GenWordPolynomial

java.lang.Object
- edu.jas.poly.GenWordPolynomial<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

AbelianGroupElem<GenWordPolynomial<C>>, Element<GenWordPolynomial<C>>, MonoidElem<GenWordPolynomial<C>>, RingElem<GenWordPolynomial<C>>, java.io.Serializable, java.lang.Comparable<GenWordPolynomial<C>>, java.lang.Iterable<WordMonomial<C>>
```
public final class GenWordPolynomial<C extends RingElem<C>>
extends java.lang.Object
implements RingElem<GenWordPolynomial<C>>, java.lang.Iterable<WordMonomial<C>>
```
GenWordPolynomial generic polynomials implementing RingElem. Non-commutative string polynomials over C. Objects of this class are intended to be immutable. The implementation is based on TreeMap respectively SortedMap from words to coefficients. Only the coefficients are modeled with generic types, the "exponents" are fixed to Word. C can also be a non integral domain, e.g. a ModInteger, i.e. it may contain zero divisors, since multiply() does check for zeros.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

GenWordPolynomialRing<C> ring
The factory for the polynomial ring.

Fields
Modifier and Type	Field and Description
`GenWordPolynomialRing<C>`	`ring` The factory for the polynomial ring.

Constructor Summary

Constructors
Modifier	Constructor and Description
	`GenWordPolynomial(GenWordPolynomialRing<C> r)` Constructor for zero GenWordPolynomial.
	`GenWordPolynomial(GenWordPolynomialRing<C> r, C c)` Constructor for GenWordPolynomial c * x⁰.
	`GenWordPolynomial(GenWordPolynomialRing<C> r, C c, ExpVector e)` Constructor for GenWordPolynomial c * x^e.
	`GenWordPolynomial(GenWordPolynomialRing<C> r, C c, Word e)` Constructor for GenWordPolynomial c * x^e.
	`GenWordPolynomial(GenWordPolynomialRing<C> r, ExpVector e)` Constructor for GenWordPolynomial x^e.
`protected`	`GenWordPolynomial(GenWordPolynomialRing<C> r, java.util.SortedMap<Word,C> v)` Constructor for GenWordPolynomial.
	`GenWordPolynomial(GenWordPolynomialRing<C> r, Word e)` Constructor for GenWordPolynomial x^e.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`GenWordPolynomial<C>`	`abs()` GenWordPolynomial absolute value, i.e. leadingCoefficient > 0.
`C`	`coefficient(Word e)` Coefficient.
`java.util.Iterator<C>`	`coefficientIterator()` Iterator over coefficients.
`int`	`compareTo(GenWordPolynomial<C> b)` GenWordPolynomial comparison.
`GenWordPolynomial<C>`	`contract(GenWordPolynomialRing<C> fac)` GenWordPolynomial contraction.
`GenWordPolynomial<C>`	`copy()` Copy this GenWordPolynomial.
`long`	`degree()` Maximal degree.
`GenWordPolynomial<C>`	`divide(C s)` GenWordPolynomial division.
`GenWordPolynomial<C>`	`divide(GenWordPolynomial<C> S)` GenWordPolynomial division.
`void`	`doPutToMap(java.util.SortedMap<Word,C> vals)` Put an a sorted map of words to coefficients into the internal map of this GenWordPolynomial.
`void`	`doPutToMap(Word e, C c)` Put a Word to coefficient entry into the internal map of this GenWordPolynomial.
`void`	`doRemoveFromMap(Word e, C c)` Remove a Word to coefficient entry from the internal map of this GenWordPolynomial.
`GenWordPolynomial<C>[]`	`egcd(GenWordPolynomial<C> S)` GenWordPolynomial extended greatest comon divisor.
`boolean`	`equals(java.lang.Object B)` Comparison with any other object.
`GenWordPolynomialRing<C>`	`factory()` Get the corresponding element factory.
`GenWordPolynomial<C>`	`gcd(GenWordPolynomial<C> S)` GenWordPolynomial greatest common divisor.
`java.util.SortedMap<Word,C>`	`getMap()` Word to coefficient map of GenWordPolynomial.
`int`	`hashCode()` Hash code for this polynomial.
`GenWordPolynomial<C>[]`	`hegcd(GenWordPolynomial<C> S)` GenWordPolynomial half extended greatest comon divisor.
