
t140 = t69 ** 2
t141 = 0.1D1 / t140
t142 = 0.1D1 / t138 * t141
Arho = 0.66725D-1 * t142 * cg4 * t68
t145 = t66 * t
t146 = t81 * trho
t149 = Arho * t72
t150 = A * t
t152 = 0.2D1 * t150 * trho
t153 = t149 + t152
t154 = t153 * t80
t157 = t79 ** 2
t158 = 0.1D1 / t157
t159 = t75 * t158
t160 = A * t77
t163 = t72 * t
t164 = t76 * t163
t167 = t149 + t152 + 0.2D1 * t160 * Arho + 0.4D1 * t164 * trho
t168 = t159 * t167
t171 = 0.133450D0 * t145 * t146 + 0.66725D-1 * t73 * t154 - 0.66
#725D-1 * t73 * t168
t172 = cg59 * t171
t173 = 0.1D1 / t84
cg11 = cg4 + t172 * t173
kfrho = cg62
cg12 = -0.3D1 / 0.4D1 * t5 * kfrho
t177 = kf ** 2
t178 = 0.1D1 / t177
t179 = cg * t178
t180 = t6 * kfrho
t182 = t89 * t102
srho = -t179 * t180 / 0.2D1 - t182 / 0.2D1
t184 = t94 ** 2
t186 = 0.1D1 / t184 * mu
Fxrho = 0.2000000001D1 * t186 * s * srho
t190 = rho * cg12
exc_rho = cg16 * Fx + t190 * Fx + t97 * Fxrho + cg3 + rho * cg11
cg33 = t63 * t6 / 0.2D1
t194 = t81 * cg33
t197 = t66 * t163
t206 = 0.2D1 * t150 * cg33 + 0.4D1 * t164 * cg33
t210 = 0.133450D0 * t145 * t194 + 0.133450D0 * t197 * A * cg33 *
# t80 - 0.66725D-1 * t73 * t159 * t206
t211 = cg59 * t210
cg2 = t211 * t173
cg13 = t88 * t6 / 0.2D1
cg58 = 0.2000000001D1 * t186 * s * cg13
exc_norm_drho = t97 * cg58 + rho * cg2
t217 = 0.1D1 / t98 / t7 * t58
t218 = t101 ** 2
t219 = 0.1D1 / t218
t224 = 0.1D1 / t101 / rho
cg60 = -dble(t4) * t217 * t219 / 0.18D2 + dble(t4) * t100 * t224
# / 0.6D1
t229 = 0.1328829340D-1 * cg60 * t23
t230 = rsrho * t109
t234 = 0.1D1 / t108 / t19
t235 = t11 * t234
t236 = t120 ** 2
t237 = t236 * t121
t240 = 0.1D1 / t15
t241 = rsrho ** 2
t242 = t240 * t241
t244 = t111 * cg60
t245 = 0.3797850000D1 * t244
t246 = 0.35876D1 * cg60
t250 = 0.2457300000D1 * t12 * cg60
t253 = 0.985880D0 * t117 * cg60
t254 = -0.1898925000D1 * t242 + t245 + t246 + 0.1228650000D1 * t
#111 * t241 + t250 + 0.9858800D0 * t241 + t253
t255 = t254 * t121
t258 = t108 ** 2
t259 = 0.1D1 / t258
t260 = t11 * t259
t261 = t22 ** 2
t262 = 0.1D1 / t261
t263 = t236 * t262
cg6 = -t229 + 0.4274000000D0 * t230 * t122 - 0.2000000000D1 * t2
#35 * t237 + 0.9999999999D0 * t110 * t255 + 0.1608182432D2 * t260 *
# t263
cg55 = cg4
t269 = t57 ** 2
cg14 = -0.2D1 / 0.9D1 * dble(t1) / t125 / t59 * t269
t273 = 0.1D1 / t62 / t61
t274 = cg62 ** 2
t279 = t129 * cg14 * t5
cg20 = -t273 * t274 * t58 / 0.2D1 + t279
cg0 = cg5
t281 = 0.1D1 / t131 / cg40
t282 = cg * t281
t285 = t102 * cg5
t287 = t133 * t285 / 0.2D1
t288 = t6 * cg20
t291 = t102 * cg0
t293 = t133 * t291 / 0.2D1
t294 = t64 * t224
cg15 = t282 * t134 * cg0 + t287 - t133 * t288 / 0.2D1 + t293 + t
#294
t295 = t6 * cg0
t1rho = -t133 * t295 / 0.2D1 - t136 / 0.2D1
t299 = 0.1D1 / t138 / cg59
t301 = 0.1D1 / t140 / t69
t302 = t299 * t301
t303 = t68 ** 2
t304 = cg4 * t303
t311 = t299 * t141
cg21 = 0.133450D0 * t302 * t304 * cg55 + 0.66725D-1 * t142 * cg6
# * t68 - 0.66725D-1 * t311 * cg4 * cg55 * t68
A1rho = 0.66725D-1 * t142 * cg55 * t68
t318 = t66 * t1rho
t321 = A1rho * t72
t323 = 0.2D1 * t150 * t1rho
t324 = t321 + t323
t325 = t324 * t80
t326 = t325 * trho
t329 = t145 * t75
t330 = t158 * trho
t335 = t321 + t323 + 0.2D1 * t160 * A1rho + 0.4D1 * t164 * t1rho
t336 = t330 * t335
t339 = t81 * cg15
t342 = t154 * t1rho
t345 = cg21 * t72
t346 = Arho * t
t348 = 0.2D1 * t346 * t1rho
t349 = A1rho * t
t351 = 0.2D1 * t349 * trho
t352 = A * t1rho
t354 = 0.2D1 * t352 * trho
t356 = 0.2D1 * t150 * cg15
t357 = t345 + t348 + t351 + t354 + t356
t358 = t357 * t80
t361 = t153 * t158
t365 = t158 * t167
t366 = t365 * t1rho
t369 = t324 * t158
t373 = t73 * t75
t375 = 0.1D1 / t157 / t79
t376 = t375 * t167
t377 = t376 * t335
t380 = A1rho * t77
t383 = A * t163
t384 = Arho * t1rho
t389 = trho * A1rho
t392 = t76 * t72
t393 = trho * t1rho
t398 = t345 + t348 + t351 + t354 + t356 + 0.2D1 * t380 * Arho +
#0.8D1 * t383 * t384 + 0.2D1 * t160 * cg21 + 0.8D1 * t383 * t389 +
#0.12D2 * t392 * t393 + 0.4D1 * t164 * cg15
t402 = 0.133450D0 * t318 * t146 + 0.133450D0 * t145 * t326 - 0.1
#33450D0 * t329 * t336 + 0.133450D0 * t145 * t339 + 0.133450D0 * t1
#45 * t342 + 0.66725D-1 * t73 * t358 - 0.66725D-1 * t73 * t361 * t3
#35 - 0.133450D0 * t329 * t366 - 0.66725D-1 * t73 * t369 * t167 + 0
#.133450D0 * t373 * t377 - 0.66725D-1 * t73 * t159 * t398
t403 = cg59 * t402
t405 = t84 ** 2
t406 = 0.1D1 / t405
t407 = t81 * t1rho
t415 = 0.133450D0 * t145 * t407 + 0.66725D-1 * t73 * t325 - 0.66
#725D-1 * t73 * t159 * t335
t416 = t406 * t415
t418 = cg59 * t415
cg10 = cg6 + t403 * t173 - t172 * t416
cg32 = cg14
cg61 = -0.3D1 / 0.4D1 * t5 * cg32
cg24 = cg12
t423 = 0.1D1 / t177 / kf
t424 = cg * t423
t425 = kfrho ** 2
t426 = t6 * t425
t428 = t102 * kfrho
t429 = t179 * t428
t430 = t6 * cg32
t432 = t179 * t430 / 0.2D1
t433 = t89 * t224
cg57 = t424 * t426 + t429 - t432 + t433
s1rho = srho
t436 = mu ** 2
t437 = 0.1D1 / t184 / t94 * t436
t438 = t91 * srho
t442 = s1rho * srho
cg25 = -0.9950248765D1 * t437 * t438 * s1rho + 0.2000000001D1 *
#t186 * t442 + 0.2000000001D1 * t186 * s * cg57
Fx1rho = 0.2000000001D1 * t186 * s * s1rho
t453 = rho * cg61
t457 = rho * cg24
exc_rho_rho = cg24 * Fx + cg16 * Fx1rho + cg12 * Fx + t453 * Fx
#+ t190 * Fx1rho + cg16 * Fxrho + t457 * Fxrho + t97 * cg25 + cg55
#+ t418 * t173 + cg11 + rho * cg10
t460 = t132 * t6
t462 = t63 * t102
cg18 = -t460 * cg5 / 0.2D1 - t462 / 0.2D1
t464 = t66 * trho
t467 = t154 * cg33
t470 = t158 * cg33
t471 = t470 * t167
t474 = t81 * cg18
t477 = t73 * A
t478 = cg33 * t80
t479 = t478 * trho
t482 = Arho * cg33
t486 = A * cg18
t490 = t197 * A
t493 = t158 * t206
t494 = t493 * trho
t500 = t375 * t206
t501 = t500 * t167
t506 = A * trho
t513 = cg33 * trho
t518 = 0.2D1 * t346 * cg33 + 0.2D1 * t506 * cg33 + 0.2D1 * t150
#* cg18 + 0.8D1 * t383 * t482 + 0.12D2 * t392 * t513 + 0.4D1 * t164
# * cg18
t522 = 0.133450D0 * t464 * t194 + 0.133450D0 * t145 * t467 - 0.1
#33450D0 * t329 * t471 + 0.133450D0 * t145 * t474 + 0.400350D0 * t4
#77 * t479 + 0.133450D0 * t197 * t482 * t80 + 0.133450D0 * t197 * t
#486 * t80 - 0.133450D0 * t490 * t471 - 0.133450D0 * t329 * t494 -
#0.66725D-1 * t73 * t361 * t206 + 0.133450D0 * t373 * t501 - 0.6672
#5D-1 * t73 * t159 * t518
t523 = cg59 * t522
t525 = t406 * t171
cg19 = t523 * t173 - t211 * t525
t528 = t178 * t6
cg47 = -t528 * kfrho / 0.2D1 - t88 * t102 / 0.2D1
t532 = t91 * cg13
t536 = srho * cg13
cg48 = -0.9950248765D1 * t437 * t532 * srho + 0.2000000001D1 * t
#186 * t536 + 0.2000000001D1 * t186 * s * cg47
exc_norm_drho_rho = cg16 * cg58 + t190 * cg58 + t97 * cg48 + cg2
# + rho * cg19
t545 = cg33 ** 2
t546 = t66 * t545
t549 = A * t545
t553 = t470 * t206
t559 = t206 ** 2
t566 = 0.2D1 * t549 + 0.12D2 * t392 * t545
t571 = cg59 * (0.133450D0 * t546 * t81 + 0.667250D0 * t73 * t549
# * t80 - 0.266900D0 * t329 * t553 - 0.266900D0 * t490 * t553 + 0.1
#33450D0 * t73 * t75 * t375 * t559 - 0.66725D-1 * t73 * t159 * t566
#)
t573 = t210 ** 2
t574 = cg59 * t573
cg9 = t571 * t173 - t574 * t406
t576 = cg13 ** 2
cg28 = -0.9950248765D1 * t437 * t91 * t576 + 0.2000000001D1 * t1
#86 * t576
exc_norm_drho_norm_drho = t97 * cg28 + rho * cg9
t586 = 0.1D1 / t57 / 0.3141592654D1
cg42 = -0.5D1 / 0.54D2 * dble(t4) / t98 / t58 / t102 * t586 / t2
#18 / t101 + dble(t4) * t217 / t218 / rho / 0.3D1 - dble(t4) * t100
# * t219 / 0.2D1
rs2rho = rsrho
t603 = cg60 * t109
t611 = 0.3797850000D1 * t111 * rs2rho + 0.35876D1 * rs2rho + 0.2
#457300000D1 * t12 * rs2rho + 0.985880D0 * t117 * rs2rho
t612 = t611 * t121
t618 = t122 * t611
t628 = -0.1898925000D1 * t240 * rsrho * rs2rho + t245 + t246 + 0
#.1228650000D1 * t112 * rs2rho + t250 + 0.9858800D0 * rsrho * rs2rh
#o + t253
t629 = t628 * t121
t634 = t120 * t262 * t611
t652 = rs2rho * t109
t658 = rs ** 2
t664 = t240 * cg60
t686 = 0.2848387500D1 / t12 / t658 * t241 * rs2rho - 0.379785000
#0D1 * t664 * rsrho - 0.1898925000D1 * t664 * rs2rho + 0.3797850000
#D1 * t111 * cg42 + 0.35876D1 * cg42 - 0.6143250000D0 * t242 * rs2r
#ho + 0.2457300000D1 * t244 * rsrho + 0.1228650000D1 * t244 * rs2rh
#o + 0.2457300000D1 * t12 * cg42 + 0.19717600D1 * cg60 * rsrho + 0.
