GenPolynomial

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

Type Parameters:
C - coefficient type

All Implemented Interfaces:

AbelianGroupElem<GenPolynomial<C>>, Element<GenPolynomial<C>>, MonoidElem<GenPolynomial<C>>, RingElem<GenPolynomial<C>>, java.io.Serializable, java.lang.Comparable<GenPolynomial<C>>, java.lang.Iterable<Monomial<C>>

Direct Known Subclasses:

GenSolvablePolynomial
```
public class GenPolynomial<C extends RingElem<C>>
extends java.lang.Object
implements RingElem<GenPolynomial<C>>, java.lang.Iterable<Monomial<C>>
```
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 ExpVector 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

See Also:
Serialized Form

Field Summary

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

Constructor Summary

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

Method Summary

Methods
Modifier and Type	Method and Description
`GenPolynomial<C>`	`abs()` GenPolynomial absolute value, i.e. leadingCoefficient > 0.
`C`	`coefficient(ExpVector e)` Coefficient.
`java.util.Iterator<C>`	`coefficientIterator()` Iterator over coefficients.
`int`	`compareTo(GenPolynomial<C> b)` GenPolynomial comparison.
`java.util.Map<ExpVector,GenPolynomial<C>>`	`contract(GenPolynomialRing<C> pfac)` Contract variables.
`GenPolynomial<C>`	`contractCoeff(GenPolynomialRing<C> pfac)` Contract variables to coefficient polynomial.
`GenPolynomial<C>`	`copy()` Copy this GenPolynomial.
`long`	`degree()` Maximal degree.
`long`	`degree(int i)` Degree in variable i.
`ExpVector`	`degreeVector()` Maximal degree vector.
`GenPolynomial<C>`	`deHomogenize(GenPolynomialRing<C> pfac)` Dehomogenize.
`GenPolynomial<C>`	`divide(C s)` GenPolynomial division.
`GenPolynomial<C>`	`divide(GenPolynomial<C> S)` GenPolynomial division.
`GenPolynomial<C>[]`	`divideAndRemainder(GenPolynomial<C> S)` Deprecated. use quotientRemainder()
`void`	`doPutToMap(ExpVector e, C c)` Put an ExpVector to coefficient entry into the internal map of this GenPolynomial.
`void`	`doPutToMap(java.util.SortedMap<ExpVector,C> vals)` Put an a sorted map of exponents to coefficients into the internal map of this GenPolynomial.
`void`	`doRemoveFromMap(ExpVector e, C c)` Remove an ExpVector to coefficient entry from the internal map of this GenPolynomial.
`GenPolynomial<C>[]`	`egcd(GenPolynomial<C> S)` GenPolynomial extended greatest comon divisor.
`boolean`	`equals(java.lang.Object B)` Comparison with any other object.
`java.util.Iterator<ExpVector>`	`exponentIterator()` Iterator over exponents.
`GenPolynomial<C>`	`extend(GenPolynomialRing<C> pfac, int j, long k)` Extend variables.
`GenPolynomial<C>`	`extendLower(GenPolynomialRing<C> pfac, int j, long k)` Extend lower variables.
`GenPolynomial<C>`	`extendUnivariate(GenPolynomialRing<C> pfac, int i)` Extend univariate to multivariate polynomial.
`GenPolynomialRing<C>`	`factory()` Get the corresponding element factory.
`GenPolynomial<C>`	`gcd(GenPolynomial<C> S)` GenPolynomial greatest common divisor.
`java.util.SortedMap<ExpVector,C>`	`getMap()` ExpVector to coefficient map of GenPolynomial.
`int`	`hashCode()` Hash code for this polynomial.
`GenPolynomial<C>[]`	`hegcd(GenPolynomial<C> S)` GenPolynomial half extended greatest comon divisor.
`GenPolynomial<C>`	`homogenize(GenPolynomialRing<C> pfac)` Make homogeneous.
`GenPolynomial<C>`	`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`	`isZERO()` Is GenPolynomial<C> zero.
`java.util.Iterator<Monomial<C>>`	`iterator()` Iterator over monomials.
`C`	`leadingBaseCoefficient()` Leading base coefficient.
`ExpVector`	`leadingExpVector()` Leading exponent vector.
`java.util.Map.Entry<ExpVector,C>`	`leadingMonomial()` Leading monomial.
`int`	`length()` Length of GenPolynomial.
`GenPolynomial<C>`	`map(UnaryFunctor<? super C,C> f)` Map a unary function to the coefficients.
`C`	`maxNorm()` GenPolynomial maximum norm.
`GenPolynomial<C>`	`modInverse(GenPolynomial<C> m)` GenPolynomial modular inverse.
`GenPolynomial<C>`	`monic()` GenPolynomial monic, i.e. leadingCoefficient == 1.
`GenPolynomial<C>`	`multiply(C s)` GenPolynomial multiplication.
`GenPolynomial<C>`	`multiply(C s, ExpVector e)` GenPolynomial multiplication.
`GenPolynomial<C>`	`multiply(ExpVector e)` GenPolynomial multiplication.
`GenPolynomial<C>`	`multiply(GenPolynomial<C> S)` GenPolynomial multiplication.
`GenPolynomial<C>`	`multiply(java.util.Map.Entry<ExpVector,C> m)` GenPolynomial multiplication.
`GenPolynomial<C>`	`negate()` GenPolynomial negation.
`int`	`numberOfVariables()` Number of variables.
`GenPolynomial<C>[]`	`quotientRemainder(GenPolynomial<C> S)` GenPolynomial division with remainder.
`GenPolynomial<C>`	`reductum()` Reductum.
`GenPolynomial<C>`	`remainder(GenPolynomial<C> S)` GenPolynomial remainder.
`GenPolynomial<C>`	`reverse(GenPolynomialRing<C> oring)` Reverse variables.
`GenPolynomial<C>`	`scaleSubtractMultiple(C b, C a, ExpVector e, GenPolynomial<C> S)` GenPolynomial scale and subtract a multiple.
`GenPolynomial<C>`	`scaleSubtractMultiple(C b, ExpVector g, C a, ExpVector e, GenPolynomial<C> S)` GenPolynomial scale and subtract a multiple.
`int`	`signum()` GenPolynomial signum.
`GenPolynomial<C>`	`subtract(C a)` GenPolynomial subtract.
`GenPolynomial<C>`	`subtract(C a, ExpVector e)` GenPolynomial subtraction.
`GenPolynomial<C>`	`subtract(GenPolynomial<C> S)` GenPolynomial subtraction.
`GenPolynomial<C>`	`subtractMultiple(C a, ExpVector e, GenPolynomial<C> S)` GenPolynomial subtract a multiple.
`GenPolynomial<C>`	`subtractMultiple(C a, GenPolynomial<C> S)` GenPolynomial subtract a multiple.
`GenPolynomial<C>`	`sum(C a)` GenPolynomial addition.
`GenPolynomial<C>`	`sum(C a, ExpVector e)` GenPolynomial addition.
`GenPolynomial<C>`	`sum(GenPolynomial<C> S)` GenPolynomial summation.
`C`	`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(java.lang.String[] v)` String representation of GenPolynomial.
`long`	`totalDegree()` Total degree.
`C`	`trailingBaseCoefficient()` Trailing base coefficient.
`ExpVector`	`trailingExpVector()` Trailing exponent vector.

