public void TestParseAndToString()
{
string[] toTest = new string[]
{
"a*b*c*d - w*x*y*z",
"X - 1",
"2*X^4 + 13*X^3 + 29*X^2 + 29*X + 13",
"w^2*x*y + w*x + w*y + 1",
"x*y + x + y + 1",
"7*x*y + 14*y - 3*x - 1",
"4*x*y - 2*y - 3*x - 1",
"4*x*y - 11*y - 12*x",
"12*x",
"x",
"1",
"0"
};
int counter = 1;
foreach (string testString in toTest)
{
MultivariatePolynomial testPolynomial = MultivariatePolynomial.Parse(testString);
string expected = testString; //.Replace(" ", "");
string actual = testPolynomial.ToString(); //.Replace(" ", "");
bool isMatch = (expected == actual);
string passFailString = isMatch ? "PASS" : "FAIL";
string inputOutputString = isMatch ? $"Polynomial: \'{testPolynomial.ToString()}\"" : $"Expected: \"{expected}\"; Actual: \"{actual}\"";
TestContext.WriteLine($"Test #{counter} => Pass/Fail: \"{passFailString}\" {inputOutputString}");
Assert.AreEqual(expected, actual, $"Test #{counter}: MultivariatePolynomial.Parse(\"{testString}\").ToString();");
counter++;
}
}
public void TestInstantiateNull()
{
MultivariatePolynomial testPolynomial = new MultivariatePolynomial(null);
string expected = "0";
string actual = testPolynomial.ToString();
Assert.AreEqual(expected, actual, $"Expected: \"{expected}\"; Actual: \"{actual}\"");
}
public void TestMonomialOrdering()
{
string toParse = "3*X^2*Y^3 + 6*X* Y^4 + X^3*Y^2 + 4*X^5 - 6*X^2*Y + 3*X* Y*Z - 5*X^2 + 3*Y^3 + 24*X* Y - 4";
string expected = "4*X^5 + 6*X*Y^4 + 3*X^2*Y^3 + X^3*Y^2 + 3*Y^3 - 6*X^2*Y + 3*X*Y*Z - 5*X^2 + 24*X*Y - 4";
MultivariatePolynomial poly = MultivariatePolynomial.Parse(toParse);
string actual = poly.ToString();
TestContext.WriteLine($"Result: \"{actual}\".");
Assert.AreEqual(expected, actual, $"Test of: Monomial Ordering");
}
public void TestInstantiateZeroCoefficient()
{
Indeterminate indt = new Indeterminate('X', 2);
Term term = new Term(0, new Indeterminate[] { indt });
MultivariatePolynomial testPolynomial = new MultivariatePolynomial(new Term[] { term });
string expected = "0";
string actual = testPolynomial.ToString();
Assert.AreEqual(expected, actual, $"Expected: \"{expected}\"; Actual: \"{actual}\"");
}
public void TestParse_ConstantPolynomial004()
{
string toTest = "-X";
MultivariatePolynomial testPolynomial = MultivariatePolynomial.Parse(toTest);
string expected = toTest; //.Replace(" ", "");
string actual = testPolynomial.ToString(); //.Replace(" ", "");
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
TestContext.WriteLine($"Pass/Fail: \"{((expected == actual) ? "PASS" : "FAIL")}\"");
Assert.AreEqual(expected, actual, $"MultivariatePolynomial.Parse(\"{toTest}\").ToString();");
}
public void TestGetDerivative2()
{
string polyString = "4*X^2*Y^4 - 4*X*Y^2 + 1";
string expected = "8*X*Y^4 - 4*Y^2";
MultivariatePolynomial poly = MultivariatePolynomial.Parse(polyString);
MultivariatePolynomial derivative = MultivariatePolynomial.GetDerivative(poly, 'X');
string actual = derivative.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.GetDerivative({polyString});");
}
public void TestPow()
{
string polyBaseString = "2*X*Y^2 - 1";
int exponent = 2;
string expected = "4*X^2*Y^4 - 4*X*Y^2 + 1";
MultivariatePolynomial polyBase = MultivariatePolynomial.Parse(polyBaseString);
MultivariatePolynomial power = MultivariatePolynomial.Pow(polyBase, exponent);
string actual = power.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Pow({polyBaseString}, {exponent});");
}
public void TestParse001()
{
string toTest = "X*Y*Z^2 + X*Y + X*Z + Y*Z - 1";
MultivariatePolynomial testPolynomial = MultivariatePolynomial.Parse(toTest);
string expected = toTest; //.Replace(" ", "");
string actual = testPolynomial.ToString(); //.Replace(" ", "");
bool isMatch = (expected == actual);
