Shapiro and Shapiro: Hypersurface Schubert conditions

Outdated Archival Version

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Maple Scripts

The data m,p in the table above are each linked to a Maple script whose comments have a record of all computations archived.

m,p	5,2	3,3	6,2
d_m,p	42	42	132
Number checked	1000	550	55

Each of these scripts generate files that can be run to test instances of Conjecture 1. The Maple scripts generate a Singular file which contains many instances of Conjecture 1 for that m,p as polynomial systems. The values of s₁,s₂,...,s_mp for each of these instances are generated in the maple script. When the Singular script is run (It must be edited first!), it generates a Maple script containg eliminants of the systems for each instance, computed by a 2-step process, first computing a degree reverse lexicographic Gröbner basis, and then with the FGLM conversion algorithm to compute the eliminant. When this new Maple script is run (edit it first!), it checks that all zeroes of the eliminant are real. If not, it prints an error message.

We use local coordinates which reduce the number of parameters by 2. While this complicates the first degree reverse lexicographic Gröbner basis (Strange, that fewer variables slow the computation!), it greatly expediates the computation of the eliminant.