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NextTest("Gaussian Integers");
/* TestGaussianFactors: test if Gaussian Factors Really works!
Computes in r the product of the factors, and checks if each
one is a Gaussian prime and if r is associated to z (i.e. if r/z
is a Gaussian Unit */
TestGaussianFactors(z_IsGaussianInteger) <--
[
Local(r,gfactors,Ok);
// Echo("TestGaussianFactors: factoring ",z);
gfactors := GaussianFactors(z);
// Echo(gfactors);
Ok := True;
r :=1;
ForEach(p,gfactors)
[
r := r*p[1]^p[2];
Ok := Ok And IsGaussianPrime(p[1]);
];
// Echo(r);
Ok := Ok And IsGaussianUnit(r/z);
If(Ok,True,Echo("FAILED: GaussianFactors(", z, ")=", gfactors, " which is wrong."));
];
TestGaussianFactors((9!)+1);
TestGaussianFactors(2+3*I);
TestGaussianFactors(-1+2*I);
TestGaussianFactors(17);
TestGaussianFactors(41);
Verify(GaussianFactors(157+28*I), {{Complex(5,2),1},{Complex(-29,6),1}});
Verify(GaussianFactors(1), {}); // is this the correct behavior? why not {{}} or {{1,1}}?
Verify(GaussianFactors(-1), {}); // is this the correct behavior?
Verify(GaussianFactors(I), {}); // is this the correct behavior?
Verify(GaussianFactors(0), {}); // is this the correct behavior?
Verify(GaussianFactors(2), {{Complex(1,1),1},{Complex(1,-1),1}});
Verify(GaussianFactors(-2), {{Complex(1,1),1},{Complex(1,-1),1}});
Verify(GaussianFactors(3), {{3,1}});
Verify(GaussianFactors(3*I), {{3,1}});
Verify(GaussianFactors(4), {{Complex(1,1),2},{Complex(1,-1),2}});
Verify(GaussianFactors(-5*I), {{Complex(2,1),1},{Complex(2,-1),1}});
Verify(GaussianFactors(Complex(1,1)^11*163^4),{{Complex(1,1),11},{163,4}});
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