ExprPolynomial

java.lang.Object
- org.matheclipse.core.polynomials.ExprPolynomial

Type Parameters:

C - coefficient type

All Implemented Interfaces:

java.lang.Iterable<ExprMonomial>
```
public class ExprPolynomial
extends java.lang.Object
implements java.lang.Iterable<ExprMonomial>
```
GenPolynomial generic polynomials implementing RingElem. n-variate ordered polynomials over C. Objects of this class are intended to be immutable. The implementation is based on TreeMap respectively SortedMap from exponents to coefficients. Only the coefficients are modeled with generic types, the exponents are fixed to ExpVectorLong with long entries (this will eventually be changed in the future). C can also be a non integral domain, e.g. a ModInteger, i.e. it may contain zero divisors, since multiply() does now check for zeros. Note: multiply() now checks for wrong method dispatch for GenSolvablePolynomial.

Author:

Heinz Kredel

Field Summary

Fields
Modifier and Type	Field and Description
`ExprPolynomialRing`	`ring` The factory for the polynomial ring.
`protected java.util.SortedMap<ExpVectorLong,IExpr>`	`val` The data structure for polynomials.

Constructor Summary

Constructors
Modifier	Constructor and Description
	`ExprPolynomial(ExprPolynomialRing r)` Constructor for zero GenPolynomial.
	`ExprPolynomial(ExprPolynomialRing r, ExpVectorLong e)` Constructor for GenPolynomial x^e.
	`ExprPolynomial(ExprPolynomialRing r, IExpr c)` Constructor for GenPolynomial c * x⁰.
	`ExprPolynomial(ExprPolynomialRing r, IExpr c, ExpVectorLong e)` Constructor for GenPolynomial c * x^e.
`protected`	`ExprPolynomial(ExprPolynomialRing r, java.util.SortedMap<ExpVectorLong,IExpr> v)` Constructor for GenPolynomial.

