public void NormalizeCoefficients()
{
RadicalSumRatio total = 0;
foreach (KeyValuePair <Tuple <Rational, Rational>, CBNode> kvp in grid)
{
if (kvp.Value.m1 + kvp.Value.m2 == m)
{
total += (kvp.Value.rawCoefficient * kvp.Value.rawCoefficient);
}
}
foreach (KeyValuePair <Tuple <Rational, Rational>, CBNode> kvp in grid)
{
if (kvp.Value.m1 + kvp.Value.m2 == m)
{
if (total.IsRational)
{
var normalizer = new Radical(total.ToRational());
kvp.Value.normalizedCoefficient = kvp.Value.rawCoefficient / normalizer;
kvp.Value.status = CBNode.NormalizationStatus.NORMALIZED;
}
else
{
kvp.Value.normalizedCoefficient = (kvp.Value.rawCoefficient * kvp.Value.rawCoefficient) / total;
kvp.Value.sign = kvp.Value.rawCoefficient >= 0 ? 1 : -1;
kvp.Value.status = CBNode.NormalizationStatus.NORM_SQUARED;
}
}
}
}
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 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 void DivisionTests()
{
// (3*sqrt(2)) / ((5/3)*sqrt(3)) = (9/5)*sqrt(2/3) = (3/5)*sqrt(6)
var b11 = new RadicalSumRatio(3, 2);
var b12 = new RadicalSumRatio(new Rational(5, 3), 3);
var actual1 = b11 / b12;
var expected1 = new RadicalSumRatio(new Rational(3, 5), 6);
// 11 / sqrt(4/9) = 33/2
var b21 = new RadicalSumRatio(11, 1);
var b22 = new RadicalSumRatio(new Rational(4, 9));
var actual2 = b21 / b22;
var expected2 = new RadicalSumRatio(new Rational(33, 2), 1);
// sqrt(4/9) / 11 = 2/33
var b41 = new RadicalSumRatio(new Rational(4, 9));
var b42 = 11;
var actual4 = b41 / b42;
var expected4 = new RadicalSumRatio(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 RadicalSumRatio(new Rational(3, 2), 2);
var b52 = new RadicalSumRatio(new Rational(7, 3), 5);
var b53 = new RadicalSumRatio(new Rational(1, 3), 2);
var b54 = new RadicalSumRatio(new Rational(7, 5), 5);
var b55 = new RadicalSumRatio(new Rational(11, 4), 2);
var actual5 = (b51 - b52 + b53 - b54) / b55;
var expected5 = new RadicalSumRatio(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 RadicalSumRatio(new Rational(3, 2), 5);
var b62 = new RadicalSumRatio(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 RadicalSumRatio(new Rational(3, 2), 5);
// (3/2)*sqrt(5) / -1 = (-3/2)*sqrt(5)
var b71 = new RadicalSumRatio(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 RadicalSumRatio(new Rational(-3, 2), 5);
// {[(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)]}
// = {[(2/3)*sqrt(3) - (3/2)*sqrt(2)] / [(2/3)*sqrt(3) + (3/2)*sqrt(2)]} * {[(4/3)*sqrt(3) - (5/7)*sqrt(2)] / [(5/6)*sqrt(3) + (7/3)*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]
// = [(101/21) - (52/21)*sqrt(6)] / [(26/3) + (101/36)*sqrt(6)]
