MathAction CommonDenominator for polynomials

Topics

FrontPage
- AxiomContributions
  - CommonDenominator for polynomials <-- You are here.

This package extends UnivariatePolynomialCommonDenominator? for arbitrary polynomial categories. In fact, I don't understand why the original package is so restrictive.

spad

)abbrev package PCDEN PolynomialCommonDenominator
PolynomialCommonDenominator(R, Q, P, E, VarSet): Exports == Impl where
  R : IntegralDomain
  Q : QuotientFieldCategory R
  E : OrderedAbelianMonoidSup
  VarSet: OrderedSet
  P: PolynomialCategory(Q, E,VarSet)

  Exports ==> with
    commonDenominator: P -> R
      ++ commonDenominator(q) returns a common denominator d for
      ++ the coefficients of q.
    clearDenominator : P -> P
      ++ clearDenominator(q) returns p such that \spad{q = p/d} where d is
      ++ a common denominator for the coefficients of q.
    splitDenominator : P -> Record(num: P, den: R)
      ++ splitDenominator(q) returns \spad{[p, d]} such that \spad{q = p/d} and d
      ++ is a common denominator for the coefficients of q.

  Impl ==> add
    import CommonDenominator(R, Q, List Q)

    commonDenominator p == commonDenominator coefficients p

    clearDenominator p ==
      d := commonDenominator p
      map(numer(d * #1)::Q, p)

    splitDenominator p ==
      d := commonDenominator p
      [map(numer(d * #1)::Q, p), d]

spad

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/3743324978057018076-25px001.spad using 
      old system compiler.
   PCDEN abbreviates package PolynomialCommonDenominator 
   processing macro definition Exports ==> -- the constructor category 
   processing macro definition Impl ==> -- the constructor capsule 
------------------------------------------------------------------------
   initializing NRLIB PCDEN for PolynomialCommonDenominator 
   compiling into NRLIB PCDEN 
   importing CommonDenominator(R,Q,List Q)
   compiling exported commonDenominator : P -> R
Time: 0.20 SEC.

   compiling exported clearDenominator : P -> P
Time: 0.01 SEC.

   compiling exported splitDenominator : P -> Record(num: P,den: R)
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |PolynomialCommonDenominator| REDEFINED

;;;     ***       |PolynomialCommonDenominator| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor PolynomialCommonDenominator
      Time: 0.21 seconds

   finalizing NRLIB PCDEN 
   Processing PolynomialCommonDenominator for Browser database:
--------(commonDenominator (R P))---------
--------(clearDenominator (P P))---------
--------(splitDenominator ((Record (: num P) (: den R)) P))---------
--->-->PolynomialCommonDenominator(constructor): Not documented!!!!
--->-->PolynomialCommonDenominator(): Missing Description
------------------------------------------------------------------------
   PolynomialCommonDenominator is now explicitly exposed in frame 
      initial 
   PolynomialCommonDenominator will be automatically loaded when needed
      from /var/zope2/var/LatexWiki/PCDEN.NRLIB/code

Example use:

axiom

)set mess type off

dom:=DMP([x,y], FRAC DMP([z],INT));

p:dom:=x*y^3/(z^2-1) + 3*x*y/(z^3-1)

(1)

axiom

commonDenominator p

(2)

axiom

clearDenominator p

(3)

axiom

splitDenominator p

(4)

subject:

	( 7 subscribers )