`GenWordPolynomial<C>`	`inverse()` GenWordPolynomial inverse.
`boolean`	`isConstant()` Is GenWordPolynomial<C> a constant.
`boolean`	`isHomogeneous()` Is GenWordPolynomial<C> homogeneous.
`boolean`	`isONE()` Is GenWordPolynomial<C> one.
`boolean`	`isUnit()` Is GenWordPolynomial<C> a unit.
`boolean`	`isZERO()` Is GenWordPolynomial<C> zero.
`java.util.Iterator<WordMonomial<C>>`	`iterator()` Iterator over monomials.
`C`	`leadingBaseCoefficient()` Leading base coefficient.
`java.util.Map.Entry<Word,C>`	`leadingMonomial()` Leading monomial.
`Word`	`leadingWord()` Leading word.
`int`	`length()` Length of GenWordPolynomial.
`GenWordPolynomial<C>`	`map(UnaryFunctor<? super C,C> f)` Map a unary function to the coefficients.
`C`	`maxNorm()` GenWordPolynomial maximum norm.
`GenWordPolynomial<C>`	`modInverse(GenWordPolynomial<C> m)` GenWordPolynomial modular inverse.
`GenWordPolynomial<C>`	`monic()` GenWordPolynomial monic, i.e. leadingCoefficient == 1.
`GenWordPolynomial<C>`	`multiply(C s)` GenWordPolynomial multiplication.
`GenWordPolynomial<C>`	`multiply(C s, C t)` GenWordPolynomial multiplication.
`GenWordPolynomial<C>`	`multiply(C s, Word e)` GenWordPolynomial multiplication.
`GenWordPolynomial<C>`	`multiply(C s, Word e, C t, Word f)` GenWordPolynomial left and right multiplication.
`GenWordPolynomial<C>`	`multiply(C s, Word e, Word f)` GenWordPolynomial left and right multiplication.
`GenWordPolynomial<C>`	`multiply(GenWordPolynomial<C> S)` GenWordPolynomial multiplication.
`GenWordPolynomial<C>`	`multiply(GenWordPolynomial<C> S, GenWordPolynomial<C> T)` GenWordPolynomial left and right multiplication.
`GenWordPolynomial<C>`	`multiply(java.util.Map.Entry<Word,C> m)` GenWordPolynomial multiplication.
`GenWordPolynomial<C>`	`multiply(Word e)` GenWordPolynomial multiplication.
`GenWordPolynomial<C>`	`multiply(Word e, Word f)` GenWordPolynomial left and right multiplication.
`GenWordPolynomial<C>`	`negate()` GenWordPolynomial negation.
`int`	`numberOfVariables()` Number of variables.
`GenWordPolynomial<C>[]`	`quotientRemainder(GenWordPolynomial<C> S)` GenWordPolynomial division with remainder.
`GenWordPolynomial<C>`	`reductum()` Reductum.
`GenWordPolynomial<C>`	`remainder(GenWordPolynomial<C> S)` GenWordPolynomial remainder.
`int`	`signum()` GenWordPolynomial signum.
`GenWordPolynomial<C>`	`subtract(C a)` GenWordPolynomial subtract.
`GenWordPolynomial<C>`	`subtract(C a, Word e)` GenWordPolynomial subtraction.
`GenWordPolynomial<C>`	`subtract(GenWordPolynomial<C> S)` GenWordPolynomial subtraction.
`GenWordPolynomial<C>`	`sum(C a)` GenWordPolynomial addition.
`GenWordPolynomial<C>`	`sum(C a, Word e)` GenWordPolynomial addition.
`GenWordPolynomial<C>`	`sum(GenWordPolynomial<C> S)` GenWordPolynomial summation.
`C`	`sumNorm()` GenWordPolynomial 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 GenWordPolynomial.
`C`	`trailingBaseCoefficient()` Trailing base coefficient.
`Word`	`trailingWord()` Trailing word.
`java.util.Iterator<Word>`	`wordIterator()` Iterator over words.

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

Methods inherited from interface edu.jas.structure.RingElem
leftGcd, rightGcd

Methods inherited from interface edu.jas.structure.MonoidElem
leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

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

- Field Detail
  - ring
```
public final GenWordPolynomialRing<C extends RingElem<C>> ring
```
    The factory for the polynomial ring.
- Constructor Detail
  - GenWordPolynomial
```
public GenWordPolynomial(GenWordPolynomialRing<C> r)
```
    Constructor for zero GenWordPolynomial.
    
