public void ExtractTermsContainingNthRoot(
BigInteger radicand,
int index,
out Polynomial p_reduced,
out Polynomial p_extract)
{
p_reduced = Polynomial.Zero;
p_extract = Polynomial.Zero;
for (int i = 0; i < Terms.Length; i++)
{
var coeff = Terms[i].Coefficient;
RadicalSum coeff_reduced = coeff;
RadicalSum coeff_target = RadicalSum.Zero;
for (int j = 0; j < coeff.Radicals.Length; j++)
{
if (coeff.Radicals[j].Index == index)
{
if (coeff.Radicals[j].Radicand % radicand == 0)
{
coeff_target += coeff.Radicals[j];
coeff_reduced -= coeff.Radicals[j];
}
}
}
p_reduced += new PolynomialTerm(coeff_reduced, Terms[i].Degree);
p_extract += new PolynomialTerm(coeff_target, Terms[i].Degree);
}
}
public void ConversionTests()
{
// [3*sqrt(2) + (7/2)*sqrt(3)] / [(-9/3)*sqrt(2) + (-14/4)*sqrt(3)] = -1
var b11 = new Radical(3, 2);
var b12 = new Radical(new Rational(7, 2), 3);
var b13 = new Radical(new Rational(-9, 3), 2);
var b14 = new Radical(new Rational(-14, 4), 3);
var c11 = new RadicalSum(new Radical[2] {
b11, b12
});
var c12 = new RadicalSum(new Radical[2] {
b13, b14
});
var cr1 = new RadicalSumRatio(c11, c12);
bool actual11 = cr1.IsRational;
var actual12 = cr1.ToRational();
bool expected11 = true;
var expected12 = new Rational(-1);
// (3*sqrt(2)) / ((5/3)*sqrt(3)) = (9/5)*sqrt(2/3) = (3/5)*sqrt(6)
var b21 = new RadicalSumRatio(3, 2);
var b22 = new RadicalSumRatio(new Rational(5, 3), 3);
var b23 = b21 / b22;
var actual21 = b23.IsRational;
var actual22 = b23.ToDouble();
var expected21 = false;
double expected22 = 1.4696938456699068589183704448235;
Assert.Equal(expected11, actual11);
Assert.Equal(expected12, actual12);
Assert.Equal(expected21, actual21);
Assert.Equal(expected22.ToString("0.000000"), actual22.ToString("0.000000"));
}
public void ConstructorTests()
{
// (3/4) * sqrt(12)
// = (2*3/4) * sqrt(3)
// = (3/2) * sqrt(3)
var actual1 = new RadicalSum(new Rational(3, 4), 12);
var expected1 = new RadicalSum(new Rational(3, 2), 3);
// sqrt(2/9) = (1/3)sqrt(2)
var actual2 = new RadicalSum(new Rational(2, 9));
var expected2 = new RadicalSum(new Rational(1, 3), 2);
// sqrt(1/2) = (1/2)sqrt(2)
var actual3 = new RadicalSum(new Rational(1, 2));
var expected3 = new RadicalSum(new Rational(1, 2), 2);
// 0 = 0
RadicalSum actual41 = 0;
var actual42 = new RadicalSum(0);
var actual43 = new RadicalSum(0, 0);
var actual44 = new RadicalSum();
var actual45 = new RadicalSum(3, 0);
var actual46 = new RadicalSum(0, 5);
var expected4 = RadicalSum.Zero;
// 1 = 1
RadicalSum actual51 = 1;
var actual52 = new RadicalSum(1, 1);
var actual53 = new RadicalSum(1);
var expected5 = RadicalSum.One;
// assert
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual3);
Assert.Equal(expected4, actual41);
Assert.Equal(expected4, actual42);
Assert.Equal(expected4, actual43);
Assert.Equal(expected4, actual44);
Assert.Equal(expected4, actual45);
Assert.Equal(expected4, actual46);
Assert.True(actual41.IsZero);
Assert.True(actual42.IsZero);
Assert.True(actual43.IsZero);
Assert.True(actual44.IsZero);
Assert.True(actual45.IsZero);
Assert.True(actual46.IsZero);
Assert.Equal(expected5, actual51);
Assert.Equal(expected5, actual52);
Assert.Equal(expected5, actual53);
Assert.True(actual51.IsOne);
Assert.True(actual52.IsOne);
Assert.True(actual53.IsOne);
}
public RadicalSum EvaluateAt(RadicalSum value)
{
RadicalSum result = RadicalSum.Zero;
for (int i = 0; i < Terms.Length; i++)
{
RadicalSum termValue = Terms[i].Coefficient;
for (int j = 0; j < Terms[i].Degree; j++)
{
termValue *= value;
}
result += termValue;
}
return(result);
}
public PolynomialTerm(RadicalSum coefficient, int degree)
{
if (degree < 0)
{
throw new ArgumentException("Degree cannot be negative", nameof(degree));
}
_coefficient = coefficient;
if (coefficient == RadicalSum.Zero)
{
_degree = 0;
}
else
{
_degree = degree;
}
}
public static Polynomial Pow(Polynomial value, int exponent)
{
// Naive implementation is SLOW
// Attempt to make more efficient using multinomial theorem:
// https://en.wikipedia.org/wiki/Multinomial_theorem
// Replace x1, x2, ..., xm with polynomial terms X^0, X^1, ..., X^m-1
// Need to partition exponent as a sum of at most value.Terms.Length === m integers
// Pre-calculate powers of each term's coefficient in the polynomial, and cache them
// Item1: term index
// Item2: power
var polynomialTermCoefficientPowers = new Dictionary <Tuple <int, int>, RadicalSum>();
for (int termIndex = 0; termIndex < value.Terms.Length; termIndex++)
{
for (int power = 0; power <= exponent; power++)
{
var key = new Tuple <int, int>(termIndex, power);
var termPower = RadicalSum.Pow(value.Terms[termIndex].Coefficient, power);
polynomialTermCoefficientPowers.Add(key, termPower);
}
}
// Get the unique partitions first, along with the multinomial coefficient associated with them
// These correspond to unique integers k1, k2, ..., km such that k1 + k2 + ... + km = n
var maxTerms = Math.Min(exponent, value.Terms.Length);
var degreePartitions = Combinatorics.IntegerPartition.GetIntegerPartitions(exponent, maxTerms);
