Computational evidence

2.vii. Computational evidence

The purpose of this document is to present considerable detail about computations in support of the conjectures of Shapiro and Shapiro. The table below gives the number of instances of Conjecture 1 that are known to have been tested, as of 1 January 1999.

An instance means a given m,p and a single choice of real parameters, s₁, s₂, ..., s_mp. This gives a specific polynomial system of Conjecture 1, which may then be checked to see if it has only real solutions. Those instances checked by Sottile are archived here. They were done on several different computers. The data m,p in the table above are each linked to a description of the computations.

Instances checked:

m,p 4,2 5,2 3,3 6,2 7,2 4,3 8,2
d_m,p 14 42 42 132 429 462 1430
Number checked >12000 1000 550 55 3 2 1