org.matheclipse.core.polynomials

Class QuarticSolver

java.lang.Object

org.matheclipse.core.polynomials.QuarticSolver

public class QuarticSolver
extends java.lang.Object

Solve polynomial equations up to fourth degree (Solve(a*x^4+b*x^3+c*x^2+d*x+e==0,x)). See Wikipedia - Quadratic equation See Wikipedia - Cubic function See Wikipedia - Quartic equation
TODO not completly tested. Especially if a division through zero occurs.

Constructor Summary

Constructors

Constructor and Description
QuarticSolver()

Method Summary

Modifier and Type	Method and Description
static IAST	biQuadraticSolve(IExpr a, IExpr c, IExpr e, IExpr sum) Solve the bi-quadratic expression.
static IAST	createSet(IAST result)
static IAST	cubicSolve(IExpr a, IExpr b, IExpr c, IExpr d, IExpr additionalSulution) Solve(a*x^3+b*x^2+c*x+d==0,x).
static IAST	depressedQuarticSolve(IExpr A, IExpr B, IExpr a, IExpr b, IExpr c) Solve(a*x^4+b*x^3+c*x^2+d*x+e==0,x).
static IAST	quadraticSolve(IExpr a, IExpr b, IExpr c, IExpr solution1, IExpr solution2) Solve(a*x^2+b*x+c==0,x).
static IAST	quarticSolve(IExpr a, IExpr b, IExpr c, IExpr d, IExpr e) Solve(a*x^4+b*x^3+c*x^2+d*x+e==0,x).
static IAST	quarticSolveN(IExpr a, IExpr b, IExpr c, IExpr d, IExpr e)
static IAST	quasiSymmetricQuarticSolve(IExpr a, IExpr b, IExpr c) Solve the special case of a "Quasi-symmetric equations" Solve(a*x^4+b*x^3+c*x^2+b*x+a==0,x).
static IAST	solve(IExpr exprPoly, IExpr x)

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

QuarticSolver

public QuarticSolver()

Method Detail

solve

public static IAST solve(IExpr exprPoly,
                         IExpr x)
                  throws java.lang.ArithmeticException

Throws:

java.lang.ArithmeticException

quarticSolveN

public static IAST quarticSolveN(IExpr a,
                                 IExpr b,
                                 IExpr c,
                                 IExpr d,
                                 IExpr e)

quarticSolve

public static IAST quarticSolve(IExpr a,
                                IExpr b,
                                IExpr c,
                                IExpr d,
                                IExpr e)

Solve(a*x^4+b*x^3+c*x^2+d*x+e==0,x). See Wikipedia - Quartic equation

Parameters:

e -

a -

b -

c -

d -

Returns:

depressedQuarticSolve

public static IAST depressedQuarticSolve(IExpr A,
                                         IExpr B,
                                         IExpr a,
                                         IExpr b,
                                         IExpr c)

Solve(a*x^4+b*x^3+c*x^2+d*x+e==0,x). See Wikipedia - Quartic equation

Parameters:

e -

a -

b -

c -

d -

Returns:

cubicSolve

public static IAST cubicSolve(IExpr a,
                              IExpr b,
                              IExpr c,
                              IExpr d,
                              IExpr additionalSulution)

Solve(a*x^3+b*x^2+c*x+d==0,x). See Wikipedia - Cubic function

Parameters:

a -

b -

c -

d -

additionalSulution - TODO

Returns:

createSet

public static IAST createSet(IAST result)

quadraticSolve

public static IAST quadraticSolve(IExpr a,
                                  IExpr b,
                                  IExpr c,
                                  IExpr solution1,
                                  IExpr solution2)

Solve(a*x^2+b*x+c==0,x). See Wikipedia - Quadratic equation

Parameters:

a -

b -

c -

solution1 - TODO

solution2 - TODO

Returns:

biQuadraticSolve

public static IAST biQuadraticSolve(IExpr a,
                                    IExpr c,
                                    IExpr e,
                                    IExpr sum)

Solve the bi-quadratic expression. Solve(a*x^4+bc*x^2+e==0,x). See Bronstein 1.6.2.4

Parameters:

a -

c -

e -

subtrahend - TODO

Returns:

quasiSymmetricQuarticSolve

public static IAST quasiSymmetricQuarticSolve(IExpr a,
                                              IExpr b,
                                              IExpr c)

Solve the special case of a "Quasi-symmetric equations" Solve(a*x^4+b*x^3+c*x^2+b*x+a==0,x). See Wikipedia - Quartic equation. See Bronstein 1.6.2.4

Parameters:

a -

c -

e -

Returns: