/// <summary>
/// Divides the two given polynomials using polynomial long division and returns the division result
/// </summary>
/// <param name="x">First polynomial</param>
/// <param name="y">Second polynomial</param>
/// <returns>Divison quotient and remainder</returns>
public static (poly Quotient, poly Remainder) PolynomialDivision(poly x, poly y)
{
int nd = x.Degree;
int dd = y.Degree;
if (dd < 0)
{
throw new ArgumentException("Divisor must have at least one one-zero coefficient");
}
if (nd < dd)
{
throw new ArgumentException("The degree of the divisor cannot exceed that of the numerator");
}
poly r = (poly)x.Clone();
scalar[] q = new scalar[nd * 2];
while (nd >= dd)
{
poly d2 = y >> (nd - dd);
q[nd - dd] = r[nd] / d2[nd];
d2 *= q[nd - dd];
r -= d2;
nd = r.Degree;
}
return(q, r);
}
public DateTime getSystemTime()
{
OracleQuery request = buildGetSystemTimeQuery();
scalar resultDelegate = delegate() { return(request.Command.ExecuteScalar()); };
return((DateTime)_cxn.query(request, resultDelegate));
}
public static mat4 inverse(this in mat4 m)
{
scalar Coef00 = m[2, 2] * m[3, 3] - m[3, 2] * m[2, 3];
scalar Coef02 = m[1, 2] * m[3, 3] - m[3, 2] * m[1, 3];
scalar Coef03 = m[1, 2] * m[2, 3] - m[2, 2] * m[1, 3];
scalar Coef04 = m[2, 1] * m[3, 3] - m[3, 1] * m[2, 3];
scalar Coef06 = m[1, 1] * m[3, 3] - m[3, 1] * m[1, 3];
scalar Coef07 = m[1, 1] * m[2, 3] - m[2, 1] * m[1, 3];
scalar Coef08 = m[2, 1] * m[3, 2] - m[3, 1] * m[2, 2];
scalar Coef10 = m[1, 1] * m[3, 2] - m[3, 1] * m[1, 2];
scalar Coef11 = m[1, 1] * m[2, 2] - m[2, 1] * m[1, 2];
scalar Coef12 = m[2, 0] * m[3, 3] - m[3, 0] * m[2, 3];
scalar Coef14 = m[1, 0] * m[3, 3] - m[3, 0] * m[1, 3];
scalar Coef15 = m[1, 0] * m[2, 3] - m[2, 0] * m[1, 3];
scalar Coef16 = m[2, 0] * m[3, 2] - m[3, 0] * m[2, 2];
scalar Coef18 = m[1, 0] * m[3, 2] - m[3, 0] * m[1, 2];
scalar Coef19 = m[1, 0] * m[2, 2] - m[2, 0] * m[1, 2];
scalar Coef20 = m[2, 0] * m[3, 1] - m[3, 0] * m[2, 1];
scalar Coef22 = m[1, 0] * m[3, 1] - m[3, 0] * m[1, 1];
scalar Coef23 = m[1, 0] * m[2, 1] - m[2, 0] * m[1, 1];
vec4 Fac0 = new vec4(Coef00, Coef00, Coef02, Coef03);
vec4 Fac1 = new vec4(Coef04, Coef04, Coef06, Coef07);
vec4 Fac2 = new vec4(Coef08, Coef08, Coef10, Coef11);
vec4 Fac3 = new vec4(Coef12, Coef12, Coef14, Coef15);
vec4 Fac4 = new vec4(Coef16, Coef16, Coef18, Coef19);
vec4 Fac5 = new vec4(Coef20, Coef20, Coef22, Coef23);
vec4 Vec0 = new vec4(m[1, 0], m[0, 0], m[0, 0], m[0, 0]);
vec4 Vec1 = new vec4(m[1, 1], m[0, 1], m[0, 1], m[0, 1]);
vec4 Vec2 = new vec4(m[1, 2], m[0, 2], m[0, 2], m[0, 2]);
vec4 Vec3 = new vec4(m[1, 3], m[0, 3], m[0, 3], m[0, 3]);
vec4 Inv0 = new vec4(Vec1 * Fac0 - Vec2 * Fac1 + Vec3 * Fac2);
vec4 Inv1 = new vec4(Vec0 * Fac0 - Vec2 * Fac3 + Vec3 * Fac4);
vec4 Inv2 = new vec4(Vec0 * Fac1 - Vec1 * Fac3 + Vec3 * Fac5);
vec4 Inv3 = new vec4(Vec0 * Fac2 - Vec1 * Fac4 + Vec2 * Fac5);
vec4 SignA = new vec4(+1, -1, +1, -1);
vec4 SignB = new vec4(-1, +1, -1, +1);