Method Summary

All Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`ExprPolynomial`	`abs()` GenPolynomial absolute value, i.e. leadingCoefficient > 0.
`IExpr`	`coefficient(ExpVectorLong e)` Coefficient.
`java.util.Iterator`	`coefficientIterator()` Iterator over coefficients.
`IAST`	`coefficientList()` Get the coefficients of a univariate polynomial up to n degree.
`IAST`	`coefficientRules()` Get the coefficient rules of a polynomial `List()` form
`int`	`compareTo(ExprPolynomial b)` GenPolynomial comparison.
`java.util.Map<ExpVectorLong,ExprPolynomial>`	`contract(ExprPolynomialRing pfac)` Contract variables.
`ExprPolynomial`	`contractCoeff(ExprPolynomialRing pfac)` Contract variables to coefficient polynomial.
`ExprPolynomial`	`copy()` Copy this GenPolynomial.
`long`	`degree()` Maximal degree.
`long`	`degree(int i)` Degree in variable i.
`ExpVectorLong`	`degreeVector()` Maximal degree vector.
`ExprPolynomial`	`deHomogenize(ExprPolynomialRing pfac)` Dehomogenize.
`ExprPolynomial`	`derivative()` Derivative of a polynomial.
`ExprPolynomial`	`divide(ExprPolynomial S)` GenPolynomial division.
`ExprPolynomial`	`divide(IExpr s)` GenPolynomial division.
`ExprPolynomial[]`	`divideAndRemainder(ExprPolynomial S)` Deprecated. use quotientRemainder()
`void`	`doAddTo(ExprPolynomial S)` GenPolynomial destructive summation.
`void`	`doAddTo(IExpr a)` GenPolynomial destructive summation.
`void`	`doAddTo(IExpr a, ExpVectorLong e)` GenPolynomial destructive summation.
`void`	`doPutToMap(ExpVectorLong e, IExpr c)` Put an ExpVectorLong to coefficient entry into the internal map of this GenPolynomial.
`void`	`doPutToMap(java.util.SortedMap<ExpVectorLong,IExpr> vals)` Put an a sorted map of exponents to coefficients into the internal map of this GenPolynomial.
`void`	`doRemoveFromMap(ExpVectorLong e, IExpr c)` Remove an ExpVectorLong to coefficient entry from the internal map of this GenPolynomial.
`ExprPolynomial[]`	`egcd(ExprPolynomial S)` GenPolynomial extended greatest comon divisor.
`boolean`	`equals(java.lang.Object B)` Comparison with any other object.
`java.util.Iterator<ExpVectorLong>`	`exponentIterator()` Iterator over exponents.
`ExprPolynomial`	`extend(ExprPolynomialRing pfac, int j, long k)` Extend variables.
`ExprPolynomial`	`extendLower(ExprPolynomialRing pfac, int j, long k)` Extend lower variables.
`ExprPolynomial`	`extendUnivariate(ExprPolynomialRing pfac, int i)` Extend univariate to multivariate polynomial.
`ExprPolynomialRing`	`factory()` Get the corresponding element factory.
`ExprPolynomial`	`gcd(ExprPolynomial S)` GenPolynomial greatest common divisor.
`IExpr`	`getExpr()` Converts a JAS polynomial to a MathEclipse AST with head `Plus`
`java.util.SortedMap<ExpVectorLong,IExpr>`	`getMap()` ExpVectorLong to coefficient map of GenPolynomial.
`int`	`hashCode()` Hash code for this polynomial.
`ExprPolynomial[]`	`hegcd(ExprPolynomial S)` GenPolynomial half extended greatest comon divisor.
`ExprPolynomial`	`homogenize(ExprPolynomialRing pfac)` Make homogeneous.
`ExprPolynomial`	`inverse()` GenPolynomial inverse.
`boolean`	`isConstant()` Is GenPolynomial<C> a constant.
`boolean`	`isHomogeneous()` Is GenPolynomial<C> homogeneous.
`boolean`	`isOne()` Is GenPolynomial<C> one.
`boolean`	`isUnit()` Is GenPolynomial<C> a unit.
`boolean`	`isWeightHomogeneous()` Is GenPolynomial<C> homogeneous with respect to a weight.
`boolean`	`isZero()` Is GenPolynomial<C> zero.
`java.util.Iterator<ExprMonomial>`	`iterator()` Iterator over monomials.
`IExpr`	`leadingBaseCoefficient()` Leading base coefficient.
`ExpVectorLong`	`leadingExpVectorLong()` Leading exponent vector.
`java.util.Map.Entry<ExpVectorLong,IExpr>`	`leadingMonomial()` Leading monomial.
`ExprPolynomial`	`leadingWeightPolynomial()` Leading weight polynomial.
`int`	`length()` Length of GenPolynomial.
`ExprPolynomial`	`map(java.util.function.Function<IExpr,IExpr> f)` Map a unary function to the coefficients.
`IExpr`	`maxNorm()` GenPolynomial maximum norm.
`ExprPolynomial`	`modInverse(ExprPolynomial m)` GenPolynomial modular inverse.
`ExprPolynomial`	`monic()` GenPolynomial monic, i.e. leadingCoefficient == 1.
`IAST`	`monomialList()` Get the monomials of a polynomial in `List()` form
`ExprPolynomial`	`multiply(ExprPolynomial S)` GenPolynomial multiplication.
`ExprPolynomial`	`multiply(ExpVectorLong e)` GenPolynomial multiplication.
`ExprPolynomial`	`multiply(IExpr s)` GenPolynomial multiplication.
`ExprPolynomial`	`multiply(IExpr s, ExpVectorLong e)` GenPolynomial multiplication.
`ExprPolynomial`	`multiply(java.util.Map.Entry<ExpVectorLong,IExpr> m)` GenPolynomial multiplication.
`ExprPolynomial`	`negate()` GenPolynomial negation.
`int`	`numberOfVariables()` Number of variables.
`ExprPolynomial[]`	`quotientRemainder(ExprPolynomial S)` GenPolynomial division with remainder.
`ExprPolynomial`	`reductum()` Reductum.
`ExprPolynomial`	`remainder(ExprPolynomial S)` GenPolynomial remainder.
`ExprPolynomial`	`reverse(ExprPolynomialRing oring)` Reverse variables.
`ExprPolynomial`	`scaleSubtractMultiple(IExpr b, ExpVectorLong g, IExpr a, ExpVectorLong e, ExprPolynomial S)` GenPolynomial scale and subtract a multiple.
`ExprPolynomial`	`scaleSubtractMultiple(IExpr b, IExpr a, ExprPolynomial S)` GenPolynomial scale and subtract a multiple.
`ExprPolynomial`	`scaleSubtractMultiple(IExpr b, IExpr a, ExpVectorLong e, ExprPolynomial S)` GenPolynomial scale and subtract a multiple.
`ExprPolynomial`	`subtract(ExprPolynomial S)` GenPolynomial subtraction.
`ExprPolynomial`	`subtract(IExpr a)` GenPolynomial subtract.
`ExprPolynomial`	`subtract(IExpr a, ExpVectorLong e)` GenPolynomial subtraction.
`ExprPolynomial`	`subtractMultiple(IExpr a, ExprPolynomial S)` GenPolynomial subtract a multiple.
`ExprPolynomial`	`subtractMultiple(IExpr a, ExpVectorLong e, ExprPolynomial S)` GenPolynomial subtract a multiple.
`ExprPolynomial`	`sum(ExprPolynomial S)` GenPolynomial summation.
`ExprPolynomial`	`sum(IExpr a)` GenPolynomial addition.
`ExprPolynomial`	`sum(IExpr a, ExpVectorLong e)` GenPolynomial addition.
`IExpr`	`sumNorm()` GenPolynomial sum norm.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toScriptFactory()` Get a scripting compatible string representation of the factory.
`java.lang.String`	`toString()` String representation of GenPolynomial.
`java.lang.String`	`toString(IAST v)` String representation of GenPolynomial.
`long`	`totalDegree()` Total degree.
`ExpVectorLong`	`trailingExpVectorLong()` Trailing exponent vector.
`long`	`weightDegree()` Weight degree.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.lang.Iterable
forEach, spliterator

