Class GenPolynomialRing<C extends RingElem<C>>

java.lang.Object
edu.jas.poly.GenPolynomialRing<C>
Type Parameters:
C - coefficient type
All Implemented Interfaces:
AbelianGroupFactory<GenPolynomial<C>>, ElemFactory<GenPolynomial<C>>, MonoidFactory<GenPolynomial<C>>, RingFactory<GenPolynomial<C>>, Serializable, Iterable<GenPolynomial<C>>
Direct Known Subclasses:
GenSolvablePolynomialRing
public class GenPolynomialRing<C extends RingElem<C>> extends Object implements RingFactory<GenPolynomial<C>>, Iterable<GenPolynomial<C>>
GenPolynomialRing generic polynomial factory. It implements RingFactory for n-variate ordered polynomials over coefficients C. The variables commute with each other and with the coefficients. For non-commutative coefficients some care is taken to respect the multiplication order. Almost immutable object, except variable names.
See Also:

  • Field Details

    • coFac

      public final RingFactory<C extends RingElem<C>> coFac
      The factory for the coefficients.

    • nvar

      public final int nvar
      The number of variables.

    • tord

      public final TermOrder tord
      The term order.

    • partial

      protected boolean partial
      True for partially reversed variables.

    • vars

      protected String[] vars
      The names of the variables. This value can be modified.

    • varCounter

      private static AtomicLong varCounter
      Counter to distinguish new variables.

    • ZERO

      public GenPolynomial<C extends RingElem<C>> ZERO
      The constant polynomial 0 for this ring.

    • ONE

      public GenPolynomial<C extends RingElem<C>> ONE
      The constant polynomial 1 for this ring.

    • evzero

      public final ExpVector evzero
      The constant exponent vector 0 for this ring.

    • random

      protected static final Random random
      A default random sequence generator.

    • isField

      protected int isField
      Indicator if this ring is a field.

    • logger

      private static final org.apache.logging.log4j.Logger logger
      Log4j logger object.

    • creations

      static int creations
      Count for number of polynomial creations.

    • checkPreempt

      volatile boolean checkPreempt
      Flag to enable if preemptive interrupt is checked.

  • Constructor Details

    • GenPolynomialRing

      public GenPolynomialRing(RingFactory<C> cf, int n)
      The constructor creates a polynomial factory object with the default term order.
      Parameters:
      cf - factory for coefficients of type C.
      n - number of variables.

    • GenPolynomialRing

      public GenPolynomialRing(RingFactory<C> cf, int n, TermOrder t)
      The constructor creates a polynomial factory object.
      Parameters:
      cf - factory for coefficients of type C.
      n - number of variables.
      t - a term order.

    • GenPolynomialRing

      public GenPolynomialRing(RingFactory<C> cf, String[] v)
      The constructor creates a polynomial factory object.
      Parameters:
      cf - factory for coefficients of type C.
      v - names for the variables.

    • GenPolynomialRing

      public GenPolynomialRing(RingFactory<C> cf, int n, String[] v)
      The constructor creates a polynomial factory object.
      Parameters:
      cf - factory for coefficients of type C.
      n - number of variables.
      v - names for the variables.

    • GenPolynomialRing

      public GenPolynomialRing(RingFactory<C> cf, TermOrder t, String[] v)
      The constructor creates a polynomial factory object.
      Parameters:
      cf - factory for coefficients of type C.
      t - a term order.
      v - names for the variables.

    • GenPolynomialRing

      public GenPolynomialRing(RingFactory<C> cf, String[] v, TermOrder t)
      The constructor creates a polynomial factory object.
      Parameters:
      cf - factory for coefficients of type C.
      v - names for the variables.
      t - a term order.

    • GenPolynomialRing

      public GenPolynomialRing(RingFactory<C> cf, int n, TermOrder t, String[] v)
      The constructor creates a polynomial factory object.
      Parameters:
      cf - factory for coefficients of type C.
      n - number of variables.
      t - a term order.
      v - names for the variables.

