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footPrint -- generalized footprint function of an ideal

Description

Returns the value of the generalized footprint function of the ideal I on the parameters d and r. Given an ideal I, a monomial is called standard of I if it is not a leading monomial of any polynomial of I. The parameters d and r are used as follows. The function computes the degree of the ideal generated by sets of r standard monomials of degree at most d. The footprint function is a lower bound of the generalized minimum function genMinDisIdeal. More information about the footprint function can be found in Definition 1.3 at https://arxiv.org/pdf/1812.06529v1.pdf

i1 : K=QQ;
i2 : R=K[t1,t2,t3];
i3 : I=ideal(t1^3,t2*t3);

o3 : Ideal of R
i4 : footPrint(2,3,I)

o4 = 4

Ways to use footPrint:

  • footPrint(ZZ,ZZ,Ideal)

For the programmer

The object footPrint is a method function.


The source of this document is in CodingTheory.m2:3847:0.