- Field Detail
  - ring
```
public final ExprPolynomialRing ring
```
    The factory for the polynomial ring.
  - val
```
protected final java.util.SortedMap<ExpVectorLong,IExpr> val
```
    The data structure for polynomials.
- Constructor Detail
  - ExprPolynomial
```
public ExprPolynomial(ExprPolynomialRing r)
```
    Constructor for zero GenPolynomial.
    
    Parameters:
    
    r - polynomial ring factory.
  - ExprPolynomial
```
public ExprPolynomial(ExprPolynomialRing r,
                      IExpr c,
                      ExpVectorLong e)
```
    Constructor for GenPolynomial c * x^e.
    
    Parameters:
    
    r - polynomial ring factory.
    
    c - coefficient.
    
    e - exponent.
  - ExprPolynomial
```
public ExprPolynomial(ExprPolynomialRing r,
                      IExpr c)
```
    Constructor for GenPolynomial c * x⁰.
    
    Parameters:
    
    r - polynomial ring factory.
    
    c - coefficient.
  - ExprPolynomial
```
public ExprPolynomial(ExprPolynomialRing r,
                      ExpVectorLong e)
```
    Constructor for GenPolynomial x^e.
    
    Parameters:
    
    r - polynomial ring factory.
    
    e - exponent.
  - ExprPolynomial
```
protected ExprPolynomial(ExprPolynomialRing r,
                         java.util.SortedMap<ExpVectorLong,IExpr> v)
```
    Constructor for GenPolynomial.
    
    Parameters:
    
    r - polynomial ring factory.
    
    v - the SortedMap of some other polynomial.
- Method Detail
  - factory
```
public ExprPolynomialRing factory()
```
    Get the corresponding element factory.
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - copy
```
public ExprPolynomial copy()
```
    Copy this GenPolynomial.
    
    Returns:
    
    copy of this.
  - length
```
public int length()
```
    Length of GenPolynomial.
    
    Returns:
    
    number of coefficients of this GenPolynomial.
  - getMap
```
public java.util.SortedMap<ExpVectorLong,IExpr> getMap()
```
    ExpVectorLong to coefficient map of GenPolynomial.
    