    • GenPolynomialRing

      public GenPolynomialRing(RingFactory<C> cf, GenPolynomialRing o)
      The constructor creates a polynomial factory object with the the same term order, number of variables and variable names as the given polynomial factory, only the coefficient factories differ.
      Parameters:
      cf - factory for coefficients of type C.
      o - other polynomial ring.

    • GenPolynomialRing

      public GenPolynomialRing(GenPolynomialRing<C> o, TermOrder to)
      The constructor creates a polynomial factory object with the the same coefficient factory, number of variables and variable names as the given polynomial factory, only the term order differs.
      Parameters:
      o - other polynomial ring.
      to - term order.

  • Method Details

    • copy

      public GenPolynomialRing<C> copy()
      Copy this factory.
      Returns:
      a clone of this.

    • toString

      public String toString()
      Get the String representation.
      Overrides:
      toString in class Object
      See Also:

    • toScript

      public String toScript()
      Get a scripting compatible string representation.
      Specified by:
      toScript in interface ElemFactory<C extends RingElem<C>>
      Returns:
      script compatible representation for this Element.
      See Also:

    • toScript

      public String toScript(ExpVector e)
      Get a scripting compatible string representation of an ExpVector of this ring.
      Parameters:
      e - exponent vector
      Returns:
      script compatible representation for the ExpVector.

    • equals

      public boolean equals(Object other)
      Comparison with any other object.
      Overrides:
      equals in class Object
      See Also:

    • hashCode

      public int hashCode()
      Hash code for this polynomial ring.
      Overrides:
      hashCode in class Object
      See Also:

    • getCreations

      public int getCreations()
      Get the number of polynomial creations.
      Returns:
      creations.

    • getVars

      public String[] getVars()
      Get the variable names.
      Returns:
      vars.

    • setVars

      public String[] setVars(String[] v)
      Set the variable names.
      Returns:
      old vars.

    • varsToString

      public String varsToString()
      Get a String representation of the variable names.
      Returns:
      names separated by commas.

    • getZEROCoefficient

      public C getZEROCoefficient()
      Get the zero element from the coefficients.
      Returns:
      0 as C.

    • getONECoefficient

      public C getONECoefficient()
      Get the one element from the coefficients.
      Returns:
      1 as C.

    • getZERO

      public GenPolynomial<C> getZERO()
      Get the zero element.
      Specified by:
      getZERO in interface AbelianGroupFactory<C extends RingElem<C>>
      Returns:
      0 as GenPolynomial.

    • getONE

      public GenPolynomial<C> getONE()
      Get the one element.
      Specified by:
      getONE in interface MonoidFactory<C extends RingElem<C>>
      Returns:
      1 as GenPolynomial.

    • isCommutative

      public boolean isCommutative()
      Query if this ring is commutative.
      Specified by:
      isCommutative in interface MonoidFactory<C extends RingElem<C>>
      Returns:
      true if this ring is commutative, else false.

    • isAssociative

      public boolean isAssociative()
      Query if this ring is associative.
      Specified by:
      isAssociative in interface MonoidFactory<C extends RingElem<C>>
      Returns:
      true if this ring is associative, else false.

    • isField

      public boolean isField()
      Query if this ring is a field.
      Specified by:
      isField in interface RingFactory<C extends RingElem<C>>
      Returns:
      false.

    • characteristic

      public BigInteger characteristic()
      Characteristic of this ring.
      Specified by:
      characteristic in interface RingFactory<C extends RingElem<C>>
      Returns:
      characteristic of this ring.

    • valueOf

      public GenPolynomial<C> valueOf(C a)
      Get a (constant) GenPolynomial<C> element from a coefficient value.
      Parameters:
      a - coefficient.
      Returns:
      a GenPolynomial<C>.

    • valueOf

      public GenPolynomial<C> valueOf(ExpVector e)
      Get a GenPolynomial<C> element from an exponent vector.
      Parameters:
      e - exponent vector.
      Returns:
      a GenPolynomial<C>.

    • valueOf

      public List<GenPolynomial<C>> valueOf(Iterable<ExpVector> E)
      Get a GenPolynomial<C> element from a list of exponent vectors.
      Parameters:
      E - list of exponent vector.
      Returns:
      a GenPolynomial<C>.