#9858800D0 * cg60 * rs2rho + 0.985880D0 * t117 * cg42
cg7 = -0.1328829340D-1 * cg42 * t23 + 0.2137000000D0 * t603 * t6
#12 + 0.4274000000D0 * t603 * t122 - 0.8548000000D0 * rsrho * t234
#* t618 + 0.4274000000D0 * t230 * t629 + 0.6873371714D1 * rsrho * t
#259 * t634 - 0.4274000000D0 * rs2rho * t234 * t237 + 0.6000000000D
#1 * t260 * t237 * t611 - 0.4000000000D1 * t235 * t629 * t120 - 0.9
#649094592D2 * t11 / t258 / t19 * t263 * t611 + 0.2137000000D0 * t6
#52 * t255 - 0.2000000000D1 * t235 * t255 * t611 + 0.9999999999D0 *
# t110 * t686 * t121 + 0.1608182432D2 * t260 * t254 * t262 * t611 +
# 0.3436685857D1 * rs2rho * t259 * t263 + 0.3216364864D2 * t260 * t
#628 * t262 * t120 + 0.5172501469D3 * t11 / t258 / t108 * t236 / t2
#61 / t22 * t611
cg37 = -t229 + 0.2137000000D0 * t230 * t612 + 0.2137000000D0 * t
#652 * t122 - 0.2000000000D1 * t235 * t618 + 0.9999999999D0 * t110
#* t629 + 0.1608182432D2 * t260 * t634
cg64 = cg37
cg27 = -0.1328829340D-1 * rs2rho * t23 + 0.9999999999D0 * t110 *
# t612
cg65 = 0.10D2 / 0.27D2 * dble(t1) / t125 / t101 * t57
cg44 = kfrho
t730 = cg1 ** 2
t738 = t273 * cg14
t741 = t58 * cg44
cg46 = -t273 * cg62 * t741 / 0.2D1 + t279
cg54 = cg46
cg45 = t129 * cg44 * t5
t750 = t131 ** 2
t754 = cg5 * cg0
t760 = t6 * cg46
cg41 = -0.3D1 * cg / t750 * t6 * t754 * cg45 - t282 * t285 * cg0
# + t282 * t760 * cg0 + t282 * t134 * cg54 - t282 * t285 * cg45 - t
#133 * t224 * cg5 + t133 * t102 * cg46 / 0.2D1 + t282 * t288 * cg45
# + t133 * t102 * cg20 / 0.2D1 - t133 * t6 * (0.3D1 / 0.4D1 / t62 /
# t730 / t58 * t274 * t586 * cg44 - t738 * t58 * cg62 - t738 * t741
# / 0.2D1 + t129 * cg65 * t5) / 0.2D1 - t282 * t291 * cg45 - t133 *
# t224 * cg0 + t133 * t102 * cg54 / 0.2D1 - t133 * t224 * cg45 - 0.
#3D1 * t64 * t219
t797 = t133 * t102 * cg45 / 0.2D1
cg23 = t282 * t134 * cg45 + t287 - t133 * t760 / 0.2D1 + t797 +
#t294
cg43 = t282 * t295 * cg45 + t293 - t133 * t6 * cg54 / 0.2D1 + t7
#97 + t294
t2rho = -t133 * t6 * cg45 / 0.2D1 - t136 / 0.2D1
t806 = t138 ** 2
t807 = 0.1D1 / t806
t808 = t140 ** 2
t824 = t303 * cg55 * cg27
t852 = cg55 * cg27 * t68
cg56 = 0.400350D0 * t807 / t808 * cg4 * t303 * t68 * cg55 * cg27
# + 0.133450D0 * t302 * cg37 * t303 * cg55 - 0.400350D0 * t807 * t3
#01 * cg4 * t824 + 0.133450D0 * t302 * t304 * cg64 + 0.133450D0 * t
#302 * cg6 * t303 * cg27 + 0.66725D-1 * t142 * cg7 * t68 - 0.66725D
#-1 * t311 * cg6 * cg27 * t68 - 0.66725D-1 * t311 * cg37 * cg55 * t
#68 - 0.66725D-1 * t311 * cg4 * cg64 * t68 + 0.66725D-1 * t807 * t1
#41 * cg4 * t852
cg35 = 0.133450D0 * t302 * t304 * cg27 + 0.66725D-1 * t142 * cg3
#7 * t68 - 0.66725D-1 * t311 * cg4 * cg27 * t68
cg34 = 0.133450D0 * t302 * t824 + 0.66725D-1 * t142 * cg64 * t68
# - 0.66725D-1 * t311 * t852
A2rho = 0.66725D-1 * t142 * cg27 * t68
t874 = A2rho * t72
t876 = 0.2D1 * t150 * t2rho
t877 = t874 + t876
t878 = t877 * t80
t879 = t878 * trho
t882 = t66 * t2rho
t890 = t874 + t876 + 0.2D1 * t160 * A2rho + 0.4D1 * t164 * t2rho
t891 = t335 * t890
t898 = t73 * t153
t900 = t375 * t335 * t890
t903 = cg35 * t72
t905 = 0.2D1 * t346 * t2rho
t906 = A2rho * t
t908 = 0.2D1 * t906 * trho
t909 = A * t2rho
t911 = 0.2D1 * t909 * trho
t913 = 0.2D1 * t150 * cg23
t914 = t903 + t905 + t908 + t911 + t913
t915 = t914 * t80
t921 = t882 * t75
t927 = A2rho * t77
t930 = Arho * t2rho
t943 = t903 + t905 + t908 + t911 + t913 + 0.2D1 * t927 * Arho +
#0.8D1 * t383 * t930 + 0.2D1 * t160 * cg35 + 0.8D1 * t383 * trho *
#A2rho + 0.12D2 * t392 * trho * t2rho + 0.4D1 * t164 * cg23
t951 = 0.133450D0 * t318 * t879 + 0.133450D0 * t882 * t339 + 0.2
#66900D0 * t329 * t375 * trho * t891 + 0.133450D0 * t145 * t325 * c
#g23 + 0.133450D0 * t898 * t900 + 0.133450D0 * t145 * t915 * t1rho
#+ 0.133450D0 * t882 * t326 - 0.133450D0 * t921 * t336 + 0.133450D0
# * t145 * t154 * cg43 + 0.133450D0 * t373 * t375 * t943 * t335 + 0
#.133450D0 * t73 * t877 * t377
t956 = cg34 * t72
t958 = 0.2D1 * t349 * t2rho
t960 = 0.2D1 * t906 * t1rho
t962 = 0.2D1 * t909 * t1rho
t964 = 0.2D1 * t150 * cg43
t967 = A1rho * t2rho
t972 = t1rho * A2rho
t980 = t956 + t958 + t960 + t962 + t964 + 0.2D1 * t927 * A1rho +
# 0.8D1 * t383 * t967 + 0.2D1 * t160 * cg34 + 0.8D1 * t383 * t972 +
# 0.12D2 * t392 * t1rho * t2rho + 0.4D1 * t164 * cg43
t984 = t956 + t958 + t960 + t962 + t964
t992 = t357 * t158
t996 = t145 * t877
t1004 = t145 * t153
t1006 = t158 * t335 * t2rho
t1019 = -0.133450D0 * t329 * t158 * cg23 * t335 - 0.66725D-1 * t
#73 * t361 * t980 - 0.66725D-1 * t73 * t984 * t158 * t167 + 0.13345
#0D0 * t145 * t358 * t2rho - 0.66725D-1 * t73 * t992 * t890 - 0.133
#450D0 * t996 * t336 - 0.133450D0 * t996 * t366 - 0.133450D0 * t329
# * t330 * t980 - 0.133450D0 * t1004 * t1006 + 0.266900D0 * t329 *
#t376 * t1rho * t890 - 0.133450D0 * t329 * t365 * cg43 - 0.66725D-1
# * t73 * t369 * t943
t1021 = t984 * t80
t1049 = t73 * t324
t1050 = t376 * t890
t1053 = t318 * t75
t1054 = t330 * t890
t1058 = t158 * t1rho * t890
t1061 = 0.133450D0 * t145 * t1021 * trho - 0.133450D0 * t921 * t
#366 + 0.266900D0 * t329 * t376 * t335 * t2rho + 0.133450D0 * t373
#* t375 * t398 * t890 - 0.66725D-1 * t73 * t914 * t158 * t335 + 0.1
#33450D0 * t145 * t878 * cg15 - 0.133450D0 * t329 * t158 * cg15 * t
#890 + 0.133450D0 * t66 * cg43 * t146 + 0.133450D0 * t1049 * t1050
#- 0.133450D0 * t1053 * t1054 - 0.133450D0 * t1004 * t1058
t1068 = t145 * t324
t1071 = t967 * trho
t1074 = cg21 * t
t1076 = 0.2D1 * t1074 * t2rho
t1079 = 0.2D1 * cg35 * t * t1rho
t1080 = t930 * t1rho
t1081 = 0.2D1 * t1080
t1083 = 0.2D1 * t346 * cg43
t1086 = 0.2D1 * cg34 * t * trho
t1087 = 0.2D1 * t1071
t1089 = 0.2D1 * t349 * cg23
t1090 = t972 * trho
t1091 = 0.2D1 * t1090
t1094 = 0.2D1 * A * cg43 * trho
t1096 = 0.2D1 * t352 * cg23
t1098 = 0.2D1 * t906 * cg15
t1100 = 0.2D1 * t909 * cg15
t1102 = 0.2D1 * t150 * cg41
t1105 = t76 * t
t1111 = 0.24D2 * t74 * t1071 + t1076 + t1079 + t1081 + t1083 + t
#1086 + t1087 + t1089 + t1091 + t1094 + t1096 + t1098 + t1100 + t11
#02 + 0.24D2 * t74 * t1090 + 0.24D2 * t1105 * t393 * t2rho + 0.24D2
# * t74 * t1080
t1112 = cg56 * t72
t1130 = A2rho * t163
t1133 = A1rho * t163
t1159 = t1112 + 0.2D1 * t380 * cg35 + 0.2D1 * t927 * cg21 + 0.4D
#1 * t164 * cg41 + 0.2D1 * t160 * cg56 + 0.8D1 * t383 * trho * cg34
# + 0.12D2 * t392 * trho * cg43 + 0.8D1 * t383 * cg23 * A1rho + 0.8
#D1 * t1130 * t389 + 0.8D1 * t1133 * t930 + 0.12D2 * t392 * cg23 *
#t1rho + 0.8D1 * t383 * cg35 * t1rho + 0.2D1 * cg34 * t77 * Arho +
#0.8D1 * t1130 * t384 + 0.12D2 * t392 * cg15 * t2rho + 0.8D1 * t383
# * Arho * cg43 + 0.8D1 * t383 * cg21 * t2rho + 0.8D1 * t383 * cg15
# * A2rho
t1166 = t157 ** 2
t1167 = 0.1D1 / t1166
t1172 = t877 * t158
t1176 = t1112 + t1076 + t1079 + t1081 + t1083 + t1086 + t1087 +
#t1089 + t1091 + t1094 + t1096 + t1098 + t1100 + t1102
t1180 = t365 * t2rho
t1187 = t81 * cg23
t1194 = 0.133450D0 * t145 * t81 * cg41 + 0.133450D0 * t373 * t37
#6 * t980 - 0.133450D0 * t1068 * t1054 - 0.66725D-1 * t73 * t159 *
#(t1111 + t1159) + 0.133450D0 * t882 * t342 - 0.400350D0 * t373 * t
#1167 * t167 * t891 - 0.66725D-1 * t73 * t1172 * t398 + 0.66725D-1
#* t73 * t1176 * t80 - 0.133450D0 * t1068 * t1180 - 0.133450D0 * t3
#29 * t158 * t398 * t2rho + 0.133450D0 * t318 * t1187 - 0.133450D0
#* t329 * t158 * t943 * t1rho
t1207 = 0.133450D0 * t145 * t81 * t2rho + 0.66725D-1 * t73 * t87
#8 - 0.66725D-1 * t73 * t159 * t890
t1208 = t406 * t1207
t1236 = 0.133450D0 * t882 * t146 + 0.133450D0 * t145 * t879 - 0.
#133450D0 * t329 * t1054 + 0.133450D0 * t145 * t1187 + 0.133450D0 *
# t145 * t154 * t2rho + 0.66725D-1 * t73 * t915 - 0.66725D-1 * t73
#* t361 * t890 - 0.133450D0 * t329 * t1180 - 0.66725D-1 * t73 * t11
#72 * t167 + 0.133450D0 * t373 * t1050 - 0.66725D-1 * t73 * t159 *
#t943
t1237 = cg59 * t1236
t1240 = 0.1D1 / t405 / t84
t1273 = 0.133450D0 * t882 * t407 + 0.133450D0 * t145 * t878 * t1
#rho - 0.133450D0 * t329 * t1058 + 0.133450D0 * t145 * t81 * cg43 +
# 0.133450D0 * t145 * t325 * t2rho + 0.66725D-1 * t73 * t1021 - 0.6
#6725D-1 * t73 * t369 * t890 - 0.133450D0 * t329 * t1006 - 0.66725D
#-1 * t73 * t1172 * t335 + 0.133450D0 * t373 * t900 - 0.66725D-1 *
#t73 * t159 * t980
cg36 = cg65
kf2rho = cg44
cg50 = cg61
cg51 = cg50
cg49 = -0.3D1 / 0.4D1 * t5 * kf2rho
t1286 = t177 ** 2
cg17 = t424 * t180 * kf2rho + t429 / 0.2D1 - t432 + t179 * t102
#* kf2rho / 0.2D1 + t433
cg39 = cg17
s2rho = -t179 * t6 * kf2rho / 0.2D1 - t182 / 0.2D1
t1324 = t184 ** 2
t1327 = 0.1D1 / t1324 * t436 * mu
t1328 = t91 * s
t1329 = t1327 * t1328
t1330 = t442 * s2rho
t1333 = t437 * s
cg29 = -0.9950248765D1 * t437 * t438 * s2rho + 0.2000000001D1 *
#t186 * s2rho * srho + 0.2000000001D1 * t186 * s * cg17
cg30 = -0.9950248765D1 * t437 * t91 * s1rho * s2rho + 0.20000000
#01D1 * t186 * s2rho * s1rho + 0.2000000001D1 * t186 * s * cg39
Fx2rho = 0.2000000001D1 * t186 * s * s2rho
cg52 = cg51 * Fx + cg24 * Fx2rho + cg49 * Fx1rho + cg16 * cg30 +
# cg50 * Fx + cg12 * Fx2rho + cg61 * Fx - 0.3D1 / 0.4D1 * rho * t5
#* cg36 * Fx + t453 * Fx2rho + cg12 * Fx1rho + rho * cg50 * Fx1rho
#+ t190 * cg30 + cg49 * Fxrho + cg16 * cg29 + cg24 * Fxrho + rho *
#cg51 * Fxrho + t457 * cg29 + cg16 * cg25 + rho * cg49 * cg25 + t97
# * (0.7425558783D2 * t1329 * t1330 - 0.2985074630D2 * t1333 * t133
#0 - 0.9950248765D1 * t437 * t91 * cg17 * s1rho - 0.9950248765D1 *
#t437 * t438 * cg39 + 0.2000000001D1 * t186 * cg39 * srho + 0.20000
#00001D1 * t186 * s1rho * cg17 - 0.9950248765D1 * t437 * t91 * cg57
# * s2rho + 0.2000000001D1 * t186 * s2rho * cg57 + 0.2000000001D1 *
# t186 * s * (-0.3D1 * cg / t1286 * t426 * kf2rho - t424 * t102 * t
#425 + 0.2D1 * t424 * t430 * kfrho - 0.2D1 * t424 * t428 * kf2rho -
# 0.2D1 * t179 * t224 * kfrho + 0.3D1 / 0.2D1 * t179 * t102 * cg32
#+ t424 * t430 * kf2rho - t179 * t6 * cg36 / 0.2D1 - t179 * t224 *
#kf2rho - 0.3D1 * t89 * t219))
exc_rho_rho_rho = cg52 + cg64 + cg59 * t1273 * t173 - t418 * t12
#08 + cg37 + t1237 * t173 - t172 * t1208 + cg10 + rho * (cg7 + cg59
# * (t951 + t1019 + t1061 + t1194) * t173 - t403 * t1208 - t1237 *
#t416 + 0.2D1 * t172 * t1240 * t415 * t1207 - t172 * t406 * t1273)
t1406 = t132 * t102
cg38 = t281 * t6 * t754 + t1406 * cg5 / 0.2D1 - t460 * cg20 / 0.
