Data update
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Ingy döt Net
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10248 changed files with 63654 additions and 6775 deletions
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/*REXX pgm computes & shows a value grid of the Möbius function for a range of integers.*/
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call time('r')
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parse arg LO HI grp . /*obtain optional arguments from the CL*/
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numeric digits 100
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if LO=='' | LO=="," then LO= 0 /*Not specified? Then use the default.*/
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if HI=='' | HI=="," then HI= 199 /* " " " " " " */
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if grp=='' | grp=="," then grp= 20 /* " " " " " " */
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/* ______ */
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call genP HI /*generate primes up to the √ HI */
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say center(' The Möbius sequence from ' LO " ──► " HI" ", max(50, grp*3), '═') /*title*/
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$= /*variable holds output grid of GRP #s.*/
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do j=LO to HI; $= $ right( mobius(j), 2) /*process some numbers from LO ──► HI.*/
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if words($)==grp then do; say substr($, 2); $= /*show grid if fully populated,*/
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end /* and nullify it for more #s.*/
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/* uuuuuuuuuuuu */
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call genP HI /*generate primes up to the v HI */
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say center(' The Moebius sequence from ' LO " --> " HI" ", max(50, grp*3), '=') /*title*/
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dd='' /*variable holds output grid of GRP hhs.*/
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do j=LO to HI; dd= dd right( moebius(j), 2) /*process some numbers from LO --> HI.*/
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if words(dd)==grp then do; say substr(dd, 2); dd='' /*show grid if fully populated,*/
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end /* and nullify it for more hhs.*/
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end /*j*/ /*for small grids, using wordCnt is OK.*/
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if $\=='' then say substr($, 2) /*handle any residual numbers not shown*/
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if dd\=='' then say substr(dd, 2) /*handle any residual numbers not shown*/
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say format(time('e'),,3) 'seconds'
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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mobius: procedure expose @.; parse arg x /*obtain a integer to be tested for mu.*/
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if x<1 then return '∙' /*special? Then return symbol for null.*/
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#= 0 /*start with a value of zero. */
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do k=1; p= @.k /*get the Kth (pre─generated) prime.*/
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/*--------------------------------------------------------------------------------------*/
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moebius: procedure expose aa.; parse arg x /*obtain a integer to be tested for mu.*/
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if x<1 then return '*' /*special? Then return symbol for null.*/
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hh= 0 /*start with a value of zero. */
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do k=1; p= aa.k /*get the Kth (pre-generated) prime.*/
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if p>x then leave /*prime (P) > X? Then we're done. */
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if p*p>x then do; #= #+1; leave /*prime (P**2 > X? Bump # and leave.*/
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if p*p>x then do; hh= hh+1; leave /*prime (P**2 > X? Bump hh and leave.*/
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end
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if x//p==0 then do; #= #+1 /*X divisible by P? Bump mu number. */
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if x//p==0 then do; hh= hh+1 /*X divisible by P? Bump mu number. */
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x= x % p /* Divide by prime. */
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if x//p==0 then return 0 /*X÷by P? Then return zero*/
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end
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end /*k*/ /*# (below) is almost always small, <9*/
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if #//2==0 then return 1 /*Is # even? Then return postive 1 */
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end /*k*/ /*hh (below) is almost always small, <9*/
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if hh//2==0 then return 1 /*Is hh even? Then return postive 1 */
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return -1 /* " " odd? " " negative 1. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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genP: @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6= 13; nP=6 /*assign low primes; # primes.*/
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/*--------------------------------------------------------------------------------------*/
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genP: aa.1=2; aa.2=3; aa.3=5; aa.4=7; aa.5=11; aa.6= 13; nP=6 /*assign low primes; hh primes.*/
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do lim=nP until lim*lim>=HI /*only keep primes up to the sqrt(HI).*/
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end /*lim*/
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do j=@.nP+4 by 2 to HI /*only find odd primes from here on. */
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parse var j '' -1 _;if _==5 then iterate /*Is last digit a "5"? Then not prime*/
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do j=aa.nP+4 by 2 to HI /*only find odd primes from here on. */
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parse var j '' -1 uu;if uu==5 then iterate /*Is last digit a "5"? Then not prime*/
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if j// 3==0 then iterate /*is J divisible by 3? " " " */
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if j// 7==0 then iterate /* " " " " 7? " " " */
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if j//11==0 then iterate /* " " " " 11? " " " */
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if j//13==0 then iterate /* " " " " 13? " " " */
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do k=7 while k*k<=j /*divide by some generated odd primes. */
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if j // @.k==0 then iterate j /*Is J divisible by P? Then not prime*/
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end /*k*/ /* [↓] a prime (J) has been found. */
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nP= nP+1; if nP<=HI then @.nP= j /*bump prime count; assign prime to @.*/
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if j // aa.k==0 then iterate j /*Is J divisible by P? Then not prime*/
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end /*k*/ /* [?] a prime (J) has been found. */
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nP= nP+1; if nP<=HI then aa.nP= j /*bump prime count; assign prime to aa.*/
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end /*j*/; return
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40
Task/M-bius-function/REXX/m-bius-function-2.rexx
Normal file
40
Task/M-bius-function/REXX/m-bius-function-2.rexx
Normal file
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@ -0,0 +1,40 @@
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include Settings
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say version; say 'Moebius sequence'; say
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parse arg LO HI grp . /*obtain optional arguments from the CL*/
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numeric digits 100
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if LO=='' | LO=="," then LO= 0 /*Not specified? Then use the default.*/
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if HI=='' | HI=="," then HI= 199 /* " " " " " " */
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if grp=='' | grp=="," then grp= 20 /* " " " " " " */
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/* ______ */
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say Center(' The Moebius sequence from ' LO " --> " HI" ", Max(50, grp*3), '=') /*title*/
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dd='' /*variable holds output grid of GRP #s.*/
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do j=LO to HI; dd= dd Right( Moebius(j), 2) /*process some numbers from LO --> HI.*/
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if Words(dd)==grp then do; say Substr(dd, 2); dd='' /*show grid if fully populated,*/
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end /* and nullify it for more #s.*/
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end /*j*/ /*for small grids, using wordCnt is OK.*/
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if dd\=='' then say Substr(dd, 2) /*handle any residual numbers not shown*/
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say Format(Time('e'),,3) 'seconds'
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exit /*stick a fork in it, we're all done. */
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Moebius:
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/* Moebius sequence */
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procedure expose fact. ufac.
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arg x
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/* Special value */
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if x = 0 then
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return '*'
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/* Using # of (unique) prime factors */
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call Factors(x)
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call Ufactors(x)
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if fact.0 = ufac.0 then
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if IsEven(fact.factor.0) then
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return 1
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else
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return -1
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else
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return 0
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include Functions
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include Numbers
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include Abend
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