var degreePartitionsWithMultinomialCoefficient =
degreePartitions
.Select(p => new Tuple <Combinatorics.IntegerPartition, BigInteger>(
p,
GetMultinomialCoefficient(p.Values, exponent)))
.ToList();
// From the unique partitions, get all permutations
// These correspond to all possible k1 + k2 + ... + km = n in the multinomial theorem
// For each permutation, calculate the degree in X; this will be used to help group terms later
// Item1: permutation
// Item2: multinomial coefficient
// Item3: degree in X (e.g., X^2, X^3, etc)
var termDescriptions = new List <Tuple <Combinatorics.Permutation, BigInteger, int> >();
foreach (Tuple <Combinatorics.IntegerPartition, BigInteger> partition in degreePartitionsWithMultinomialCoefficient)
{
var permutations =
Combinatorics.Permutation.ArrangeInSlots(partition.Item1.Values, value.Terms.Length, false);
foreach (Combinatorics.Permutation p in permutations)
{
var degreeX = GetPermutationDegree(p.Values, value);
var termDescription =
new Tuple <Combinatorics.Permutation, BigInteger, int>(
p,
partition.Item2,
degreeX);
termDescriptions.Add(termDescription);
}
}
// Start multithreading block
// Initialize dictionary of terms for each degree in X
var degreeRadicalSumDictionary = new Dictionary <int, List <RadicalSum> >();
int processCount = termDescriptions.Count;
var doneEvent = new ManualResetEvent(false);
for (int termDescriptionIndex = 0; termDescriptionIndex < termDescriptions.Count; termDescriptionIndex++)
{
ThreadPool.QueueUserWorkItem(new WaitCallback((obj) =>
{
var termDescription =
(Tuple <Combinatorics.Permutation, BigInteger, int>)obj;
// Calculate term for this permutation in multinomial formula
var coefficient = RadicalSum.One;
for (int i = 0; i < value.Terms.Length; i++)
{
// term index, coefficient degree
var key = new Tuple <int, int>(i, termDescription.Item1.Values[i]);
var polynomialTermCoefficientPower = polynomialTermCoefficientPowers[key];
coefficient *= polynomialTermCoefficientPower;
}
coefficient *= termDescription.Item2;
lock (degreeRadicalSumDictionary)
{
if (degreeRadicalSumDictionary.ContainsKey(termDescription.Item3))
{
var existingTermList = degreeRadicalSumDictionary[termDescription.Item3];
existingTermList.Add(coefficient);
}
else
{
var termList = new List <RadicalSum>();
termList.Add(coefficient);
degreeRadicalSumDictionary.Add(termDescription.Item3, termList);
}
}
if (Interlocked.Decrement(ref processCount) == 0)
{
doneEvent.Set();
}
}), termDescriptions[termDescriptionIndex]);
}
doneEvent.WaitOne();
// Combine terms for each degree in X
var polynomialTerms = new List <PolynomialTerm>();
doneEvent = new ManualResetEvent(false);
processCount = degreeRadicalSumDictionary.Count;
foreach (KeyValuePair <int, List <RadicalSum> > kvp in degreeRadicalSumDictionary)
{
ThreadPool.QueueUserWorkItem(new WaitCallback((obj) =>
{
var key =
(KeyValuePair <int, List <RadicalSum> >)obj;
// Combine terms
var coefficient = RadicalSum.Zero;
foreach (RadicalSum radicalSum in key.Value)
{
coefficient += radicalSum;
}
var term = new PolynomialTerm(coefficient, key.Key);
lock (polynomialTerms)
{
polynomialTerms.Add(term);
}
if (Interlocked.Decrement(ref processCount) == 0)
{
doneEvent.Set();
}
}), kvp);
}
doneEvent.WaitOne();
var result = new Polynomials.Polynomial(polynomialTerms.OrderBy(p => p.Degree).ToArray());
return(result);
}
public void AdditionTests()
{
// sqrt(2) + sqrt(3)
var b11 = new RadicalSum(1, 2);
var b12 = new RadicalSum(1, 3);
var actual1 = b11 + b12;
var expected1 = new RadicalSum(new Radical[2] {
new Radical(1, 2), new Radical(1, 3)
});
// sqrt(2) + 2 * sqrt(2) = 3 * sqrt(2)
var b21 = new RadicalSum(1, 2);
var b22 = new RadicalSum(2, 2);
var actual2 = b21 + b22;
var expected2 = new RadicalSum(new Radical(3, 2));
// 5*sqrt(27) + 7*sqrt(12) = 15*sqrt(3) + 14*sqrt(3) = 29*sqrt(3)
var b31 = new RadicalSum(5, 27);
var b32 = new RadicalSum(7, 12);
var actual3 = b31 + b32;
var expected3 = new RadicalSum(new Radical(29, 3));
// 3*sqrt(2) + 2*sqrt(3)
var b41 = new RadicalSum(3, 2);
var b42 = new RadicalSum(2, 3);
var actual4 = b41 + b42;
var expected4 = new RadicalSum(new Radical[2] {
new Radical(3, 2), new Radical(2, 3)
});
// 2*sqrt(2) + 5*sqrt(28) + sqrt(1/2) + 3 + sqrt(7/9) + 11*sqrt(4) = 25 + (5/2)sqrt(2) + (31/3)*sqrt(7)
var b51 = new RadicalSum(2, 2);
var b52 = new RadicalSum(5, 28);
var b53 = new RadicalSum(new Rational(1, 2));
var b54 = new RadicalSum(3, 1);
var b55 = new RadicalSum(new Rational(7, 9));
var b56 = new RadicalSum(11, 4);
var actual5 = b51 + b52 + b53 + b54 + b55 + b56;
var expected5 = new RadicalSum(new Radical[3] {
new Radical(25, 1),
new Radical(new Rational(5, 2), 2),
new Radical(new Rational(31, 3), 7)
});
// (3/2)*sqrt(5) + 0 = (3/2)*sqrt(5)
// 0 + (3/2)*sqrt(5) = (3/2)*sqrt(5)
var b61 = new RadicalSum(new Rational(3, 2), 5);
var b62 = RadicalSum.Zero;
var actual61 = b61 + b62;
var actual62 = b62 + b61;
var expected6 = new RadicalSum(new Radical(new Rational(3, 2), 5));