#2D1 + t1406 * cg0 / 0.2D1 + t63 * t224
cg53 = -t460 * cg0 / 0.2D1 - t462 / 0.2D1
t1425 = cg33 * A1rho
t1433 = 0.2D1 * t349 * cg33 + 0.2D1 * t352 * cg33 + 0.2D1 * t150
# * cg53 + 0.8D1 * t383 * t1425 + 0.12D2 * t392 * cg33 * t1rho + 0.
#4D1 * t164 * cg53
t1438 = t197 * Arho
t1439 = t470 * t335
t1442 = cg18 * t158
t1443 = t1442 * t335
t1446 = Arho * cg53
t1451 = t167 * t335
t1455 = t464 * t75
t1458 = t375 * cg33
t1459 = t1458 * t1451
t1477 = 0.133450D0 * t66 * cg15 * t194 + 0.133450D0 * t373 * t37
#5 * t1433 * t167 - 0.133450D0 * t1438 * t1439 - 0.133450D0 * t490
#* t1443 + 0.133450D0 * t197 * t1446 * t80 - 0.400350D0 * t373 * t1
#167 * t206 * t1451 - 0.133450D0 * t1455 * t1439 + 0.266900D0 * t32
#9 * t1459 - 0.66725D-1 * t73 * t369 * t518 + 0.133450D0 * t373 * t
#500 * t398 + 0.133450D0 * t145 * t325 * cg18 + 0.133450D0 * t318 *
# t474 - 0.133450D0 * t329 * t158 * t518 * t1rho
t1480 = t500 * t335
t1484 = t478 * t1rho
t1497 = trho * t335
t1501 = t81 * cg53
t1506 = t145 * A
t1514 = t158 * cg53 * t167
t1517 = t470 * t398
t1520 = -0.133450D0 * t329 * t1443 + 0.133450D0 * t898 * t1480 +
# 0.400350D0 * t73 * Arho * t1484 - 0.66725D-1 * t73 * t361 * t1433
# + 0.400350D0 * t477 * cg18 * t80 * t1rho + 0.133450D0 * t145 * t3
#58 * cg33 - 0.400350D0 * t477 * t470 * t1497 + 0.133450D0 * t464 *
# t1501 - 0.133450D0 * t1068 * t494 + 0.800700D0 * t1506 * t478 * t
#393 + 0.400350D0 * t73 * A1rho * t479 - 0.133450D0 * t329 * t1514
#- 0.133450D0 * t490 * t1517
t1533 = t375 * t518
t1552 = cg21 * cg33
t1563 = 0.133450D0 * t197 * A * cg38 * t80 - 0.133450D0 * t197 *
# A1rho * t471 + 0.400350D0 * t477 * cg53 * t80 * trho + 0.133450D0
# * t373 * t1533 * t335 - 0.133450D0 * t490 * t1514 - 0.133450D0 *
#t1004 * t1439 + 0.133450D0 * t145 * t81 * cg38 + 0.266900D0 * t490
# * t1459 + 0.133450D0 * t145 * t154 * cg53 + 0.400350D0 * t477 * t
#478 * cg15 + 0.133450D0 * t197 * t1552 * t80 - 0.133450D0 * t329 *
# t158 * t1433 * trho - 0.133450D0 * t329 * t493 * cg15
t1564 = t167 * t1rho
t1571 = t325 * cg33
t1578 = A1rho * cg18
t1584 = t384 * cg33
t1588 = t389 * cg33
t1627 = 0.2D1 * t1074 * cg33 + 0.2D1 * t1584 + 0.2D1 * t346 * cg
#53 + 0.2D1 * t1588 + 0.2D1 * A * cg15 * cg33 + 0.2D1 * t506 * cg53
# + 0.2D1 * t349 * cg18 + 0.2D1 * t352 * cg18 + 0.2D1 * t150 * cg38
# + 0.8D1 * t1133 * t482 + 0.24D2 * t74 * t1584 + 0.8D1 * t383 * t1
#446 + 0.8D1 * t383 * t1552 + 0.24D2 * t74 * t1588 + 0.24D2 * t1105
# * t513 * t1rho + 0.12D2 * t392 * cg53 * trho + 0.12D2 * t392 * cg
#33 * cg15 + 0.8D1 * t383 * t1578 + 0.12D2 * t392 * cg18 * t1rho +
#0.4D1 * t164 * cg38
t1636 = t493 * t1rho
t1648 = -0.400350D0 * t477 * t470 * t1564 + 0.266900D0 * t329 *
#t500 * t1497 + 0.133450D0 * t464 * t1571 - 0.133450D0 * t1053 * t4
#71 - 0.133450D0 * t1053 * t494 + 0.133450D0 * t197 * t1578 * t80 -
# 0.66725D-1 * t73 * t159 * t1627 - 0.66725D-1 * t73 * t992 * t206
#+ 0.133450D0 * t1049 * t501 - 0.133450D0 * t1004 * t1636 - 0.13345
#0D0 * t1068 * t471 + 0.133450D0 * t318 * t467 + 0.266900D0 * t329
#* t500 * t1564 - 0.133450D0 * t329 * t1517
t1683 = 0.133450D0 * t318 * t194 + 0.133450D0 * t145 * t1571 - 0
#.133450D0 * t329 * t1439 + 0.133450D0 * t145 * t1501 + 0.400350D0
#* t477 * t1484 + 0.133450D0 * t197 * t1425 * t80 + 0.133450D0 * t1
#97 * A * cg53 * t80 - 0.133450D0 * t490 * t1439 - 0.133450D0 * t32
#9 * t1636 - 0.66725D-1 * t73 * t369 * t206 + 0.133450D0 * t373 * t
#1480 - 0.66725D-1 * t73 * t159 * t1433
t1684 = cg59 * t1683
t1686 = t1240 * t171
cg31 = cg47
t1702 = t536 * s1rho
t1720 = t91 * cg47
cg26 = -0.9950248765D1 * t437 * t532 * s1rho + 0.2000000001D1 *
#t186 * s1rho * cg13 + 0.2000000001D1 * t186 * s * cg31
exc_norm_drho_rho_rho = cg24 * cg58 + cg16 * cg26 + cg12 * cg58
#+ t453 * cg58 + t190 * cg26 + cg16 * cg48 + t457 * cg48 + t97 * (0
#.7425558783D2 * t1329 * t1702 - 0.2985074630D2 * t1333 * t1702 - 0
#.9950248765D1 * t437 * t91 * cg31 * srho - 0.9950248765D1 * t437 *
# t532 * cg57 + 0.2000000001D1 * t186 * cg57 * cg13 + 0.2000000001D
#1 * t186 * srho * cg31 - 0.9950248765D1 * t437 * t1720 * s1rho + 0
#.2000000001D1 * t186 * s1rho * cg47 + 0.2000000001D1 * t186 * s *
#(t423 * t6 * t425 + t178 * t102 * kfrho - t528 * cg32 / 0.2D1 + t8
#8 * t224)) + t1684 * t173 - t211 * t416 + cg19 + rho * (cg59 * (t1
#477 + t1520 + t1563 + t1648) * t173 - t523 * t416 - t1684 * t525 +
# 0.2D1 * t211 * t1686 * t415 - t211 * t406 * t402)
t1747 = t470 * t518
t1759 = t375 * t559
t1766 = Arho * t545
t1786 = t1442 * t206
t1794 = -0.266900D0 * t490 * t1747 - 0.800700D0 * t477 * t470 *
#t206 * trho + 0.1334500D1 * t477 * t478 * cg18 - 0.266900D0 * t100
#4 * t553 + 0.266900D0 * t329 * t1759 * trho + 0.266900D0 * t373 *
#t1533 * t206 - 0.66725D-1 * t73 * t159 * (0.2D1 * t1766 + 0.4D1 *
#t486 * cg33 + 0.24D2 * t74 * t1766 + 0.24D2 * t1105 * t545 * trho
#+ 0.24D2 * t392 * cg18 * cg33) - 0.266900D0 * t1455 * t553 - 0.133
#450D0 * t546 * t168 - 0.266900D0 * t490 * t1786 - 0.266900D0 * t32
#9 * t1786 + 0.266900D0 * t66 * cg18 * t194
t1806 = t500 * cg33 * t167
t1811 = t545 * t80
t1815 = t375 * t566
t1829 = t545 * t158
t1833 = t1167 * t559
t1837 = 0.133450D0 * t73 * t153 * t375 * t559 - 0.133450D0 * t32
#9 * t158 * t566 * trho - 0.266900D0 * t1438 * t553 + 0.533800D0 *
#t329 * t1806 - 0.266900D0 * t329 * t1747 + 0.1334500D1 * t1506 * t
#1811 * trho + 0.133450D0 * t373 * t1815 * t167 + 0.133450D0 * t546
# * t154 + 0.533800D0 * t490 * t1806 - 0.66725D-1 * t73 * t361 * t5
#66 + 0.667250D0 * t73 * t1766 * t80 - 0.667250D0 * t477 * t1829 *
#t167 - 0.400350D0 * t373 * t1833 * t167
t1842 = t406 * t210
t1848 = t1328 * t576
t1852 = s * t576
exc_norm_drho_norm_drho_rho = cg16 * cg28 + t190 * cg28 + t97 *
#(0.7425558783D2 * t1327 * t1848 * srho - 0.2985074630D2 * t437 * t
#1852 * srho - 0.1990049753D2 * t437 * t1720 * cg13 + 0.4000000002D
#1 * t186 * cg47 * cg13) + cg9 + rho * (cg59 * (t1794 + t1837) * t1
#73 - t571 * t525 - 0.2D1 * t523 * t1842 + 0.2D1 * t574 * t1686)
cg63 = cg33
t1865 = A * cg63
t1871 = 0.2D1 * t1865 * cg33 + 0.12D2 * t392 * cg33 * cg63
t1876 = cg63 * t158 * t566
t1883 = 0.2D1 * t150 * cg63 + 0.4D1 * t164 * cg63
t1885 = t1458 * t206 * t1883
t1891 = t158 * t1871 * cg33
t1910 = t1759 * cg63
t1913 = t66 * cg63
t1924 = t159 * t1883
t1932 = 0.266900D0 * t373 * t500 * t1871 - 0.133450D0 * t490 * t
#1876 + 0.533800D0 * t490 * t1885 + 0.533800D0 * t329 * t1885 - 0.2
#66900D0 * t329 * t1891 - 0.266900D0 * t490 * t1891 + 0.133450D0 * </Text-field></Output><Output><Text-field layout="Normal" style="Line Printed Output"> #t373 * t1815 * t1883 - 0.1601400D1 * t197 * t75 * t158 * t76 * t54
#5 * cg63 - 0.133450D0 * t329 * t1876 + 0.1601400D1 * t1506 * t1811
# * cg63 + 0.266900D0 * t329 * t1910 - 0.266900D0 * t1913 * t75 * t
#553 - 0.1334500D1 * t477 * t470 * t206 * cg63 - 0.667250D0 * t477
#* t1829 * t1883 - 0.133450D0 * t546 * t1924 + 0.266900D0 * t490 *
#t1910 - 0.400350D0 * t373 * t1833 * t1883
t1943 = 0.133450D0 * t145 * t81 * cg63 + 0.133450D0 * t197 * t18
#65 * t80 - 0.66725D-1 * t73 * t1924
t1951 = t470 * t1883
t1956 = t493 * cg63
cg8 = cg13
exc_norm_drho_norm_drho_norm_drho = t97 * (0.7425558783D2 * t132
#7 * t1848 * cg8 - 0.2985074630D2 * t437 * t1852 * cg8) + rho * (cg
#59 * t1932 * t173 - t571 * t406 * t1943 - 0.2D1 * cg59 * (0.133450
#D0 * t1913 * t194 + 0.667250D0 * t477 * t478 * cg63 - 0.133450D0 *
# t329 * t1951 - 0.133450D0 * t490 * t1951 - 0.133450D0 * t329 * t1
#956 - 0.133450D0 * t490 * t1956 + 0.133450D0 * t373 * t500 * t1883
# - 0.66725D-1 * t73 * t159 * t1871) * t1842 + 0.2D1 * t574 * t1240
# * t1943)
cg66 = exc_norm_drho_norm_drho_norm_drho
return
end</Text-field></Output></Group></Section></Section><Text-field/><Section><Title><Text-field layout="Heading 1" style="Heading 1">LSD</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc(eqs_ex_lda)intersect loc(eqs_pbec2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8I0klYmV0YUc2Ig==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">loc(eqs_ex_lda);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8Kkkic0c2Ikkma2FwcGFHRiVJI0Z4R0YlSSNrZkdGJUknZXhfbGRhR0YlSShleF91bmlmR0YlSSNtdUdGJUklYmV0YUdGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">toRn:=convert(loc(eqs_ex_lda)minus {beta,kappa,mu},list);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSV0b1JuRzYiNydJInNHRiVJI0Z4R0YlSSNrZkdGJUknZXhfbGRhR0YlSShleF91bmlmR0Yl</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_ex_a:=subs(op(map(x-&gt;x=x||_a,toRn)),rho=2*rhoa,norm_drho=2*norm_drhoa,eqs_ex_lda);
eqs_ex_b:=subs(op(map(x-&gt;x=x||_b,toRn)),rho=2*rhob,norm_drho=2*norm_drhob,eqs_ex_lda);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSllcXNfZXhfYUc2IjcqL0kma2FwcGFHRiUkIiQvKSEiJC9JJWJldGFHRiUkIiZEbichIicvSSNtdUdGJSwkKiZGLSIiIkkjUGlHSSpwcm90ZWN0ZWRHRjciIiMjRjUiIiQvSSVrZl9hR0YlKihGOkY5RjhGOSomRjZGOEklcmhvYUdGJUY1RjkvSSpleF91bmlmX2FHRiUsJComRjYhIiJGPEY1I0YrIiIlL0kkc19hR0YlLCQqKEkrbm9ybV9kcmhvYUdGJUY1RjxGREY/RkQjRjVGOC9JJUZ4X2FHRiUsKEY1RjVGKEY1KiZGKEY1LCZGNUY1KihGMkY1RkhGOEYoRkRGNUZERkQvSSlleF9sZGFfYUdGJSwkKihGP0Y1RkFGNUZORjVGOA==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSllcXNfZXhfYkc2IjcqL0kma2FwcGFHRiUkIiQvKSEiJC9JJWJldGFHRiUkIiZEbichIicvSSNtdUdGJSwkKiZGLSIiIkkjUGlHSSpwcm90ZWN0ZWRHRjciIiMjRjUiIiQvSSVrZl9iR0YlKihGOkY5RjhGOSomRjZGOEklcmhvYkdGJUY1RjkvSSpleF91bmlmX2JHRiUsJComRjYhIiJGPEY1I0YrIiIlL0kkc19iR0YlLCQqKEkrbm9ybV9kcmhvYkdGJUY1RjxGREY/RkQjRjVGOC9JJUZ4X2JHRiUsKEY1RjVGKEY1KiZGKEY1LCZGNUY1KihGMkY1RkhGOEYoRkRGNUZERkQvSSlleF9sZGFfYkdGJSwkKihGP0Y1RkFGNUZORjVGOA==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">unk(eqs_ex_a);
unk(eqs_ex_b);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8JUklcmhvYUc2IkkjUGlHSSpwcm90ZWN0ZWRHRidJK25vcm1fZHJob2FHRiU=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8JUklcmhvYkc2IkkjUGlHSSpwcm90ZWN0ZWRHRidJK25vcm1fZHJob2JHRiU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sameNameSameDef(eqs_pbec2,eqs_ex_a);
sameNameSameDef(eqs_pbec2,eqs_ex_b);
sameNameSameDef(eqs_ex_a,eqs_ex_b);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_lsd:=combineEqs([[rho=rhoa+rhob],eqs_pbec2,eqs_ex_a,eqs_ex_b,[scale_ec=1,scale_ex=1,exc=scale_ex*(ex_lda_a+ex_lda_b)/2+scale_ec*ec]]):
