hyp -- hyp function of an ideal

Synopsis

Usage:

hyp(d,r,I)
Inputs:
- d, an integer,
- r, an integer,
- I, an ideal,
Outputs:
- an integer,

Description

Returns the value of the hyp function (HypF) of the ideal I on the parameters d and r. The HypF computes the maximum degree of the ideals generated by r-tuples of polynomials of degree at most d that are linearly independent modulo the ideal I. Finding upper bounds for this functions is equivalent to finding lower bounds for the generalized minimum distance function genMinDisIdeal. More information about the Hyp can be found in Definition 1.2 at https://arxiv.org/pdf/1812.06529v1.pdf.

i1 : K=ZZ/3;

i2 : R=K[t1,t2,t3,t4,t5,t6];

i3 : I=ideal(t1*t6-t3*t4,t2*t6-t3*t5);

o3 : Ideal of R

i4 : hyp(1,1,I)

o4 = 1

Ways to use hyp :

hyp(ZZ,ZZ,Ideal)

For the programmer

The object hyp is a method function.