September 2017 Update

Task/Polynomial-long-division/SPAD/polynomial-long-division.spad

@@ -0,0 +1,6 @@
+(1) -> monicDivide(x^3-12*x^2-42,x-3,'x)
+
+                     2
+   (1)  [quotient = x  - 9x - 27,remainder = - 123]
+
+   Type: Record(quotient: Polynomial(Integer),remainder: Polynomial(Integer))

Task/Polynomial-long-division/Sidef/polynomial-long-division-1.sidef

@@ -1,20 +1,20 @@
 func poly_long_div(rn, rd) {
-
+ 
     var n = rn.map{_}
     var gd = rd.len
-
+ 
     if (n.len >= gd) {
         return(gather {
             while (n.len >= gd) {
                 var piv = n[0]/rd[0]
                 take(piv)
-                0.to(n.len.min(gd)-1).each { |i|
+                { |i|
                     n[i] -= (rd[i] * piv)
-                }
+                } << ^(n.len `min` gd)
                 n.shift
             }
         }, n)
     }
-
+ 
     return([0], rn)
 }

Task/Polynomial-long-division/Zkl/polynomial-long-division-1.zkl

@@ -0,0 +1,22 @@
+fcn polyLongDivision(a,b){  // (a0 + a1x + a2x^2 + a3x^3 ...)
+   _assert_(degree(b)>=0,"degree(%s) < 0".fmt(b));
+   q:=List.createLong(a.len(),0.0);
+   while((ad:=degree(a)) >= (bd:=degree(b))){
+      z,d,m := ad-bd, List.createLong(z,0.0).extend(b), a[ad]/b[bd];;
+      q[z]=m;
+      d,a = d.apply('*(m)), a.zipWith('-,d);
+   }
+   return(q,a);		// may have trailing zero elements
+}
+fcn degree(v){  // -1,0,..len(v)-1, -1 if v==0
+   v.len() - v.copy().reverse().filter1n('!=(0)) - 1;
+}
+fcn polyString(terms){ // (a0,a1,a2...)-->"a0 + a1x + a2x^2 ..."
+   str:=[0..].zipWith('wrap(n,a){ if(a) "+ %sx^%s ".fmt(a,n) else "" },terms)
+   .pump(String)
+   .replace("x^0 "," ").replace(" 1x"," x").replace("x^1 ","x ")
+   .replace("+ -", "- ");
+   if(not str)     return(" ");  // all zeros
+   if(str[0]=="+") str[1,*];     // leave leading space
+   else            String("-",str[2,*]);
+}

Task/Polynomial-long-division/Zkl/polynomial-long-division-2.zkl

@@ -0,0 +1,3 @@
+q,r:=polyLongDivision(T(-42.0, 0.0, -12.0, 1.0),T(-3.0, 1.0));
+println("Quotient  = ",polyString(q));
+println("Remainder = ",polyString(r));