# reorderPolynomialRing -- produces an isomorphic polynomial ring with a different, randomized, monomial order

## Synopsis

• Usage:
R1 = reorderPolynomialRing(orderType, R)
• Inputs:
• R, a ring, a polynomial ring
• orderType, , a valid monomial order, such as GRevLex
• Outputs:
• S, a ring, a polynomial ring with a new random monomial order

## Description

This function takes a polynomial ring and produces a new polynomial ring with MonomialOrder of type orderType. The order of the variables is randomized.

 i1 : R = QQ[x,y,z,w]; i2 : x > y and y > z and z > w o2 = true i3 : use reorderPolynomialRing(GRevLex, R) o3 = QQ[z, w..y] o3 : PolynomialRing i4 : x > y o4 = true i5 : y > z o5 = false i6 : z > w o6 = true

## Ways to use reorderPolynomialRing :

• "reorderPolynomialRing(Symbol,Ring)"

## For the programmer

The object reorderPolynomialRing is .