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

- Field Detail
  - ring
```
public final GenPolynomialRing<C extends RingElem<C>> ring
```
    The factory for the polynomial ring.
  - val
```
protected final java.util.SortedMap<ExpVector,C extends RingElem<C>> val
```
    The data structure for polynomials.
- Constructor Detail
  - GenPolynomial
```
public GenPolynomial(GenPolynomialRing<C> r)
```
    Constructor for zero GenPolynomial.
    
    Parameters:
    r - polynomial ring factory.
  - GenPolynomial
```
public GenPolynomial(GenPolynomialRing<C> r,
             C c,
             ExpVector e)
```
    Constructor for GenPolynomial c * x^e.
    
    Parameters:
    r - polynomial ring factory.
    c - coefficient.
    e - exponent.
  - GenPolynomial
```
public GenPolynomial(GenPolynomialRing<C> r,
             C c)
```
    Constructor for GenPolynomial c * x⁰.
    
    Parameters:
    r - polynomial ring factory.
    c - coefficient.
  - GenPolynomial
```
public GenPolynomial(GenPolynomialRing<C> r,
             ExpVector e)
```
    Constructor for GenPolynomial x^e.
    
    Parameters:
    r - polynomial ring factory.
    e - exponent.
  - GenPolynomial
```
protected GenPolynomial(GenPolynomialRing<C> r,
             java.util.SortedMap<ExpVector,C> v)
```
    Constructor for GenPolynomial.
    