unk(eqs_lsd);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM8KEklcmhvYkc2IkklcmhvYUdGJUkjUGlHSSpwcm90ZWN0ZWRHRihJKm5vcm1fZHJob0dGJUkrbm9ybV9kcmhvYUdGJUkrbm9ybV9kcmhvYkdGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">arg_lsd_names:=[rhoa,rhob,norm_drho,norm_drhoa,norm_drhob]; </Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SS5hcmdfbHNkX25hbWVzRzYiNydJJXJob2FHRiVJJXJob2JHRiVJKm5vcm1fZHJob0dGJUkrbm9ybV9kcmhvYUdGJUkrbm9ybV9kcmhvYkdGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_lsd2:=rmDefs(costanti,eqs_lsd):
unk(eqs_lsd2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">deriv_lsd1:=calcDerivs(eqs_lsd2,arg_lsd_names):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">deriv_lsd2:=[seq(seq(op(calcDerivs(deriv_lsd1[i],[arg_lsd_names[j]])),i=1..j),j=1..nops(arg_lsd_names))]:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">#deriv_lsd3:=[seq(seq(op(calcDerivs(deriv_lsd2[i],[arg_lsd_names[j]])),i=1..((j+1)*j/2)),j=1..nops(arg_lsd_names))]:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">n_deriv1:=map(x-&gt;lhs(op(-1,x)),deriv_lsd1);
n_deriv2:=map(x-&gt;lhs(op(-1,x)),deriv_lsd2);
#n_deriv3:=map(x-&gt;lhs(op(-1,x)),deriv_lsd3);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSluX2Rlcml2MUc2IjcnSSlleGNfcmhvYUdGJUkpZXhjX3Job2JHRiVJLmV4Y19ub3JtX2RyaG9HRiVJL2V4Y19ub3JtX2RyaG9hR0YlSS9leGNfbm9ybV9kcmhvYkdGJQ==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">'sameNameSameDef(eqs_lsd2,deriv_lsd1[i])'$i=1..nops(deriv_lsd1);
'sameNameSameDef(eqs_lsd2,deriv_lsd2[i])'$i=1..nops(deriv_lsd1);
#foldl(`and`,sameNameSameDef(eqs_lsd2,deriv_lsd3[i])$i=1..nops(deriv_lsd3));
foldl(`and`,seq(sameNameSameDef(deriv_lsd1[i],deriv_lsd2[j])$i=1..nops(deriv_lsd1),j=1..nops(deriv_lsd2)));
#foldl(`and`,seq(sameNameSameDef(deriv_lsd1[i],deriv_lsd3[j])$i=1..nops(deriv_lsd1),j=1..nops(deriv_lsd3)));
#foldl(`and`,seq(sameNameSameDef(deriv_lsd2[i],deriv_lsd3[j])$i=1..nops(deriv_lsd2),j=1..nops(deriv_lsd3)));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NidJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGIw==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NidJJXRydWVHSSpwcm90ZWN0ZWRHRiRGI0YjRiNGIw==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_lsd3:=combineEqs([eqs_lsd2,op(deriv_lsd1),op(deriv_lsd2)]): # ,op(deriv_lsd3) # removed 3 deriv</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eqs_lsd4:=enforceDependencies([my_rhoa=rhoa,my_rhob=rhob,
my_norm_drho=norm_drho,my_norm_drhoa=norm_drhoa,my_norm_drhob=norm_drhob,
op(subs(rhoa=my_rhoa,rhob=my_rhob,norm_drho=my_norm_drho,
norm_drhoa=my_norm_drhoa,norm_drhob=my_norm_drhob,eqs_lsd3))]):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">res_eqs_lsd:=[exc,op(n_deriv1),op(n_deriv2)]:#,op(n_deriv3)]: # removed 3 deriv
res_eqs_lsd2:=[]:
for my_symb in res_eqs_lsd do
if not rhs(getDef(my_symb,eqs_lsd4))=0 then
res_eqs_lsd2:=[op(res_eqs_lsd2),my_symb]:
end if;
end do;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">for my_symb in res_eqs_lsd2 do
print(my_symb,unk([op(eqs_lsd4),result=my_symb]));
end do;
my_symb:='my_symb':</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJLmV4Y19ub3JtX2RyaG9HNiI8PkklcmhvYkdGJEkqZ2FtbWFfdmFyR0YkSSVyaG9hR0YkSSRBXzJHRiRJJHBfM0dGJEkkQV8zR0YkSSRBXzFHRiRJJHBfMkdGJEkpYmV0YV80XzNHRiRJKWJldGFfM18zR0YkSSphbHBoYV8xXzNHRiRJKWJldGFfMV8zR0YkSSliZXRhXzJfM0dGJEkjUGlHSSpwcm90ZWN0ZWRHRjRJKWJldGFfM18xR0YkSSphbHBoYV8xXzJHRiRJKWJldGFfMV8yR0YkSSliZXRhXzJfMkdGJEkpYmV0YV80XzJHRiRJKWJldGFfM18yR0YkSSliZXRhXzJfMUdGJEkpYmV0YV80XzFHRiRJKm5vcm1fZHJob0dGJEklYmV0YUdGJEkpYmV0YV8xXzFHRiRJKXNjYWxlX2VjR0YkSSRwXzFHRiRJKmFscGhhXzFfMUdGJA==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJL2V4Y19ub3JtX2RyaG9hRzYiPChJJXJob2FHRiRJJmthcHBhR0YkSSNQaUdJKnByb3RlY3RlZEdGKUkjbXVHRiRJKXNjYWxlX2V4R0YkSStub3JtX2RyaG9hR0Yk</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJL2V4Y19ub3JtX2RyaG9iRzYiPChJJXJob2JHRiRJJmthcHBhR0YkSSNQaUdJKnByb3RlY3RlZEdGKUkjbXVHRiRJKXNjYWxlX2V4R0YkSStub3JtX2RyaG9iR0Yk</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJLmV4Y19yaG9hX3Job2JHNiI8PkklcmhvYkdGJEkqZ2FtbWFfdmFyR0YkSSVyaG9hR0YkSSRBXzJHRiRJJHBfM0dGJEkkQV8zR0YkSSRBXzFHRiRJJHBfMkdGJEkpYmV0YV80XzNHRiRJKWJldGFfM18zR0YkSSphbHBoYV8xXzNHRiRJKWJldGFfMV8zR0YkSSliZXRhXzJfM0dGJEkjUGlHSSpwcm90ZWN0ZWRHRjRJKWJldGFfM18xR0YkSSphbHBoYV8xXzJHRiRJKWJldGFfMV8yR0YkSSliZXRhXzJfMkdGJEkpYmV0YV80XzJHRiRJKWJldGFfM18yR0YkSSliZXRhXzJfMUdGJEkpYmV0YV80XzFHRiRJKm5vcm1fZHJob0dGJEklYmV0YUdGJEkpYmV0YV8xXzFHRiRJKXNjYWxlX2VjR0YkSSRwXzFHRiRJKmFscGhhXzFfMUdGJA==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJM2V4Y19yaG9hX25vcm1fZHJob0c2Ijw+SSVyaG9iR0YkSSpnYW1tYV92YXJHRiRJJXJob2FHRiRJJEFfMkdGJEkkcF8zR0YkSSRBXzNHRiRJJEFfMUdGJEkkcF8yR0YkSSliZXRhXzRfM0dGJEkpYmV0YV8zXzNHRiRJKmFscGhhXzFfM0dGJEkpYmV0YV8xXzNHRiRJKWJldGFfMl8zR0YkSSNQaUdJKnByb3RlY3RlZEdGNEkpYmV0YV8zXzFHRiRJKmFscGhhXzFfMkdGJEkpYmV0YV8xXzJHRiRJKWJldGFfMl8yR0YkSSliZXRhXzRfMkdGJEkpYmV0YV8zXzJHRiRJKWJldGFfMl8xR0YkSSliZXRhXzRfMUdGJEkqbm9ybV9kcmhvR0YkSSViZXRhR0YkSSliZXRhXzFfMUdGJEkpc2NhbGVfZWNHRiRJJHBfMUdGJEkqYWxwaGFfMV8xR0Yk</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJM2V4Y19yaG9iX25vcm1fZHJob0c2Ijw+SSVyaG9iR0YkSSpnYW1tYV92YXJHRiRJJXJob2FHRiRJJEFfMkdGJEkkcF8zR0YkSSRBXzNHRiRJJEFfMUdGJEkkcF8yR0YkSSliZXRhXzRfM0dGJEkpYmV0YV8zXzNHRiRJKmFscGhhXzFfM0dGJEkpYmV0YV8xXzNHRiRJKWJldGFfMl8zR0YkSSNQaUdJKnByb3RlY3RlZEdGNEkpYmV0YV8zXzFHRiRJKmFscGhhXzFfMkdGJEkpYmV0YV8xXzJHRiRJKWJldGFfMl8yR0YkSSliZXRhXzRfMkdGJEkpYmV0YV8zXzJHRiRJKWJldGFfMl8xR0YkSSliZXRhXzRfMUdGJEkqbm9ybV9kcmhvR0YkSSViZXRhR0YkSSliZXRhXzFfMUdGJEkpc2NhbGVfZWNHRiRJJHBfMUdGJEkqYWxwaGFfMV8xR0Yk</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJOGV4Y19ub3JtX2RyaG9fbm9ybV9kcmhvRzYiPD5JJXJob2JHRiRJKmdhbW1hX3ZhckdGJEklcmhvYUdGJEkkQV8yR0YkSSRwXzNHRiRJJEFfM0dGJEkkQV8xR0YkSSRwXzJHRiRJKWJldGFfNF8zR0YkSSliZXRhXzNfM0dGJEkqYWxwaGFfMV8zR0YkSSliZXRhXzFfM0dGJEkpYmV0YV8yXzNHRiRJI1BpR0kqcHJvdGVjdGVkR0Y0SSliZXRhXzNfMUdGJEkqYWxwaGFfMV8yR0YkSSliZXRhXzFfMkdGJEkpYmV0YV8yXzJHRiRJKWJldGFfNF8yR0YkSSliZXRhXzNfMkdGJEkpYmV0YV8yXzFHRiRJKWJldGFfNF8xR0YkSSpub3JtX2RyaG9HRiRJJWJldGFHRiRJKWJldGFfMV8xR0YkSSlzY2FsZV9lY0dGJEkkcF8xR0YkSSphbHBoYV8xXzFHRiQ=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJNGV4Y19yaG9hX25vcm1fZHJob2FHNiI8KEklcmhvYUdGJEkma2FwcGFHRiRJI1BpR0kqcHJvdGVjdGVkR0YpSSNtdUdGJEkpc2NhbGVfZXhHRiRJK25vcm1fZHJob2FHRiQ=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJOmV4Y19ub3JtX2RyaG9hX25vcm1fZHJob2FHNiI8KEklcmhvYUdGJEkma2FwcGFHRiRJI1BpR0kqcHJvdGVjdGVkR0YpSSNtdUdGJEkpc2NhbGVfZXhHRiRJK25vcm1fZHJob2FHRiQ=</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJNGV4Y19yaG9iX25vcm1fZHJob2JHNiI8KEklcmhvYkdGJEkma2FwcGFHRiRJI1BpR0kqcHJvdGVjdGVkR0YpSSNtdUdGJEkpc2NhbGVfZXhHRiRJK25vcm1fZHJob2JHRiQ=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiRJOmV4Y19ub3JtX2RyaG9iX25vcm1fZHJob2JHNiI8KEklcmhvYkdGJEkma2FwcGFHRiRJI1BpR0kqcHJvdGVjdGVkR0YpSSNtdUdGJEkpc2NhbGVfZXhHRiRJK25vcm1fZHJob2JHRiQ=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">for i from 1 to nops(eqs_lsd3) do
for j from i+1 to nops(eqs_lsd3) do
if eqUses(eqs_lsd3[i],eqs_lsd3[j]) then
print(i,j,eqs_lsd3[i],uses,eqs_lsd3[j]);
end if;
end do;
end do;
i:='i':j:='j':</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">glob_eqs_lsd4:=[my_rhoa,my_rhob,my_norm_drho,my_norm_drhoa,my_norm_drhob,op(res_eqs_lsd2)];
args_lsd:=[rhoa,rhob,norm_drho,norm_drhoa,norm_drhob];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation>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</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation>NiM+SSlhcmdzX2xzZEc2IjcnSSVyaG9hR0YlSSVyaG9iR0YlSSpub3JtX2RyaG9HRiVJK25vcm1fZHJob2FHRiVJK25vcm1fZHJob2JHRiU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cs_eqs_lsd4:=CompSeq(locals=loc2(eqs_lsd4)minus convert(glob_eqs_lsd4,set),
globals=[op(glob_eqs_lsd4),op(costanti)],params=args_lsd,eqs_lsd4):
r_eqs_lsd4:=convert(cs_eqs_lsd4,procedure):</Text-field></Input></Group><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Fortran code</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Fortran(r_eqs_lsd4,defaulttype=float,optimize);</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, The following variable name replacements were made: ["cg", "cg0", "cg1", "cg10", "cg11", "cg12", "cg13", "cg14", "cg15", "cg16", "cg17", "cg18", "cg19", "cg2", "cg20", "cg21", "cg22", "cg23", "cg24", "cg25", "cg26", "cg27", "cg28", "cg29", "cg3", "cg30", "cg31", "cg32", "cg33", "cg34", "cg35", "cg36", "cg37", "cg38", "cg39", "cg4", "cg40", "cg41", "cg42", "cg43", "cg44", "cg45", "cg46", "cg47", "cg48", "cg49", "cg5", "cg50", "cg51", "cg52", "cg53", "cg54", "cg55", "cg56", "cg57", "cg58", "cg59", "cg6", "cg60", "cg61", "cg62", "cg63", "cg64", "cg65", "cg66", "cg67", "cg68", "cg69", "cg7", "cg70", "cg71", "cg72", "cg73", "cg74", "cg75", "cg76", "cg77", "cg78", "cg79", "cg8", "cg80", "cg81", "cg82", "cg83", "cg84", "cg85", "cg86", "cg87", "cg88", "cg89", "cg9", "cg90", "cg91", "cg92", "cg93"] = ["norm_drho", "norm_drhoa", "norm_drhob", "e_c_u_0rhoarhob", "rsrhoarhob", "Arhobrhob", "alpha_c1rhoa", "epsilon_c_unifrhoarhob", "phi1rhoa", "s_anorm_drhoa", "e_c_u_0", "ex_unif_arhoa", "alpha_c", "s_b1rhob", "epsilon_c_unif", "k_s", "kf_a", "Fx_a", "kf_b", "Fx_b", "chirhoa", "epsilon_cGGA", "e_c_u_0rhobrhob", "s_a", "s_a1rhoa", "Fx_a1rhoa", "ex_unif_b", "s_b", "Arhoarhoa", "ex_unif_brhob", "rsrhobrhob", "Fx_b1rhob", "frhoarhob", "k_frhoa", "k_srhoa", "epsilon_cGGArhob", "chirhoarhob", "epsilon_c_unifrhoarhoa", "phirhoa", "s_arhoa", "chirhob", "Fx_arhoa", "kf_arhoarhoa", "ex_unif_a1rhoa", "kf_brhobrhob", "ex_unif_b1rhob", "epsilon_c_unifrhob", "trhoanorm_drho", "kf_arhoa", "phirhob", "k_frhob", "k_srhob", "Arhoarhob", "trhoarhob", "Fx_brhob", "rsrhoarhoa", "s_brhob", "epsilon_cGGArhoa", "Hnorm_drho", "frhobrhob", "kf_brhob", "tnorm_drho", "e_c_u_01rhob", "chirhobrhob", "alpha_crhob", "e_c_u_0rhob", "e_c_u_1rhob", "Fx_anorm_drhoa", "epsilon_c_unifrhoa", "s_bnorm_drhob", "Fx_bnorm_drhob", "e_c_u_0rhoarhoa", "alpha_crhoa", "e_c_u_1rhoa", "phirhoarhoa", "e_c_u_0rhoa", "chirhoarhoa", "trhobnorm_drho", "k_s1rhob", "epsilon_c_unif1rhoa", "phirhobrhob", "alpha_c1rhob", "epsilon_c_unif1rhob", "ex_unif_a", "k_frhoarhob", "e_c_u_01rhoa", "trhoarhoa", "k_s1rhoa", "k_frhoarhoa", "phi1rhob", "trhobrhob", "epsilon_c_unifrhobrhob", "phirhoarhob", "frhoarhoa", "r_eqs_lsd4"]
