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CommonDenominator for polynomials

Edit detail for CommonDenominator for polynomials revision 3 of 3

	1 2 3
Editor: test1 Time: 2018/04/13 15:44:45 GMT+0
Note:

changed:
-Note: Common denominator in FriCAS is extended in such a way.
-
-This package extends UnivariatePolynomialCommonDenominator for arbitrary polynomial categories. In fact, I don't understand why the original package is so restrictive.
-
-\begin{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]
-\end{spad}
This page presented extension of UnivariatePolynomialCommonDenominator for arbitrary polynomial categories.  FriCAS now
contains such extension, so we just present an example. 

added:
)expose PCDEN

This page presented extension of UnivariatePolynomialCommonDenominator? for arbitrary polynomial categories. FriCAS now contains such extension, so we just present an example.

Example use:

fricas

)set mess type off

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)expose PCDEN

   PolynomialCommonDenominator is now explicitly exposed in frame 
      initial 
dom:=DMP([x,y], FRAC DMP([z],INT));

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

$\label{eq1}{{1 \over{{{z}^{2}}- 1}}\ x \ {{y}^{3}}}+{{3 \over{{{z}^{3}}- 1}}\ x \ y}$

(1)

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commonDenominator p

$\label{eq2}{{z}^{4}}+{{z}^{3}}- z - 1$

(2)

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clearDenominator p

$\label{eq3}{{\left({{z}^{2}}+ z + 1 \right)}\ x \ {{y}^{3}}}+{{\left({3 \ z}+ 3 \right)}\ x \ y}$

(3)

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splitDenominator p

$\label{eq4}\begin{array}{@{}l} \displaystyle \left[{num ={{{\left({{z}^{2}}+ z + 1 \right)}\ x \ {{y}^{3}}}+{{\left({3 \ z}+ 3 \right)}\ x \ y}}}, \: \right. \ \ \displaystyle \left.{den ={{{z}^{4}}+{{z}^{3}}- z - 1}}\right]$

(4)