    • valueOf

      public GenPolynomial<C> valueOf(C a, ExpVector e)
      Get a GenPolynomial<C> element from a coefficient and an exponent vector.
      Parameters:
      a - coefficient.
      e - exponent vector.
      Returns:
      a GenPolynomial<C>.

    • valueOf

      public GenPolynomial<C> valueOf(Monomial<C> m)
      Get a GenPolynomial<C> element from a monomial.
      Parameters:
      m - monomial.
      Returns:
      a GenPolynomial<C>.

    • fromInteger

      public GenPolynomial<C> fromInteger(long a)
      Get a (constant) GenPolynomial<C> element from a long value.
      Specified by:
      fromInteger in interface ElemFactory<C extends RingElem<C>>
      Parameters:
      a - long.
      Returns:
      a GenPolynomial<C>.

    • fromInteger

      public GenPolynomial<C> fromInteger(BigInteger a)
      Get a (constant) GenPolynomial<C> element from a BigInteger value.
      Specified by:
      fromInteger in interface ElemFactory<C extends RingElem<C>>
      Parameters:
      a - BigInteger.
      Returns:
      a GenPolynomial<C>.

    • fromVector

      public GenPolynomial<C> fromVector(GenVector<C> a)
      Get a GenPolynomial<C> from a GenVector<C>.
      Parameters:
      a - GenVector<C>.
      Returns:
      a GenPolynomial<C>.

    • random

      public GenPolynomial<C> random(int n)
      Random polynomial. Generates a random polynomial with k = 5, l = n, d = (nvar == 1) ? n : 3, q = (nvar == 1) ? 0.7 : 0.3.
      Specified by:
      random in interface ElemFactory<C extends RingElem<C>>
      Parameters:
      n - number of terms.
      Returns:
      a random polynomial.

    • random

      public GenPolynomial<C> random(int n, Random rnd)
      Random polynomial. Generates a random polynomial with k = 5, l = n, d = n, q = (nvar == 1) ? 0.5 : 0.3.
      Specified by:
      random in interface ElemFactory<C extends RingElem<C>>
      Parameters:
      n - number of terms.
      rnd - is a source for random bits.
      Returns:
      a random polynomial.

    • random

      public GenPolynomial<C> random(int k, int l, int d, float q)
      Generate a random polynomial.
      Parameters:
      k - bitsize of random coefficients.
      l - number of terms.
      d - maximal degree in each variable.
      q - density of nozero exponents.
      Returns:
      a random polynomial.

    • random

      public GenPolynomial<C> random(int k, int l, int d, float q, Random rnd)
      Generate a random polynomial.
      Parameters:
      k - bitsize of random coefficients.
      l - number of terms.
      d - maximal degree in each variable.
      q - density of nozero exponents.
      rnd - is a source for random bits.
      Returns:
      a random polynomial.

    • copy

      public GenPolynomial<C> copy(GenPolynomial<C> c)
      Copy polynomial c.
      Specified by:
      copy in interface ElemFactory<C extends RingElem<C>>
      Parameters:
      c -
      Returns:
      a copy of c.

    • copy

      public List<GenPolynomial<C>> copy(List<GenPolynomial<C>> L)
      Copy polynomial list.
      Parameters:
      L - polynomial list
      Returns:
      a copy of L in this ring.

    • parse

      public GenPolynomial<C> parse(String s)
      Parse a polynomial with the use of GenPolynomialTokenizer.
      Specified by:
      parse in interface ElemFactory<C extends RingElem<C>>
      Parameters:
      s - String.
      Returns:
      GenPolynomial from s.

    • parse

      public GenPolynomial<C> parse(Reader r)
      Parse a polynomial with the use of GenPolynomialTokenizer.
      Specified by:
      parse in interface ElemFactory<C extends RingElem<C>>
      Parameters:
      r - Reader.
      Returns:
      next GenPolynomial from r.

    • univariate

      public GenPolynomial<C> univariate(String x)
      Generate univariate polynomial in a given variable with given exponent.
      Parameters:
      x - the name of a variable.
      Returns:
      x as univariate polynomial.