</Text-field></Output><Output><Text-field layout="Normal" style="Line Printed Output"> doubleprecision function cg93 (rhoa, rhob, cg, cg0, cg1)
doubleprecision my_rhoa
doubleprecision my_rhob
doubleprecision my_norm_drho
doubleprecision my_norm_drhoa
doubleprecision my_norm_drhob
doubleprecision exc
doubleprecision exc_rhoa
doubleprecision exc_rhob
doubleprecision exc_norm_drho
doubleprecision exc_norm_drhoa
doubleprecision exc_norm_drhob
doubleprecision exc_rhoa_rhoa
doubleprecision exc_rhoa_rhob
doubleprecision exc_rhob_rhob
doubleprecision exc_rhoa_norm_drho
doubleprecision exc_rhob_norm_drho
doubleprecision exc_norm_drho_norm_drho
doubleprecision exc_rhoa_norm_drhoa
doubleprecision exc_norm_drhoa_norm_drhoa
doubleprecision exc_rhob_norm_drhob
doubleprecision exc_norm_drhob_norm_drhob
doubleprecision kappa
doubleprecision beta
doubleprecision mu
doubleprecision gamma_var
doubleprecision p_1
doubleprecision A_1
doubleprecision alpha_1_1
doubleprecision beta_1_1
doubleprecision beta_2_1
doubleprecision beta_3_1
doubleprecision beta_4_1
doubleprecision p_2
doubleprecision A_2
doubleprecision alpha_1_2
doubleprecision beta_1_2
doubleprecision beta_2_2
doubleprecision beta_3_2
doubleprecision beta_4_2
doubleprecision p_3
doubleprecision A_3
doubleprecision alpha_1_3
doubleprecision beta_1_3
doubleprecision beta_2_3
doubleprecision beta_3_3
doubleprecision beta_4_3
doubleprecision scale_ec
doubleprecision scale_ex
common my_rhoa, my_rhob, my_norm_drho, my_norm_drhoa, my_norm_dr
#hob, exc, exc_rhoa, exc_rhob, exc_norm_drho, exc_norm_drhoa, exc_n
#orm_drhob, exc_rhoa_rhoa, exc_rhoa_rhob, exc_rhob_rhob, exc_rhoa_n
#orm_drho, exc_rhob_norm_drho, exc_norm_drho_norm_drho, exc_rhoa_no
#rm_drhoa, exc_norm_drhoa_norm_drhoa, exc_rhob_norm_drhob, exc_norm
#_drhob_norm_drhob, kappa, beta, mu, gamma_var, p_1, A_1, alpha_1_1
#, beta_1_1, beta_2_1, beta_3_1, beta_4_1, p_2, A_2, alpha_1_2, bet
#a_1_2, beta_2_2, beta_3_2, beta_4_2, p_3, A_3, alpha_1_3, beta_1_3
#, beta_2_3, beta_3_3, beta_4_3, scale_ec, scale_ex
doubleprecision rhoa
doubleprecision rhob
doubleprecision cg
doubleprecision cg0
doubleprecision cg1
doubleprecision t187
doubleprecision t190
doubleprecision t191
doubleprecision t192
doubleprecision t194
doubleprecision t153
doubleprecision t156
integer t66
doubleprecision t1440
doubleprecision t1550
doubleprecision t1552
doubleprecision t56
doubleprecision t57
doubleprecision t58
doubleprecision t59
doubleprecision t1228
doubleprecision t1231
doubleprecision cg2
doubleprecision cg3
doubleprecision t198
doubleprecision t199
doubleprecision t200
doubleprecision t201
doubleprecision t205
doubleprecision t1865
doubleprecision t1739
doubleprecision t1765
doubleprecision t1767
doubleprecision cg4
doubleprecision cg5
doubleprecision cg6
doubleprecision cg7
doubleprecision cg8
doubleprecision t1346
doubleprecision t1630
doubleprecision t1501
doubleprecision t212
doubleprecision t213
doubleprecision t215
doubleprecision t1829
doubleprecision t211
doubleprecision t74
doubleprecision t75
doubleprecision t1283
doubleprecision t219
doubleprecision t220
doubleprecision t222
doubleprecision t226
doubleprecision t221
doubleprecision t232
doubleprecision t233
doubleprecision t234
doubleprecision t1193
doubleprecision t240
doubleprecision t242
doubleprecision t244
doubleprecision t245
doubleprecision t246
doubleprecision t248
doubleprecision t249
doubleprecision t250
doubleprecision t252
doubleprecision t254
doubleprecision t1293
integer t69
doubleprecision t12
doubleprecision t1922
doubleprecision t1674
doubleprecision t1677
doubleprecision t1680
doubleprecision t256
doubleprecision t257
doubleprecision t259
doubleprecision t262
doubleprecision t266
doubleprecision t268
doubleprecision t269
doubleprecision t274
doubleprecision t272
doubleprecision t273
doubleprecision t277
doubleprecision t278
doubleprecision t280
doubleprecision t281
doubleprecision t282
doubleprecision t284
doubleprecision t285
doubleprecision t286
doubleprecision t289
doubleprecision t456
doubleprecision t1462
doubleprecision t1465
doubleprecision cg9
doubleprecision t293
doubleprecision t294
doubleprecision t297
doubleprecision t298
doubleprecision t302
doubleprecision t303
doubleprecision t306
doubleprecision t299
doubleprecision t310
doubleprecision t311
doubleprecision t312
doubleprecision t313
doubleprecision t314
doubleprecision t317
doubleprecision t318
doubleprecision t324
doubleprecision t325
doubleprecision t326
doubleprecision t578
doubleprecision t321
doubleprecision t329
doubleprecision t335
doubleprecision t337
doubleprecision t340
doubleprecision t341
doubleprecision t344
doubleprecision t346
doubleprecision t350
doubleprecision t368
doubleprecision t396
doubleprecision t403
doubleprecision t405
doubleprecision t407
doubleprecision t409
doubleprecision t410
doubleprecision t411
doubleprecision t413
doubleprecision t415
doubleprecision t417
doubleprecision t427
doubleprecision t429
doubleprecision t432
doubleprecision t436
doubleprecision t1327
doubleprecision t439
doubleprecision t442
doubleprecision t444
doubleprecision t445
doubleprecision t453
doubleprecision t457
doubleprecision t460
doubleprecision t466
doubleprecision t467
doubleprecision t471
doubleprecision t468
doubleprecision t477
doubleprecision t676
doubleprecision t481
doubleprecision t475
doubleprecision t488
doubleprecision t1050
doubleprecision t494
doubleprecision t493
doubleprecision t506
doubleprecision t505
doubleprecision cg10
doubleprecision cg11
doubleprecision t519
doubleprecision t518
doubleprecision t525
doubleprecision t523
doubleprecision t536
doubleprecision t538
doubleprecision t543
doubleprecision t544
doubleprecision t548
doubleprecision t549
doubleprecision t561
doubleprecision t556
doubleprecision t576
doubleprecision t579
doubleprecision t563
doubleprecision t580
doubleprecision t588
doubleprecision t1555
doubleprecision t590
doubleprecision t595
doubleprecision t596
doubleprecision t600
doubleprecision t611
doubleprecision t606
doubleprecision t624
doubleprecision t626
doubleprecision t627
doubleprecision t628
doubleprecision t1377
doubleprecision t636
doubleprecision t638
doubleprecision t1288
doubleprecision t643
doubleprecision t644
doubleprecision t648
doubleprecision t659
doubleprecision t654
doubleprecision t672
doubleprecision t1285
doubleprecision t1286
doubleprecision t1291
doubleprecision t674
doubleprecision t675
doubleprecision t681
doubleprecision t687
doubleprecision t63
doubleprecision t64
doubleprecision t705
doubleprecision t708
doubleprecision t711
doubleprecision t1743
doubleprecision t726
doubleprecision t733
doubleprecision t736
doubleprecision t745
doubleprecision t750
doubleprecision t755
doubleprecision t763
doubleprecision t767
doubleprecision t768
doubleprecision cg12
doubleprecision t775
doubleprecision t779
doubleprecision t776
doubleprecision t785
doubleprecision t789
doubleprecision t795
doubleprecision t798
doubleprecision t801
doubleprecision f1rhoa
doubleprecision cg13
doubleprecision cg14
doubleprecision t812
doubleprecision t820
doubleprecision t821
doubleprecision t822
doubleprecision t823
doubleprecision t825
doubleprecision t828
doubleprecision t839
doubleprecision t840
doubleprecision t851
doubleprecision cg15
doubleprecision t858
doubleprecision t865
doubleprecision t867
doubleprecision t1713
doubleprecision t876
doubleprecision t879
doubleprecision t880
doubleprecision t904
doubleprecision t914
doubleprecision t908
doubleprecision t909
doubleprecision t911
doubleprecision t917
doubleprecision t919
doubleprecision cg16
doubleprecision t924
doubleprecision t936
doubleprecision t944
doubleprecision t953
doubleprecision t959
doubleprecision t962
doubleprecision t965
doubleprecision cg17
doubleprecision t967
doubleprecision t966
doubleprecision t1603
doubleprecision t985
doubleprecision t998
doubleprecision t999
doubleprecision t1000
doubleprecision t1001
doubleprecision t1033
doubleprecision t1031
doubleprecision rs
doubleprecision rho
doubleprecision chi
doubleprecision t1038
doubleprecision t1514
doubleprecision cg18
doubleprecision cg19
doubleprecision cg20
doubleprecision f
doubleprecision t1069
doubleprecision t1071
doubleprecision phi
doubleprecision cg21
doubleprecision t
doubleprecision A
doubleprecision cg22
doubleprecision cg23
doubleprecision cg24
doubleprecision cg25
doubleprecision cg26
doubleprecision rsrhoa
doubleprecision cg27
doubleprecision cg28
doubleprecision t1104
doubleprecision t1106
doubleprecision cg29
doubleprecision t77
doubleprecision t78
doubleprecision t14
doubleprecision t15
doubleprecision cg30
doubleprecision cg31
doubleprecision t162
doubleprecision t163
doubleprecision t164
doubleprecision t165
doubleprecision cg32
doubleprecision t130
doubleprecision t79
doubleprecision t80
doubleprecision cg33
doubleprecision cg34
doubleprecision cg35
doubleprecision t305
doubleprecision t1741
doubleprecision t1640
doubleprecision t18
doubleprecision t82
doubleprecision cg36
doubleprecision t682
doubleprecision t84
doubleprecision t85
doubleprecision t112
doubleprecision t113
doubleprecision t115
doubleprecision t116
doubleprecision t118
doubleprecision t119
doubleprecision t123
doubleprecision t20
doubleprecision t21
doubleprecision t22
doubleprecision t23
doubleprecision cg37
doubleprecision t27
doubleprecision t28
doubleprecision t564
doubleprecision t1520
doubleprecision t167
doubleprecision t171
doubleprecision t1830
doubleprecision t1831
doubleprecision frhoa
doubleprecision cg38
doubleprecision cg39
doubleprecision trhoa
doubleprecision Arhoa
doubleprecision t1748
doubleprecision t1871
doubleprecision t1876
doubleprecision cg40
doubleprecision cg41
doubleprecision cg42
doubleprecision t122
doubleprecision t1330
doubleprecision t1rhoa
doubleprecision t32
doubleprecision t868
doubleprecision cg43
doubleprecision cg44
doubleprecision rsrhob
doubleprecision cg45
integer t124
doubleprecision t125
doubleprecision t126
doubleprecision t129
doubleprecision t131
doubleprecision cg46
doubleprecision cg47
doubleprecision t1411
doubleprecision t34
doubleprecision t87
doubleprecision t88
doubleprecision cg48
doubleprecision cg49