// (3/2)*sqrt(5) + (-3/2)*sqrt(5) = 0
var b71 = new RadicalSum(new Rational(3, 2), 5);
var b72 = new RadicalSum(new Rational(-3, 2), 5);
var actual7 = b71 + b72;
var expected7 = RadicalSum.Zero;
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual3);
Assert.Equal(expected4, actual4);
Assert.Equal(expected5, actual5);
Assert.Equal(expected6, actual61);
Assert.Equal(expected6, actual62);
Assert.Equal(expected7, actual7);
}
public PolynomialTerm(RadicalSum constant)
: this(constant, 0)
{
}
public void MultiplicationTests()
{
// (3*sqrt(2)) * ((5/3)*sqrt(3)) = (15/3)*sqrt(6) = 5*sqrt(6)
var b11 = new RadicalSum(3, 2);
var b12 = new RadicalSum(new Rational(5, 3), 3);
var actual1 = b11 * b12;
var expected1 = new RadicalSum(5, 6);
// 11 * sqrt(4/9) = 22/3
var b21 = new RadicalSum(11, 1);
var b22 = new RadicalSum(new Rational(4, 9));
var actual2 = b21 * b22;
var expected2 = new RadicalSum(new Rational(22, 3), 1);
// 11 * sqrt(4/9) = 22/3
var b31 = 11;
var b32 = new RadicalSum(new Rational(4, 9));
var actual31 = b31 * b32;
var actual32 = b32 * b31;
var expected3 = new RadicalSum(new Rational(22, 3), 1);
// [(3/2)*sqrt(2) - (7/3)*sqrt(5) + (1/3)*sqrt(2) - (7/5)*sqrt(5)] * (11/4)*sqrt(2)
// = [(11/6)*sqrt(2) - (56/15)*sqrt(5)] * (11/4)*sqrt(2)
// = (121/24)*2 - (154/15)*sqrt(10)
// = (121/12) - (56/15)*sqrt(10)
var b41 = new RadicalSum(new Rational(3, 2), 2);
var b42 = new RadicalSum(new Rational(7, 3), 5);
var b43 = new RadicalSum(new Rational(1, 3), 2);
var b44 = new RadicalSum(new Rational(7, 5), 5);
var b45 = new RadicalSum(new Rational(11, 4), 2);
var actual41 = (b41 - b42 + b43 - b44) * b45;
var actual42 = b45 * (b41 - b42 + b43 - b44);
var expected4 = new RadicalSum(new Radical[2] {
new Radical(new Rational(121, 12), 1),
new Radical(new Rational(-154, 15), 10)
});
// (3/2)*sqrt(5) * 1 = (3/2)*sqrt(5)
var b51 = new RadicalSum(new Rational(3, 2), 5);
var b52 = new RadicalSum(1, 1);
var b53 = 1;
var b54 = new RadicalSum(1);
var b55 = RadicalSum.One;
var actual51 = b51 * b52;
var actual52 = b51 * b53;
var actual53 = b51 * b54;
var actual54 = b51 * b55;
var actual55 = b52 * b51;
var actual56 = b53 * b51;
var actual57 = b54 * b51;
var actual58 = b55 * b51;
var expected5 = new RadicalSum(new Rational(3, 2), 5);
// (3/2)*sqrt(5) * -1 = (-3/2)*sqrt(5)
var b61 = new RadicalSum(new Rational(3, 2), 5);
var b62 = -RadicalSum.One;
var b63 = -1;
var b64 = new RadicalSum(-1, 1);
var actual61 = b61 * b62;
var actual62 = b61 * b63;
var actual63 = b61 * b64;
var actual64 = b62 * b61;
var actual65 = b63 * b61;
var actual66 = b64 * b61;
var expected6 = new RadicalSum(new Rational(-3, 2), 5);
// (3/2)*sqrt(5) * 0 = 0
var b71 = new RadicalSum(new Rational(3, 2), 5);
var b72 = 0;
var b73 = RadicalSum.Zero;
var b74 = new RadicalSum(0);
var b75 = new RadicalSum(0, 0);
var actual71 = b71 * b72;
var actual72 = b71 * b73;
var actual73 = b71 * b74;
var actual74 = b71 * b75;
var actual75 = b72 * b71;
var actual76 = b73 * b71;
var actual77 = b74 * b71;
var actual78 = b75 * b71;
var expected7 = RadicalSum.Zero;
// [(5/3)*sqrt(7) - (2/9)*sqrt(11) - 6*sqrt(13)] * [2*sqrt(6) - 3*sqrt(8)]
// = (10/3)*sqrt(42) - (4/9)*sqrt(66) - 12*sqrt(78) - 5*sqrt(56) + (2/3)*sqrt(88) + 18*sqrt(104)
// = (10/3)*sqrt(42) - 5*sqrt(56) - (4/9)*sqrt(66) - (34/3)*sqrt(88) + 18*sqrt(104) - 12*sqrt(78)
// = -10*sqrt(14) + (4/3)*sqrt(22) + 36*sqrt(26) + (10/3)*sqrt(42) - (4/9)*sqrt(66) - 12*sqrt(78)
var b81 = new RadicalSum(new Rational(5, 3), 7);
var b82 = new RadicalSum(new Rational(2, 9), 11);
var b83 = new RadicalSum(6, 13);
var b84 = new RadicalSum(2, 6);
var b85 = new RadicalSum(3, 8);
var c81 = b81 - b82 - b83;
var c82 = b84 - b85;
var actual8 = c81 * c82;
var expected8 = new RadicalSum(new Radical[6] {
new Radical(-10, 14),
new Radical(new Rational(4, 3), 22),
new Radical(36, 26),
new Radical(new Rational(10, 3), 42),
new Radical(new Rational(-4, 9), 66),
new Radical(-12, 78)
});
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual31);
Assert.Equal(expected3, actual32);
Assert.Equal(expected4, actual41);
Assert.Equal(expected4, actual42);
Assert.Equal(expected5, actual51);
Assert.Equal(expected5, actual52);
Assert.Equal(expected5, actual53);
Assert.Equal(expected5, actual54);
Assert.Equal(expected5, actual55);
Assert.Equal(expected5, actual56);
Assert.Equal(expected5, actual57);
Assert.Equal(expected5, actual58);
Assert.Equal(expected6, actual61);
Assert.Equal(expected6, actual62);
Assert.Equal(expected6, actual63);
Assert.Equal(expected6, actual64);
Assert.Equal(expected6, actual65);
Assert.Equal(expected6, actual66);
Assert.Equal(expected7, actual71);
Assert.Equal(expected7, actual72);
Assert.Equal(expected7, actual73);
Assert.Equal(expected7, actual74);
Assert.Equal(expected7, actual75);
Assert.Equal(expected7, actual76);
Assert.Equal(expected7, actual77);
Assert.Equal(expected7, actual78);
Assert.Equal(expected8, actual8);
}
public void DivisionTests()
{