    • univariate

      public GenPolynomial<C> univariate(String x, long e)
      Generate univariate polynomial in a given variable with given exponent.
      Parameters:
      x - the name of the variable.
      e - the exponent of the variable.
      Returns:
      x^e as univariate polynomial.

    • univariate

      public GenPolynomial<C> univariate(int i)
      Generate univariate polynomial in a given variable.
      Parameters:
      i - the index of the variable.
      Returns:
      X_i as univariate polynomial.

    • univariate

      public GenPolynomial<C> univariate(int i, long e)
      Generate univariate polynomial in a given variable with given exponent.
      Parameters:
      i - the index of the variable.
      e - the exponent of the variable.
      Returns:
      X_i^e as univariate polynomial.

    • univariate

      public GenPolynomial<C> univariate(int modv, int i, long e)
      Generate univariate polynomial in a given variable with given exponent.
      Parameters:
      modv - number of module variables.
      i - the index of the variable.
      e - the exponent of the variable.
      Returns:
      X_i^e as univariate polynomial.

    • getGenerators

      public List<GenPolynomial<C>> getGenerators()
      Get the generating elements excluding the generators for the coefficient ring.
      Returns:
      a list of generating elements for this ring.

    • generators

      public List<GenPolynomial<C>> generators()
      Get a list of the generating elements.
      Specified by:
      generators in interface ElemFactory<C extends RingElem<C>>
      Returns:
      list of generators for the algebraic structure.
      See Also:

    • generators

      public List<GenPolynomial<C>> generators(int modv)
      Get a list of the generating elements excluding the module variables.
      Parameters:
      modv - number of module variables
      Returns:
      list of generators for the polynomial ring.

    • isFinite

      public boolean isFinite()
      Is this structure finite or infinite.
      Specified by:
      isFinite in interface ElemFactory<C extends RingElem<C>>
      Returns:
      true if this structure is finite, else false.
      See Also:

    • univariateList

      public List<? extends GenPolynomial<C>> univariateList()
      Generate list of univariate polynomials in all variables.
      Returns:
      List(X_1,...,X_n) a list of univariate polynomials.

    • univariateList

      public List<? extends GenPolynomial<C>> univariateList(int modv)
      Generate list of univariate polynomials in all variables.
      Parameters:
      modv - number of module variables.
      Returns:
      List(X_1,...,X_n) a list of univariate polynomials.

    • univariateList

      public List<? extends GenPolynomial<C>> univariateList(int modv, long e)
      Generate list of univariate polynomials in all variables with given exponent.
      Parameters:
      modv - number of module variables.
      e - the exponent of the variables.
      Returns:
      List(X_1^e,...,X_n^e) a list of univariate polynomials.

    • extend

      public GenPolynomialRing<C> extend(int i)
      Extend variables. Used e.g. in module embedding. Extend number of variables by i.
      Parameters:
      i - number of variables to extend.
      Returns:
      extended polynomial ring factory.

    • extend

      public GenPolynomialRing<C> extend(int i, boolean top)
      Extend variables. Used e.g. in module embedding. Extend number of variables by i.
      Parameters:
      i - number of variables to extend.
      top - true for TOP term order, false for POT term order.
      Returns:
      extended polynomial ring factory.

    • extend

      public GenPolynomialRing<C> extend(String[] vn)
      Extend variables. Used e.g. in module embedding. Extend number of variables by length(vn).
      Parameters:
      vn - names for extended variables.
      Returns:
      extended polynomial ring factory.

    • extend

      public GenPolynomialRing<C> extend(String[] vn, boolean top)
      Extend variables. Used e.g. in module embedding. Extend number of variables by length(vn).
      Parameters:
      vn - names for extended variables.
      top - true for TOP term order, false for POT term order.
      Returns:
      extended polynomial ring factory.

    • extendLower

      public GenPolynomialRing<C> extendLower(int i)
      Extend lower variables. Extend number of variables by i.
      Parameters:
      i - number of variables to extend.
      Returns:
      extended polynomial ring factory.

    • extendLower

      public GenPolynomialRing<C> extendLower(String[] vn)
      Extend lower variables. Extend number of variables by length(vn).
      Parameters:
      vn - names for extended lower variables.
      Returns:
      extended polynomial ring factory.