doubleprecision cg50
doubleprecision t1632
doubleprecision t1635
doubleprecision t1638
doubleprecision cg51
doubleprecision t1698
doubleprecision t550
doubleprecision t1801
doubleprecision t90
doubleprecision t91
doubleprecision t1766
doubleprecision t1529
doubleprecision frhob
doubleprecision cg52
doubleprecision cg53
doubleprecision cg54
doubleprecision trhob
doubleprecision t38
doubleprecision f1rhob
doubleprecision t1164
doubleprecision A1rhoa
doubleprecision cg55
doubleprecision cg56
doubleprecision t1949
doubleprecision cg57
doubleprecision t1588
doubleprecision t1590
doubleprecision t1591
doubleprecision t175
doubleprecision t176
doubleprecision t177
doubleprecision t178
doubleprecision t179
doubleprecision t183
doubleprecision Arhob
doubleprecision t382
doubleprecision t39
doubleprecision t92
doubleprecision t93
doubleprecision t94
doubleprecision cg58
doubleprecision cg59
doubleprecision cg60
doubleprecision cg61
doubleprecision cg62
doubleprecision t40
doubleprecision t41
doubleprecision cg63
doubleprecision t1482
doubleprecision cg64
doubleprecision cg65
doubleprecision cg66
doubleprecision cg67
doubleprecision cg68
doubleprecision t95
doubleprecision t96
doubleprecision cg69
doubleprecision cg70
doubleprecision cg71
doubleprecision cg72
doubleprecision cg73
doubleprecision t1
doubleprecision cg74
doubleprecision t100
doubleprecision t101
doubleprecision t102
doubleprecision t1599
doubleprecision t1602
doubleprecision cg75
doubleprecision cg76
doubleprecision cg77
doubleprecision t97
doubleprecision t98
doubleprecision t1888
doubleprecision t70
doubleprecision t71
doubleprecision t45
doubleprecision t46
doubleprecision t336
doubleprecision cg78
doubleprecision cg79
doubleprecision cg80
doubleprecision cg81
doubleprecision cg82
doubleprecision cg83
doubleprecision cg84
doubleprecision t133
doubleprecision t135
doubleprecision t137
doubleprecision t140
doubleprecision t2
integer t3
doubleprecision t472
doubleprecision t502
doubleprecision t1711
doubleprecision t1712
doubleprecision t1rhob
doubleprecision t50
doubleprecision cg85
doubleprecision cg86
doubleprecision cg87
doubleprecision t52
doubleprecision t1269
doubleprecision t1342
doubleprecision t1489
doubleprecision t1492
integer t4
integer t5
integer t6
doubleprecision t1901
doubleprecision t72
doubleprecision t73
doubleprecision cg88
doubleprecision A1rhob
doubleprecision cg89
doubleprecision t142
doubleprecision t143
doubleprecision t7
doubleprecision t8
doubleprecision t9
doubleprecision cg90
doubleprecision t103
doubleprecision t104
doubleprecision t105
doubleprecision t107
doubleprecision t108
doubleprecision t110
doubleprecision t111
doubleprecision cg91
doubleprecision t1304
doubleprecision t146
doubleprecision t147
doubleprecision t148
doubleprecision t150
doubleprecision cg92
my_rhoa = rhoa
my_rhob = rhob
my_norm_drho = cg
my_norm_drhoa = cg0
my_norm_drhob = cg1
rho = rhoa + rhob
t1 = rhoa - rhob
t2 = 0.1D1 / rho
chi = t1 * t2
t3 = 3 ** (0.1D1 / 0.3D1)
t4 = 4 ** (0.1D1 / 0.3D1)
t5 = t4 ** 2
t6 = t3 * t5
t7 = 0.1D1 / 0.3141592654D1
t8 = t7 * t2
t9 = t8 ** (0.1D1 / 0.3D1)
rs = dble(t6) * t9 / 0.4D1
t12 = 0.1D1 + alpha_1_1 * rs
t14 = 0.1D1 / A_1
t15 = sqrt(rs)
t18 = t15 * rs
t20 = p_1 + 0.1D1
t21 = rs ** t20
t22 = beta_4_1 * t21
t23 = beta_1_1 * t15 + beta_2_1 * rs + beta_3_1 * t18 + t22
t27 = 0.1D1 + t14 / t23 / 0.2D1
t28 = log(t27)
cg17 = -0.2D1 * A_1 * t12 * t28
t32 = 0.1D1 + alpha_1_2 * rs
t34 = 0.1D1 / A_2
t38 = p_2 + 0.1D1
t39 = rs ** t38
t40 = beta_4_2 * t39
t41 = beta_1_2 * t15 + beta_2_2 * rs + beta_3_2 * t18 + t40
t45 = 0.1D1 + t34 / t41 / 0.2D1
t46 = log(t45)
t50 = 0.1D1 + alpha_1_3 * rs
t52 = 0.1D1 / A_3
t56 = p_3 + 0.1D1
t57 = rs ** t56
t58 = beta_4_3 * t57
t59 = beta_1_3 * t15 + beta_2_3 * rs + beta_3_3 * t18 + t58
t63 = 0.1D1 + t52 / t59 / 0.2D1
t64 = log(t63)
cg19 = 0.2D1 * A_3 * t50 * t64
t66 = 2 ** (0.1D1 / 0.3D1)
t69 = 1 / (2 * t66 - 2)
t70 = 0.1D1 + chi
t71 = t70 ** (0.1D1 / 0.3D1)
t72 = t71 * t70
t73 = 0.1D1 - chi
t74 = t73 ** (0.1D1 / 0.3D1)
t75 = t74 * t73
f = (t72 + t75 - 0.2D1) * dble(t69)
t77 = cg19 * f
t78 = 0.9D1 / 0.8D1 / dble(t69)
t79 = chi ** 2
t80 = t79 ** 2
t82 = t78 * (0.1D1 - t80)
t84 = -0.2D1 * A_2 * t32 * t46 - cg17
t85 = t84 * f
cg20 = cg17 + t77 * t82 + t85 * t80
t87 = t71 ** 2
t88 = t74 ** 2
phi = t87 / 0.2D1 + t88 / 0.2D1
t90 = 0.3141592654D1 ** 2
t91 = t90 * rho
t92 = t91 ** (0.1D1 / 0.3D1)
t93 = dble(t3) * t92 * t7
t94 = sqrt(t93)
cg21 = 0.2D1 * t94
t95 = 0.1D1 / phi
t96 = cg * t95
t97 = 0.1D1 / cg21
t98 = t97 * t2
t = t96 * t98 / 0.2D1
t100 = 0.1D1 / gamma_var
t101 = beta * t100
t102 = cg20 * t100
t103 = phi ** 2
t104 = t103 * phi
t105 = 0.1D1 / t104
t107 = exp(-t102 * t105)
t108 = t107 - 0.1D1
A = t101 / t108
t110 = gamma_var * t104
t111 = t ** 2
t112 = A * t111
t113 = 0.1D1 + t112
t115 = A ** 2
t116 = t111 ** 2
t118 = 0.1D1 + t112 + t115 * t116
t119 = 0.1D1 / t118
t122 = 0.1D1 + t101 * t111 * t113 * t119
t123 = log(t122)
cg27 = cg20 + t110 * t123
t124 = t3 * t66
t125 = t90 * rhoa
t126 = t125 ** (0.1D1 / 0.3D1)
cg22 = dble(t124) * t126
cg83 = -0.3D1 / 0.4D1 * t7 * cg22
t129 = 0.1D1 / cg22
t130 = cg0 * t129
t131 = 0.1D1 / rhoa
cg29 = t130 * t131 / 0.2D1
t133 = cg29 ** 2
t135 = 0.1D1 / kappa
t137 = 0.1D1 + mu * t133 * t135
cg23 = 0.1D1 + kappa - kappa / t137
t140 = rhoa * cg83
t142 = t90 * rhob
t143 = t142 ** (0.1D1 / 0.3D1)
cg24 = dble(t124) * t143
cg31 = -0.3D1 / 0.4D1 * t7 * cg24
t146 = 0.1D1 / cg24
t147 = cg1 * t146
t148 = 0.1D1 / rhob
cg32 = t147 * t148 / 0.2D1
t150 = cg32 ** 2
t153 = 0.1D1 + mu * t150 * t135
cg25 = 0.1D1 + kappa - kappa / t153
t156 = rhob * cg31
exc = scale_ex * (0.2D1 * t140 * cg23 + 0.2D1 * t156 * cg25) / 0
#.2D1 + scale_ec * rho * cg27
t162 = rho ** 2
t163 = 0.1D1 / t162
t164 = t1 * t163
cg26 = t2 - t164
t165 = t9 ** 2
t167 = 0.1D1 / t165 * t7
rsrhoa = -dble(t6) * t167 * t163 / 0.12D2
t171 = A_1 * alpha_1_1
t175 = t23 ** 2
t176 = 0.1D1 / t175
t177 = t12 * t176
t178 = 0.1D1 / t15
t179 = beta_1_1 * t178
t183 = beta_3_1 * t15
t187 = 0.1D1 / rs
t190 = t179 * rsrhoa / 0.2D1 + beta_2_1 * rsrhoa + 0.3D1 / 0.2D1
# * t183 * rsrhoa + t22 * t20 * rsrhoa * t187
t191 = 0.1D1 / t27
t192 = t190 * t191
cg76 = -0.2D1 * t171 * rsrhoa * t28 + t177 * t192
t194 = A_2 * alpha_1_2
t198 = t41 ** 2
t199 = 0.1D1 / t198
t200 = t32 * t199
t201 = beta_1_2 * t178
t205 = beta_3_2 * t15
t211 = t201 * rsrhoa / 0.2D1 + beta_2_2 * rsrhoa + 0.3D1 / 0.2D1
# * t205 * rsrhoa + t40 * t38 * rsrhoa * t187
t212 = 0.1D1 / t45
t213 = t211 * t212
cg74 = -0.2D1 * t194 * rsrhoa * t46 + t200 * t213
t215 = A_3 * alpha_1_3
t219 = t59 ** 2
t220 = 0.1D1 / t219
t221 = t50 * t220
t222 = beta_1_3 * t178
t226 = beta_3_3 * t15
t232 = t222 * rsrhoa / 0.2D1 + beta_2_3 * rsrhoa + 0.3D1 / 0.2D1
# * t226 * rsrhoa + t58 * t56 * rsrhoa * t187
t233 = 0.1D1 / t63
t234 = t232 * t233
cg73 = 0.2D1 * t215 * rsrhoa * t64 - t221 * t234
frhoa = (0.4D1 / 0.3D1 * t71 * cg26 - 0.4D1 / 0.3D1 * t74 * cg26
#) * dble(t69)
t240 = cg73 * f
t242 = cg19 * frhoa
t244 = t79 * chi
t245 = t78 * t244
t246 = t245 * cg26
t248 = 0.4D1 * t77 * t246
t249 = cg74 - cg76
t250 = t249 * f
t252 = t84 * frhoa
t254 = t244 * cg26
t256 = 0.4D1 * t85 * t254
cg7 = cg76 + t240 * t82 + t242 * t82 - t248 + t250 * t80 + t252
#* t80 + t256
t257 = 0.1D1 / t71
t259 = 0.1D1 / t74
cg42 = t257 * cg26 / 0.3D1 - t259 * cg26 / 0.3D1
t262 = t92 ** 2
cg38 = dble(t3) / t262 * t90 / 0.3D1
t266 = 0.1D1 / t94
cg39 = t266 * cg38 * t7
t268 = 0.1D1 / t103
t269 = cg * t268
t272 = cg21 ** 2
t273 = 0.1D1 / t272
t274 = t273 * t2
t277 = t97 * t163
t278 = t96 * t277
trhoa = -t269 * t98 * cg42 / 0.2D1 - t96 * t274 * cg39 / 0.2D1 -
# t278 / 0.2D1
t280 = t108 ** 2
t281 = 0.1D1 / t280
t282 = cg7 * t100
t284 = t103 ** 2
t285 = 0.1D1 / t284
t286 = t285 * cg42
t289 = -t282 * t105 + 0.3D1 * t102 * t286
Arhoa = -t101 * t281 * t289 * t107
t293 = gamma_var * t103
t294 = t123 * cg42
t297 = t101 * t
t298 = t113 * t119
t299 = t298 * trhoa
t302 = Arhoa * t111
t303 = A * t
t305 = 0.2D1 * t303 * trhoa
t306 = t302 + t305
t310 = t101 * t111
t311 = t118 ** 2
t312 = 0.1D1 / t311
t313 = t113 * t312
t314 = A * t116
t317 = t111 * t
t318 = t115 * t317
t321 = t302 + t305 + 0.2D1 * t314 * Arhoa + 0.4D1 * t318 * trhoa
t324 = 0.2D1 * t297 * t299 + t101 * t111 * t306 * t119 - t310 *
#t313 * t321
t325 = 0.1D1 / t122
t326 = t324 * t325
cg6 = cg7 + 0.3D1 * t293 * t294 + t110 * t326
t329 = t126 ** 2
cg51 = dble(t124) / t329 * t90 / 0.3D1
cg18 = -0.3D1 / 0.4D1 * t7 * cg51
t335 = cg22 ** 2
t336 = 0.1D1 / t335
t337 = cg0 * t336
t340 = rhoa ** 2
t341 = 0.1D1 / t340
cg43 = -t337 * t131 * cg51 / 0.2D1 - t130 * t341 / 0.2D1
t344 = t137 ** 2
t346 = 0.1D1 / t344 * mu
cg45 = 0.2D1 * t346 * cg29 * cg43
t350 = rhoa * cg18
exc_rhoa = scale_ex * (0.2D1 * cg83 * cg23 + 0.2D1 * t350 * cg23
# + 0.2D1 * t140 * cg45) / 0.2D1 + scale_ec * (cg27 + rho * cg6)
cg44 = -t2 - t164
rsrhob = rsrhoa
t368 = t179 * rsrhob / 0.2D1 + beta_2_1 * rsrhob + 0.3D1 / 0.2D1
# * t183 * rsrhob + t22 * t20 * rsrhob * t187
cg67 = -0.2D1 * t171 * rsrhob * t28 + t177 * t368 * t191
t382 = t201 * rsrhob / 0.2D1 + beta_2_2 * rsrhob + 0.3D1 / 0.2D1
# * t205 * rsrhob + t40 * t38 * rsrhob * t187
cg68 = -0.2D1 * t194 * rsrhob * t46 + t200 * t382 * t212
t396 = t222 * rsrhob / 0.2D1 + beta_2_3 * rsrhob + 0.3D1 / 0.2D1
# * t226 * rsrhob + t58 * t56 * rsrhob * t187
cg66 = 0.2D1 * t215 * rsrhob * t64 - t221 * t396 * t233
frhob = (0.4D1 / 0.3D1 * t71 * cg44 - 0.4D1 / 0.3D1 * t74 * cg44
#) * dble(t69)
t403 = cg66 * f
t405 = cg19 * frhob
t407 = t245 * cg44
t409 = 0.4D1 * t77 * t407
t410 = cg68 - cg67
t411 = t410 * f
t413 = t84 * frhob
t415 = t244 * cg44
t417 = 0.4D1 * t85 * t415
cg5 = cg67 + t403 * t82 + t405 * t82 - t409 + t411 * t80 + t413
#* t80 + t417
cg52 = t257 * cg44 / 0.3D1 - t259 * cg44 / 0.3D1
cg53 = cg38
cg54 = t266 * cg53 * t7
trhob = -t269 * t98 * cg52 / 0.2D1 - t96 * t274 * cg54 / 0.2D1 -
# t278 / 0.2D1
t427 = cg5 * t100
t429 = t285 * cg52
t432 = -t427 * t105 + 0.3D1 * t102 * t429
Arhob = -t101 * t281 * t432 * t107
t436 = t123 * cg52
t439 = t298 * trhob
t442 = Arhob * t111
t444 = 0.2D1 * t303 * trhob
t445 = t442 + t444
t453 = t442 + t444 + 0.2D1 * t314 * Arhob + 0.4D1 * t318 * trhob
t456 = 0.2D1 * t297 * t439 + t101 * t111 * t445 * t119 - t310 *
#t313 * t453
t457 = t456 * t325
cg4 = cg5 + 0.3D1 * t293 * t436 + t110 * t457
t460 = t143 ** 2
cg62 = dble(t124) / t460 * t90 / 0.3D1
cg34 = -0.3D1 / 0.4D1 * t7 * cg62
t466 = cg24 ** 2
t467 = 0.1D1 / t466
t468 = cg1 * t467
t471 = rhob ** 2
t472 = 0.1D1 / t471
cg59 = -t468 * t148 * cg62 / 0.2D1 - t147 * t472 / 0.2D1
t475 = t153 ** 2
t477 = 0.1D1 / t475 * mu
cg57 = 0.2D1 * t477 * cg32 * cg59
t481 = rhob * cg34
exc_rhob = scale_ex * (0.2D1 * cg31 * cg25 + 0.2D1 * t481 * cg25
# + 0.2D1 * t156 * cg57) / 0.2D1 + scale_ec * (cg27 + rho * cg4)
t488 = t95 * t97
cg63 = t488 * t2 / 0.2D1
t493 = t101 * t317
t494 = A * cg63
t502 = 0.2D1 * t303 * cg63 + 0.4D1 * t318 * cg63
t505 = 0.2D1 * t297 * t298 * cg63 + 0.2D1 * t493 * t494 * t119 -
# t310 * t313 * t502
t506 = t505 * t325
cg60 = t110 * t506
exc_norm_drho = scale_ec * rho * cg60
cg16 = t129 * t131 / 0.2D1
cg69 = 0.2D1 * t346 * cg29 * cg16
exc_norm_drhoa = scale_ex * t140 * cg69
cg70 = t146 * t148 / 0.2D1
cg71 = 0.2D1 * t477 * cg32 * cg70
exc_norm_drhob = scale_ex * t156 * cg71
t518 = 0.1D1 / t162 / rho</Text-field></Output><Output><Text-field layout="Normal" style="Line Printed Output"> t519 = t1 * t518
cg77 = -0.2D1 * t163 + 0.2D1 * t519
t523 = 0.1D1 / t90
t525 = t162 ** 2
cg58 = -dble(t6) / t165 / t8 * t523 / t525 / 0.18D2 + dble(t6) *
# t167 * t518 / 0.6D1
t536 = alpha_1_1 * rsrhoa
t538 = t176 * t190 * t191
t543 = t12 / t175 / t23
t544 = t190 ** 2
t548 = 0.1D1 / t18
t549 = beta_1_1 * t548
t550 = rsrhoa ** 2
t556 = beta_3_1 * t178
t561 = t20 ** 2
t563 = rs ** 2
t564 = 0.1D1 / t563
t576 = t175 ** 2
t578 = t12 / t576
t579 = t27 ** 2
t580 = 0.1D1 / t579
cg72 = -0.2D1 * t171 * cg58 * t28 + 0.2D1 * t536 * t538 - 0.2D1
#* t543 * t544 * t191 + t177 * (-t549 * t550 / 0.4D1 + t179 * cg58
#/ 0.2D1 + beta_2_1 * cg58 + 0.3D1 / 0.4D1 * t556 * t550 + 0.3D1 /
#0.2D1 * t183 * cg58 + t22 * t561 * t550 * t564 + t22 * t20 * cg58
#* t187 - t22 * t20 * t550 * t564) * t191 + t578 * t544 * t580 * t1
#4 / 0.2D1
cg85 = cg76
t588 = alpha_1_2 * rsrhoa
t590 = t199 * t211 * t212
t595 = t32 / t198 / t41
t596 = t211 ** 2
t600 = beta_1_2 * t548
t606 = beta_3_2 * t178
t611 = t38 ** 2
t624 = t198 ** 2
t626 = t32 / t624
t627 = t45 ** 2
t628 = 0.1D1 / t627
t636 = alpha_1_3 * rsrhoa
t638 = t220 * t232 * t233
t643 = t50 / t219 / t59
t644 = t232 ** 2
t648 = beta_1_3 * t548
t654 = beta_3_3 * t178
t659 = t56 ** 2
t672 = t219 ** 2
t674 = t50 / t672
t675 = t63 ** 2
t676 = 0.1D1 / t675
cg13 = cg73
t681 = 0.1D1 / t87
t682 = cg26 ** 2
t687 = 0.1D1 / t88
cg92 = (0.4D1 / 0.9D1 * t681 * t682 + 0.4D1 / 0.3D1 * t71 * cg77
# + 0.4D1 / 0.9D1 * t687 * t682 - 0.4D1 / 0.3D1 * t74 * cg77) * dbl
#e(t69)
f1rhoa = frhoa
t705 = cg13 * f
t708 = cg19 * f1rhoa
t711 = t78 * t79
t726 = cg74 - cg85
t733 = t726 * f
t736 = t84 * f1rhoa
t745 = -0.4D1 * t77 * t245 * cg77 + (-0.2D1 * t194 * cg58 * t46
#+ 0.2D1 * t588 * t590 - 0.2D1 * t595 * t596 * t212 + t200 * (-t600
# * t550 / 0.4D1 + t201 * cg58 / 0.2D1 + beta_2_2 * cg58 + 0.3D1 /
#0.4D1 * t606 * t550 + 0.3D1 / 0.2D1 * t205 * cg58 + t40 * t611 * t
#550 * t564 + t40 * t38 * cg58 * t187 - t40 * t38 * t550 * t564) *
#t212 + t626 * t596 * t628 * t34 / 0.2D1 - cg72) * f * t80 + t249 *
# f1rhoa * t80 + 0.4D1 * t250 * t254 + t726 * frhoa * t80 + t84 * c
#g92 * t80 + 0.4D1 * t252 * t254 + 0.4D1 * t733 * t254 + 0.4D1 * t7
#36 * t254 + 0.12D2 * t85 * t79 * t682 + 0.4D1 * t85 * t244 * cg77
cg41 = cg72 + (0.2D1 * t215 * cg58 * t64 - 0.2D1 * t636 * t638 +
# 0.2D1 * t643 * t644 * t233 - t221 * (-t648 * t550 / 0.4D1 + t222
#* cg58 / 0.2D1 + beta_2_3 * cg58 + 0.3D1 / 0.4D1 * t654 * t550 + 0
#.3D1 / 0.2D1 * t226 * cg58 + t58 * t659 * t550 * t564 + t58 * t56
#* cg58 * t187 - t58 * t56 * t550 * t564) * t233 - t674 * t644 * t6
#76 * t52 / 0.2D1) * f * t82 + cg73 * f1rhoa * t82 - 0.4D1 * t240 *
# t246 + cg13 * frhoa * t82 + cg19 * cg92 * t82 - 0.4D1 * t242 * t2
#46 - 0.4D1 * t705 * t246 - 0.4D1 * t708 * t246 - 0.12D2 * t77 * t7
#11 * t682 + t745
cg8 = cg85 + t705 * t82 + t708 * t82 - t248 + t733 * t80 + t736
#* t80 + t256
t750 = 0.1D1 / t72
t755 = 0.1D1 / t75
cg75 = -t750 * t682 / 0.9D1 + t257 * cg77 / 0.3D1 - t755 * t682
#/ 0.9D1 - t259 * cg77 / 0.3D1
cg15 = cg42
t763 = t90 ** 2
cg88 = -0.2D1 / 0.9D1 * dble(t3) / t262 / t91 * t763
t767 = 0.1D1 / t94 / t93
t768 = cg38 ** 2
cg87 = cg39
t775 = cg * t105 * t97
t776 = t2 * cg42
t779 = t269 * t273
t785 = t269 * t277 * cg42 / 0.2D1
t789 = t2 * cg39
t795 = t96 / t272 / cg21
t798 = t273 * t163
t801 = t96 * t798 * cg39 / 0.2D1
t812 = t96 * t97 * t518
cg86 = t775 * t776 * cg15 + t779 * t776 * cg87 / 0.2D1 + t785 -
#t269 * t98 * cg75 / 0.2D1 + t779 * t789 * cg15 / 0.2D1 + t795 * t7
#89 * cg87 + t801 - t96 * t274 * (-t767 * t768 * t523 / 0.2D1 + t26
#6 * cg88 * t7) / 0.2D1 + t269 * t277 * cg15 / 0.2D1 + t96 * t798 *
# cg87 / 0.2D1 + t812
t1rhoa = -t269 * t98 * cg15 / 0.2D1 - t96 * t274 * cg87 / 0.2D1
#- t278 / 0.2D1
t820 = t101 / t280 / t108
t821 = t107 ** 2
t822 = t289 * t821
t823 = cg8 * t100
t825 = t285 * cg15
t828 = -t823 * t105 + 0.3D1 * t102 * t825
t839 = 0.1D1 / t284 / phi
t840 = t839 * cg42
t851 = t101 * t281
cg33 = 0.2D1 * t820 * t822 * t828 - t101 * t281 * (-cg41 * t100
#* t105 + 0.3D1 * t282 * t825 + 0.3D1 * t823 * t286 - 0.12D2 * t102
# * t840 * cg15 + 0.3D1 * t102 * t285 * cg75) * t107 - t851 * t289
#* t828 * t107
A1rhoa = -t101 * t281 * t828 * t107
t858 = gamma_var * phi
t865 = A1rhoa * t111
t867 = 0.2D1 * t303 * t1rhoa
t868 = t865 + t867
t876 = t865 + t867 + 0.2D1 * t314 * A1rhoa + 0.4D1 * t318 * t1rh
#oa
t879 = 0.2D1 * t297 * t298 * t1rhoa + t101 * t111 * t868 * t119
#- t310 * t313 * t876
t880 = t879 * t325
t904 = t306 * t119
t908 = cg33 * t111
t909 = Arhoa * t
t911 = 0.2D1 * t909 * t1rhoa
t914 = 0.2D1 * A1rhoa * t * trhoa
t917 = 0.2D1 * A * t1rhoa * trhoa
t919 = 0.2D1 * t303 * cg86
t924 = t306 * t312
t936 = t113 / t311 / t118
t944 = A * t317
t953 = t115 * t111
t959 = t908 + t911 + t914 + t917 + t919 + 0.2D1 * A1rhoa * t116
#* Arhoa + 0.8D1 * t944 * Arhoa * t1rhoa + 0.2D1 * t314 * cg33 + 0.
#8D1 * t944 * trhoa * A1rhoa + 0.12D2 * t953 * trhoa * t1rhoa + 0.4
#D1 * t318 * cg86
t962 = 0.2D1 * t101 * t1rhoa * t299 + 0.2D1 * t297 * t868 * t119
# * trhoa - 0.2D1 * t297 * t313 * trhoa * t876 + 0.2D1 * t297 * t29
#8 * cg86 + 0.2D1 * t297 * t904 * t1rhoa + t101 * t111 * (t908 + t9
#11 + t914 + t917 + t919) * t119 - t310 * t924 * t876 - 0.2D1 * t29
#7 * t313 * t321 * t1rhoa - t310 * t868 * t312 * t321 + 0.2D1 * t31
#0 * t936 * t321 * t876 - t310 * t313 * t959
t965 = t122 ** 2
t966 = 0.1D1 / t965
t967 = t324 * t966
cg46 = -0.2D1 / 0.9D1 * dble(t124) / t329 / t125 * t763
cg47 = cg18
t985 = cg51 ** 2
cg3 = cg43
t998 = mu ** 2
t999 = 0.1D1 / t344 / t137 * t998
t1000 = t999 * t133
t1001 = cg43 * t135
cg30 = 0.2D1 * t346 * cg29 * cg3
exc_rhoa_rhoa = scale_ex * (0.2D1 * cg47 * cg23 + 0.2D1 * cg83 *
# cg30 + 0.2D1 * cg18 * cg23 - 0.3D1 / 0.2D1 * rhoa * t7 * cg46 * c
#g23 + 0.2D1 * t350 * cg30 + 0.2D1 * cg83 * cg45 + 0.2D1 * rhoa * c
#g47 * cg45 + 0.2D1 * t140 * (-0.8D1 * t1000 * t1001 * cg3 + 0.2D1
#* t346 * cg3 * cg43 + 0.2D1 * t346 * cg29 * (cg0 / t335 / cg22 * t
#131 * t985 + t337 * t341 * cg51 - t337 * t131 * cg46 / 0.2D1 + t13
#0 / t340 / rhoa))) / 0.2D1 + scale_ec * (cg8 + 0.3D1 * t293 * t123
# * cg15 + t110 * t880 + cg6 + rho * (cg41 + 0.6D1 * t858 * t294 *
#cg15 + 0.3D1 * t293 * t880 * cg42 + 0.3D1 * t293 * t123 * cg75 + 0
#.3D1 * t293 * t326 * cg15 + t110 * t962 * t325 - t110 * t967 * t87
#9))
cg40 = 0.2D1 * t519
cg11 = cg58
t1031 = t176 * t368 * t191
t1033 = alpha_1_1 * rsrhob
t1038 = rsrhoa * rsrhob
t1050 = rsrhob * t564 * rsrhoa
cg10 = -0.2D1 * t171 * cg11 * t28 + t536 * t1031 + t1033 * t538
#- 0.2D1 * t543 * t192 * t368 + t177 * (-t549 * t1038 / 0.4D1 + t17
#9 * cg11 / 0.2D1 + beta_2_1 * cg11 + 0.3D1 / 0.4D1 * t556 * t1038
#+ 0.3D1 / 0.2D1 * t183 * cg11 + t22 * t561 * t1050 + t22 * t20 * c
#g11 * t187 - t22 * t20 * t1050) * t191 + t578 * t190 * t580 * t14
#* t368 / 0.2D1
t1069 = t199 * t382 * t212
t1071 = alpha_1_2 * rsrhob
t1104 = t220 * t396 * t233
t1106 = alpha_1_3 * rsrhob
cg37 = (0.4D1 / 0.9D1 * t681 * cg26 * cg44 + 0.4D1 / 0.3D1 * t71
# * cg40 + 0.4D1 / 0.9D1 * t687 * cg26 * cg44 - 0.4D1 / 0.3D1 * t74
# * cg40) * dble(t69)
t1164 = t79 * cg26 * cg44
t1193 = -0.4D1 * t77 * t245 * cg40 + (-0.2D1 * t194 * cg11 * t46
# + t588 * t1069 + t1071 * t590 - 0.2D1 * t595 * t213 * t382 + t200
# * (-t600 * t1038 / 0.4D1 + t201 * cg11 / 0.2D1 + beta_2_2 * cg11
#+ 0.3D1 / 0.4D1 * t606 * t1038 + 0.3D1 / 0.2D1 * t205 * cg11 + t40
# * t611 * t1050 + t40 * t38 * cg11 * t187 - t40 * t38 * t1050) * t
#212 + t626 * t211 * t628 * t34 * t382 / 0.2D1 - cg10) * f * t80 +
#t249 * frhob * t80 + 0.4D1 * t250 * t415 + t410 * frhoa * t80 + t8
#4 * cg37 * t80 + 0.4D1 * t252 * t415 + 0.4D1 * t411 * t254 + 0.4D1
# * t413 * t254 + 0.12D2 * t85 * t1164 + 0.4D1 * t85 * t244 * cg40
cg14 = cg10 + (0.2D1 * t215 * cg11 * t64 - t636 * t1104 - t1106
#* t638 + 0.2D1 * t643 * t234 * t396 - t221 * (-t648 * t1038 / 0.4D
#1 + t222 * cg11 / 0.2D1 + beta_2_3 * cg11 + 0.3D1 / 0.4D1 * t654 *
# t1038 + 0.3D1 / 0.2D1 * t226 * cg11 + t58 * t659 * t1050 + t58 *
#t56 * cg11 * t187 - t58 * t56 * t1050) * t233 - t674 * t232 * t676
# * t52 * t396 / 0.2D1) * f * t82 + cg73 * frhob * t82 - 0.4D1 * t2
#40 * t407 + cg66 * frhoa * t82 + cg19 * cg37 * t82 - 0.4D1 * t242
#* t407 - 0.4D1 * t403 * t246 - 0.4D1 * t405 * t246 - 0.12D2 * t77
#* t78 * t1164 + t1193
cg91 = -t750 * cg26 * cg44 / 0.9D1 + t257 * cg40 / 0.3D1 - t755
#* cg26 * cg44 / 0.9D1 - t259 * cg40 / 0.3D1
cg84 = cg88
t1228 = t269 * t277 * cg52 / 0.2D1
t1231 = t96 * t798 * cg54 / 0.2D1
cg56 = t775 * t776 * cg52 + t779 * t776 * cg54 / 0.2D1 + t785 -
#t269 * t98 * cg91 / 0.2D1 + t779 * t789 * cg52 / 0.2D1 + t795 * t7
#89 * cg54 + t801 - t96 * t274 * (-t767 * cg38 * t523 * cg53 / 0.2D
#1 + t266 * cg84 * t7) / 0.2D1 + t1228 + t1231 + t812
cg55 = 0.2D1 * t820 * t822 * t432 - t101 * t281 * (-cg14 * t100
#* t105 + 0.3D1 * t282 * t429 + 0.3D1 * t427 * t286 - 0.12D2 * t102
# * t840 * cg52 + 0.3D1 * t102 * t285 * cg91) * t107 - t851 * t289
#* t432 * t107
t1269 = t445 * t119
t1283 = cg55 * t111
t1285 = 0.2D1 * t909 * trhob
t1286 = Arhob * t
t1288 = 0.2D1 * t1286 * trhoa
t1291 = 0.2D1 * A * trhob * trhoa
