Package org.matheclipse.core.polynomials

Class QuarticSolver

java.lang.Object

org.matheclipse.core.polynomials.QuarticSolver

public class QuarticSolver
extends 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	Description
QuarticSolver()

Method Summary

Modifier and Type	Method	Description
static IASTAppendable	biQuadraticSolve(IExpr a, IExpr c, IExpr e, IExpr sum)	Solve the bi-quadratic expression.
static IASTAppendable	biQuadraticSolve(IExpr a, IExpr c, IExpr e, IExpr sum, boolean createSet, boolean sort)	Solve the bi-quadratic expression.
static IASTAppendable	createSet(IASTAppendable result)
static IASTAppendable	cubicSolve(IExpr a, IExpr b, IExpr c, IExpr d, IExpr additionalSolution)	Solve(a*x^3+b*x^2+c*x+d==0,x).
static IASTAppendable	cubicSolve(IExpr a, IExpr b, IExpr c, IExpr d, IExpr additionalSolution, boolean createSet, boolean sort)	Solve(a*x^3+b*x^2+c*x+d==0,x).
static IASTAppendable	evalAndSort(IASTAppendable result, boolean sort)
static IASTAppendable	quadraticSolve(IExpr a, IExpr b, IExpr c)	Solve(a*x^2+b*x+c==0,x).
static IASTAppendable	quadraticSolve(IExpr a, IExpr b, IExpr c, boolean createSet)	Solve(a*x^2+b*x+c==0,x).
static IASTAppendable	quadraticSolve(IExpr a, IExpr b, IExpr c, boolean createSet, boolean sort)	Solve(a*x^2+b*x+c==0,x).
static IASTAppendable	quadraticSolve(IExpr a, IExpr b, IExpr c, IExpr solution1, IExpr solution2)	Solve(a*x^2+b*x+c==0,x).
static IASTAppendable	quadraticSolve(IExpr a, IExpr b, IExpr c, IExpr solution1, IExpr solution2, boolean createSet, boolean sort)	Solve(a*x^2+b*x+c==0,x).
static IASTAppendable	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 IASTAppendable	quarticSolve(IExpr a, IExpr b, IExpr c, IExpr d, IExpr e, boolean createSet, boolean sort)	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 IASTAppendable	quasiSymmetricQuarticSolve(IExpr a, IExpr b, IExpr c)	Solve the special case of a "Quasi-symmetric equation" Solve(a*x^4+b*x^3+c*x^2+b*x+a==0,x).
static IASTAppendable	quasiSymmetricQuarticSolve(IExpr a, IExpr b, IExpr c, boolean createSet, boolean sort)	Solve the special case of a "Quasi-symmetric equation" Solve(a*x^4+b*x^3+c*x^2+b*x+a==0,x).
static IASTMutable	solve(IExpr exprPoly, IExpr x)
static IASTMutable	solve(IExpr exprPoly, IExpr x, boolean createSet, boolean sort)
static IASTMutable	sortASTArguments(IASTMutable resultList)	Sort the arguments of a list.

Methods inherited from class java.lang.Object

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

Constructor Detail

QuarticSolver

public QuarticSolver()

Method Detail

solve

public static IASTMutable solve(IExpr exprPoly,
                                IExpr x)
                         throws ArithmeticException

Throws:

ArithmeticException

solve

public static IASTMutable solve(IExpr exprPoly,
                                IExpr x,
                                boolean createSet,
                                boolean sort)
                         throws ArithmeticException

Throws:

ArithmeticException

quarticSolveN

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

quarticSolve

public static IASTAppendable 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:

a - coefficient for x^4

b - coefficient for x^3

c - coefficient for x^2

d - coefficient for x

e - coefficient for 1

Returns:

quarticSolve

public static IASTAppendable quarticSolve(IExpr a,
                                          IExpr b,
                                          IExpr c,
                                          IExpr d,
                                          IExpr e,
                                          boolean createSet,
                                          boolean sort)

