eliminatingDual -- eliminating dual space of a polynomial ideal

Synopsis

Usage:

S = eliminatingDual(p, I, v, d)
Inputs:
- p, a point,
- 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 tolerance
Outputs:
- S, an instance of the type DualSpace,

Description

Given a list of variable indices, this method computes 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

Caveat

The space of dual elements satisfying the conditions is not in general of finite dimension. If the dimension is infinite, this function will not terminate. This is not checked. To ensure termination, the local dimension of I at p should not exceed the length of v, and certain genericity constraints on the coordinates must be met.

Ways to use eliminatingDual :

eliminatingDual(AbstractPoint,Ideal,List,ZZ)
eliminatingDual(AbstractPoint,Matrix,List,ZZ)

For the programmer

The object eliminatingDual is a method function with options.