Class MultiVarPowerSeries<C extends RingElem<C>>

java.lang.Object
edu.jas.ps.MultiVarPowerSeries<C>
Type Parameters:
C - ring element type
All Implemented Interfaces:
AbelianGroupElem<MultiVarPowerSeries<C>>, Element<MultiVarPowerSeries<C>>, MonoidElem<MultiVarPowerSeries<C>>, RingElem<MultiVarPowerSeries<C>>, Serializable, Comparable<MultiVarPowerSeries<C>>
public class MultiVarPowerSeries<C extends RingElem<C>> extends Object implements RingElem<MultiVarPowerSeries<C>>
Multivariate power series implementation. Uses inner classes and lazy evaluated generating function for coefficients. All ring element methods use lazy evaluation except where noted otherwise. Eager evaluated methods are toString(), compareTo(), equals(), evaluate(), or methods which use the order() or orderExpVector() methods, like signum(), abs(), divide(), remainder() and gcd(). Note: Currently the term order is fixed to the order defined by the iterator over exponent vectors in class ExpVectorIterator.
See Also:

  • Field Details

    • ring

      public final MultiVarPowerSeriesRing<C extends RingElem<C>> ring
      Power series ring factory.

    • lazyCoeffs

      MultiVarCoefficients<C extends RingElem<C>> lazyCoeffs
      Data structure / generating function for coefficients. Cannot be final because of fixPoint, must be accessible in factory.

    • truncate

      private int truncate
      Truncation of computations.

    • order

      private int order
      Order of power series.

    • evorder

      private ExpVector evorder
      ExpVector of order of power series.

  • Constructor Details

    • MultiVarPowerSeries

      private MultiVarPowerSeries()
      Private constructor.

    • MultiVarPowerSeries

      MultiVarPowerSeries(MultiVarPowerSeriesRing<C> ring)
      Package constructor. Use in fixPoint only, must be accessible in factory.
      Parameters:
      ring - power series ring.

    • MultiVarPowerSeries

      public MultiVarPowerSeries(MultiVarPowerSeriesRing<C> ring, MultiVarCoefficients<C> lazyCoeffs)
      Constructor.
      Parameters:
      ring - power series ring.
      lazyCoeffs - generating function for coefficients.

    • MultiVarPowerSeries

      public MultiVarPowerSeries(MultiVarPowerSeriesRing<C> ring, MultiVarCoefficients<C> lazyCoeffs, int trunc)
      Constructor.
      Parameters:
      ring - power series ring.
      lazyCoeffs - generating function for coefficients.
      trunc - truncate parameter for this power series.

  • Method Details

    • factory

      public MultiVarPowerSeriesRing<C> factory()
      Get the corresponding element factory.
      Specified by:
      factory in interface Element<C extends RingElem<C>>
      Returns:
      factory for this Element.
      See Also:

    • copy

      public MultiVarPowerSeries<C> copy()
      Clone this power series.
      Specified by:
      copy in interface Element<C extends RingElem<C>>
      Returns:
      Creates and returns a copy of this Element.
      See Also:

    • toString

      public String toString()
      String representation of power series.
      Overrides:
      toString in class Object
      See Also:

    • toString

      public String toString(int trunc)
      To String with given truncate.
      Parameters:
      trunc - truncate parameter for this power series.
      Returns:
      string representation of this to given truncate.

    • toScript

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

    • toScriptFactory

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

    • coefficient

      public C coefficient(ExpVector index)
      Get coefficient.
      Parameters:
      index - number of requested coefficient.
      Returns:
      coefficient at index.

    • homogeneousPart

      public GenPolynomial<C> homogeneousPart(long tdeg)
      Homogeneous part.
      Parameters:
      tdeg - requested degree.
      Returns:
      polynomial part of given degree.

    • asPolynomial

      public GenPolynomial<C> asPolynomial()
      Get a GenPolynomial<C> from this.
      Returns:
      a GenPolynomial<C> from this up to truncate homogeneous parts.

    • leadingCoefficient

      public C leadingCoefficient()
      Leading base coefficient.
      Returns:
      first coefficient.

    • prepend

      public MultiVarPowerSeries<C> prepend(C h, int r)
      Prepend a new leading coefficient.
      Parameters:
      h - new coefficient.
      r - variable for the direction.
      Returns:
      new power series.

    • shift

      public MultiVarPowerSeries<C> shift(int k, int r)
      Shift coefficients.
      Parameters:
      k - shift index.
      r - variable for the direction.
      Returns:
      new power series with coefficient(i) = old.coefficient(i-k).

    • reductum

      public MultiVarPowerSeries<C> reductum(int r)
      Reductum.
      Parameters:
      r - variable for taking the reductum.
      Returns:
      this - leading monomial in the direction of r.

    • reductum

      public MultiVarPowerSeries<C> reductum()
      Reductum.
      Returns:
      this - leading monomial.