    Parameters:
    
    r - polynomial ring factory.
  - GenWordPolynomial
```
public GenWordPolynomial(GenWordPolynomialRing<C> r,
                         C c,
                         Word e)
```
    Constructor for GenWordPolynomial c * x^e.
    
    Parameters:
    
    r - polynomial ring factory.
    
    c - coefficient.
    
    e - word.
  - GenWordPolynomial
```
public GenWordPolynomial(GenWordPolynomialRing<C> r,
                         C c)
```
    Constructor for GenWordPolynomial c * x⁰.
    
    Parameters:
    
    r - polynomial ring factory.
    
    c - coefficient.
  - GenWordPolynomial
```
public GenWordPolynomial(GenWordPolynomialRing<C> r,
                         Word e)
```
    Constructor for GenWordPolynomial x^e.
    
    Parameters:
    
    r - polynomial ring factory.
    
    e - word.
  - GenWordPolynomial
```
public GenWordPolynomial(GenWordPolynomialRing<C> r,
                         ExpVector e)
```
    Constructor for GenWordPolynomial x^e.
    
    Parameters:
    
    r - polynomial ring factory.
    
    e - exponent vector.
  - GenWordPolynomial
```
public GenWordPolynomial(GenWordPolynomialRing<C> r,
                         C c,
                         ExpVector e)
```
    Constructor for GenWordPolynomial c * x^e.
    
    Parameters:
    
    r - polynomial ring factory.
    
    c - coefficient.
    
    e - exponent vector.
  - GenWordPolynomial
```
protected GenWordPolynomial(GenWordPolynomialRing<C> r,
                            java.util.SortedMap<Word,C> v)
```
    Constructor for GenWordPolynomial.
    
    Parameters:
    
    r - polynomial ring factory.
    
