org.matheclipse.core.reflection.system

Class Roots

java.lang.Object

org.matheclipse.core.eval.interfaces.AbstractEvaluator

org.matheclipse.core.eval.interfaces.AbstractFunctionEvaluator

org.matheclipse.core.reflection.system.Roots

All Implemented Interfaces:

IFunctionEvaluator, IEvaluator

public class Roots
extends AbstractFunctionEvaluator

Determine the roots of a univariate polynomial See Wikipedia entries for: Quadratic equation , Cubic function and Quartic function

Constructor Summary

Constructors

Constructor and Description
Roots()

Method Summary

Modifier and Type	Method and Description
IExpr	evaluate(IAST ast, EvalEngine engine) Symbolic evaluation of a function.
static IAST	findRoots(double... coefficients) Given a set of polynomial coefficients, compute the roots of the polynomial.
protected static IAST	roots(IExpr arg1, boolean numericSolutions, IAST variables, EvalEngine engine)
protected static IAST	rootsOfVariable(IExpr expr, IExpr denom, IAST variables, boolean numericSolutions, EvalEngine engine)

Methods inherited from class org.matheclipse.core.eval.interfaces.AbstractFunctionEvaluator

createRuleFromMethod, getNormalizedNegativeExpression, getNormalizedNegativeExpression, getPeriodicParts, getPureImaginaryPart, getRuleAST, initSerializedRules, isNegativeExpression, setUp

Methods inherited from class org.matheclipse.core.eval.interfaces.AbstractEvaluator

numericEval

Methods inherited from class java.lang.Object

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

Constructor Detail

Roots

public Roots()

Method Detail

evaluate

public IExpr evaluate(IAST ast,
                      EvalEngine engine)

Description copied from class: AbstractFunctionEvaluator

Symbolic evaluation of a function. ast.get(0) (or alternatively ast.head()) contains the head (i.e. the function symbol) of this abstract syntax tree (AST).
From ast.arg1() to ast.get(n) the ast contains the first to n-th argument of the function (alternatively you get the first to fifth argument with the methods arg1(), arg2(),... arg5()).
If necessary use the methods from the Validate class to check the number or types of arguments in the evaluate method.
Note: if the symbolic evaluation isn't possible or no result is found the evaluate method returns with a null value without throwing an exception!

Specified by:

evaluate in interface IFunctionEvaluator

Specified by:

evaluate in class AbstractFunctionEvaluator

Parameters:

ast - the abstract syntax tree (AST) which should be evaluated

engine - the users current evaluation engine

Returns:

the evaluated object or null, if evaluation isn't possible

See Also:

Validate, IExpr.head(), IAST.arg1(), IAST.arg2(), IAST.arg3()

roots

protected static IAST roots(IExpr arg1,
                            boolean numericSolutions,
                            IAST variables,
                            EvalEngine engine)

findRoots

public static IAST findRoots(double... coefficients)

Given a set of polynomial coefficients, compute the roots of the polynomial. Depending on the polynomial being considered the roots may contain complex number. When complex numbers are present they will come in pairs of complex conjugates.

Parameters:

coefficients - coefficients of the polynomial.

Returns:

the roots of the polynomial

rootsOfVariable

protected static IAST rootsOfVariable(IExpr expr,
                                      IExpr denom,
                                      IAST variables,
                                      boolean numericSolutions,
                                      EvalEngine engine)

Parameters:

expr -

denom -

variables -

numericSolutions -

engine -

Returns:

F.NIL if no evaluation was possible.