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/*
TESTS:
- random-test code for roots, be generating random roots and
multiplicities.
- find an example where bisection is needed, or better, a group
of examples where bisection is needed, for tests
- GarbageCollect in TryRandomPoly causes some corruption, as is
visible when turning show file/line on.
*/
BuiltinPrecisionSet(5);
VerifyZero(x) := (Abs(x)<10^ -BuiltinPrecisionGet());
sl() := []; //Echo(CurrentFile(),CurrentLine());
TryRandomPoly(deg,coefmin,coefmax):=
[
//GarbageCollect();
Local(coefs,p,roots,px);
coefs:=Table(FloorN(coefmin+Random()*(coefmax-coefmin)),i,1,deg+1,1);
p:=Add(coefs*x^(0 .. deg));
p:=Rationalize(p);
//Echo("Test polynom ",p);
Verify(Maximum(Abs(coefs))<=MaximumBound(p));
Verify(Minimum(Abs(coefs))>MinimumBound(p));
//Echo("bounds ",BoundRealRoots(p));
roots:=FindRealRoots(p);
//Echo("roots ",roots);
px := (p Where x==x);
Verify(Dot(px, px) < 0.01);
];
TryRandomRoots(deg,coefmin,coefmax):=
[
//GarbageCollect();
Local(coefs,p,roots,px,mult);
coefs:=RemoveDuplicates(Table(FloorN(coefmin+Random()*(coefmax-coefmin)),i,1,deg+1,1));
deg:=Length(coefs)-1;
mult:=1+Abs(Table(FloorN(coefmin+Random()*(coefmax-coefmin)),i,1,deg+1,1));
p:=Product((x-coefs)^mult);
p:=Rationalize(p);
Echo("Test polynom ",p);
Echo("minimum ",MinimumBound(p));
Echo("maximum ",MaximumBound(p));
Echo("bounds ",BoundRealRoots(p));
roots:=FindRealRoots(p);
Echo("roots ",roots);
Verify(Length(roots) = Length(coefs));
Verify(Length(RemoveDuplicates(roots)) = Length(coefs));
px := (p Where x==x);
Verify(Dot(px, px) < 0.01);
];
sl();
[
Local(p);
p := FindRealRoots((x+2)^9*(x-4)^5*(x-1)^4)-{-2.,1.,4.};
Verify(VerifyZero(Dot(p,p)),True);
];
sl();
/*TODO
TryRandomRoots(3,-10,10); sl();
TryRandomRoots(3,-10,10); sl();
TryRandomRoots(5,5,1000); sl();
TryRandomRoots(5,5,1000); sl();
*/
// Bounds on coefficients
Verify(MinimumBound(4),-Infinity); sl();
Verify(MaximumBound(4),Infinity); sl();
// RealRootsCount
Verify(RealRootsCount(x^2-1),2); sl();
Verify(RealRootsCount(x^2+1),0); sl();
[
Local(p);
p:=Difference(FindRealRoots(Expand((x*(x-10)^3*(x+2)^2))),{0,-2.,10.});
Verify(VerifyZero(Dot(p, p)),True);
];
Verify(FindRealRoots((x^2+20)*(x^2+10)),{});
Verify(RealRootsCount((x^2+20)*(x^2+10)),0);
sl();
// Simple test on Squarefree
TestMathPiper(Monic(SquareFree((x-1)^2*(x-3)^3)),Monic((x-1)*(x-3)));
sl();
// Check the rare case where the bounds finder lands on
// exactly a root
[
Local(p);
p:=FindRealRoots((x+4)*(x-6),1,7)-{-4.,6.};
Verify(VerifyZero(Dot(p, p)),True);
];
sl();
[
Local(p);
p:=Expand((x-3.1)*(x+6.23));
p:=FindRealRoots(p)-{-6.23,3.1};
Verify(VerifyZero(Dot(p, p)),True);
];
sl();
Verify(BuiltinPrecisionGet(),5);
[
Local(res);
res:=FindRealRoots(Expand((x-3.1)*(x+6.23)))-{-6.23,3.1};
Verify(VerifyZero(Dot(res, res)) , True);
];
sl();
TryRandomPoly(5,5,1000); sl();
sl();
TryRandomPoly(5,5,1000); sl();
sl();
TryRandomPoly(5,5,1000); sl();
sl();
TryRandomPoly(5,5,1000); sl();
sl();
TryRandomPoly(5,5,1000); sl();
sl();
TryRandomPoly(5,5,1000); sl();
sl();
//RandomPoly(_var,_degree,_coefmin,_coefmax)
//RandomIntegerList(_count,_coefmin,_coefmax)
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