    v - the SortedMap of some other polynomial.
- Method Detail
  - factory
```
public GenWordPolynomialRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - copy
```
public GenWordPolynomial<C> copy()
```
    Copy this GenWordPolynomial.
    
    Specified by:
    
    copy in interface Element<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    copy of this.
  - length
```
public int length()
```
    Length of GenWordPolynomial.
    
    Returns:
    
    number of coefficients of this GenWordPolynomial.
  - getMap
```
public java.util.SortedMap<Word,C> getMap()
```
    Word to coefficient map of GenWordPolynomial.
    
    Returns:
    
    val as unmodifiable SortedMap.
  - doPutToMap
```
public void doPutToMap(Word e,
                       C c)
```
    Put a Word to coefficient entry into the internal map of this GenWordPolynomial. 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 - word.
  - doRemoveFromMap
```
public void doRemoveFromMap(Word e,
                            C c)
```
    Remove a Word to coefficient entry from the internal map of this GenWordPolynomial. 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 - Word.
    
    c - expected coefficient, null for ignore.
  - doPutToMap
```
public void doPutToMap(java.util.SortedMap<Word,C> vals)
```
    Put an a sorted map of words to coefficients into the internal map of this GenWordPolynomial. 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 wordss and coefficients.
  - toString
```
public java.lang.String toString()
```
    String representation of GenWordPolynomial.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Specified by:
    
    toScript in interface Element<GenWordPolynomial<C extends RingElem<C>>>
    
    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.
    
    Specified by:
    
    toScriptFactory in interface Element<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - isZERO
```
public boolean isZERO()
```
    Is GenWordPolynomial<C> zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    If this is 0 then true is returned, else false.
    
    See Also:
    
    AbelianGroupElem.isZERO()
  - isONE
```
public boolean isONE()
```
    Is GenWordPolynomial<C> one.
    
    Specified by:
    
    isONE in interface MonoidElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    If this is 1 then true is returned, else false.
    
    See Also:
    
    MonoidElem.isONE()
  - isUnit
```
public boolean isUnit()
```
    Is GenWordPolynomial<C> a unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    If this is a unit then true is returned, else false.
    
    See Also:
    
    MonoidElem.isUnit()
  - isConstant
```
public boolean isConstant()
```
    Is GenWordPolynomial<C> a constant.
    
    Returns:
    
    If this is a constant polynomial then true is returned, else false.
  - isHomogeneous
```
public boolean isHomogeneous()
```
    Is GenWordPolynomial<C> homogeneous.
    
    Returns:
    
    true, if this is homogeneous, else false.
  - equals
```
public boolean equals(java.lang.Object B)
```
    Comparison with any other object.
    
    Specified by:
    
    equals in interface Element<GenWordPolynomial<C extends RingElem<C>>>
    
    Overrides:
    
    equals in class java.lang.Object
    
    Returns:
    
    true if this is equal to b, else false.
    
    See Also:
    
    Object.equals(java.lang.Object)
  - hashCode
```
public int hashCode()
```
    Hash code for this polynomial.
    
    Specified by:
    
    hashCode in interface Element<GenWordPolynomial<C extends RingElem<C>>>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
    
    See Also:
    
    Object.hashCode()
  - compareTo
```
public int compareTo(GenWordPolynomial<C> b)
```
    GenWordPolynomial comparison.
    
    Specified by:
    
    compareTo in interface Element<GenWordPolynomial<C extends RingElem<C>>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    b - GenWordPolynomial.
    
    Returns:
    
    sign(this-b).
  - signum
```
public int signum()
```
    GenWordPolynomial signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    sign(ldcf(this)).
  - numberOfVariables
```
public int numberOfVariables()
```
    Number of variables.
    
    Returns:
    
    ring.alphabet.length().
  - leadingMonomial
```
public java.util.Map.Entry<Word,C> leadingMonomial()
```
    Leading monomial.
    
    Returns:
    
    first map entry.
  - leadingWord
```
public Word leadingWord()
```
    Leading word.
    
    Returns:
    
    first highest word.
  - trailingWord
```
public Word trailingWord()
```
    Trailing word.
    
    Returns:
    
    last lowest word.
  - leadingBaseCoefficient
```
public C leadingBaseCoefficient()
```
    Leading base coefficient.
    
    Returns:
    
    first coefficient.
  - trailingBaseCoefficient
```
public C trailingBaseCoefficient()
```
    Trailing base coefficient.
    
    Returns:
    
    coefficient of constant term.
  - coefficient
```
public C coefficient(Word e)
```
    Coefficient.
    
    Parameters:
    
    e - word.
    
    Returns:
    
    coefficient for given word.
  - reductum
```
public GenWordPolynomial<C> reductum()
```
    Reductum.
    
    Returns:
    
    this - leading monomial.
  - degree
```
public long degree()
```
    Maximal degree.
    
    Returns:
    
    maximal degree in any variables.
  - maxNorm
```
public C maxNorm()
```
    GenWordPolynomial maximum norm.
    
    Returns:
    
