permutePolynomial -- permutes a RingElement or a PolynomialExpression of RingElements

Synopsis

Usage:

permutePolynomial(perm,f)

permutePolynomial(perm,prod)

permutePolynomial(perm,s)

permutePolynomial(perm,pow)

permutePolynomial(perm,minu)
Inputs:
- f, a ring element, a ring element
- prod, a product expression, a Product expression
- s, a sum expression, a sum expression
- pow, a power expression, a power expression
- minu, a minus expression, a minus expression
- perm, a permutation
Outputs:
- a ring element, the result of applying perm to f
- an expression, the result of applying f to the given expression

Description

This method applies permutations to polynomial ring elements by permuting the variables. Therefore the size of the permutation must be equal to the number of generators of the ring of the elements.

i1 : R = QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing

i2 : l = {1,0,2,3,4}

o2 = {1, 0, 2, 3, 4}

o2 : List

i3 : f = x_1*x_2*x_3

o3 = x x x
      1 2 3

o3 : R

i4 : permutePolynomial(l,f)

o4 = x x x
      0 2 3

o4 : R

This method can also permute polynomial expressions that are constructed from ring elements either by sums, products or powers.

i5 : ex = factor(x_1*x_2*x_3)+factor(x_1*x_3*x_4)

o5 = (x )(x )(x ) + (x )(x )(x )
       3   2   1      4   3   1

o5 : Expression of class Sum

i6 : permutePolynomial(l,ex)

o6 = (x )(x )(x ) + (x )(x )(x )
       3   2   0      4   3   0

o6 : Expression of class Sum

Ways to use permutePolynomial:

permutePolynomial(List,Minus)
permutePolynomial(List,Power)
permutePolynomial(List,Product)
permutePolynomial(List,RingElement)
permutePolynomial(List,Sum)
permutePolynomial(List,Holder) (missing documentation)
permutePolynomial(List,Number) (missing documentation)

For the programmer

The object permutePolynomial is a method function.