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 symbol, 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 a method function with options.