mat4 Inverse = new mat4(Inv0 * SignA, Inv1 * SignB, Inv2 * SignA, Inv3 * SignB);
vec4 Row0 = new vec4(Inverse[0, 0], Inverse[1, 0], Inverse[2, 0], Inverse[3, 0]);
vec4 Dot0 = new vec4(m[0] * Row0);
scalar det = Dot0.X + Dot0.Y + (Dot0.Z + Dot0.W);
return(Inverse / det);
}
/// <inheritdoc/> public poly Multiply(scalar factor) => this * factor;
/// <summary>
/// Solves the current polynomial for any given y-value
/// </summary>
/// <param name="y">y-value</param>
/// <returns>X-values</returns>
public IEnumerable <scalar> Solve(scalar y)
{
scalar[] co = _coeff;
poly llc = this << 1;
int deg = Degree;
IEnumerable <scalar> __solve()
{
if (deg == 0)
{
if (co[0].@is(y))
{
foreach (scalar f in glm.AllNumbers())
{
yield return(f);
}
}
}
else if (deg == 1)
{
yield return((y - co[0]) / co[1]);
}
else if (co[0].@is(y))
{
yield return(0);
foreach (scalar f in llc.Solve(y))
{
yield return(f);
}
}
else
{
if (deg == 2)
{
scalar a = co[2];
scalar b = co[1];
scalar c = co[0] - y;
scalar q = b * b - 4 * a * c;
if (q > -scalar.Epsilon)
{
q = (scalar)(-.5 * Math.Sqrt(q));
yield return(q / a);
if (!q.is_zero())
{
yield return(c / q);
}
}
}
else if (deg == 3)
{
foreach ((double real, double imag) in glm.SolveCardano(co[3], co[2], co[1], co[0] - y))
{
if (imag.is_zero())
{
yield return((scalar)real);
}
}
}
else if (deg == 4)
{
// solve for
// 0 = ax⁴ + bx³ + cx² + dx + e
// = (((ax + b)x + c)x + d)x + e
throw new NotImplementedException();
}
else
{
throw new NotImplementedException();
}
}
}
foreach (scalar x in __solve().Distinct())
{
yield return(x);
}
}
public static bool @is(this scalar x, scalar y) => is_zero(x - y);
public static scalar tanh(scalar angle) => (scalar)Math.Tanh(angle);
/// <inheritdoc cref="this"/> public scalar Evaluate(scalar x) => this[x];
public static scalar acosh(scalar x) => x < 1 ? 0 : (scalar)Math.Log(x + Math.Sqrt(x * x - 1));
public static scalar sinh(scalar angle) => (scalar)Math.Sinh(angle);
public static bool is_zero(this scalar x) => Math.Abs(x) <= 2 * scalar.Epsilon;
public static scalar degrees(scalar radians) => radians * 57.295779513082320876798154814105f;
public static scalar atan(scalar y_over_x) => (scalar)Math.Atan(y_over_x);
public static scalar atanh(scalar x) => Math.Abs(x) >= 1 ? 0 : .5f * (scalar)Math.Log((1 + x) / (1 - x));
public static scalar atan(scalar y, scalar x) => (scalar)Math.Atan2(y, x);
public static scalar asinh(scalar x) => (x < 0 ? -1 : x > 0 ? 1 : 0) * (scalar)Math.Log(Math.Abs(x) + Math.Sqrt(1 + x * x));
public static scalar asin(scalar x) => (scalar)Math.Asin(x);
/// <summary> /// Evaluates the polynomial at the given X value /// </summary> /// <param name="x">X value</param> /// <returns>Polynomial value at X</returns> public scalar this[scalar x] => _coeff.Reverse().Aggregate((acc, c) => acc * x + c);
public static scalar radians(scalar degrees) => degrees * 0.01745329251994329576923690768489f;
public static scalar cosh(scalar angle) => (scalar)Math.Cosh(angle);
public static scalar acos(scalar x) => (scalar)Math.Acos(x);