// (3*sqrt(2)) / ((5/3)*sqrt(3)) = (9/5)*sqrt(2/3) = (3/5)*sqrt(6)
var b11 = new RadicalSum(3, 2);
var b12 = new Radical(new Rational(5, 3), 3);
var actual1 = b11 / b12;
var expected1 = new RadicalSum(new Rational(3, 5), 6);
// 11 / sqrt(4/9) = 33/2
var b21 = new RadicalSum(11, 1);
var b22 = new Radical(new Rational(4, 9));
var actual2 = b21 / b22;
var expected2 = new RadicalSum(new Rational(33, 2), 1);
// sqrt(4/9) / 11 = 2/33
var b41 = new RadicalSum(new Rational(4, 9));
var b42 = 11;
var actual4 = b41 / b42;
var expected4 = new RadicalSum(new Rational(2, 33), 1);
// [(3/2)*sqrt(2) - (7/3)*sqrt(5) + (1/3)*sqrt(2) - (7/5)*sqrt(5)] / (11/4)*sqrt(2)
// = [(11/6)*sqrt(2) - (56/15)*sqrt(5)] / (11/4)*sqrt(2)
// = (2/3) - (224/165)*sqrt(5/2)
// = (2/3) - (112/165)*sqrt(10)
var b51 = new RadicalSum(new Rational(3, 2), 2);
var b52 = new RadicalSum(new Rational(7, 3), 5);
var b53 = new RadicalSum(new Rational(1, 3), 2);
var b54 = new RadicalSum(new Rational(7, 5), 5);
var b55 = new Radical(new Rational(11, 4), 2);
var actual5 = (b51 - b52 + b53 - b54) / b55;
var expected5 = new RadicalSum(new Radical[2] {
new Radical(new Rational(2, 3), 1),
new Radical(new Rational(-112, 165), 10)
});
// (3/2)*sqrt(5) / 1 = (3/2)*sqrt(5)
var b61 = new RadicalSum(new Rational(3, 2), 5);
var b62 = new Radical(1, 1);
var b63 = 1;
var b64 = new Radical(1);
var b65 = Radical.One;
var actual61 = b61 / b62;
var actual62 = b61 / b63;
var actual63 = b61 / b64;
var actual64 = b61 / b65;
var expected6 = new RadicalSum(new Rational(3, 2), 5);
// (3/2)*sqrt(5) / -1 = (-3/2)*sqrt(5)
var b71 = new RadicalSum(new Rational(3, 2), 5);
var b72 = new Radical(-1, 1);
var b73 = -1;
var b74 = -Radical.One;
var actual71 = b71 / b72;
var actual72 = b71 / b73;
var actual73 = b71 / b74;
var expected7 = new RadicalSum(new Rational(-3, 2), 5);
// 3*sqrt(2) + 2*sqrt(3)
var b81 = new RadicalSum(3, 2);
var b82 = new RadicalSum(2, 3);
var s81 = b81 + b82;
var rationalizer81 = RadicalSum.GetRationalizer(s81);
var actual81 = s81 * rationalizer81;
// sqrt(2) + sqrt(3) + sqrt(11)
var b91 = new RadicalSum(1, 2);
var b92 = new RadicalSum(1, 3);
var b93 = new RadicalSum(1, 11);
var s91 = b91 + b92 + b93;
var rationalizer91 = RadicalSum.GetRationalizer(s91);
var actual91 = s91 * rationalizer91;
// 8*sqrt(6) - 3*sqrt(10) - 5*sqrt(12) + 2*sqrt(14)
var b10_1 = new RadicalSum(8, 6);
var b10_2 = new RadicalSum(-3, 10);
var b10_3 = new RadicalSum(-5, 12);
var b10_4 = new RadicalSum(2, 14);
var s10_1 = b10_1 + b10_2 + b10_3 + b10_4;
var rationalizer10_1 = RadicalSum.GetRationalizer(s10_1);
var actual10_1 = s10_1 * rationalizer10_1;
// [3*sqrt(2) + (7/2)*sqrt(3)] / [(-9/3)*sqrt(2) + (-14/4)*sqrt(3)] = -1
var b11_1 = new Radical(3, 2);
var b11_2 = new Radical(new Rational(7, 2), 3);
var b11_3 = new Radical(new Rational(-9, 3), 2);
var b11_4 = new Radical(new Rational(-14, 4), 3);
var c11_1 = new RadicalSum(new Radical[2] {
b11_1, b11_2
});
var c11_2 = new RadicalSum(new Radical[2] {
b11_3, b11_4
});
var actual11 = c11_1 / c11_2;
var expected11 = -1;
// Multiplicative inverse of sqrt(2) * Root[3](5)
// Inverse: (10/17) + (-4/17)*Sqrt(2) + (4/17)*Root[3](5) + (5/17)*Root[3](25) + (-5/17)*Root[6](200) + (-2/17)*Root[6](5000)
var b12_1 = Radical.Sqrt(2);
var b12_2 = Radical.NthRoot(5, 3);
var c12_1 = b12_1 + b12_2;
var c12_2 = RadicalSum.GetRationalizer(c12_1);
var actual12 = c12_1 * c12_2;
var expected12 = RadicalSum.One;
// Multiplicative inverse of sqrt(2) + root[3](3)
var b13_1 = Radical.Sqrt(2);
var b13_2 = Radical.NthRoot(3, 3);
var c13_1 = b13_1 + b13_2;
var c13_2 = RadicalSum.GetRationalizer(c13_1);
var actual13 = c13_1 * c13_2;
var expected13 = RadicalSum.One;
// Group division: sqrt(7) / [sqrt(2) * root[3](5)]
// = Sqrt(7) * [(10/17) + (-4/17)*Sqrt(2) + (4/17)*Root[3](5) + (5/17)*Root[3](25) + (-5/17)*Root[6](200) + (-2/17)*Root[6](5000)]
// = (10/17)*Sqrt(7) + (-4/17)*Sqrt(14) + (4/17)*Root[6](8575) + (5/17)*Root[6](214375) + (-5/17)*Root[6](68600) + (-2/17)*Root[6](1715000)
var b14_1 = Radical.Sqrt(7);
var b14_2 = Radical.Sqrt(2);
var b14_3 = Radical.NthRoot(5, 3);
RadicalSum c14_1 = b14_1;
var c14_2 = b14_2 + b14_3;
var actual14 = RadicalSum.GroupDivide(c14_1, c14_2);
var expected14 =
((Rational)10 / 17) * Radical.Sqrt(7)
+ ((Rational)(-4) / 17) * Radical.Sqrt(14)
+ ((Rational)4 / 17) * Radical.NthRoot(8575, 6)
+ ((Rational)5 / 17) * Radical.NthRoot(214375, 6)
+ ((Rational)(-5) / 17) * Radical.NthRoot(68600, 6)
+ ((Rational)(-2) / 17) * Radical.NthRoot(1715000, 6);
//// sqrt(2) + sqrt(3) + sqrt(6) + root[3](3) + root[3](4) + root[6](2) + root[6](3)
//// Warning: was not able to complete due to memory/cpu/time constraints
//var b15_1 = Radical.Sqrt(2);
//var b15_2 = Radical.Sqrt(3);
//var b15_3 = Radical.Sqrt(6);
//var b15_4 = Radical.NthRoot(3, 3);
//var b15_5 = Radical.NthRoot(4, 3);
//var b15_6 = Radical.NthRoot(2, 6);
//var b15_7 = Radical.NthRoot(3, 6);
//var c15_1 = b15_1 + b15_2 + b15_3 + b15_4 + b15_5 + b15_6 + b15_7;
//var c15_2 = RadicalSum.GetRationalizer(c15_1);