    Returns:
    
    val as unmodifiable SortedMap.
  - doPutToMap
```
public void doPutToMap(ExpVectorLong e,
                       IExpr c)
```
    Put an ExpVectorLong to coefficient entry into the internal map of this GenPolynomial. Note: Do not use this method unless you are constructing a new polynomial. this is modified and breaks the immutability promise of this class.
    
    Parameters:
    
    c - coefficient.
    
    e - exponent.
  - doRemoveFromMap
```
public void doRemoveFromMap(ExpVectorLong e,
                            IExpr c)
```
    Remove an ExpVectorLong to coefficient entry from the internal map of this GenPolynomial. Note: Do not use this method unless you are constructing a new polynomial. this is modified and breaks the immutability promise of this class.
    
    Parameters:
    
    e - exponent.
    
    c - expected coefficient, null for ignore.
  - doPutToMap
```
public void doPutToMap(java.util.SortedMap<ExpVectorLong,IExpr> vals)
```
    Put an a sorted map of exponents to coefficients into the internal map of this GenPolynomial. Note: Do not use this method unless you are constructing a new polynomial. this is modified and breaks the immutability promise of this class.
    
    Parameters:
    
    vals - sorted map of exponents and coefficients.
  - toString
```
public java.lang.String toString()
```
    String representation of GenPolynomial.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - toString
```
public java.lang.String toString(IAST v)
```
    String representation of GenPolynomial.
    
    Parameters:
    
    v - names for variables.
    
    See Also:
    
    Object.toString()
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Returns:
    
    script compatible representation for this Element.
    
    See Also:
    
    Element.toScript()
  - toScriptFactory
```
public java.lang.String toScriptFactory()
```
    Get a scripting compatible string representation of the factory.
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - isZero
```
public boolean isZero()
```
    Is GenPolynomial<C> zero.
    
    Returns:
    
    If this is 0 then true is returned, else false.
    
    See Also:
    
    edu.jas.structure.RingElem#isZero()
  - isOne
```
public boolean isOne()
```
    Is GenPolynomial<C> one.
    
    Returns:
    
    If this is 1 then true is returned, else false.
    
    See Also:
    
    edu.jas.structure.RingElem#isOne()
  - isUnit
```
public boolean isUnit()
```
    Is GenPolynomial<C> a unit.
    
    Returns:
    
    If this is a unit then true is returned, else false.
    
    See Also:
    
    MonoidElem.isUnit()
  - isConstant
```
public boolean isConstant()
```
    Is GenPolynomial<C> a constant.
    
    Returns:
    
    If this is a constant polynomial then true is returned, else false.
  - isHomogeneous
```
public boolean isHomogeneous()
```
    Is GenPolynomial<C> homogeneous.
    
    Returns:
    
    true, if this is homogeneous, else false.
  - equals
```
public boolean equals(java.lang.Object B)
```
    Comparison with any other object.
    
    Overrides:
    
    equals in class java.lang.Object
    
    See Also:
    
    Object.equals(java.lang.Object)
  - hashCode
```
public int hashCode()
```
    Hash code for this polynomial.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    See Also:
    
    Object.hashCode()
  - compareTo
```
public int compareTo(ExprPolynomial b)
```
    GenPolynomial comparison.
    
    Parameters:
    
    b - GenPolynomial.
    
    Returns:
    
    sign(this-b).
  - numberOfVariables
```
public int numberOfVariables()
```
    Number of variables.
    
    Returns:
    
    ring.nvar.
  - leadingMonomial
```
public java.util.Map.Entry<ExpVectorLong,IExpr> leadingMonomial()
```
    Leading monomial.
    
    Returns:
    
    first map entry.
  - leadingExpVectorLong
```
public ExpVectorLong leadingExpVectorLong()
```
    Leading exponent vector.
    
    Returns:
    
    first exponent.
  - trailingExpVectorLong
```
public ExpVectorLong trailingExpVectorLong()
```
    Trailing exponent vector.
    
    Returns:
    
    last exponent.
  - leadingBaseCoefficient
```
public IExpr leadingBaseCoefficient()
```
    Leading base coefficient.
    
    Returns:
    
    first coefficient.
  - coefficient
```
public IExpr coefficient(ExpVectorLong e)
```
    Coefficient.
    
    Parameters:
    
    e - exponent.
    
