canonicalForm -- computes the canonical form of a neural ideal

Usage:

canonicalForm(I) or canonicalForm(C)
Inputs:
- I, a squarefree pseudomonomial ideal, or C, a NeuralCode
Outputs:
- a List of pseudomonomials in ring(I) (resp. ring(C))

Description

Optional Inputs =>SharedIndex => ...,default value true, when true uses the shared index method of Geller and R.G. to compute the canonical form instead of the primary decomposition method of Curto, Itskov, et alIterative => ...,default value true, when true computes the canonical form of a neural code using the iterative method of Petersen, Youngs, et al instead of computing the neural ideal and then its canonical formComputes the canonical form of a neural ideal or a neural code, with several options for how to compute it.

i1 : R=ZZ/2[x_1..x_3];

i2 : I=ideal(x_1*x_3,x_2*(1-x_1));

o2 : Ideal of R

i3 : canonicalForm(I)

o3 = {x x , x x  + x , x x }
       1 3   1 2    2   2 3

o3 : List

i4 : R=ZZ/2[x_1..x_3];

i5 : C=neuralCode({"000","001"});

i6 : canonicalForm(C)

o6 = {x , x }
       1   2

o6 : List

Ways to use canonicalForm:

canonicalForm(Ideal)
canonicalForm(NeuralCode)

For the programmer

The object canonicalForm is a method function with options.

The source of this document is in NeuralIdeals.m2:792:0.