//var actual15 = c15_1 * c15_2;
//var expected15 = RadicalSum.One;
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
//Assert.Equal(expected3, actual3);
Assert.Equal(expected4, actual4);
Assert.Equal(expected5, actual5);
Assert.Equal(expected6, actual61);
Assert.Equal(expected6, actual62);
Assert.Equal(expected6, actual63);
Assert.Equal(expected6, actual64);
Assert.Equal(expected7, actual71);
Assert.Equal(expected7, actual72);
Assert.Equal(expected7, actual73);
Assert.True(actual81.IsRational);
Assert.True(actual91.IsRational);
Assert.True(actual10_1.IsRational);
Assert.Equal(expected11, actual11);
Assert.Equal(expected12, actual12);
Assert.Equal(actual13, expected13);
Assert.Equal(actual14, expected14);
//Assert.Equal(actual15, expected15);
}
public void MultiplicationTests()
{
// (3*sqrt(2)) * ((5/3)*sqrt(3)) = (15/3)*sqrt(6) = 5*sqrt(6)
var b11 = new Radical(3, 2);
var b12 = new Radical(new Rational(5, 3), 3);
var actual1 = b11 * b12;
var expected1 = new Radical(5, 6);
// 11 * sqrt(4/9) = 22/3
var b21 = new Radical(11, 1);
var b22 = new Radical(new Rational(4, 9));
var actual2 = b21 * b22;
var expected2 = new Radical(new Rational(22, 3), 1);
// 11 * sqrt(4/9) = 22/3
var b31 = 11;
var b32 = new Radical(new Rational(4, 9));
var actual31 = b31 * b32;
var actual32 = b32 * b31;
var expected3 = new Radical(new Rational(22, 3), 1);
// [(3/2)*sqrt(2) - (7/3)*sqrt(5) + (1/3)*sqrt(2) - (7/5)*sqrt(5)] * (11/4)*sqrt(2)
// = [(11/6)*sqrt(2) - (56/15)*sqrt(5)] * (11/4)*sqrt(2)
// = (121/24)*2 - (154/15)*sqrt(10)
// = (121/12) - (56/15)*sqrt(10)
var b41 = new Radical(new Rational(3, 2), 2);
var b42 = new Radical(new Rational(7, 3), 5);
var b43 = new Radical(new Rational(1, 3), 2);
var b44 = new Radical(new Rational(7, 5), 5);
var b45 = new Radical(new Rational(11, 4), 2);
var actual41 = (b41 - b42 + b43 - b44) * b45;
var actual42 = b45 * (b41 - b42 + b43 - b44);
var expected4 = new RadicalSum(new Radical[2] {
new Radical(new Rational(121, 12), 1),
new Radical(new Rational(-154, 15), 10)
});
// (3/2)*sqrt(5) * 1 = (3/2)*sqrt(5)
var b51 = new Radical(new Rational(3, 2), 5);
var b52 = new Radical(1, 1);
var b53 = 1;
var b54 = new Radical(1);
var b55 = Radical.One;
var actual51 = b51 * b52;
var actual52 = b51 * b53;
var actual53 = b51 * b54;
var actual54 = b51 * b55;
var actual55 = b52 * b51;
var actual56 = b53 * b51;
var actual57 = b54 * b51;
var actual58 = b55 * b51;
var expected5 = new Radical(new Rational(3, 2), 5);
// (3/2)*sqrt(5) * -1 = (-3/2)*sqrt(5)
var b61 = new Radical(new Rational(3, 2), 5);
var b62 = -Radical.One;
var b63 = -1;
var b64 = new Radical(-1, 1);
var actual61 = b61 * b62;
var actual62 = b61 * b63;
var actual63 = b61 * b64;
var actual64 = b62 * b61;
var actual65 = b63 * b61;
var actual66 = b64 * b61;
var expected6 = new Radical(new Rational(-3, 2), 5);
// (3/2)*sqrt(5) * 0 = 0
var b71 = new Radical(new Rational(3, 2), 5);
var b72 = 0;
var b73 = Radical.Zero;
var b74 = new Radical(0);
var b75 = new Radical(0, 0);
var actual71 = b71 * b72;
var actual72 = b71 * b73;
var actual73 = b71 * b74;
var actual74 = b71 * b75;
var actual75 = b72 * b71;
var actual76 = b73 * b71;
var actual77 = b74 * b71;
var actual78 = b75 * b71;
var expected7 = Radical.Zero;
// (3/2)*sqrt(5) Inverse
var b8_1 = new Radical((Rational)3 / 2, 5);
var b8_2 = Radical.Invert(b8_1);
var actual8 = b8_1 * b8_2;
var expected8 = Radical.One;
// Sqrt(2) * Root[3](5) = Root[6](2^3) * Root[6](5^2)
// = Root[6](8*25) = Root[6](200)
var b9_1 = new Radical(2);
var b9_2 = Radical.NthRoot(5, 3);
var actual9 = b9_1 * b9_2;
var expected9 = new Radical(1, 200, 6);
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual31);
Assert.Equal(expected3, actual32);
Assert.Equal(expected4, actual41);
Assert.Equal(expected4, actual42);
Assert.Equal(expected5, actual51);
Assert.Equal(expected5, actual52);
Assert.Equal(expected5, actual53);
Assert.Equal(expected5, actual54);
Assert.Equal(expected5, actual55);
Assert.Equal(expected5, actual56);
Assert.Equal(expected5, actual57);
Assert.Equal(expected5, actual58);
Assert.Equal(expected6, actual61);
Assert.Equal(expected6, actual62);
Assert.Equal(expected6, actual63);
Assert.Equal(expected6, actual64);
Assert.Equal(expected6, actual65);
Assert.Equal(expected6, actual66);
Assert.Equal(expected7, actual71);
Assert.Equal(expected7, actual72);
Assert.Equal(expected7, actual73);
Assert.Equal(expected7, actual74);
Assert.Equal(expected7, actual75);
Assert.Equal(expected7, actual76);
Assert.Equal(expected7, actual77);
Assert.Equal(expected7, actual78);
Assert.Equal(expected8, actual8);
Assert.Equal(expected9, actual9);
}
public void SubtractionTests()
{
// sqrt(2) - sqrt(3)
var b11 = new RadicalSum(1, 2);
var b12 = new RadicalSum(1, 3);
var actual1 = b11 - b12;
var expected1 = new RadicalSum(new Radical[2] {
new Radical(1, 2), new Radical(-1, 3)
});
// sqrt(2) - 2 * sqrt(2) = -1 * sqrt(2)
var b21 = new RadicalSum(1, 2);
var b22 = new RadicalSum(2, 2);
var actual2 = b21 - b22;