    Parameters:
    r - polynomial ring factory.
    v - the SortedMap of some other polynomial.
- Method Detail
  - factory
```
public GenPolynomialRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    factory for this Element.
    See Also:
    Element.factory()
  - copy
```
public GenPolynomial<C> copy()
```
    Copy this GenPolynomial.
    
    Specified by:
    
    copy in interface Element<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    copy of this.
  - length
```
public int length()
```
    Length of GenPolynomial.
    
    Returns:
    number of coefficients of this GenPolynomial.
  - getMap
```
public java.util.SortedMap<ExpVector,C> getMap()
```
    ExpVector to coefficient map of GenPolynomial.
    
    Returns:
    val as unmodifiable SortedMap.
  - doPutToMap
```
public void doPutToMap(ExpVector e,
              C c)
```
    Put an ExpVector 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(ExpVector e,
                   C c)
```
    Remove an ExpVector 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<ExpVector,C> 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(java.lang.String[] 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.
    
    Specified by:
    
    toScript in interface Element<GenPolynomial<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<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    script compatible representation for this ElemFactory.
    See Also:
    Element.toScriptFactory()
  - isZERO
```
public boolean isZERO()
```
    Is GenPolynomial<C> zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    If this is 0 then true is returned, else false.
    See Also:
    AbelianGroupElem.isZERO()
  - isONE
```
public boolean isONE()
```
    Is GenPolynomial<C> one.
    
    Specified by:
    
    isONE in interface MonoidElem<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    If this is 1 then true is returned, else false.
    See Also:
    MonoidElem.isONE()
  - isUnit
```
public boolean isUnit()
```
    Is GenPolynomial<C> a unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<GenPolynomial<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 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.
    
    Specified by:
    
    equals in interface Element<GenPolynomial<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<GenPolynomial<C extends RingElem<C>>>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    the hashCode.
    See Also:
    Object.hashCode()
  - compareTo
```
public int compareTo(GenPolynomial<C> b)
```
    GenPolynomial comparison.
    
    Specified by:
    
    compareTo in interface Element<GenPolynomial<C extends RingElem<C>>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    b - GenPolynomial.
    
    Returns:
    sign(this-b).
  - signum
```
public int signum()
```
    GenPolynomial signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    sign(ldcf(this)).
  - numberOfVariables
```
public int numberOfVariables()
```
    Number of variables.
    
    Returns:
    ring.nvar.
  - leadingMonomial
```
public java.util.Map.Entry<ExpVector,C> leadingMonomial()
```
    Leading monomial.
    
    Returns:
    first map entry.
  - leadingExpVector
```
public ExpVector leadingExpVector()
```
    Leading exponent vector.
    
    Returns:
    first exponent.
  - trailingExpVector
```
public ExpVector trailingExpVector()
```
    Trailing exponent vector.
    
    Returns:
    last exponent.
  - 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(ExpVector e)
```
    Coefficient.
    
    Parameters:
    e - exponent.
    
    Returns:
    coefficient for given exponent.
  - reductum
```
public GenPolynomial<C> 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.
  - degreeVector
```
public ExpVector degreeVector()
```
    Maximal degree vector.
    
    Returns:
    maximal degree vector of all variables.
  - maxNorm
```
public C maxNorm()
```
    GenPolynomial maximum norm.
    
    Returns:
    ||this||.
  - sumNorm
```
public C sumNorm()
```
    GenPolynomial sum norm.
    
    Returns:
    sum of all absolute values of coefficients.
  - sum
```
public GenPolynomial<C> sum(GenPolynomial<C> S)
```
    GenPolynomial summation.
    
    Specified by:
    
    sum in interface AbelianGroupElem<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    S - GenPolynomial.
    
    Returns:
    this+S.
  - sum
```
public GenPolynomial<C> sum(C a,
                   ExpVector 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 GenPolynomial<C> sum(C a)
```
    GenPolynomial addition. This method is not very efficient, since this is copied.
    
    Parameters:
    a - coefficient.
    
    Returns:
    this + a x⁰.
  - subtract
```
public GenPolynomial<C> subtract(GenPolynomial<C> S)
```
    GenPolynomial subtraction.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    S - GenPolynomial.
    
    Returns:
    this-S.
  - subtract
```
public GenPolynomial<C> subtract(C a,
                        ExpVector 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 GenPolynomial<C> subtract(C a)
```
    GenPolynomial subtract. This method is not very efficient, since this is copied.
    
    Parameters:
    a - coefficient.
    