    • shift

      public MultiVarPowerSeries<C> shift(ExpVector k)
      Shift coefficients. Multiply by exponent vector.
      Parameters:
      k - shift ExpVector.
      Returns:
      new power series with coefficient(i) = old.coefficient(i-k).

    • multiply

      public MultiVarPowerSeries<C> multiply(C c, ExpVector k)
      Multiply by exponent vector and coefficient.
      Parameters:
      c - coefficient multiplier.
      k - shift ExpVector.
      Returns:
      new power series with coefficient(i) = old.coefficient(i-k)*c.

    • sum

      public MultiVarPowerSeries<C> sum(Map.Entry<ExpVector, C> m)
      Sum monomial.
      Parameters:
      m - ExpVector , coefficient pair
      Returns:
      this + ONE.multiply(m.coefficient,m.exponent).

    • sum

      public MultiVarPowerSeries<C> sum(C c, ExpVector k)
      Sum exponent vector and coefficient.
      Parameters:
      c - coefficient.
      k - ExpVector.
      Returns:
      this + ONE.multiply(c,k).

    • subtract

      public MultiVarPowerSeries<C> subtract(C c, ExpVector k)
      Subtract exponent vector and coefficient.
      Parameters:
      c - coefficient.
      k - ExpVector.
      Returns:
      this - ONE.multiply(c,k).

    • sum

      public MultiVarPowerSeries<C> sum(MultiVarCoefficients<C> mvc)
      Sum exponent vector and coefficient.
      Parameters:
      mvc - cached coefficients.
      Returns:
      this + mvc.

    • select

      public MultiVarPowerSeries<C> select(Selector<? super C> sel)
      Select coefficients.
      Parameters:
      sel - selector functor.
      Returns:
      new power series with selected coefficients.

    • shiftSelect

      public MultiVarPowerSeries<C> shiftSelect(Selector<? super C> sel)
      Shift select coefficients. Not selected coefficients are removed from the result series.
      Parameters:
      sel - selector functor.
      Returns:
      new power series with shifted selected coefficients.

    • map

      public MultiVarPowerSeries<C> map(UnaryFunctor<? super C, C> f)
      Map a unary function to this power series.
      Parameters:
      f - evaluation functor.
      Returns:
      new power series with coefficients f(this(i)).

    • zip

      public MultiVarPowerSeries<C> zip(BinaryFunctor<? super C, ? super C, C> f, MultiVarPowerSeries<C> ps)
      Map a binary function to this and another power series.
      Parameters:
      f - evaluation functor with coefficients f(this(i),other(i)).
      ps - other power series.
      Returns:
      new power series.

    • sumZip

      public MultiVarPowerSeries<C> sumZip(MultiVarPowerSeries<C> ps)
      Sum of two power series, using zip().
      Parameters:
      ps - other power series.
      Returns:
      this + ps.

    • subtractZip

      public MultiVarPowerSeries<C> subtractZip(MultiVarPowerSeries<C> ps)
      Subtraction of two power series, using zip().
      Parameters:
      ps - other power series.
      Returns:
      this - ps.

    • multiply

      public MultiVarPowerSeries<C> multiply(C a)
      Multiply by coefficient.
      Parameters:
      a - coefficient.
      Returns:
      this * a.

    • monic

      public MultiVarPowerSeries<C> monic()
      Monic.
      Returns:
      1/orderCoeff() * this.

    • negate

      public MultiVarPowerSeries<C> negate()
      Negate.
      Specified by:
      negate in interface AbelianGroupElem<C extends RingElem<C>>
      Returns:
      - this.

    • abs

      public MultiVarPowerSeries<C> abs()
      Absolute value.
      Specified by:
      abs in interface AbelianGroupElem<C extends RingElem<C>>
      Returns:
      abs(this).

    • evaluate

      public C evaluate(List<C> a)
      Evaluate at given point.
      Returns:
      ps(a).

    • order

      public int order()
      Order.
      Returns:
      index of first non zero coefficient.

    • orderExpVector

      public ExpVector orderExpVector()
      Order ExpVector.
      Returns:
      ExpVector of first non zero coefficient.

    • orderMonomial

      public Map.Entry<ExpVector, C> orderMonomial()
      Order monomial.
      Returns:
      first map entry or null.

    • truncate

      public int truncate()
      Truncate.
      Returns:
      truncate index of power series.

    • setTruncate

      public int setTruncate(int t)
      Set truncate.
      Parameters:
      t - new truncate index.
      Returns:
      old truncate index of power series.

    • ecart

      public long ecart()
      Ecart.
      Returns:
      ecart.

    • signum

      public int signum()
      Signum.
      Specified by:
      signum in interface AbelianGroupElem<C extends RingElem<C>>
      Returns:
      sign of first non zero coefficient.