    ||this||.
  - sumNorm
```
public C sumNorm()
```
    GenWordPolynomial sum norm.
    
    Returns:
    
    sum of all absolute values of coefficients.
  - sum
```
public GenWordPolynomial<C> sum(GenWordPolynomial<C> S)
```
    GenWordPolynomial summation.
    
    Specified by:
    
    sum in interface AbelianGroupElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    S - GenWordPolynomial.
    
    Returns:
    
    this+S.
  - sum
```
public GenWordPolynomial<C> sum(C a,
                                Word e)
```
    GenWordPolynomial addition. This method is not very efficient, since this is copied.
    
    Parameters:
    
    a - coefficient.
    
    e - word.
    
    Returns:
    
    this + a e.
  - sum
```
public GenWordPolynomial<C> sum(C a)
```
    GenWordPolynomial addition. This method is not very efficient, since this is copied.
    
    Parameters:
    
    a - coefficient.
    
    Returns:
    
    this + a x⁰.
  - subtract
```
public GenWordPolynomial<C> subtract(GenWordPolynomial<C> S)
```
    GenWordPolynomial subtraction.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    S - GenWordPolynomial.
    
    Returns:
    
    this-S.
  - subtract
```
public GenWordPolynomial<C> subtract(C a,
                                     Word e)
```
    GenWordPolynomial subtraction. This method is not very efficient, since this is copied.
    
    Parameters:
    
    a - coefficient.
    
    e - word.
    
    Returns:
    
    this - a e.
  - subtract
```
public GenWordPolynomial<C> subtract(C a)
```
    GenWordPolynomial subtract. This method is not very efficient, since this is copied.
    
    Parameters:
    
    a - coefficient.
    
    Returns:
    
    this + a x⁰.
  - negate
```
public GenWordPolynomial<C> negate()
```
    GenWordPolynomial negation.
    
    Specified by:
    
    negate in interface AbelianGroupElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    -this.
  - abs
```
public GenWordPolynomial<C> abs()
```
    GenWordPolynomial absolute value, i.e. leadingCoefficient > 0.
    
    Specified by:
    
    abs in interface AbelianGroupElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    abs(this).
  - multiply
```
public GenWordPolynomial<C> multiply(GenWordPolynomial<C> S)
```
    GenWordPolynomial multiplication.
    
    Specified by:
    
    multiply in interface MonoidElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    S - GenWordPolynomial.
    
    Returns:
    
    this*S.
  - multiply
```
public GenWordPolynomial<C> multiply(GenWordPolynomial<C> S,
                                     GenWordPolynomial<C> T)
```
    GenWordPolynomial left and right multiplication. Product with two polynomials.
    
    Parameters:
    
    S - GenWordPolynomial.
    
    T - GenWordPolynomial.
    
    Returns:
    
    S*this*T.
  - multiply
```
public GenWordPolynomial<C> multiply(C s)
```
    GenWordPolynomial multiplication. Product with coefficient ring element.
    
    Parameters:
    
    s - coefficient.
    
    Returns:
    
    this*s.
  - multiply
```
public GenWordPolynomial<C> multiply(C s,
                                     C t)
```
    GenWordPolynomial multiplication. Product with coefficient ring element.
    
    Parameters:
    
    s - coefficient.
    
    t - coefficient.
    
    Returns:
    
    s*this*t.
  - monic
```
public GenWordPolynomial<C> monic()
```
    GenWordPolynomial monic, i.e. leadingCoefficient == 1. If leadingCoefficient is not invertible returns this unmodified.
    
    Returns:
    
    monic(this).
  - multiply
```
public GenWordPolynomial<C> multiply(C s,
                                     Word e)
```
    GenWordPolynomial multiplication. Product with ring element and word.
    
    Parameters:
    
    s - coefficient.
    
    e - left word.
    
    Returns:
    
    this * s e.
  - multiply
```
public GenWordPolynomial<C> multiply(Word e,
                                     Word f)
```
    GenWordPolynomial left and right multiplication. Product with ring element and two words.
    
    Parameters:
    
    e - left word.
    
    f - right word.
    
    Returns:
    
    e * this * f.
  - multiply
```
public GenWordPolynomial<C> multiply(C s,
                                     Word e,
                                     Word f)
```
    GenWordPolynomial left and right multiplication. Product with ring element and two words.
    
    Parameters:
    
    s - coefficient.
    
    e - left word.
    
    f - right word.
    
    Returns:
    
    e * this * s * f.
  - multiply
```
public GenWordPolynomial<C> multiply(C s,
                                     Word e,
                                     C t,
                                     Word f)
```
    GenWordPolynomial left and right multiplication. Product with ring element and two words.
    
    Parameters:
    
    s - coefficient.
    
    e - left word.
    
    t - coefficient.
    
    f - right word.
    
    Returns:
    
    s * e * this * t * f.
  - multiply
```
public GenWordPolynomial<C> multiply(Word e)
```
    GenWordPolynomial multiplication. Product with word.
    
    Parameters:
    
    e - word (!= null).
    
    Returns:
    
    this * e.
  - multiply
```
public GenWordPolynomial<C> multiply(java.util.Map.Entry<Word,C> m)
```
    GenWordPolynomial multiplication. Product with 'monomial'.
    
    Parameters:
    
    m - 'monomial'.
    
    Returns:
    
    this * m.
  - divide