// = [(101/7) - (52/7)*sqrt(6)] / [26 + (101/12)*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(101, 7), 1),
new Radical(new Rational(-52, 7), 6)
}),
new RadicalSum(new Radical[2] {
new Radical(new Rational(26), 1),
new Radical(new Rational(101, 12), 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);
}
public void MultiplicationTests()
{
// (3*sqrt(2)) * ((5/3)*sqrt(3)) = (15/3)*sqrt(6) = 5*sqrt(6)
var b11 = new RadicalSumRatio(3, 2);
var b12 = new RadicalSumRatio(new Rational(5, 3), 3);
var actual1 = b11 * b12;
var expected1 = new RadicalSumRatio(5, 6);
// 11 * sqrt(4/9) = 22/3
var b21 = new RadicalSumRatio(11, 1);
var b22 = new RadicalSumRatio(new Rational(4, 9));
var actual2 = b21 * b22;
var expected2 = new RadicalSumRatio(new Rational(22, 3), 1);
// 11 * sqrt(4/9) = 22/3
var b31 = 11;
var b32 = new RadicalSumRatio(new Rational(4, 9));
var actual31 = b31 * b32;
var actual32 = b32 * b31;
var expected3 = new RadicalSumRatio(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 RadicalSumRatio(new Rational(3, 2), 2);
var b42 = new RadicalSumRatio(new Rational(7, 3), 5);
var b43 = new RadicalSumRatio(new Rational(1, 3), 2);
var b44 = new RadicalSumRatio(new Rational(7, 5), 5);
var b45 = new RadicalSumRatio(new Rational(11, 4), 2);
var actual41 = (b41 - b42 + b43 - b44) * b45;
var actual42 = b45 * (b41 - b42 + b43 - b44);
var expected4 = new RadicalSumRatio(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 RadicalSumRatio(new Rational(3, 2), 5);
var b52 = new RadicalSumRatio(1, 1);
var b53 = 1;
var b54 = new RadicalSumRatio(1);
var b55 = RadicalSumRatio.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 RadicalSumRatio(new Rational(3, 2), 5);
// (3/2)*sqrt(5) * -1 = (-3/2)*sqrt(5)
var b61 = new RadicalSumRatio(new Rational(3, 2), 5);
var b62 = -RadicalSumRatio.One;
var b63 = -1;
var b64 = new RadicalSumRatio(-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 RadicalSumRatio(new Rational(-3, 2), 5);
// (3/2)*sqrt(5) * 0 = 0
var b71 = new RadicalSumRatio(new Rational(3, 2), 5);
var b72 = 0;
var b73 = RadicalSumRatio.Zero;
var b74 = new RadicalSumRatio(0);
var b75 = new RadicalSumRatio(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 = RadicalSumRatio.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 RadicalSumRatio(new Rational(5, 3), 7);
var b82 = new RadicalSumRatio(new Rational(2, 9), 11);
var b83 = new RadicalSumRatio(6, 13);
var b84 = new RadicalSumRatio(2, 6);
var b85 = new RadicalSumRatio(3, 8);
var c81 = b81 - b82 - b83;
var c82 = b84 - b85;
var actual8 = c81 * c82;
var expected8 = new RadicalSumRatio(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)
