fix the issue with sign of a and b in a*x^n==b equations

Task #140 - solve gives wrong answers for some polynomial equations
grzegorzmazur · Oct 13, 2015 · 1bd8c69 · 1bd8c69
1 parent 4466691
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diff --git a/scripts/univar.rep/code.ys b/scripts/univar.rep/code.ys
@@ -492,9 +492,10 @@ Rule("PSolve", 1, 1, IsUniVar(uni) And Degree(uni) > 1 And Coef(uni, 0 .. Degree
 
 // Special case: a * x^n + b, solution generated by roots of unity
 Rule("PSolve", 1, 1, IsUniVar(uni) And Degree(uni) > 1 And ConstantTerm(uni) != 0 And Coef(uni, 1 .. Degree(uni) - 1) = ZeroVector(Degree(uni) - 1)) [
-    Local(n, k);
+    Local(n, k, phi0);
     n := Degree(uni);
-    (-ConstantTerm(uni))^(1/n) / Abs(LeadingCoef(uni))^(1/n) * MapSingle({{k}, Complex(Cos(2 * k * Pi / n), Sin(2 * k * Pi / n))}, 0 .. n - 1);
+    phi0 := If (Sign(LeadingCoef(uni)) * Sign(ConstantTerm(uni)) < 0, 0, Pi);
+    (Abs(ConstantTerm(uni) / LeadingCoef(uni)))^(1/n) * MapSingle({{k}, Complex(Cos((phi0 + 2 * k * Pi) / n), Sin((phi0 + 2 * k * Pi) / n))}, 0 .. n - 1);
 ];
 
 Rule("PSolve", 1, 10, IsUniVar(uni) And Degree(uni) = 2)

diff --git a/tests/solve.yts b/tests/solve.yts
@@ -85,6 +85,18 @@ VerifySolve(Solve(x^5 == 1, x),
             { x == 1, x == Exp(2/5*I*Pi), x == Exp(4/5*I*Pi), 
               x == Exp(-2/5*I*Pi), x == Exp(-4/5*I*Pi)});
 
+VerifySolve(Solve(x^3 == 1, x),
+            {x==1,x==Complex((-1)/2,Sqrt(3/4)),x==Complex((-1)/2,-Sqrt(3/4))});
+
+VerifySolve(Solve(x^3 == -1, x),
+            {x==Complex(1/2,Sqrt(3/4)),x==(-1),x==Complex(1/2,-Sqrt(3/4))});
+
+VerifySolve(Solve(-x^3 == 1, x),
+            {x==Complex(1/2,Sqrt(3/4)),x==(-1),x==Complex(1/2,-Sqrt(3/4))});
+
+VerifySolve(Solve(-x^3 == -1, x),
+            {x==1,x==Complex((-1)/2,Sqrt(3/4)),x==Complex((-1)/2,-Sqrt(3/4))});
+
 VerifySolve(Solve(Sqrt(x) == 1, x),  { x == 1 });
 VerifySolve(Solve(Sqrt(x) == -1, x), { });
 VerifySolve(Solve(Sqrt(x) == I, x),  { x == -1 });