    Returns:
    
    coefficient for given exponent.
  - reductum
```
public ExprPolynomial reductum()
```
    Reductum.
    
    Returns:
    
    this - leading monomial.
  - degree
```
public long degree(int i)
```
    Degree in variable i.
    
    Returns:
    
    maximal degree in the variable i.
  - degree
```
public long degree()
```
    Maximal degree.
    
    Returns:
    
    maximal degree in any variables.
  - totalDegree
```
public long totalDegree()
```
    Total degree.
    
    Returns:
    
    total degree in any variables.
  - weightDegree
```
public long weightDegree()
```
    Weight degree.
    
    Returns:
    
    weight degree in all variables.
  - leadingWeightPolynomial
```
public ExprPolynomial leadingWeightPolynomial()
```
    Leading weight polynomial.
    
    Returns:
    
    polynomial with terms of maximal weight degree.
  - isWeightHomogeneous
```
public boolean isWeightHomogeneous()
```
    Is GenPolynomial<C> homogeneous with respect to a weight.
    
    Returns:
    
    true, if this is weight homogeneous, else false.
  - degreeVector
```
public ExpVectorLong degreeVector()
```
    Maximal degree vector.
    
    Returns:
    
    maximal degree vector of all variables.
  - maxNorm
```
public IExpr maxNorm()
```
    GenPolynomial maximum norm.
    
    Returns:
    
    ||this||.
  - sumNorm
```
public IExpr sumNorm()
```
    GenPolynomial sum norm.
    
    Returns:
    
    sum of all absolute values of coefficients.
  - sum
```
public ExprPolynomial sum(ExprPolynomial S)
```
    GenPolynomial summation.
    
    Parameters:
    
    S - GenPolynomial.
    
    Returns:
    
    this+S.
  - sum
```
public ExprPolynomial sum(IExpr a,
                          ExpVectorLong e)
```
    GenPolynomial addition. This method is not very efficient, since this is copied.
    
    Parameters:
    
    a - coefficient.
    
    e - exponent.
    
    Returns:
    
    this + a x^e.
  - sum
```
public ExprPolynomial sum(IExpr a)
```
    GenPolynomial addition. This method is not very efficient, since this is copied.
    
    Parameters:
    
    a - coefficient.
    
    Returns:
    
    this + a x⁰.
  - doAddTo
```
public void doAddTo(ExprPolynomial S)
```
    GenPolynomial destructive summation.
    
    Parameters:
    
    S - GenPolynomial.
  - doAddTo
```
public void doAddTo(IExpr a,
                    ExpVectorLong e)
```
    GenPolynomial destructive summation.
    
    Parameters:
    
    a - coefficient.
    
    e - exponent.
  - doAddTo
```
public void doAddTo(IExpr a)
```
    GenPolynomial destructive summation.
    
    Parameters:
    
    a - coefficient.
  - subtract
```
public ExprPolynomial subtract(ExprPolynomial S)
```
    GenPolynomial subtraction.
    
    Parameters:
    
    S - GenPolynomial.
    
    Returns:
    
    this-S.
  - subtract
```
public ExprPolynomial subtract(IExpr a,
                               ExpVectorLong e)
```
    GenPolynomial subtraction. This method is not very efficient, since this is copied.
    
    Parameters:
    
    a - coefficient.
    
    e - exponent.
    
    Returns:
    
    this - a x^e.
  - subtract
```
public ExprPolynomial subtract(IExpr a)
```
    GenPolynomial subtract. This method is not very efficient, since this is copied.
    
    Parameters:
    
    a - coefficient.
    
    Returns:
    
    this + a x⁰.
  - subtractMultiple
```
public ExprPolynomial subtractMultiple(IExpr a,
                                       ExprPolynomial S)
```
    GenPolynomial subtract a multiple.
    
    Parameters:
    
    a - coefficient.
    
    S - GenPolynomial.
    
    Returns:
    
    this - a S.
  - subtractMultiple
```
public ExprPolynomial subtractMultiple(IExpr a,
                                       ExpVectorLong e,
                                       ExprPolynomial S)
```
    GenPolynomial subtract a multiple.
    
    Parameters:
    
    a - coefficient.
    
    e - exponent.
    