string passFailString = isMatch ? "PASS" : "FAIL";
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
TestContext.WriteLine($"Pass/Fail: \"{passFailString}\"");
Assert.AreEqual(expected, actual, $"MultivariatePolynomial.Parse(\"{toTest}\").ToString();");
}
public void TestParseNegativeLeadingCoefficient()
{
string polynomialExpected = "-8*X^2 - X + 8";
string leadingTermExpected = "-8*X^2";
string secondTermExpected = "-X";
MultivariatePolynomial testPolynomial = MultivariatePolynomial.Parse(polynomialExpected);
string polynomialActual = testPolynomial.ToString();
string leadingTermActual = testPolynomial.Terms[2].ToString();
string secondTermActual = testPolynomial.Terms[1].ToString();
Assert.AreEqual(polynomialExpected, polynomialActual, $"Expected: \"{polynomialExpected}\"; Actual: \"{polynomialActual}\"");
Assert.AreEqual(leadingTermExpected, leadingTermActual, $"Expected: \"{leadingTermExpected}\"; Actual: \"{leadingTermActual}\"");
Assert.AreEqual(secondTermExpected, secondTermActual, $"Expected: \"{secondTermExpected}\"; Actual: \"{secondTermActual}\"");
}
public void TestSubtract2()
{
string minuend = "36*X*Y + 6*X + 6*Y + 1";
string subtrahend = "36*X*Y + 1";
string expected = "6*X + 6*Y";
MultivariatePolynomial polyMinuend = MultivariatePolynomial.Parse(minuend);
MultivariatePolynomial polySubtrahend = MultivariatePolynomial.Parse(subtrahend);
MultivariatePolynomial difference = MultivariatePolynomial.Subtract(polyMinuend, polySubtrahend);
string actual = difference.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Subtract: ({minuend}) - ({subtrahend})");
}
public void TestAddUnlikeTerms()
{
string augend = "X^2";
string addend = "6";
string expected = "X^2 + 6";
MultivariatePolynomial polyAugend = MultivariatePolynomial.Parse(augend);
MultivariatePolynomial polyAddend = MultivariatePolynomial.Parse(addend);
MultivariatePolynomial sum = MultivariatePolynomial.Add(polyAugend, polyAddend);
string actual = sum.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Add({augend}, {addend});");
}
public void TestSubtract4()
{
string minuend = "3*X^2*Y^3 + 2*X^3*Y^2 + 6*X*Y^2 + 4*X^3 - 6*X^2*Y + 3*X*Y - 2*X^2 + 12*X - 6";
string subtrahend = "X^3*Y^2 + 3*X^2 - 3*Y^2 - 12*X - 2";
string expected = "3*X^2*Y^3 + X^3*Y^2 + 4*X^3 + 6*X*Y^2 - 6*X^2*Y + 3*Y^2 - 5*X^2 + 3*X*Y + 24*X - 4";
MultivariatePolynomial polyMinuend = MultivariatePolynomial.Parse(minuend);
MultivariatePolynomial polySubtrahend = MultivariatePolynomial.Parse(subtrahend);
MultivariatePolynomial difference = MultivariatePolynomial.Subtract(polyMinuend, polySubtrahend);
string actual = difference.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Subtract: ({minuend}) - ({subtrahend})");
}
public void TestDivide2()
{
string dividend = "2*X*Y^2 + 3*X*Y + 4*Y^2 + 6*Y";
string divisor = "X + 2";
string expected = "2*Y^2 + 3*Y";
MultivariatePolynomial polyDivedend = MultivariatePolynomial.Parse(dividend);
MultivariatePolynomial polyDivisor = MultivariatePolynomial.Parse(divisor);
MultivariatePolynomial quotient = MultivariatePolynomial.Divide(polyDivedend, polyDivisor);
string actual = quotient.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Divide({dividend}, {divisor});");
}
public void TestMultiplySameSymbols()
{
string lhs = "6*X + 1";
string rhs = "6*X - 1";
string expected = "36*X^2 - 1";
MultivariatePolynomial polylhs = MultivariatePolynomial.Parse(lhs);
MultivariatePolynomial polyrhs = MultivariatePolynomial.Parse(rhs);
MultivariatePolynomial polyProdcut = MultivariatePolynomial.Multiply(polylhs, polyrhs);
string actual = polyProdcut.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Multiply({lhs}, {rhs});");
}
public void TestSubtract5()