    Returns:
    this + a x⁰.
  - subtractMultiple
```
public GenPolynomial<C> subtractMultiple(C a,
                                GenPolynomial<C> S)
```
    GenPolynomial subtract a multiple.
    
    Parameters:
    a - coefficient.
    S - GenPolynomial.
    
    Returns:
    this - a x^e S.
  - subtractMultiple
```
public GenPolynomial<C> subtractMultiple(C a,
                                ExpVector e,
                                GenPolynomial<C> S)
```
    GenPolynomial subtract a multiple.
    
    Parameters:
    a - coefficient.
    e - exponent.
    S - GenPolynomial.
    
    Returns:
    this - a x^e S.
  - scaleSubtractMultiple
```
public GenPolynomial<C> scaleSubtractMultiple(C b,
                                     C a,
                                     ExpVector e,
                                     GenPolynomial<C> 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 GenPolynomial<C> scaleSubtractMultiple(C b,
                                     ExpVector g,
                                     C a,
                                     ExpVector e,
                                     GenPolynomial<C> 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 GenPolynomial<C> negate()
```
    GenPolynomial negation.
    
    Specified by:
    
    negate in interface AbelianGroupElem<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    -this.
  - abs
```
public GenPolynomial<C> abs()
```
    GenPolynomial absolute value, i.e. leadingCoefficient > 0.
    
    Specified by:
    
    abs in interface AbelianGroupElem<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    abs(this).
  - multiply
```
public GenPolynomial<C> multiply(GenPolynomial<C> S)
```
    GenPolynomial multiplication.
    
    Specified by:
    
    multiply in interface MonoidElem<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    S - GenPolynomial.
    
    Returns:
    this*S.
  - multiply
```
public GenPolynomial<C> multiply(C s)
```
    GenPolynomial multiplication. Product with coefficient ring element.
    
    Parameters:
    s - coefficient.
    
    Returns:
    this*s.
  - monic
```
public GenPolynomial<C> monic()
```
    GenPolynomial monic, i.e. leadingCoefficient == 1. If leadingCoefficient is not invertible returns this unmodified.
    
    Returns:
    monic(this).
  - multiply
```
public GenPolynomial<C> multiply(C s,
                        ExpVector e)
```
    GenPolynomial multiplication. Product with ring element and exponent vector.
    
    Parameters:
    s - coefficient.
    e - exponent.
    
    Returns:
    this * s x^e.
  - multiply
```
public GenPolynomial<C> multiply(ExpVector e)
```
    GenPolynomial multiplication. Product with exponent vector.
    
    Parameters:
    e - exponent (!= null).
    
    Returns:
    this * x^e.
  - multiply
```
public GenPolynomial<C> multiply(java.util.Map.Entry<ExpVector,C> m)
```
    GenPolynomial multiplication. Product with 'monomial'.
    
    Parameters:
    m - 'monomial'.
    
    Returns:
    this * m.
  - divide
```
public GenPolynomial<C> divide(C s)
```
    GenPolynomial division. Division by coefficient ring element. Fails, if exact division is not possible.
    
    Parameters:
    s - coefficient.
    
    Returns:
    this/s.
  - quotientRemainder
```
public GenPolynomial<C>[] quotientRemainder(GenPolynomial<C> 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:
    .
  - divideAndRemainder
```
@Deprecated
public GenPolynomial<C>[] divideAndRemainder(GenPolynomial<C> 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:
    .
  - divide
```
public GenPolynomial<C> divide(GenPolynomial<C> 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.
    
    Specified by:
    
    divide in interface MonoidElem<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    S - nonzero GenPolynomial with invertible leading coefficient.
    
    Returns:
    quotient with this = quotient * S + remainder.
    See Also:
    .
  - remainder
```
public GenPolynomial<C> remainder(GenPolynomial<C> 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.
    
    Specified by:
    
    remainder in interface MonoidElem<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    S - nonzero GenPolynomial with invertible leading coefficient.
    
    Returns:
    remainder with this = quotient * S + remainder.
    See Also:
    .
  - gcd
```
public GenPolynomial<C> gcd(GenPolynomial<C> S)
```
    GenPolynomial greatest common divisor. Only for univariate polynomials over fields.
    
    Specified by:
    
    gcd in interface RingElem<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    S - GenPolynomial.
    
    Returns:
    gcd(this,S).
  - egcd
```
public GenPolynomial<C>[] egcd(GenPolynomial<C> S)
```
    GenPolynomial extended greatest comon divisor. Only for univariate polynomials over fields.
    