```
public GenWordPolynomial<C> divide(C s)
```
    GenWordPolynomial division. Division by coefficient ring element. Fails, if exact division is not possible.
    
    Parameters:
    
    s - coefficient.
    
    Returns:
    
    this/s.
  - quotientRemainder
```
public GenWordPolynomial<C>[] quotientRemainder(GenWordPolynomial<C> S)
```
    GenWordPolynomial 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.
    
    Specified by:
    
    quotientRemainder in interface MonoidElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    S - nonzero GenWordPolynomial with invertible leading coefficient.
    
    Returns:
    
    [ quotient , remainder ] with this = quotient * S + remainder and deg(remainder) < deg(S) or remiander = 0.
    
    See Also:
    
    .
  - divide
```
public GenWordPolynomial<C> divide(GenWordPolynomial<C> S)
```
    GenWordPolynomial division. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.
    
    Specified by:
    
    divide in interface MonoidElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    S - nonzero GenWordPolynomial with invertible leading coefficient.
    
    Returns:
    
    quotient with this = quotient * S + remainder.
    
    See Also:
    
    .
  - remainder
```
public GenWordPolynomial<C> remainder(GenWordPolynomial<C> S)
```
    GenWordPolynomial remainder. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.
    
    Specified by:
    
    remainder in interface MonoidElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    S - nonzero GenWordPolynomial with invertible leading coefficient.
    
    Returns:
    
    remainder with this = quotient * S + remainder.
    
    See Also:
    
    .
  - gcd
```
public GenWordPolynomial<C> gcd(GenWordPolynomial<C> S)
```
    GenWordPolynomial greatest common divisor. Only for univariate polynomials over fields.
    
    Specified by:
    
    gcd in interface RingElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    S - GenWordPolynomial.
    
    Returns:
    
    gcd(this,S).
  - egcd
```
public GenWordPolynomial<C>[] egcd(GenWordPolynomial<C> S)
```
    GenWordPolynomial extended greatest comon divisor. Only for univariate polynomials over fields.
    
    Specified by:
    
    egcd in interface RingElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    S - GenWordPolynomial.
    
    Returns:
    
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
  - hegcd
```
public GenWordPolynomial<C>[] hegcd(GenWordPolynomial<C> S)
```
    GenWordPolynomial half extended greatest comon divisor. Only for univariate polynomials over fields.
    
    Parameters:
    
    S - GenWordPolynomial.
    
    Returns:
    
    [ gcd(this,S), a ] with a*this + b*S = gcd(this,S).
  - inverse
```
public GenWordPolynomial<C> inverse()
```
    GenWordPolynomial inverse. Required by RingElem. Throws not invertible exception.
    
    Specified by:
    
    inverse in interface MonoidElem<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    x with this * x = 1, if it exists.
  - modInverse
```
public GenWordPolynomial<C> modInverse(GenWordPolynomial<C> m)
```
    GenWordPolynomial modular inverse. Only for univariate polynomials over fields.
    
    Parameters:
    
    m - GenWordPolynomial.
    
    Returns:
    
    a with with a*this = 1 mod m.
  - coefficientIterator
```
public java.util.Iterator<C> coefficientIterator()
```
    Iterator over coefficients.
    
    Returns:
    
    val.values().iterator().
  - wordIterator
```
public java.util.Iterator<Word> wordIterator()
```
    Iterator over words.
    
    Returns:
    
    val.keySet().iterator().
  - iterator
```
public java.util.Iterator<WordMonomial<C>> iterator()
```
    Iterator over monomials.
    
    Specified by:
    
    iterator in interface java.lang.Iterable<WordMonomial<C extends RingElem<C>>>
    
    Returns:
    
    a PolyIterator.
  - map
```
public GenWordPolynomial<C> map(UnaryFunctor<? super C,C> f)
```
    Map a unary function to the coefficients.
    
    Parameters:
    
    f - evaluation functor.
    
    Returns:
    
    new polynomial with coefficients f(this(e)).
  - contract
```
public GenWordPolynomial<C> contract(GenWordPolynomialRing<C> fac)
```
    GenWordPolynomial contraction.
    
    Parameters:
    
    fac - GenWordPolynomialRing.
    
    Returns:
    
    this contracted to fac ring, if this in fac ring, null else.

Class GenWordPolynomial<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface edu.jas.structure.RingElem

Methods inherited from interface edu.jas.structure.MonoidElem

Methods inherited from interface java.lang.Iterable

Field Detail

ring

Constructor Detail

GenWordPolynomial

GenWordPolynomial

GenWordPolynomial

GenWordPolynomial

GenWordPolynomial

GenWordPolynomial

GenWordPolynomial

Method Detail

factory

copy

length

getMap

doPutToMap

doRemoveFromMap

doPutToMap

toString

toScript

toScriptFactory

isZERO

isONE

isUnit

isConstant

isHomogeneous

equals

hashCode

compareTo

signum

numberOfVariables

leadingMonomial

leadingWord

trailingWord

leadingBaseCoefficient

trailingBaseCoefficient

coefficient

reductum

degree

maxNorm

sumNorm

sum

sum

sum

subtract

subtract

subtract

negate

abs

multiply

multiply

multiply

multiply

monic

multiply

multiply

multiply

multiply

multiply

multiply

divide

quotientRemainder

divide

remainder

gcd

egcd

hegcd

inverse

modInverse

coefficientIterator

wordIterator

iterator