public void TestComplicatedParseSqrt2()
{
string somePolynomial = "(x*x + sqrt2*x + 1)*(x*x - sqrt2*x + 1)";
SlowOperatorBasedField<double> rationalField = new SlowOperatorBasedField<double>();
PolynomialOverFieldRing<double> rationalPolynomialRing = new PolynomialOverFieldRing<double>(rationalField);
IRing<Polynomial<double>> rationalWithSqrt2Ring =
new QuotientRing<Polynomial<double>>
(new PrincipalIdeal<Polynomial<double>>
(rationalPolynomialRing,
new Polynomial<double>(new double[] {-2, 0, 1}, rationalField)));
var sqrt2 = rationalField.CreateMonomial(1, 1);
PolynomialParser parser = new PolynomialParser
(new PolynomialParserOptions()
{
Aliases = new Dictionary<string, object>()
{
{"sqrt2", sqrt2}
}
});
Polynomial<Polynomial<double>> parsed =
parser.Parse(somePolynomial, rationalWithSqrt2Ring);
PolynomialRing<Polynomial<double>> complexPolynomialRing =
new PolynomialRing<Polynomial<double>>(rationalWithSqrt2Ring);
Polynomial<Polynomial<double>> expectedResult =
complexPolynomialRing.Add(
rationalWithSqrt2Ring.CreateMonomial(rationalWithSqrt2Ring.Identity, 4),
complexPolynomialRing.Identity);
Assert.IsTrue(complexPolynomialRing.Comparer.Equals(parsed, expectedResult));
}
public void TestDivision()
{
PolynomialOverFieldRing<double> ring =
new PolynomialOverFieldRing<double>(new SlowOperatorBasedField<double>());
Polynomial<double> remainder;
var quotient =
ring.Divide(new Polynomial<double>(new double[] {-1, 0, 0, 1}, ring.CoefficientsRing),
new Polynomial<double>(new double[] {-1, 1}, ring.CoefficientsRing), out remainder);
Assert.IsTrue(ring.Comparer.Equals(remainder, ring.Zero));
Assert.IsTrue(ring.Comparer.Equals(quotient,
new Polynomial<double>(new double[] {1, 1, 1}, ring.CoefficientsRing)));
}
public void TestInverse()
{
SlowOperatorBasedField<double> rationalField = new SlowOperatorBasedField<double>();
PolynomialOverFieldRing<double> rationalPolynomialRing = new PolynomialOverFieldRing<double>(rationalField);
IField<Polynomial<double>> rationalWithSqrt2Ring =
new QuotientField<Polynomial<double>>
(new PrincipalIdeal<Polynomial<double>>
(rationalPolynomialRing,
new Polynomial<double>(new double[] {-2, 0, 1}, rationalField)));
var sqrt2 = rationalField.CreateMonomial(1, 1);
var number = rationalWithSqrt2Ring.Add(sqrt2, rationalWithSqrt2Ring.Identity);
var result = rationalWithSqrt2Ring.Inverse(number);
Polynomial<double> inverse = rationalWithSqrt2Ring.Add(sqrt2,
rationalWithSqrt2Ring.Negative(
rationalWithSqrt2Ring.Identity));
Assert.IsTrue(rationalWithSqrt2Ring.Comparer.Equals
(result,
inverse));
}