var expected2 = new RadicalSum(new Radical(-1, 2));
// 5*sqrt(27) - 7*sqrt(12) = 15*sqrt(3) - 14*sqrt(3) = 1*sqrt(3)
var b31 = new RadicalSum(5, 27);
var b32 = new RadicalSum(7, 12);
var actual3 = b31 - b32;
var expected3 = new RadicalSum(new Radical(1, 3));
// 3*sqrt(2) - 2*sqrt(3)
var b41 = new RadicalSum(3, 2);
var b42 = new RadicalSum(2, 3);
var actual4 = b41 - b42;
var expected4 = new RadicalSum(new Radical[2] {
new Radical(3, 2), new Radical(-2, 3)
});
// 2*sqrt(2) + 5*sqrt(28) - sqrt(1/2) + 3 - sqrt(7/9) + 11*sqrt(4) = 25 + (3/2)sqrt(2) + (29/3)*sqrt(7)
var b51 = new RadicalSum(2, 2);
var b52 = new RadicalSum(5, 28);
var b53 = new RadicalSum(new Rational(1, 2));
var b54 = new RadicalSum(3, 1);
var b55 = new RadicalSum(new Rational(7, 9));
var b56 = new RadicalSum(11, 4);
var actual5 = b51 + b52 - b53 + b54 - b55 + b56;
var expected5 = new RadicalSum(new Radical[3] {
new Radical(25, 1),
new Radical(new Rational(3, 2), 2),
new Radical(new Rational(29, 3), 7)
});
// (3/2)*sqrt(5) - 0 = (3/2)*sqrt(5)
var b61 = new RadicalSum(new Rational(3, 2), 5);
var b62 = RadicalSum.Zero;
var actual6 = b61 - b62;
var expected6 = new RadicalSum(new Radical(new Rational(3, 2), 5));
// 0 - (3/2)*sqrt(5) = (-3/2)*sqrt(5)
var b71 = RadicalSum.Zero;
var b72 = new RadicalSum(new Rational(3, 2), 5);
var actual7 = b71 - b72;
var expected7 = new RadicalSum(new Radical(new Rational(-3, 2), 5));
// (3/2)*sqrt(5) - (3/2)*sqrt(5) = 0
var b81 = new RadicalSum(new Rational(3, 2), 5);
var b82 = new RadicalSum(new Rational(3, 2), 5);
var actual8 = b81 - b82;
var expected8 = RadicalSum.Zero;
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual3);
Assert.Equal(expected4, actual4);
Assert.Equal(expected5, actual5);
Assert.Equal(expected6, actual6);
Assert.Equal(expected7, actual7);
Assert.Equal(expected8, actual8);
}
public void AdditionTests()
{
// sqrt(2) + sqrt(3)
var b11 = new RadicalSumRatio(1, 2);
var b12 = new RadicalSumRatio(1, 3);
var actual1 = b11 + b12;
var expected1 = new RadicalSumRatio(new Radical[2] {
new Radical(1, 2), new Radical(1, 3)
});
// sqrt(2) + 2 * sqrt(2) = 3 * sqrt(2)
var b21 = new RadicalSumRatio(1, 2);
var b22 = new RadicalSumRatio(2, 2);
var actual2 = b21 + b22;
var expected2 = new RadicalSumRatio(new Radical(3, 2));
// 5*sqrt(27) + 7*sqrt(12) = 15*sqrt(3) + 14*sqrt(3) = 29*sqrt(3)
var b31 = new RadicalSumRatio(5, 27);
var b32 = new RadicalSumRatio(7, 12);
var actual3 = b31 + b32;
var expected3 = new RadicalSumRatio(new Radical(29, 3));
// 3*sqrt(2) + 2*sqrt(3)
var b41 = new RadicalSumRatio(3, 2);
var b42 = new RadicalSumRatio(2, 3);
var actual4 = b41 + b42;
var expected4 = new RadicalSumRatio(new Radical[2] {
new Radical(3, 2), new Radical(2, 3)
});
// 2*sqrt(2) + 5*sqrt(28) + sqrt(1/2) + 3 + sqrt(7/9) + 11*sqrt(4) = 25 + (5/2)sqrt(2) + (31/3)*sqrt(7)
var b51 = new RadicalSumRatio(2, 2);
var b52 = new RadicalSumRatio(5, 28);
var b53 = new RadicalSumRatio(new Rational(1, 2));
var b54 = new RadicalSumRatio(3, 1);
var b55 = new RadicalSumRatio(new Rational(7, 9));
var b56 = new RadicalSumRatio(11, 4);
var actual5 = b51 + b52 + b53 + b54 + b55 + b56;
var expected5 = new RadicalSumRatio(new Radical[3] {
new Radical(25, 1),
new Radical(new Rational(5, 2), 2),
new Radical(new Rational(31, 3), 7)
});
// (3/2)*sqrt(5) + 0 = (3/2)*sqrt(5)
// 0 + (3/2)*sqrt(5) = (3/2)*sqrt(5)
var b61 = new RadicalSumRatio(new Rational(3, 2), 5);
var b62 = RadicalSumRatio.Zero;
var actual61 = b61 + b62;
var actual62 = b62 + b61;
var expected6 = new RadicalSumRatio(new Radical(new Rational(3, 2), 5));
// (3/2)*sqrt(5) + (-3/2)*sqrt(5) = 0
var b71 = new RadicalSumRatio(new Rational(3, 2), 5);
var b72 = new RadicalSumRatio(new Rational(-3, 2), 5);
var actual7 = b71 + b72;
var expected7 = RadicalSumRatio.Zero;
// {[(2/3)*sqrt(3) - (3/2)*sqrt(2)] / [(2/3)*sqrt(3) + (3/2)*sqrt(2)]} + {[(5/6)*sqrt(3) + (7/3)*sqrt(2)] / [(4/3)*sqrt(3) - (5/7)*sqrt(2)]}
// = [(8/9)*3 - (10/21)*sqrt(6) - (12/6)*sqrt(6) + (15/14)*2 + (10/18)*3 + (14/9)*sqrt(6) + (15/12)*sqrt(6) + (21/6)*2] / [(8/9)*3 - (10/21)*sqrt(6) + (12/6)*sqrt(6) - (15/14)*2]
// = [(8/3) + (83/252)*sqrt(6) + (15/7) + (10/6) + (21/3)] / [(8/3) + (32/21)*sqrt(6) - (15/7)]
// = [(283/21) + (83/252)*sqrt(6)] / [(11/21) + (32/21)*sqrt(6)]
// = [(283) + (83/12)*sqrt(6)] / [(11) + 32*sqrt(6)]
var b81 = new Radical(new Rational(2, 3), 3);
var b82 = new Radical(new Rational(3, 2), 2);
var b83 = new Radical(new Rational(2, 3), 3);
var b84 = new Radical(new Rational(3, 2), 2);
var b85 = new Radical(new Rational(5, 6), 3);
var b86 = new Radical(new Rational(7, 3), 2);
var b87 = new Radical(new Rational(4, 3), 3);
var b88 = new Radical(new Rational(5, 7), 2);
var c81 = b81 - b82;
var c82 = b83 + b84;
var c83 = b85 + b86;
var c84 = b87 - b88;
var cr81 = new RadicalSumRatio(c81, c82);
var cr82 = new RadicalSumRatio(c83, c84);
var actual8 = cr81 + cr82;
var expected8 = new RadicalSumRatio(
new RadicalSum(new Radical[2] {
new Radical(new Rational(283), 1),