});
// {[(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)]}
// = [(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]
// = [(-16/3) + (11/36)*sqrt(6)] / [(11/21) + (32/21)*sqrt(6)]
// = [(-112) + (77/12)*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(-112), 1),
new Radical(new Rational(77, 12), 6)
}),
new RadicalSum(new Radical[2] {
new Radical(new Rational(11), 1),
new Radical(new Rational(32), 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 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 bool CalculateRawCoefficient(Rational j1, Rational j2, Rational j)
{
// Check if we can calculate the raw coefficient
if (IsSet)
{
return(false);
}
// x O
//
int calculationMethod = 0;
if (n_m1_00 != null &&
n_m1_00.IsSet &&
n_00_m1 == null)
{
calculationMethod = 1;
}
// O
// x
if (n_m1_00 == null &&
n_00_m1 != null &&
n_00_m1.IsSet)
{
calculationMethod = 2;
}
// x O
// x
if (n_m1_00 != null &&
n_m1_00.IsSet &&
n_00_m1 != null &&
n_00_m1.IsSet)
{
calculationMethod = 3;
}
//
// O x
if (n_p1_00 != null &&
n_p1_00.IsSet &&
n_00_p1 == null)
{
calculationMethod = 4;
}
// x
// O
if (n_p1_00 == null &&
n_00_p1 != null &&
n_00_p1.IsSet)
{
calculationMethod = 5;
}
// x
// O x
if (n_p1_00 != null &&
n_p1_00.IsSet &&
n_00_p1 != null &&
n_00_p1.IsSet)
{
calculationMethod = 6;
}
// O
// x
if (n_00_m1 != null &&
n_00_m1.IsSet &&
n_p1_m1 == null)
{
calculationMethod = 7;
}
// O
// x
if (n_00_m1 == null &&
n_p1_m1 != null &&
n_p1_m1.IsSet)
{
calculationMethod = 8;
}
// O
// x x
if (n_00_m1 != null &&
n_00_m1.IsSet &&
n_p1_m1 != null &&
n_p1_m1.IsSet)
{
calculationMethod = 9;
}
//
// x O
if (n_m1_00 != null &&
n_m1_00.IsSet &&
n_m1_p1 == null)
{
calculationMethod = 10;
}
// x
// O
if (n_m1_00 == null &&
n_m1_p1 != null &&
n_m1_p1.IsSet)
{
calculationMethod = 11;
}
// x
// x O
if (n_m1_00 != null &&
n_m1_00.IsSet &&
n_m1_p1 != null &&
n_m1_p1.IsSet)
{
calculationMethod = 12;
}
// O x
//
if (n_p1_00 != null &&
n_p1_00.IsSet &&
n_p1_m1 == null)
{
calculationMethod = 13;
}
// O
// x
if (n_p1_00 == null &&
n_p1_m1 != null &&
n_p1_m1.IsSet)
{
calculationMethod = 14;
}
// O x
// x
if (n_p1_00 != null &&
n_p1_00.IsSet &&
n_p1_m1 != null &&
n_p1_m1.IsSet)
{
calculationMethod = 15;
}
// x
// O
if (n_m1_p1 == null &&
n_00_p1 != null &&
n_00_p1.IsSet)
{
calculationMethod = 16;
}
// x
// O
if (n_m1_p1 != null &&
n_m1_p1.IsSet &&
n_00_p1 == null)
{
calculationMethod = 17;
}
// x x
// O
if (n_m1_p1 != null &&
n_m1_p1.IsSet &&
n_00_p1 != null &&
n_00_p1.IsSet)
{
calculationMethod = 18;
}
if (calculationMethod == 0)
{
return(false);
}
// J+:
