next | previous | forward | backward | up | index | toc

# gfanSubstitute -- rename the variables of a list of polynomials

## Synopsis

• Usage:
gfanSubstitute(M,R)
gfanSusbtitute(L,R)
gfanSubstitute(I,R)
• Inputs:
• M, , of polynomials
• L, a list, of polynomials
• I, an ideal,
• R, , with the same number of variables as the ring of the polynomials in M, L and I.
• Outputs:
• L, a list, of polynomials from L with variables replaced by those in R

## Description

This method replaces each variable in a marked polynomial list with variables from a different ring.

 i1 : R = QQ[z,a,b]; i2 : S = QQ[x,y,z]; i3 : L = markedPolynomialList{{x*y, z^2} , {x*y+ z^2, x*y + z^2}} 2 2 o3 = {(x*y) + z , (z ) + x*y} o3 : MarkedPolynomialList i4 : gfanSubstitute(L, R) 2 2 o4 = {(z*a) + b , (b ) + z*a} o4 : MarkedPolynomialList

Caution should be used as this method invokes use R which changes the global symbol table. It would be preferable to use the map command which is built into Macaulay 2. A ring map can be applied directly to a marked polynomial list.

 i5 : f = map(R,S, {z,a,b}) o5 = map (R, S, {z, a, b}) o5 : RingMap R <--- S i6 : f L 2 2 o6 = {(z*a) + b , (b ) + z*a} o6 : MarkedPolynomialList

gfan Documentation This program changes the variable names of a polynomial ring. The input is a polynomial ring, a polynomial set in the ring and a new polynomial ring with the same coefficient field but different variable names. The output is the polynomial set written with the variable names of the second polynomial ring.Example:Input:Q[a,b,c,d]{2a-3b,c+d}Q[b,a,c,x]Output:Q[b,a,c,x]{2*b-3*a,c+x}Options:

## Ways to use gfanSubstitute :

• "gfanSubstitute(Ideal,PolynomialRing)"
• "gfanSubstitute(List,PolynomialRing)"
• "gfanSubstitute(MarkedPolynomialList,PolynomialRing)"

## For the programmer

The object gfanSubstitute is .