new Radical(new Rational(83, 12), 6)
}),
new RadicalSum(new Radical[2] {
new Radical(new Rational(11), 1),
new Radical(new Rational(32), 6)
}));
// (2/3) + (1/3) = 1
var b91 = new Radical(2, 1);
var b92 = new Radical(3, 1);
var b93 = new Radical(1, 1);
var b94 = new Radical(3, 1);
var c91 = new RadicalSum(b91);
var c92 = new RadicalSum(b92);
var c93 = new RadicalSum(b93);
var c94 = new RadicalSum(b94);
var cr91 = new RadicalSumRatio(c91, c92);
var cr92 = new RadicalSumRatio(c93, c94);
var actual9 = cr91 + cr92;
var expected9 = RadicalSumRatio.One;
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual3);
Assert.Equal(expected4, actual4);
Assert.Equal(expected5, actual5);
Assert.Equal(expected6, actual61);
Assert.Equal(expected6, actual62);
Assert.Equal(expected7, actual7);
Assert.Equal(expected8, actual8);
Assert.Equal(expected9, actual9);
}
public Polynomial(RadicalSum constant)
: this(new PolynomialTerm[1] {
new PolynomialTerm(constant)
})
{
}
public void SubtractionTests()
{
// sqrt(2) - sqrt(3)
var b11 = new RadicalSumRatio(1, 2);
var b12 = new RadicalSumRatio(1, 3);
var actual1 = b11 - b12;
var expected1 = new RadicalSumRatio(new Radical[2] {
new Radical(1, 2), new Radical(-1, 3)
});
// sqrt(2) - 2 * sqrt(2) = -1 * sqrt(2)
var b21 = new RadicalSumRatio(1, 2);
var b22 = new RadicalSumRatio(2, 2);
var actual2 = b21 - b22;
var expected2 = new RadicalSumRatio(new Radical(-1, 2));
// 5*sqrt(27) - 7*sqrt(12) = 15*sqrt(3) - 14*sqrt(3) = 1*sqrt(3)
var b31 = new RadicalSumRatio(5, 27);
var b32 = new RadicalSumRatio(7, 12);
var actual3 = b31 - b32;
var expected3 = new RadicalSumRatio(new Radical(1, 3));
// 3*sqrt(2) - 2*sqrt(3)
var b41 = new RadicalSumRatio(3, 2);
var b42 = new RadicalSumRatio(2, 3);
var actual4 = b41 - b42;
var expected4 = new RadicalSumRatio(new Radical[2] {
new Radical(3, 2), new Radical(-2, 3)
});
// 2*sqrt(2) + 5*sqrt(28) - sqrt(1/2) + 3 - sqrt(7/9) + 11*sqrt(4) = 25 + (3/2)sqrt(2) + (29/3)*sqrt(7)
var b51 = new RadicalSumRatio(2, 2);
var b52 = new RadicalSumRatio(5, 28);
var b53 = new RadicalSumRatio(new Rational(1, 2));
var b54 = new RadicalSumRatio(3, 1);
var b55 = new RadicalSumRatio(new Rational(7, 9));
var b56 = new RadicalSumRatio(11, 4);
var actual5 = b51 + b52 - b53 + b54 - b55 + b56;
var expected5 = new RadicalSumRatio(new Radical[3] {
new Radical(25, 1),
new Radical(new Rational(3, 2), 2),
new Radical(new Rational(29, 3), 7)
});
// (3/2)*sqrt(5) - 0 = (3/2)*sqrt(5)
var b61 = new RadicalSumRatio(new Rational(3, 2), 5);
var b62 = RadicalSumRatio.Zero;
var actual6 = b61 - b62;
var expected6 = new RadicalSumRatio(new Radical(new Rational(3, 2), 5));
// 0 - (3/2)*sqrt(5) = (-3/2)*sqrt(5)
var b71 = RadicalSumRatio.Zero;
var b72 = new RadicalSumRatio(new Rational(3, 2), 5);
var actual7 = b71 - b72;
var expected7 = new RadicalSumRatio(new Radical(new Rational(-3, 2), 5));
// (3/2)*sqrt(5) - (3/2)*sqrt(5) = 0
var b81 = new RadicalSumRatio(new Rational(3, 2), 5);
var b82 = new RadicalSumRatio(new Rational(3, 2), 5);
var actual8 = b81 - b82;
var expected8 = RadicalSumRatio.Zero;
// {[(2/3)*sqrt(3) - (3/2)*sqrt(2)] / [(2/3)*sqrt(3) + (3/2)*sqrt(2)]} - {[(5/6)*sqrt(3) + (7/3)*sqrt(2)] / [(4/3)*sqrt(3) - (5/7)*sqrt(2)]}
// = [(8/9)*3 - (10/21)*sqrt(6) - (12/6)*sqrt(6) + (15/14)*2 - (10/18)*3 - (14/9)*sqrt(6) - (15/12)*sqrt(6) - (21/6)*2] / [(8/9)*3 - (10/21)*sqrt(6) + (12/6)*sqrt(6) - (15/14)*2]
// = [(8/3) - (1331/252)*sqrt(6) + (15/7) - (10/6) - (21/3)] / [(8/3) + (32/21)*sqrt(6) - (15/7)]
// = [(-27/7) - (1331/252)*sqrt(6)] / [(11/21) + (32/21)*sqrt(6)]
// = [(-81) - (1331/12)*sqrt(6)] / [(11) + 32*sqrt(6)]
var b91 = new Radical(new Rational(2, 3), 3);
var b92 = new Radical(new Rational(3, 2), 2);
var b93 = new Radical(new Rational(2, 3), 3);
var b94 = new Radical(new Rational(3, 2), 2);
var b95 = new Radical(new Rational(5, 6), 3);
var b96 = new Radical(new Rational(7, 3), 2);
var b97 = new Radical(new Rational(4, 3), 3);
var b98 = new Radical(new Rational(5, 7), 2);
var c91 = b91 - b92;
var c92 = b93 + b94;
var c93 = b95 + b96;
var c94 = b97 - b98;
var cr91 = new RadicalSumRatio(c91, c92);
var cr92 = new RadicalSumRatio(c93, c94);
var actual9 = cr91 - cr92;
var expected9 = new RadicalSumRatio(
new RadicalSum(new Radical[2] {
new Radical(new Rational(-81), 1),
new Radical(new Rational(-1331, 12), 6)
}),
new RadicalSum(new Radical[2] {
new Radical(new Rational(11), 1),
new Radical(new Rational(32), 6)
}));
// (2/3) - (1/3) = 1/3
var b101 = new Radical(2, 1);
var b102 = new Radical(3, 1);
var b103 = new Radical(1, 1);
var b104 = new Radical(3, 1);
var c101 = new RadicalSum(b101);
var c102 = new RadicalSum(b102);
var c103 = new RadicalSum(b103);
var c104 = new RadicalSum(b104);
var cr101 = new RadicalSumRatio(c101, c102);
var cr102 = new RadicalSumRatio(c103, c104);
var actual10 = cr101 - cr102;
var expected10 = new RadicalSumRatio(
new RadicalSum(new Radical(1, 1)),
new RadicalSum(new Radical(3, 1))
);
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual3);
