# eliminatingDual -- eliminating dual space of a polynomial ideal

## Synopsis

• Usage:
S = eliminatingDual(p, I, v, d)
• Inputs:
• p,
• I, an ideal, or a one-row Matrix of generators
• v, a list, a list of the integers designating which variables to bound
• d, an integer, the degree bound for the designated variables
• Optional inputs:
• Tolerance => ..., default value null, optional argument for numerical tolernace
• Outputs:

## Description

Given a list of variable indices, compute the a basis for all dual elements orthogonal to I which have total degree in the variables on the list bounded by d.

 i1 : R = CC[x,y]; i2 : I = ideal{x^2-y^3} 3 2 o2 = ideal(- y + x ) o2 : Ideal of R i3 : eliminatingDual(origin R, I, {0}, 2) o3 = | y5+x2y2 y4+x2y y3+x2 xy2 xy x y2 y 1 | o3 : DualSpace

This function generalizes truncatedDual in that if v includes all the variables in the ring, then its behavior is the same.

 i4 : eliminatingDual(origin R, I, {0,1}, 2) o4 = | xy y2 x y 1 | o4 : DualSpace