    • extendLower

      public GenPolynomialRing<C> extendLower(String[] vn, boolean top)
      Extend lower variables. Extend number of variables by length(vn).
      Parameters:
      vn - names for extended lower variables.
      top - true for TOP term order, false for POT term order.
      Returns:
      extended polynomial ring factory.

    • contract

      public GenPolynomialRing<C> contract(int i)
      Contract variables. Used e.g. in module embedding. Contract number of variables by i.
      Parameters:
      i - number of variables to remove.
      Returns:
      contracted polynomial ring factory.

    • recursive

      public GenPolynomialRing<GenPolynomial<C>> recursive(int i)
      Recursive representation as polynomial with i main variables.
      Parameters:
      i - number of main variables.
      Returns:
      recursive polynomial ring factory.

    • distribute

      public GenPolynomialRing<C> distribute()
      Distributive representation as polynomial with all main variables.
      Returns:
      distributive polynomial ring factory.

    • reverse

      public GenPolynomialRing<C> reverse()
      Reverse variables. Used e.g. in opposite rings.
      Returns:
      polynomial ring factory with reversed variables.

    • reverse

      public GenPolynomialRing<C> reverse(boolean partial)
      Reverse variables. Used e.g. in opposite rings. The coefficient ring must be commuative.
      Parameters:
      partial - true for partially reversed term orders.
      Returns:
      polynomial ring factory with reversed variables.

    • getComparator

      public PolynomialComparator<C> getComparator()
      Get PolynomialComparator.
      Returns:
      polynomial comparator.

    • getComparator

      public PolynomialComparator<C> getComparator(boolean rev)
      Get PolynomialComparator.
      Parameters:
      rev - for reverse comparator.
      Returns:
      polynomial comparator.

    • newVars

      public static String[] newVars(String prefix, int n)
      New variable names. Generate new names for variables,
      Parameters:
      prefix - name prefix.
      n - number of variables.
      Returns:
      new variable names.

    • newVars

      public String[] newVars(String prefix)
      New variable names. Generate new names for variables,
      Parameters:
      prefix - name prefix.
      Returns:
      new variable names.

    • newVars

      public static String[] newVars(int n)
      New variable names. Generate new names for variables,
      Parameters:
      n - number of variables.
      Returns:
      new variable names.

    • newVars

      public String[] newVars()
      New variable names. Generate new names for variables,
      Returns:
      new variable names.

    • permuteVars

      public static String[] permuteVars(List<Integer> P, String[] vars)
      Permute variable names.
      Parameters:
      P - permutation.
      vars - variable names.
      Returns:
      P(vars).

    • permutation

      public GenPolynomialRing<C> permutation(List<Integer> P)
      Permutation of polynomial ring variables.
      Parameters:
      P - permutation.
      Returns:
      P(this).

    • charPolynomial

      public GenPolynomial<C> charPolynomial(GenMatrix<C> A)
      Characteristic polynomial of matrix. Note: using Faddeev–LeVerrier algorithm
      Parameters:
      A - a square matrix.
      Returns:
      characteristic polynomial of A.

    • determinantFromCharPol

      public C determinantFromCharPol(GenPolynomial<C> P)
      Determinant of matrix from characteristic polynomial. Note: using Faddeev–LeVerrier algorithm
      Parameters:
      P - characteristic polynomial of a matrix.
      Returns:
      determinant from characteristic polynomial.

    • determinant

      public C determinant(GenMatrix<C> A)
      Determinant of matrix via characteristic polynomial. Note: using Faddeev–LeVerrier algorithm
      Parameters:
      A - square matrix.
      Returns:
      determinant of A from characteristic polynomial of A.

    • traceFromCharPol

      public C traceFromCharPol(GenPolynomial<C> P)
      Trace of matrix from characteristic polynomial.
      Parameters:
      P - characteristic polynomial of a matrix.
      Returns:
      trace from characteristic polynomial.

    • iterator

      public Iterator<GenPolynomial<C>> iterator()
      Get a GenPolynomial iterator.
      Specified by:
      iterator in interface Iterable<C extends RingElem<C>>
      Returns:
      an iterator over all polynomials.