    Specified by:
    
    egcd in interface RingElem<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    S - GenPolynomial.
    
    Returns:
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
  - hegcd
```
public GenPolynomial<C>[] hegcd(GenPolynomial<C> 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 GenPolynomial<C> inverse()
```
    GenPolynomial inverse. Required by RingElem. Throws not invertible exception.
    
    Specified by:
    
    inverse in interface MonoidElem<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    x with this * x = 1, if it exists.
  - modInverse
```
public GenPolynomial<C> modInverse(GenPolynomial<C> m)
```
    GenPolynomial modular inverse. Only for univariate polynomials over fields.
    
    Parameters:
    m - GenPolynomial.
    
    Returns:
    a with with a*this = 1 mod m.
  - extend
```
public GenPolynomial<C> extend(GenPolynomialRing<C> pfac,
                      int j,
                      long k)
```
    Extend variables. Used e.g. in module embedding. Extend all ExpVectors 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 GenPolynomial<C> extendLower(GenPolynomialRing<C> pfac,
                           int j,
                           long k)
```
    Extend lower variables. Used e.g. in module embedding. Extend all ExpVectors 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<ExpVector,GenPolynomial<C>> contract(GenPolynomialRing<C> pfac)
```
    Contract variables. Used e.g. in module embedding. Remove i elements of each ExpVector.
    
    Parameters:
    pfac - contracted polynomial ring factory (by i variables).
    
    Returns:
    Map of exponents and contracted polynomials. Note: could return SortedMap
  - contractCoeff
```
public GenPolynomial<C> contractCoeff(GenPolynomialRing<C> pfac)
```
    Contract variables to coefficient polynomial. Remove i elements of each ExpVector, removed elements must be zero.
    
    Parameters:
    pfac - contracted polynomial ring factory (by i variables).
    
    Returns:
    contracted coefficient polynomial.
  - extendUnivariate
```
public GenPolynomial<C> extendUnivariate(GenPolynomialRing<C> 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 GenPolynomial<C> homogenize(GenPolynomialRing<C> pfac)
```
    Make homogeneous.
    
    Parameters:
    pfac - extended polynomial ring factory (by 1 variable).
    
    Returns:
    homogeneous polynomial.
  - deHomogenize
```
public GenPolynomial<C> deHomogenize(GenPolynomialRing<C> pfac)
```
    Dehomogenize.
    
    Parameters:
    pfac - contracted polynomial ring factory (by 1 variable).
    
    Returns:
    in homogeneous polynomial.
  - reverse
```
public GenPolynomial<C> reverse(GenPolynomialRing<C> oring)
```
    Reverse variables. Used e.g. in opposite rings.
    
    Returns:
    polynomial with reversed variables.
  - coefficientIterator
```
public java.util.Iterator<C> coefficientIterator()
```
    Iterator over coefficients.
    
    Returns:
    val.values().iterator().
  - exponentIterator
```
public java.util.Iterator<ExpVector> exponentIterator()
```
    Iterator over exponents.
    
    Returns:
    val.keySet().iterator().
  - iterator
```
public java.util.Iterator<Monomial<C>> iterator()
```
    Iterator over monomials.
    
    Specified by:
    
    iterator in interface java.lang.Iterable<Monomial<C extends RingElem<C>>>
    
    Returns:
    a PolyIterator.
  - map
```
public GenPolynomial<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)).

Class GenPolynomial<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

val

Constructor Detail

GenPolynomial

GenPolynomial

GenPolynomial

GenPolynomial

GenPolynomial

Method Detail

factory

copy

length

getMap

doPutToMap

doRemoveFromMap

doPutToMap

toString

toString

toScript

toScriptFactory

isZERO

isONE

isUnit

isConstant

isHomogeneous

equals

hashCode

compareTo

signum

numberOfVariables

leadingMonomial

leadingExpVector

trailingExpVector

leadingBaseCoefficient

trailingBaseCoefficient

coefficient

reductum

degree

degree

totalDegree

degreeVector

maxNorm

sumNorm

sum

sum

sum

subtract

subtract

subtract

subtractMultiple

subtractMultiple

scaleSubtractMultiple

scaleSubtractMultiple

negate

abs

multiply

multiply

monic

multiply

multiply

multiply

divide

quotientRemainder

divideAndRemainder

divide

remainder

gcd

egcd

hegcd

inverse

modInverse

extend

extendLower

contract