t1293 = 0.2D1 * t303 * cg56
t1304 = t445 * t312
t1327 = t1283 + t1285 + t1288 + t1291 + t1293 + 0.2D1 * Arhob *
#t116 * Arhoa + 0.8D1 * t944 * Arhoa * trhob + 0.2D1 * t314 * cg55
#+ 0.8D1 * t944 * trhoa * Arhob + 0.12D2 * t953 * trhoa * trhob + 0
#.4D1 * t318 * cg56
t1330 = 0.2D1 * t101 * trhob * t299 + 0.2D1 * t297 * t1269 * trh
#oa - 0.2D1 * t297 * t313 * trhoa * t453 + 0.2D1 * t297 * t298 * cg
#56 + 0.2D1 * t297 * t904 * trhob + t101 * t111 * (t1283 + t1285 +
#t1288 + t1291 + t1293) * t119 - t310 * t924 * t453 - 0.2D1 * t297
#* t313 * t321 * trhob - t310 * t1304 * t321 + 0.2D1 * t310 * t936
#* t321 * t453 - t310 * t313 * t1327
exc_rhoa_rhob = scale_ec * (cg4 + cg6 + rho * (cg14 + 0.6D1 * t8
#58 * t294 * cg52 + 0.3D1 * t293 * t457 * cg42 + 0.3D1 * t293 * t12
#3 * cg91 + 0.3D1 * t293 * t326 * cg52 + t110 * t1330 * t325 - t110
# * t967 * t456))
cg65 = 0.2D1 * t163 + 0.2D1 * t519
cg35 = cg11
t1342 = t368 ** 2
t1346 = rsrhob ** 2
cg28 = -0.2D1 * t171 * cg35 * t28 + 0.2D1 * t1033 * t1031 - 0.2D
#1 * t543 * t1342 * t191 + t177 * (-t549 * t1346 / 0.4D1 + t179 * c
#g35 / 0.2D1 + beta_2_1 * cg35 + 0.3D1 / 0.4D1 * t556 * t1346 + 0.3
#D1 / 0.2D1 * t183 * cg35 + t22 * t561 * t1346 * t564 + t22 * t20 *
# cg35 * t187 - t22 * t20 * t1346 * t564) * t191 + t578 * t1342 * t
#580 * t14 / 0.2D1
cg64 = cg67
t1377 = t382 ** 2
t1411 = t396 ** 2
cg81 = cg66
t1440 = cg44 ** 2
cg61 = (0.4D1 / 0.9D1 * t681 * t1440 + 0.4D1 / 0.3D1 * t71 * cg6
#5 + 0.4D1 / 0.9D1 * t687 * t1440 - 0.4D1 / 0.3D1 * t74 * cg65) * d
#ble(t69)
f1rhob = frhob
t1462 = cg81 * f
t1465 = cg19 * f1rhob
t1482 = cg68 - cg64
t1489 = t1482 * f
t1492 = t84 * f1rhob
t1501 = -0.4D1 * t77 * t245 * cg65 + (-0.2D1 * t194 * cg35 * t46
# + 0.2D1 * t1071 * t1069 - 0.2D1 * t595 * t1377 * t212 + t200 * (-
#t600 * t1346 / 0.4D1 + t201 * cg35 / 0.2D1 + beta_2_2 * cg35 + 0.3
#D1 / 0.4D1 * t606 * t1346 + 0.3D1 / 0.2D1 * t205 * cg35 + t40 * t6
#11 * t1346 * t564 + t40 * t38 * cg35 * t187 - t40 * t38 * t1346 *
#t564) * t212 + t626 * t1377 * t628 * t34 / 0.2D1 - cg28) * f * t80
# + t410 * f1rhob * t80 + 0.4D1 * t411 * t415 + t1482 * frhob * t80
# + t84 * cg61 * t80 + 0.4D1 * t413 * t415 + 0.4D1 * t1489 * t415 +
# 0.4D1 * t1492 * t415 + 0.12D2 * t85 * t79 * t1440 + 0.4D1 * t85 *
# t244 * cg65
cg90 = cg28 + (0.2D1 * t215 * cg35 * t64 - 0.2D1 * t1106 * t1104
# + 0.2D1 * t643 * t1411 * t233 - t221 * (-t648 * t1346 / 0.4D1 + t
#222 * cg35 / 0.2D1 + beta_2_3 * cg35 + 0.3D1 / 0.4D1 * t654 * t134
#6 + 0.3D1 / 0.2D1 * t226 * cg35 + t58 * t659 * t1346 * t564 + t58
#* t56 * cg35 * t187 - t58 * t56 * t1346 * t564) * t233 - t674 * t1
#411 * t676 * t52 / 0.2D1) * f * t82 + cg66 * f1rhob * t82 - 0.4D1
#* t403 * t407 + cg81 * frhob * t82 + cg19 * cg61 * t82 - 0.4D1 * t
#405 * t407 - 0.4D1 * t1462 * t407 - 0.4D1 * t1465 * t407 - 0.12D2
#* t77 * t711 * t1440 + t1501
cg82 = cg64 + t1462 * t82 + t1465 * t82 - t409 + t1489 * t80 + t
#1492 * t80 + t417
cg80 = -t750 * t1440 / 0.9D1 + t257 * cg65 / 0.3D1 - t755 * t144
#0 / 0.9D1 - t259 * cg65 / 0.3D1
cg89 = cg52
t1514 = cg53 ** 2
cg79 = cg54
t1520 = t2 * cg52
t1529 = t2 * cg54
cg9 = t775 * t1520 * cg89 + t779 * t1520 * cg79 / 0.2D1 + t1228
#- t269 * t98 * cg80 / 0.2D1 + t779 * t1529 * cg89 / 0.2D1 + t795 *
# t1529 * cg79 + t1231 - t96 * t274 * (-t767 * t1514 * t523 / 0.2D1
# + t266 * cg84 * t7) / 0.2D1 + t269 * t277 * cg89 / 0.2D1 + t96 *
#t798 * cg79 / 0.2D1 + t812
t1rhob = -t269 * t98 * cg89 / 0.2D1 - t96 * t274 * cg79 / 0.2D1
#- t278 / 0.2D1
t1550 = cg82 * t100
t1552 = t285 * cg89
t1555 = -t1550 * t105 + 0.3D1 * t102 * t1552
cg12 = 0.2D1 * t820 * t432 * t821 * t1555 - t101 * t281 * (-cg90
# * t100 * t105 + 0.3D1 * t427 * t1552 + 0.3D1 * t1550 * t429 - 0.1
#2D2 * t102 * t839 * cg52 * cg89 + 0.3D1 * t102 * t285 * cg80) * t1
#07 - t851 * t432 * t1555 * t107
A1rhob = -t101 * t281 * t1555 * t107
t1588 = A1rhob * t111
t1590 = 0.2D1 * t303 * t1rhob
t1591 = t1588 + t1590
t1599 = t1588 + t1590 + 0.2D1 * t314 * A1rhob + 0.4D1 * t318 * t
#1rhob
t1602 = 0.2D1 * t297 * t298 * t1rhob + t101 * t111 * t1591 * t11
#9 - t310 * t313 * t1599
t1603 = t1602 * t325
t1630 = cg12 * t111
t1632 = 0.2D1 * t1286 * t1rhob
t1635 = 0.2D1 * A1rhob * t * trhob
t1638 = 0.2D1 * A * t1rhob * trhob
t1640 = 0.2D1 * t303 * cg9
t1674 = t1630 + t1632 + t1635 + t1638 + t1640 + 0.2D1 * A1rhob *
# t116 * Arhob + 0.8D1 * t944 * Arhob * t1rhob + 0.2D1 * t314 * cg1
#2 + 0.8D1 * t944 * trhob * A1rhob + 0.12D2 * t953 * trhob * t1rhob
# + 0.4D1 * t318 * cg9
t1677 = 0.2D1 * t101 * t1rhob * t439 + 0.2D1 * t297 * t1591 * t1
#19 * trhob - 0.2D1 * t297 * t313 * trhob * t1599 + 0.2D1 * t297 *
#t298 * cg9 + 0.2D1 * t297 * t1269 * t1rhob + t101 * t111 * (t1630
#+ t1632 + t1635 + t1638 + t1640) * t119 - t310 * t1304 * t1599 - 0
#.2D1 * t297 * t313 * t453 * t1rhob - t310 * t1591 * t312 * t453 +
#0.2D1 * t310 * t936 * t453 * t1599 - t310 * t313 * t1674
t1680 = t456 * t966
cg48 = -0.2D1 / 0.9D1 * dble(t124) / t460 / t142 * t763
cg49 = cg34
t1698 = cg62 ** 2
cg2 = cg59
t1711 = 0.1D1 / t475 / t153 * t998
t1712 = t1711 * t150
t1713 = cg59 * t135
cg36 = 0.2D1 * t477 * cg32 * cg2
exc_rhob_rhob = scale_ex * (0.2D1 * cg49 * cg25 + 0.2D1 * cg31 *
# cg36 + 0.2D1 * cg34 * cg25 - 0.3D1 / 0.2D1 * rhob * t7 * cg48 * c
#g25 + 0.2D1 * t481 * cg36 + 0.2D1 * cg31 * cg57 + 0.2D1 * rhob * c
#g49 * cg57 + 0.2D1 * t156 * (-0.8D1 * t1712 * t1713 * cg2 + 0.2D1
#* t477 * cg2 * cg59 + 0.2D1 * t477 * cg32 * (cg1 / t466 / cg24 * t
#148 * t1698 + t468 * t472 * cg62 - t468 * t148 * cg48 / 0.2D1 + t1
#47 / t471 / rhob))) / 0.2D1 + scale_ec * (cg82 + 0.3D1 * t293 * t1
#23 * cg89 + t110 * t1603 + cg4 + rho * (cg90 + 0.6D1 * t858 * t436
# * cg89 + 0.3D1 * t293 * t1603 * cg52 + 0.3D1 * t293 * t123 * cg80
# + 0.3D1 * t293 * t457 * cg89 + t110 * t1677 * t325 - t110 * t1680
# * t1602))
t1739 = t268 * t97
t1741 = t95 * t273
t1743 = t488 * t163
cg50 = -t1739 * t776 / 0.2D1 - t1741 * t789 / 0.2D1 - t1743 / 0.
#2D1
t1748 = t101 * cg63
t1765 = t909 * cg63
t1766 = t494 * trhoa
t1767 = t303 * cg50
t1801 = 0.2D1 * t1748 * t299 + 0.4D1 * t310 * t494 * t119 * trho
#a - 0.2D1 * t297 * t313 * trhoa * t502 + 0.2D1 * t297 * t298 * cg5
#0 + 0.2D1 * t297 * t904 * cg63 + t101 * t111 * (0.2D1 * t1765 + 0.
#2D1 * t1766 + 0.2D1 * t1767) * t119 - t310 * t924 * t502 - 0.2D1 *
# t297 * t313 * t321 * cg63 - 0.2D1 * t493 * t494 * t312 * t321 + 0
#.2D1 * t310 * t936 * t321 * t502 - t310 * t313 * (0.2D1 * t1765 +
#0.2D1 * t1766 + 0.2D1 * t1767 + 0.8D1 * t944 * Arhoa * cg63 + 0.12
#D2 * t953 * trhoa * cg63 + 0.4D1 * t318 * cg50)
exc_rhoa_norm_drho = scale_ec * (cg60 + rho * (0.3D1 * t293 * t5
#06 * cg42 + t110 * t1801 * t325 - t110 * t967 * t505))
cg78 = -t1739 * t1520 / 0.2D1 - t1741 * t1529 / 0.2D1 - t1743 /
#0.2D1
t1829 = t1286 * cg63
t1830 = t494 * trhob
t1831 = t303 * cg78
t1865 = 0.2D1 * t1748 * t439 + 0.4D1 * t310 * t494 * t119 * trho
#b - 0.2D1 * t297 * t313 * trhob * t502 + 0.2D1 * t297 * t298 * cg7
#8 + 0.2D1 * t297 * t1269 * cg63 + t101 * t111 * (0.2D1 * t1829 + 0
#.2D1 * t1830 + 0.2D1 * t1831) * t119 - t310 * t1304 * t502 - 0.2D1
# * t297 * t313 * t453 * cg63 - 0.2D1 * t493 * t494 * t312 * t453 +
# 0.2D1 * t310 * t936 * t453 * t502 - t310 * t313 * (0.2D1 * t1829
#+ 0.2D1 * t1830 + 0.2D1 * t1831 + 0.8D1 * t944 * Arhob * cg63 + 0.
#12D2 * t953 * trhob * cg63 + 0.4D1 * t318 * cg78)
exc_rhob_norm_drho = scale_ec * (cg60 + rho * (0.3D1 * t293 * t5
#06 * cg52 + t110 * t1865 * t325 - t110 * t1680 * t505))
t1871 = cg63 ** 2
t1876 = A * t1871
t1888 = t502 ** 2
t1901 = t505 ** 2
exc_norm_drho_norm_drho = scale_ec * rho * (t110 * (0.2D1 * t101
# * t1871 * t113 * t119 + 0.10D2 * t310 * t1876 * t119 - 0.4D1 * t2
#97 * t313 * cg63 * t502 - 0.4D1 * t493 * t494 * t312 * t502 + 0.2D
#1 * t310 * t936 * t1888 - t310 * t313 * (0.2D1 * t1876 + 0.12D2 *
#t953 * t1871)) * t325 - t110 * t1901 * t966)
exc_rhoa_norm_drhoa = scale_ex * (0.2D1 * cg83 * cg69 + 0.2D1 *
#t350 * cg69 + 0.2D1 * t140 * (-0.8D1 * t1000 * t1001 * cg16 + 0.2D
#1 * t346 * cg16 * cg43 + 0.2D1 * t346 * cg29 * (-t336 * t131 * cg5
#1 / 0.2D1 - t129 * t341 / 0.2D1))) / 0.2D1
t1922 = cg16 ** 2
exc_norm_drhoa_norm_drhoa = scale_ex * t140 * (-0.8D1 * t999 * t
#133 * t1922 * t135 + 0.2D1 * t346 * t1922)
exc_rhob_norm_drhob = scale_ex * (0.2D1 * cg31 * cg71 + 0.2D1 *
#t481 * cg71 + 0.2D1 * t156 * (-0.8D1 * t1712 * t1713 * cg70 + 0.2D
#1 * t477 * cg70 * cg59 + 0.2D1 * t477 * cg32 * (-t467 * t148 * cg6
#2 / 0.2D1 - t146 * t472 / 0.2D1))) / 0.2D1
t1949 = cg70 ** 2
exc_norm_drhob_norm_drhob = scale_ex * t156 * (-0.8D1 * t1711 *
#t150 * t1949 * t135 + 0.2D1 * t477 * t1949)
cg93 = exc_norm_drhob_norm_drhob
return
end</Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group></Section></Section><Text-field/><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalf(r_eqs_lsd4(0.1,0.1,0.3,0.15,0.15));
evalf(exc);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIStqcF4lMyIhIzU=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkISs1aGhkKSohIzY=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalf(r_eqs_lda4(0.2,0.3));
evalf(exc);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkISsqemwxKyIhIzU=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkISs1aGhkKSohIzY=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">exc:='exc':exc_rhoa:='exc_rhoa':exc_rhob:='exc_rhob':exc_norm_drho:='exc_norm_drho':
exc_norm_drhoa:='exc_norm_drhoa':exc_norm_drhob:='exc_norm_drhob':
exc_rhoa_rhoa:='exc_rhoa_rhoa':exc_rhoa_rhob:='exc_rhoa_rhob':exc_rhob_rhob:='exc_rhob_rhob':
exc_rhoa_norm_drho:='exc_rhoa_norm_drho':exc_rhob_norm_drho:='exc_rhob_norm_drho':
exc_norm_drho_norm_drho:='exc_norm_drho_norm_drho':
exc_rhoa_norm_drhoa:='exc_rhoa_norm_drhoa':exc_norm_drhoa_norm_drhoa:='exc_norm_drhoa_norm_drhoa':
exc_rhob_norm_drhob:='exc_rhob_norm_drhob':exc_norm_drhob_norm_drhob:='exc_norm_drhob_norm_drhob':
my_rho:='my_rho':my_norm_drho:='my_norm_drho':my_rhoa:='my_rhoa':my_rhob:='my_rhob':
my_norm_drhoa:='my_norm_drhoa':my_norm_drhob:='my_norm_drhob':
exc_rho:='exc_rho':exc_rho_rho:='exc_rho_rho':exc_rho_norm_drho:='exc_rho_norm_drho':
</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Text-field/><Text-field/></Worksheet>
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