Assert.Equal(expected4, actual4);
Assert.Equal(expected5, actual5);
Assert.Equal(expected6, actual6);
Assert.Equal(expected7, actual7);
Assert.Equal(expected8, actual8);
Assert.Equal(expected9, actual9);
Assert.Equal(expected10, actual10);
}
public void ConstructorTests()
{
// (3/4) * sqrt(12)
// = (2*3/4) * sqrt(3)
// = (3/2) * sqrt(3)
var actual1 = new RadicalSumRatio(new Rational(3, 4), 12);
var expected1 = new RadicalSumRatio(new Rational(3, 2), 3);
// sqrt(2/9) = (1/3)sqrt(2)
var actual2 = new RadicalSumRatio(new Rational(2, 9));
var expected2 = new RadicalSumRatio(new Rational(1, 3), 2);
// sqrt(1/2) = (1/2)sqrt(2)
var actual3 = new RadicalSumRatio(new Rational(1, 2));
var expected3 = new RadicalSumRatio(new Rational(1, 2), 2);
// 0 = 0
RadicalSumRatio actual41 = 0;
var actual42 = new RadicalSumRatio(0);
var actual43 = new RadicalSumRatio(0, 0);
var actual44 = new RadicalSumRatio();
var actual45 = new RadicalSumRatio(3, 0);
var actual46 = new RadicalSumRatio(0, 5);
var expected4 = RadicalSumRatio.Zero;
// 1 = 1
RadicalSumRatio actual51 = 1;
var actual52 = new RadicalSumRatio(1, 1);
var actual53 = new RadicalSumRatio(1);
var expected5 = RadicalSumRatio.One;
// [(3/2)*sqrt(7) - (2/3)*sqrt(5)] / [(1/2)*sqrt(7) + (4/5)*sqrt(6)]
var c61 = new RadicalSum(new Radical[2] {
new Radical(new Rational(3, 2), 7),
new Radical(new Rational(-2, 3), 5)
});
var c62 = new RadicalSum(new Radical[2] {
new Radical(new Rational(1, 2), 7),
new Radical(new Rational(4, 5), 6)
});
var actual6 = (RadicalSumRatio)c61 / c62;
var expected6 = new RadicalSumRatio(c61, c62);
// assert
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual3);
Assert.Equal(expected4, actual41);
Assert.Equal(expected4, actual42);
Assert.Equal(expected4, actual43);
Assert.Equal(expected4, actual44);
Assert.Equal(expected4, actual45);
Assert.Equal(expected4, actual46);
Assert.True(actual41.IsZero);
Assert.True(actual42.IsZero);
Assert.True(actual43.IsZero);
Assert.True(actual44.IsZero);
Assert.True(actual45.IsZero);
Assert.True(actual46.IsZero);
Assert.Equal(expected5, actual51);
Assert.Equal(expected5, actual52);
Assert.Equal(expected5, actual53);
Assert.True(actual51.IsOne);
Assert.True(actual52.IsOne);
Assert.True(actual53.IsOne);
Assert.Equal(expected6, actual6);
}
public void DivisionTests()
{
// (3*sqrt(2)) / ((5/3)*sqrt(3)) = (9/5)*sqrt(2/3) = (3/5)*sqrt(6)
var b11 = new Radical(3, 2);
var b12 = new Radical(new Rational(5, 3), 3);
var actual1 = b11 / b12;
var expected1 = new Radical(new Rational(3, 5), 6);
// 11 / sqrt(4/9) = 33/2
var b21 = new Radical(11, 1);
var b22 = new Radical(new Rational(4, 9));
var actual2 = b21 / b22;
var expected2 = new Radical(new Rational(33, 2), 1);
// 11 / sqrt(4/9) = 33/2
var b31 = 11;
var b32 = new Radical(new Rational(4, 9));
var actual3 = b31 / b32;
var expected3 = new Radical(new Rational(33, 2), 1);
// sqrt(4/9) / 11 = 2/33
var b41 = new Radical(new Rational(4, 9));
var b42 = 11;
var actual4 = b41 / b42;
var expected4 = new Radical(new Rational(2, 33), 1);
// [(3/2)*sqrt(2) - (7/3)*sqrt(5) + (1/3)*sqrt(2) - (7/5)*sqrt(5)] / (11/4)*sqrt(2)
// = [(11/6)*sqrt(2) - (56/15)*sqrt(5)] / (11/4)*sqrt(2)
// = (2/3) - (224/165)*sqrt(5/2)
// = (2/3) - (112/165)*sqrt(10)
var b51 = new Radical(new Rational(3, 2), 2);
var b52 = new Radical(new Rational(7, 3), 5);
var b53 = new Radical(new Rational(1, 3), 2);
var b54 = new Radical(new Rational(7, 5), 5);
var b55 = new Radical(new Rational(11, 4), 2);
var actual5 = (b51 - b52 + b53 - b54) / b55;
var expected5 = new RadicalSum(new Radical[2] {
new Radical(new Rational(2, 3), 1),
new Radical(new Rational(-112, 165), 10)
});
// (3/2)*sqrt(5) / 1 = (3/2)*sqrt(5)
var b61 = new Radical(new Rational(3, 2), 5);
var b62 = new Radical(1, 1);
var b63 = 1;
var b64 = new Radical(1);
var b65 = Radical.One;
var actual61 = b61 / b62;
var actual62 = b61 / b63;
var actual63 = b61 / b64;
var actual64 = b61 / b65;
var expected6 = new Radical(new Rational(3, 2), 5);
// (3/2)*sqrt(5) / -1 = (-3/2)*sqrt(5)
var b71 = new Radical(new Rational(3, 2), 5);
var b72 = new Radical(-1, 1);
var b73 = -1;
var b74 = -Radical.One;
var actual71 = b71 / b72;
var actual72 = b71 / b73;
var actual73 = b71 / b74;
var expected7 = new Radical(new Rational(-3, 2), 5);
// Sqrt(2) / Root[3](5) = Sqrt(2) * (1/5)*Root[3](5^2) = Root[6](2^3) * (1/5)*Root[6](5^4)
// = (1/5)*Root[6](8*625) = Root[6](5000)
var b9_1 = new Radical(2);
var b9_2 = Radical.NthRoot(5, 3);
var actual9 = b9_1 / b9_2;
var expected9 = new Radical((Rational)1 / 5, 5000, 6);
Assert.Equal(expected1, actual1);
Assert.Equal(expected2, actual2);
Assert.Equal(expected3, actual3);
Assert.Equal(expected4, actual4);
Assert.Equal(expected5, actual5);
Assert.Equal(expected6, actual61);
Assert.Equal(expected6, actual62);
Assert.Equal(expected6, actual63);
Assert.Equal(expected6, actual64);
Assert.Equal(expected7, actual71);
Assert.Equal(expected7, actual72);
Assert.Equal(expected7, actual73);
Assert.Equal(expected9, actual9);
}