    • compareTo

      public int compareTo(MultiVarPowerSeries<C> ps)
      Compare to. Note: compare only up to max(truncates).
      Specified by:
      compareTo in interface Comparable<C extends RingElem<C>>
      Specified by:
      compareTo in interface Element<C extends RingElem<C>>
      Parameters:
      ps -
      Returns:
      sign of first non zero coefficient of this-ps.

    • isZERO

      public boolean isZERO()
      Is power series zero. Note: compare only up to truncate.
      Specified by:
      isZERO in interface AbelianGroupElem<C extends RingElem<C>>
      Returns:
      If this is 0 then true is returned, else false.
      See Also:

    • isONE

      public boolean isONE()
      Is power series one. Note: compare only up to truncate.
      Specified by:
      isONE in interface MonoidElem<C extends RingElem<C>>
      Returns:
      If this is 1 then true is returned, else false.
      See Also:

    • equals

      public boolean equals(Object B)
      Comparison with any other object. Note: compare only up to truncate.
      Specified by:
      equals in interface Element<C extends RingElem<C>>
      Overrides:
      equals in class Object
      Parameters:
      B -
      Returns:
      true if this is equal to b, else false.
      See Also:

    • hashCode

      public int hashCode()
      Hash code for this polynomial. Note: only up to truncate.
      Specified by:
      hashCode in interface Element<C extends RingElem<C>>
      Overrides:
      hashCode in class Object
      Returns:
      the hashCode.
      See Also:

    • isUnit

      public boolean isUnit()
      Is unit.
      Specified by:
      isUnit in interface MonoidElem<C extends RingElem<C>>
      Returns:
      true, if this power series is invertible, else false.

    • sum

      public MultiVarPowerSeries<C> sum(MultiVarPowerSeries<C> ps)
      Sum a another power series.
      Specified by:
      sum in interface AbelianGroupElem<C extends RingElem<C>>
      Parameters:
      ps - other power series.
      Returns:
      this + ps.

    • subtract

      public MultiVarPowerSeries<C> subtract(MultiVarPowerSeries<C> ps)
      Subtract a another power series.
      Specified by:
      subtract in interface AbelianGroupElem<C extends RingElem<C>>
      Parameters:
      ps - other power series.
      Returns:
      this - ps.

    • multiply

      public MultiVarPowerSeries<C> multiply(MultiVarPowerSeries<C> ps)
      Multiply by another power series.
      Specified by:
      multiply in interface MonoidElem<C extends RingElem<C>>
      Parameters:
      ps - other power series.
      Returns:
      this * ps.

    • inverse

      public MultiVarPowerSeries<C> inverse()
      Inverse power series.
      Specified by:
      inverse in interface MonoidElem<C extends RingElem<C>>
      Returns:
      ps with this * ps = 1.

    • divide

      public MultiVarPowerSeries<C> divide(MultiVarPowerSeries<C> ps)
      Divide by another power series.
      Specified by:
      divide in interface MonoidElem<C extends RingElem<C>>
      Parameters:
      ps - nonzero power series with invertible coefficient.
      Returns:
      this / ps.

    • remainder

      public MultiVarPowerSeries<C> remainder(MultiVarPowerSeries<C> ps)
      Power series remainder.
      Specified by:
      remainder in interface MonoidElem<C extends RingElem<C>>
      Parameters:
      ps - nonzero power series with invertible leading coefficient.
      Returns:
      remainder with this = quotient * ps + remainder.

    • quotientRemainder

      public MultiVarPowerSeries<C>[] quotientRemainder(MultiVarPowerSeries<C> S)
      Quotient and remainder by division of this by S.
      Specified by:
      quotientRemainder in interface MonoidElem<C extends RingElem<C>>
      Parameters:
      S - a MultiVarPowerSeries
      Returns:
      [this/S, this - (this/S)*S].

    • differentiate

      public MultiVarPowerSeries<C> differentiate(int r)
      Differentiate with respect to variable r.
      Parameters:
      r - variable for the direction.
      Returns:
      differentiate(this).

    • integrate

      public MultiVarPowerSeries<C> integrate(C c, int r)
      Integrate with respect to variable r and with given constant.
      Parameters:
      c - integration constant.
      r - variable for the direction.
      Returns:
      integrate(this).

    • gcd

      public MultiVarPowerSeries<C> gcd(MultiVarPowerSeries<C> ps)
      Power series greatest common divisor.
      Specified by:
      gcd in interface RingElem<C extends RingElem<C>>
      Parameters:
      ps - power series.
      Returns:
      gcd(this,ps).

    • egcd

      public MultiVarPowerSeries<C>[] egcd(MultiVarPowerSeries<C> S)
      Power series extended greatest common divisor. Note: not implemented.
      Specified by:
      egcd in interface RingElem<C extends RingElem<C>>
      Parameters:
      S - power series.
      Returns:
      [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).