Utility for simplifying polynomials.

expreduce/builtin_power.go

@@ -272,5 +272,10 @@ func GetPowerDefinitions() (defs []Definition) {
 		Name:  "PolynomialGCD",
 	})
 	defs = append(defs, Definition{Name: "SquareFreeQ"})
+	defs = append(defs, Definition{
+		Name: "PSimplify",
+		OmitDocumentation: true,
+		ExpreduceSpecific: true,
+	})
 	return
 }

expreduce/cas_test.go

@@ -12,13 +12,16 @@ import (
 
 var testmodules = flag.String("testmodules", "",
 	"A regexp of modules to test, otherwise test all modules.")
+var testsyms = flag.String("testsyms", "",
+	"A regexp of symbols to test, otherwise test all symbols.")
 var verbosetest = flag.Bool("verbosetest", false,
 	"Print every test case that runs.")
 var deftimings = flag.Bool("deftimings", false,
 	"Show the time consuption aggregations for each definition.")
 
 func TestIncludedModules(t *testing.T) {
 	var testModEx = regexp.MustCompile(*testmodules)
+	var testSymEx = regexp.MustCompile(*testsyms)
 	defSets := GetAllDefinitions()
 	numTests := 0
 	lhsDefTimeCounter := TimeCounter{}
@@ -32,6 +35,9 @@ func TestIncludedModules(t *testing.T) {
 		}
 		fmt.Printf("Testing module %s\n", defSet.Name)
 		for _, def := range defSet.Defs {
+			if !testSymEx.MatchString(def.Name) {
+				continue
+			}
 			es := NewEvalState()
 			def.AnnotateWithDynamic(es)
 			td := TestDesc{

expreduce/resources/power.m

@@ -36,6 +36,8 @@
 PolynomialQ[p_.*v_^Optional[exp_Integer], v_] :=
   If[FreeQ[p, v] && Positive[exp], True, False];
 PolynomialQ[p_, v_] := If[FreeQ[p, v], True, False];
+(*Seemingly undocumented version with no variable specification:*)
+PolynomialQ[p_] := PolynomialQ[p, Variables[p]];
 Attributes[PolynomialQ] = {Protected};
 Tests`PolynomialQ = {
     ETests[
@@ -84,7 +86,8 @@
         ESameTest[True, PolynomialQ[x^y, 1]]
     ], EKnownFailures[
         ESameTest[True, PolynomialQ[2*x^2-3x+2, 2]],
-        ESameTest[True, PolynomialQ[2*x^2-3x, 2]]
+        ESameTest[True, PolynomialQ[2*x^2-3x, 2]],
+        ESameTest[False, PolynomialQ[x/y]]
     ]
 };
 
@@ -385,3 +388,23 @@
         ESameTest[False, SquareFreeQ[(2 x + 3)^2]]
     ]
 };
+
+PSimplify[expr_] := expr;
+PSimplify[p_?PolynomialQ/q_?PolynomialQ] := 
+  If[Length[Variables[p]] === 1 && Variables[p] === Variables[q], 
+   PolynomialQuotient[p, q, Variables[p][[1]]], p/q];
+Tests`PSimplify = {
+    ESimpleExamples[
+        ESameTest[-1 + x^2, PSimplify[(1 - 2*x^2 + x^4)/(-1 + x^2)]],
+        ESameTest[4*x, PSimplify[(-4*x + 4*x^3)/(-1 + x^2)]],
+        ESameTest[-1 - x + x^3 + x^4, PSimplify[(1 - x^2 - x^3 + x^5)/(-1 + x)]],
+        ESameTest[2*x + 5*x^2 + 5*x^3, PSimplify[(-2*x - 3*x^2 + 5*x^4)/(-1 + x)]],
+        ESameTest[-6 + 11*x - 6*x^2 + x^3, PSimplify[(18 - 39*x + 29*x^2 - 9*x^3 + x^4)/(-3 + x)]],
+        ESameTest[13 - 15*x + 4*x^2, PSimplify[(-39 + 58*x - 27*x^2 + 4*x^3)/(-3 + x)]],
+        ESameTest[-3 - x + 3*x^2 + x^3, PSimplify[(-9 - 6*x + 8*x^2 + 6*x^3 + x^4)/(3 + x)]],
+        ESameTest[-2 + 6*x + 4*x^2, PSimplify[(-6 + 16*x + 18*x^2 + 4*x^3)/(3 + x)]]
+    ], EKnownDangerous[
+        ESameTest[12 + 4*x - 15*x^2 - 5*x^3 + 3*x^4 + x^5, PSimplify[(-108 - 108*x + 207*x^2 + 239*x^3 - 81*x^4 - 153*x^5 - 27*x^6 + 21*x^7 + 9*x^8 + x^9)/(-9 - 6*x + 8*x^2 + 6*x^3 + x^4)]],
+        ESameTest[12 - 54*x - 33*x^2 + 18*x^3 + 9*x^4, PSimplify[(-108 + 414*x + 717*x^2 - 324*x^3 - 765*x^4 - 162*x^5 + 147*x^6 + 72*x^7 + 9*x^8)/(-9 - 6*x + 8*x^2 + 6*x^3 + x^4)]]
+    ],
+};