// Type 0: <m1, m2; j, m + 1> = {sqrt[(j1 - m1 + 1)(j1 + m1)]<m1 - 1, m2; j, m> + sqrt[(j2 - m2 + 1)(j2 + m2)]<m1, m2 - 1; j, m>} / sqrt[(j - m)(j + m + 1)]
// Type 4: <m1 - 1, m2; j, m> = {sqrt[(j - m)(j + m + 1)]<m1, m2; j, m + 1> - sqrt[(j2 - m2 + 1)(j2 + m2)]<m1, m2 - 1; j, m>} / sqrt[(j1 - m1 + 1)(j1 + m1)]
// Type 5: <m1, m2 - 1; j, m> = {sqrt[(j - m)(j + m + 1)]<m1, m2; j, m + 1> - sqrt[(j1 - m1 + 1)(j1 + m1)]<m1 - 1, m2; j, m>} / sqrt[(j2 - m2 + 1)(j2 + m2)]
// J-:
// Type 1: <m1, m2; j, m - 1> = {sqrt[(j1 + m1 + 1)(j1 - m1)]<m1 + 1, m2; j, m> + sqrt[(j2 + m2 + 1)(j2 - m2)]<m1, m2 + 1; j, m>} / sqrt[(j + m)(j - m + 1)]
// Type 3: <m1 + 1, m2; j, m> = {sqrt[(j + m)(j - m + 1)]<m1, m2; j, m - 1> - sqrt[(j2 + m2 + 1)(j2 - m2)]<m1, m2 + 1; j, m>} / sqrt[(j1 + m1 + 1)(j1 - m1)]
// Type 2: <m1, m2 + 1; j, m> = {sqrt[(j + m)(j - m + 1)]<m1, m2; j, m - 1> - sqrt[(j1 + m1 + 1)(j1 - m1)]<m1 + 1, m2; j, m>} / sqrt[(j2 + m2 + 1)(j2 - m2)]
int[] type0 = new int[] { 1, 2, 3 };
int[] type1 = new int[] { 4, 5, 6 };
int[] type2 = new int[] { 7, 8, 9 };
int[] type3 = new int[] { 10, 11, 12 };
int[] type4 = new int[] { 13, 14, 15 };
int[] type5 = new int[] { 16, 17, 18 };
var m = m1 + m2;
if (type0.Contains(calculationMethod))
{
// x O
// x
// J+:
// Type 0: <m1, m2; j, m + 1> = {sqrt[(j1 - m1 + 1)(j1 + m1)]<m1 - 1, m2; j, m> + sqrt[(j2 - m2 + 1)(j2 + m2)]<m1, m2 - 1; j, m>} / sqrt[(j - m)(j + m + 1)]
// => c = { a1 * c_m1_00 + a2 * c_00_m1 } / a0
m -= 1;
RadicalSumRatio c_m1_00 = n_m1_00 != null ? n_m1_00.rawCoefficient : 0;
RadicalSumRatio c_00_m1 = n_00_m1 != null ? n_00_m1.rawCoefficient : 0;
var a1 = new Radical((j1 - m1 + 1) * (j1 + m1));
var a2 = new Radical((j2 - m2 + 1) * (j2 + m2));
var a0 = new Radical((j - m) * (j + m + 1));
rawCoefficient =
((a1 * c_m1_00) + (a2 * c_00_m1)) / a0;
}
else if (type1.Contains(calculationMethod))
{
// x
// O x
// J-:
// Type 1: <m1, m2; j, m - 1> = {sqrt[(j1 + m1 + 1)(j1 - m1)]<m1 + 1, m2; j, m> + sqrt[(j2 + m2 + 1)(j2 - m2)]<m1, m2 + 1; j, m>} / sqrt[(j + m)(j - m + 1)]
// => c = { a1 * c_p1_00 + a2 * c_00_p1 } / a0
m += 1;
RadicalSumRatio c_p1_00 = n_p1_00 != null ? n_p1_00.rawCoefficient : 0;
RadicalSumRatio c_00_p1 = n_00_p1 != null ? n_00_p1.rawCoefficient : 0;
Radical a1 = new Radical((j1 + m1 + 1) * (j1 - m1));
Radical a2 = new Radical((j2 + m2 + 1) * (j2 - m2));
Radical a0 = new Radical((j + m) * (j - m + 1));
rawCoefficient =
((a1 * c_p1_00) + (a2 * c_00_p1)) / a0;
}
else if (type2.Contains(calculationMethod))
{
// O
// x x
// J-:
// Type 2: <m1, m2 + 1; j, m> = {sqrt[(j + m)(j - m + 1)]<m1, m2; j, m - 1> - sqrt[(j1 + m1 + 1)(j1 - m1)]<m1 + 1, m2; j, m>} / sqrt[(j2 + m2 + 1)(j2 - m2)]