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

Parameters:

a - coefficient for x^4

b - coefficient for x^3

c - coefficient for x^2

d - coefficient for x

e - coefficient for 1

createSet - delete duplicates from result list

Returns:

cubicSolve

public static IASTAppendable cubicSolve(IExpr a,
                                        IExpr b,
                                        IExpr c,
                                        IExpr d,
                                        IExpr additionalSolution)

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

Parameters:

a - coefficient for x^3

b - coefficient for x^2

c - coefficient for x

d - coefficient for 1

additionalSolution - ann additional solution, which should be appended to the result

Returns:

cubicSolve

public static IASTAppendable cubicSolve(IExpr a,
                                        IExpr b,
                                        IExpr c,
                                        IExpr d,
                                        IExpr additionalSolution,
                                        boolean createSet,
                                        boolean sort)

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

Parameters:

a - coefficient for x^3

b - coefficient for x^2

c - coefficient for x

d - coefficient for 1

additionalSolution - ann additional solution, which should be appended to the result

Returns:

createSet

public static IASTAppendable createSet(IASTAppendable result)

evalAndSort

public static IASTAppendable evalAndSort(IASTAppendable result,
                                         boolean sort)

quadraticSolve

public static IASTAppendable quadraticSolve(IExpr a,
                                            IExpr b,
                                            IExpr c)

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

Parameters:

a -

b -

c -

Returns:

quadraticSolve

public static IASTAppendable quadraticSolve(IExpr a,
                                            IExpr b,
                                            IExpr c,
                                            boolean createSet)

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

Parameters:

a -

b -

c -

createSet -

Returns:

quadraticSolve

public static IASTAppendable quadraticSolve(IExpr a,
                                            IExpr b,
                                            IExpr c,
                                            boolean createSet,
                                            boolean sort)

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

Parameters:

a -

b -

c -

createSet -

sort - the result

Returns:

quadraticSolve

public static IASTAppendable 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 - coefficient for x^2

b - coefficient for x

c - coefficient for 1

solution1 - possible first solution from cubicSolve(IExpr, IExpr, IExpr, IExpr, IExpr)

solution2 - possible second solution from cubicSolve(IExpr, IExpr, IExpr, IExpr, IExpr)

Returns:

quadraticSolve

public static IASTAppendable quadraticSolve(IExpr a,
                                            IExpr b,
                                            IExpr c,
                                            IExpr solution1,
                                            IExpr solution2,
                                            boolean createSet,
                                            boolean sort)

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

Parameters:

a - coefficient for x^2

b - coefficient for x

c - coefficient for 1

solution1 - possible first solution from cubicSolve(IExpr, IExpr, IExpr, IExpr, IExpr)

solution2 - possible second solution from cubicSolve(IExpr, IExpr, IExpr, IExpr, IExpr)

createSet - delete duplicate values in the result

sortResult - sort the result values

Returns:

biQuadraticSolve

public static IASTAppendable 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 -

sum -

Returns:

biQuadraticSolve

public static IASTAppendable biQuadraticSolve(IExpr a,
                                              IExpr c,
                                              IExpr e,
                                              IExpr sum,
                                              boolean createSet,
                                              boolean sort)

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 -

sum -

createSet -

Returns:

quasiSymmetricQuarticSolve

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

Solve the special case of a "Quasi-symmetric equation" 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 - coefficient for x^4 and x

b - coefficient for x^3 and x

c - coefficient for x^2

Returns:

quasiSymmetricQuarticSolve

public static IASTAppendable quasiSymmetricQuarticSolve(IExpr a,
                                                        IExpr b,
                                                        IExpr c,
                                                        boolean createSet,
                                                        boolean sort)

Solve the special case of a "Quasi-symmetric equation" 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 - coefficient for x^4 and x

b - coefficient for x^3 and x

c - coefficient for x^2

Returns:

sortASTArguments

public static IASTMutable sortASTArguments(IASTMutable resultList)

Sort the arguments of a list.

Parameters:

resultList - assumed to be of type List()

Returns:

sorted resultList