{
string minuend = "504*X*Y*Z^2 + 216*X*Y - 42*X*Z^2 - 18*X + 84*Y*Z^2 + 36*Y - 7*Z^2 - 3";
string subtrahend = "X*Y*Z^2 + 42*X*Z^2 - 8*X - X^2 - 3";
string expected = "503*X*Y*Z^2 + 84*Y*Z^2 - 84*X*Z^2 + X^2 - 7*Z^2 + 216*X*Y + 36*Y - 10*X";
MultivariatePolynomial polyMinuend = MultivariatePolynomial.Parse(minuend);
MultivariatePolynomial polySubtrahend = MultivariatePolynomial.Parse(subtrahend);
MultivariatePolynomial difference = MultivariatePolynomial.Subtract(polyMinuend, polySubtrahend);
string actual = difference.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Subtract: ({minuend}) - ({subtrahend})");
}
public void TestGCD()
{
//throw new NotImplementedException();
string polyString1 = "X^4 + 8*X^3 + 21*X^2 + 22*X + 8"; //"X^4 + 8*X^3 + 21*X^2 + 22*X + 8";
string polyString2 = "X^3 + 6*X^2 + 11*X + 6"; //"X^3 + 6*X^2 + 11*X + 6";
string expected = "X^2 + 3*X + 2"; //"X^2 + 3*X + 2";
MultivariatePolynomial poly1 = MultivariatePolynomial.Parse(polyString1);
MultivariatePolynomial poly2 = MultivariatePolynomial.Parse(polyString2);
MultivariatePolynomial gcd = MultivariatePolynomial.GCD(poly1, poly2);
string actual = gcd.ToString();
TestContext.WriteLine($"Expected: \"{expected}\"; Actual: \"{actual}\"");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.GCD({polyString1}, {polyString2});");
}
public void TestEvaluate_BigInteger()
{
string expected = "8551120982818029391";
string polyString = "2*x^4 + 13*y^3 + 29*x^2 + 29*y + 13";
MultivariatePolynomial poly = MultivariatePolynomial.Parse(polyString);
List <Tuple <char, BigInteger> > indeterminants = new List <Tuple <char, BigInteger> >()
{
new Tuple <char, BigInteger>('x', 45468),
new Tuple <char, BigInteger>('y', 63570),
};
BigInteger result = poly.Evaluate(indeterminants);
string actual = result.ToString();
TestContext.WriteLine($"Result: \"{actual}\".");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Evaluate({polyString}) where {string.Join(" and ", indeterminants.Select(tup => $"{tup.Item1} = {tup.Item2}"))}");
}
public void TestEvaluate_Double()
{
string expected = "15565";
string polyString = "10000*x^4 + 125*y^3 + 500*x^2 + 75*y + 13";
MultivariatePolynomial poly = MultivariatePolynomial.Parse(polyString);
List <Tuple <char, double> > indeterminants = new List <Tuple <char, double> >()
{
new Tuple <char, double>('x', 1.1d),
new Tuple <char, double>('y', 1.2d),
};
double result = poly.Evaluate(indeterminants);
string actual = result.ToString();
TestContext.WriteLine($"Result: \"{actual}\".");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Evaluate({polyString}) where {string.Join(" and ", indeterminants.Select(tup => $"{tup.Item1} = {tup.Item2}"))}");
}
public void TestEvaluate_Complex()
{
string expected = "(0, 0)";
string polyString = "x^2 + 1";
MultivariatePolynomial poly = MultivariatePolynomial.Parse(polyString);
List <Tuple <char, Complex> > indeterminants = new List <Tuple <char, Complex> >()
{
new Tuple <char, Complex>('x', Complex.ImaginaryOne)
};
Complex evaluated = poly.Evaluate(indeterminants);
Complex result = new Complex(Math.Round(evaluated.Real, 1), Math.Round(evaluated.Imaginary, 1));
string actual = result.ToString();
TestContext.WriteLine($"Result: \"{actual}\".");
Assert.AreEqual(expected, actual, $"Test of: MultivariatePolynomial.Evaluate({polyString}) where x = sqrt(-1)");
}
public void TestFunctionalComposition001()
{
MultivariatePolynomial indeterminateX = MultivariatePolynomial.Parse("6*X + 1");
MultivariatePolynomial zero = MultivariatePolynomial.Parse("0");
MultivariatePolynomial minusOne = MultivariatePolynomial.Parse("-1");
MultivariatePolynomial one = MultivariatePolynomial.Parse("1");
MultivariatePolynomial X = MultivariatePolynomial.Parse("X");
MultivariatePolynomial even = MultivariatePolynomial.Parse("2*Y");
MultivariatePolynomial odd = MultivariatePolynomial.Parse("2*X + 1");
string expecting1 = "1";
string expecting2 = "6*X + 1";
string expecting3 = "12*Y + 1";
//string expecting4 = "";
//string expecting5 = "";
string actual1 = MultivariatePolynomial.Pow(indeterminateX, 0).ToString();
string actual2 = MultivariatePolynomial.Pow(indeterminateX, 1).ToString();
string actual3 = indeterminateX.FunctionalComposition(new List <Tuple <char, MultivariatePolynomial> >()
{
new Tuple <char, MultivariatePolynomial>('X', even)
}).ToString();
//string actual4 = composition4.ToString();
//string actual5 = composition5.ToString();
Assert.AreEqual(expecting1, actual1);
Assert.AreEqual(expecting2, actual2);
Assert.AreEqual(expecting3, actual3);
//Assert.AreEqual(expecting4, actual4);
//Assert.AreEqual(expecting5, actual5);
}
public void TestFunctionalComposition002()
{
MultivariatePolynomial indeterminateX = MultivariatePolynomial.Parse("6*X + 1");
MultivariatePolynomial indeterminateY = MultivariatePolynomial.Parse("6*Y - 1");
MultivariatePolynomial polyn = MultivariatePolynomial.Multiply(indeterminateX, indeterminateY);
MultivariatePolynomial zero = MultivariatePolynomial.Parse("0");
MultivariatePolynomial minusOne = MultivariatePolynomial.Parse("-1");
MultivariatePolynomial six = MultivariatePolynomial.Parse("6");
MultivariatePolynomial even = MultivariatePolynomial.Parse("2*Y");
MultivariatePolynomial odd = MultivariatePolynomial.Parse("2*X + 1");
MultivariatePolynomial inversePolyn = MultivariatePolynomial.Multiply(polyn, minusOne); // -36*X*Y + 6*X - 6*Y + 1
List <Tuple <char, MultivariatePolynomial> > indeterminantsOddEven = new List <Tuple <char, MultivariatePolynomial> >()
{
new Tuple <char, MultivariatePolynomial>('X', odd),
new Tuple <char, MultivariatePolynomial>('Y', even),
};
List <Tuple <char, MultivariatePolynomial> > indeterminantsConstants = new List <Tuple <char, MultivariatePolynomial> >()
{
new Tuple <char, MultivariatePolynomial>('X', zero),
new Tuple <char, MultivariatePolynomial>('Y', minusOne),
};
List <Tuple <char, MultivariatePolynomial> > indeterminantsInverse = new List <Tuple <char, MultivariatePolynomial> >()
{
new Tuple <char, MultivariatePolynomial>('X', inversePolyn),
new Tuple <char, MultivariatePolynomial>('Y', inversePolyn),
};
List <Tuple <char, MultivariatePolynomial> > indeterminantSix = new List <Tuple <char, MultivariatePolynomial> >()
{
new Tuple <char, MultivariatePolynomial>('X', six)
};
MultivariatePolynomial composition1 = polyn.FunctionalComposition(indeterminantsOddEven); // 36*X*Y + 6*Y - 6*X - 1
MultivariatePolynomial composition2 = polyn.FunctionalComposition(indeterminantsInverse);
MultivariatePolynomial composition3 = polyn.FunctionalComposition(indeterminantsConstants);
MultivariatePolynomial composition4 = minusOne.FunctionalComposition(indeterminantSix);
MultivariatePolynomial composition5 = indeterminateX.FunctionalComposition(indeterminantsConstants);
string expecting1 = "144*X*Y - 12*X + 84*Y - 7";
string expecting2 = "46656*X^2*Y^2 + 1296*X^2 - 15552*X^2*Y + 15552*X*Y^2 + 432*X - 5184*X*Y + 1296*Y^2 - 432*Y + 35";
string expecting3 = "-7";
string expecting4 = "-1";
string expecting5 = "1";
string actual1 = composition1.ToString();
string actual2 = composition2.ToString();
string actual3 = composition3.ToString();
string actual4 = composition4.ToString();
string actual5 = composition5.ToString();
//Assert.AreEqual(expecting1, actual1);
//Assert.AreEqual(expecting2, actual2);
Assert.AreEqual(expecting3, actual3);
Assert.AreEqual(expecting4, actual4);
Assert.AreEqual(expecting5, actual5);
}