    S - GenPolynomial.
    
    Returns:
    
    this - a x^e S.
  - scaleSubtractMultiple
```
public ExprPolynomial scaleSubtractMultiple(IExpr b,
                                            IExpr a,
                                            ExprPolynomial S)
```
    GenPolynomial scale and subtract a multiple.
    
    Parameters:
    
    b - scale factor.
    
    a - coefficient.
    
    S - GenPolynomial.
    
    Returns:
    
    this * b - a S.
  - scaleSubtractMultiple
```
public ExprPolynomial scaleSubtractMultiple(IExpr b,
                                            IExpr a,
                                            ExpVectorLong e,
                                            ExprPolynomial S)
```
    GenPolynomial scale and subtract a multiple.
    
    Parameters:
    
    b - scale factor.
    
    a - coefficient.
    
    e - exponent.
    
    S - GenPolynomial.
    
    Returns:
    
    this * b - a x^e S.
  - scaleSubtractMultiple
```
public ExprPolynomial scaleSubtractMultiple(IExpr b,
                                            ExpVectorLong g,
                                            IExpr a,
                                            ExpVectorLong e,
                                            ExprPolynomial S)
```
    GenPolynomial scale and subtract a multiple.
    
    Parameters:
    
    b - scale factor.
    
    g - scale exponent.
    
    a - coefficient.
    
    e - exponent.
    
    S - GenPolynomial.
    
    Returns:
    
    this * a x^g - a x^e S.
  - negate
```
public ExprPolynomial negate()
```
    GenPolynomial negation.
    
    Returns:
    
    -this.
  - abs
```
public ExprPolynomial abs()
```
    GenPolynomial absolute value, i.e. leadingCoefficient > 0.
    
    Returns:
    
    abs(this).
  - multiply
```
public ExprPolynomial multiply(ExprPolynomial S)
```
    GenPolynomial multiplication.
    
    Parameters:
    
    S - GenPolynomial.
    
    Returns:
    
    this*S.
  - multiply
```
public ExprPolynomial multiply(IExpr s)
```
    GenPolynomial multiplication. Product with coefficient ring element.
    
    Parameters:
    
    s - coefficient.
    
    Returns:
    
    this*s.
  - monic
```
public ExprPolynomial monic()
```
    GenPolynomial monic, i.e. leadingCoefficient == 1. If leadingCoefficient is not invertible returns this unmodified.
    
    Returns:
    
    monic(this).
  - multiply
```
public ExprPolynomial multiply(IExpr s,
                               ExpVectorLong e)
```
    GenPolynomial multiplication. Product with ring element and exponent vector.
    
    Parameters:
    
    s - coefficient.
    
    e - exponent.
    
    Returns:
    
    this * s x^e.
  - multiply
```
public ExprPolynomial multiply(ExpVectorLong e)
```
    GenPolynomial multiplication. Product with exponent vector.
    
    Parameters:
    
    e - exponent (!= null).
    
    Returns:
    
    this * x^e.
  - multiply
```
public ExprPolynomial multiply(java.util.Map.Entry<ExpVectorLong,IExpr> m)
```
    GenPolynomial multiplication. Product with 'monomial'.
    
    Parameters:
    
    m - 'monomial'.
    
    Returns:
    
    this * m.
  - divide
```
public ExprPolynomial divide(IExpr s)
```
    GenPolynomial division. Division by coefficient ring element. Fails, if exact division is not possible.
    
    Parameters:
    
    s - coefficient.
    
    Returns:
    
    this/s.
  - quotientRemainder
```
public ExprPolynomial[] quotientRemainder(ExprPolynomial S)
```
    GenPolynomial division with remainder. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.
    
    Parameters:
    
    S - nonzero GenPolynomial with invertible leading coefficient.
    
    Returns:
    
    [ quotient , remainder ] with this = quotient * S + remainder and deg(remainder) < deg(S) or remiander = 0.
    
    See Also:
    
    PolyUtil.baseSparsePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial)
  - divideAndRemainder
```
@Deprecated
public ExprPolynomial[] divideAndRemainder(ExprPolynomial S)
```
    Deprecated. use quotientRemainder()
    
    GenPolynomial division with remainder. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.
    