// => c = { a1 * c_00_m1 - a2 * c_p1_m1 } / a0
var M2 = m2 - 1;
m = m1 + M2;
m += 1;
RadicalSumRatio c_00_m1 = n_00_m1 != null ? n_00_m1.rawCoefficient : 0;
RadicalSumRatio c_p1_m1 = n_p1_m1 != null ? n_p1_m1.rawCoefficient : 0;
Radical a1 = new Radical((j + m) * (j - m + 1));
Radical a2 = new Radical((j1 + m1 + 1) * (j1 - m1));
Radical a0 = new Radical((j2 + M2 + 1) * (j2 - M2));
rawCoefficient =
((a1 * c_00_m1) - (a2 * c_p1_m1)) / a0;
}
else if (type3.Contains(calculationMethod))
{
// x
// x O
// J-:
// Type 3: <m1 + 1, m2; j, m> = {sqrt[(j + m)(j - m + 1)]<m1, m2; j, m - 1> - sqrt[(j2 + m2 + 1)(j2 - m2)]<m1, m2 + 1; j, m>} / sqrt[(j1 + m1 + 1)(j1 - m1)]
// => c = { a1 * c_m1_00 - a2 * c_m1_p1 } / a0;
var M1 = m1 - 1;
m = M1 + m2;
m += 1;
RadicalSumRatio c_m1_00 = n_m1_00 != null ? n_m1_00.rawCoefficient : 0;
RadicalSumRatio c_m1_p1 = n_m1_p1 != null ? n_m1_p1.rawCoefficient : 0;
Radical a1 = new Radical((j + m) * (j - m + 1));
Radical a2 = new Radical((j2 + m2 + 1) * (j2 - m2));
Radical a0 = new Radical((j1 + M1 + 1) * (j1 - M1));
rawCoefficient =
((a1 * c_m1_00) - (a2 * c_m1_p1)) / a0;
}
else if (type4.Contains(calculationMethod))
{
// O x
// x
// J+:
// Type 4: <m1 - 1, m2; j, m> = {sqrt[(j - m)(j + m + 1)]<m1, m2; j, m + 1> - sqrt[(j2 - m2 + 1)(j2 + m2)]<m1, m2 - 1; j, m>} / sqrt[(j1 - m1 + 1)(j1 + m1)]
// => c = { a1 * c_p1_00 - a2 * c_p1_m1 } / a0
var M1 = m1 + 1;
m = M1 + m2;
m -= 1;
RadicalSumRatio c_p1_00 = n_p1_00 != null ? n_p1_00.rawCoefficient : 0;
RadicalSumRatio c_p1_m1 = n_p1_m1 != null ? n_p1_m1.rawCoefficient : 0;
Radical a1 = new Radical((j - m) * (j + m + 1));
Radical a2 = new Radical((j2 - m2 + 1) * (j2 + m2));
Radical a0 = new Radical((j1 - M1 + 1) * (j1 + M1));
rawCoefficient =
((a1 * c_p1_00) - (a2 * c_p1_m1)) / a0;
}
else if (type5.Contains(calculationMethod))
{
// x x
// O
// J+:
// Type 5: <m1, m2 - 1; j, m> = {sqrt[(j - m)(j + m + 1)]<m1, m2; j, m + 1> - sqrt[(j1 - m1 + 1)(j1 + m1)]<m1 - 1, m2; j, m>} / sqrt[(j2 - m2 + 1)(j2 + m2)]
// => c = { a1 * c_00_p1 - a2 * c_m1_p1 } / a0
var M2 = m2 + 1;
m = m1 + M2;
m -= 1;
RadicalSumRatio c_00_p1 = n_00_p1 != null ? n_00_p1.rawCoefficient : 0;
RadicalSumRatio c_m1_p1 = n_m1_p1 != null ? n_m1_p1.rawCoefficient : 0;
Radical a1 = new Radical((j - m) * (j + m + 1));
Radical a2 = new Radical((j1 - m1 + 1) * (j1 + m1));
Radical a0 = new Radical((j2 - M2 + 1) * (j2 + M2));
rawCoefficient =
((a1 * c_00_p1) - (a2 * c_m1_p1)) / a0;
}
else
{
throw new Exception("Invalid calculation method: " + calculationMethod.ToString());
}
IsSet = true;
return(true);
}
