# 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
• prod, , a Product expression
• s, , a sum expression
• pow, , a power expression
• minu, , a minus expression
• perm, a permutation
• Outputs:
• , the result of applying perm to f
• , 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)"

## For the programmer

The object permutePolynomial is .