    Parameters:
    
    S - nonzero GenPolynomial with invertible leading coefficient.
    
    Returns:
    
    [ quotient , remainder ] with this = quotient * S + remainder and deg(remainder) < deg(S) or remiander = 0.
    
    See Also:
    
    PolyUtil.baseSparsePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial)
  - divide
```
public ExprPolynomial divide(ExprPolynomial S)
```
    GenPolynomial division. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.
    
    Parameters:
    
    S - nonzero GenPolynomial with invertible leading coefficient.
    
    Returns:
    
    quotient with this = quotient * S + remainder.
    
    See Also:
    
    PolyUtil.baseSparsePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial)
  - remainder
```
public ExprPolynomial remainder(ExprPolynomial S)
```
    GenPolynomial remainder. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.
    
    Parameters:
    
    S - nonzero GenPolynomial with invertible leading coefficient.
    
    Returns:
    
    remainder with this = quotient * S + remainder.
    
    See Also:
    
    PolyUtil.baseSparsePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial)
  - gcd
```
public ExprPolynomial gcd(ExprPolynomial S)
```
    GenPolynomial greatest common divisor. Only for univariate polynomials over fields.
    
    Parameters:
    
    S - GenPolynomial.
    
    Returns:
    
    gcd(this,S).
  - egcd
```
public ExprPolynomial[] egcd(ExprPolynomial S)
```
    GenPolynomial extended greatest comon divisor. Only for univariate polynomials over fields.
    
    Parameters:
    
    S - GenPolynomial.
    
    Returns:
    
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
  - hegcd
```
public ExprPolynomial[] hegcd(ExprPolynomial S)
```
    GenPolynomial half extended greatest comon divisor. Only for univariate polynomials over fields.
    
    Parameters:
    
    S - GenPolynomial.
    
    Returns:
    
    [ gcd(this,S), a ] with a*this + b*S = gcd(this,S).
  - inverse
```
public ExprPolynomial inverse()
```
    GenPolynomial inverse. Required by RingElem. Throws not invertible exception.
  - modInverse
```
public ExprPolynomial modInverse(ExprPolynomial m)
```
    GenPolynomial modular inverse. Only for univariate polynomials over fields.
    
    Parameters:
    
    m - GenPolynomial.
    
    Returns:
    
    a with with a*this = 1 mod m.
  - extend
```
public ExprPolynomial extend(ExprPolynomialRing pfac,
                             int j,
                             long k)
```
    Extend variables. Used e.g. in module embedding. Extend all ExpVectorLongs by i elements and multiply by x_j^k.
    
    Parameters:
    
    pfac - extended polynomial ring factory (by i variables).
    
    j - index of variable to be used for multiplication.
    
    k - exponent for x_j.
    
    Returns:
    
    extended polynomial.
  - extendLower
```
public ExprPolynomial extendLower(ExprPolynomialRing pfac,
                                  int j,
                                  long k)
```
    Extend lower variables. Used e.g. in module embedding. Extend all ExpVectorLongs by i lower elements and multiply by x_j^k.
    
    Parameters:
    
    pfac - extended polynomial ring factory (by i variables).
    
    j - index of variable to be used for multiplication.
    
    k - exponent for x_j.
    
    Returns:
    
    extended polynomial.
  - contract
```
public java.util.Map<ExpVectorLong,ExprPolynomial> contract(ExprPolynomialRing pfac)
```
    Contract variables. Used e.g. in module embedding. Remove i elements of each ExpVectorLong.
    
    Parameters:
    
    pfac - contracted polynomial ring factory (by i variables).
    
    Returns:
    
    Map of exponents and contracted polynomials. Note: could return SortedMap
  - contractCoeff
```
public ExprPolynomial contractCoeff(ExprPolynomialRing pfac)
```
    Contract variables to coefficient polynomial. Remove i elements of each ExpVectorLong, removed elements must be zero.
    
    Parameters:
    
    pfac - contracted polynomial ring factory (by i variables).
    
    Returns:
    
    contracted coefficient polynomial.
  - extendUnivariate
```
public ExprPolynomial extendUnivariate(ExprPolynomialRing pfac,
                                       int i)
```
    Extend univariate to multivariate polynomial. This is an univariate polynomial in variable i of the polynomial ring, it is extended to the given polynomial ring.
    
    Parameters:
    
    pfac - extended polynomial ring factory.
    
    i - index of the variable of this polynomial in pfac.
    
    Returns:
    
    extended multivariate polynomial.
  - homogenize
```
public ExprPolynomial homogenize(ExprPolynomialRing pfac)
```
    Make homogeneous.
    
    Parameters:
    
    pfac - extended polynomial ring factory (by 1 variable).
    
    Returns:
    
    homogeneous polynomial.
  - deHomogenize
```
public ExprPolynomial deHomogenize(ExprPolynomialRing pfac)
```
    Dehomogenize.
    
    Parameters:
    
    pfac - contracted polynomial ring factory (by 1 variable).
    
    Returns:
    
    in homogeneous polynomial.
  - reverse
```
public ExprPolynomial reverse(ExprPolynomialRing oring)
```
    Reverse variables. Used e.g. in opposite rings.
    
    Returns:
    
    polynomial with reversed variables.
  - coefficientIterator
```
public java.util.Iterator coefficientIterator()
```
    Iterator over coefficients.
    
    Returns:
    
    val.values().iterator().
  - exponentIterator
```
public java.util.Iterator<ExpVectorLong> exponentIterator()
```
    Iterator over exponents.
    
    Returns:
    
    val.keySet().iterator().
  - iterator
```
public java.util.Iterator<ExprMonomial> iterator()
```
    Iterator over monomials.
    
    Specified by:
    
    iterator in interface java.lang.Iterable<ExprMonomial>
    
    Returns:
    
    a PolyIterator.
  - map
```
public ExprPolynomial map(java.util.function.Function<IExpr,IExpr> f)
```
    Map a unary function to the coefficients.
    
    Parameters:
    
    f - evaluation functor.
    
    Returns:
    
    new polynomial with coefficients f(this(e)).
  - coefficientRules
```
public IAST coefficientRules()
```
    Get the coefficient rules of a polynomial List() form
    
    Returns:
    
    the monomials of a polynomial
  - monomialList
```
public IAST monomialList()
```
    Get the monomials of a polynomial in List() form
    
    Returns:
    
    the monomials of a polynomial
  - coefficientList
```
public IAST coefficientList()
```
    Get the coefficients of a univariate polynomial up to n degree. Throws WrongNumberOfArguments if the polynomial is not univariate.
    
    Returns:
    
    the coefficients of a univariate polynomial up to n degree
  - derivative
```
public ExprPolynomial derivative()
```
    Derivative of a polynomial. This method assumes that the polynomial is univariate. Throws WrongNumberOfArguments if the polynomial is not univariate.
    
    Returns:
    
    the derivative polynomia if the polynomial isn't univariate
  - getExpr
```
public IExpr getExpr()
```
    Converts a JAS polynomial to a MathEclipse AST with head Plus
    
    Returns:

Class ExprPolynomial

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface java.lang.Iterable

Field Detail

ring

val

Constructor Detail

ExprPolynomial

ExprPolynomial

ExprPolynomial

ExprPolynomial

ExprPolynomial

Method Detail

factory

copy

length

getMap

doPutToMap

doRemoveFromMap

doPutToMap

toString

toString

toScript

toScriptFactory

isZero

isOne

isUnit

isConstant

isHomogeneous

equals

hashCode

compareTo

numberOfVariables

leadingMonomial

leadingExpVectorLong

trailingExpVectorLong

leadingBaseCoefficient

coefficient

reductum

degree

degree

totalDegree

weightDegree

leadingWeightPolynomial

isWeightHomogeneous

degreeVector

maxNorm

sumNorm

sum

sum

sum

doAddTo

doAddTo

doAddTo

subtract

subtract

subtract

subtractMultiple

subtractMultiple

scaleSubtractMultiple

scaleSubtractMultiple

scaleSubtractMultiple

negate

abs

multiply

multiply

monic

multiply

multiply

multiply

divide

quotientRemainder

divideAndRemainder

divide

remainder

gcd

egcd