Computational evidence

3.vi. Computational evidence

The table below shows the number of different instances of Conjecture 2 that have been checked by Sottile as of 1 January 1999. The notation here is the same as the previous page: Given a Schubert condition a, and a positive integer j, (a)^j means that a is repeated j times, and
J_i = 1, 2, ..., p-1, p+i, .
The Schubert condition J_i is a Pieri-type condition, it is the condition that a general p-plane H meet a fixed m+1-i-plane nontrivially.

The links in the table are to to documented Maple V.5 scripts that were used to test these cases. These scripts, when run, create a Singular-1.2.1 script (which may need to be slightly edited) containing the resulting polynomial systems. Running that script will generate a Maple script which will check the eliminants for real roots and print a message with the input data if the eliminant has fewer real roots than expected.

General Schubert data tested:

Schubert data   (J₂)⁵ (J₂)⁶ (J₂)⁷   (J₃)⁵ (J₂)⁶ (135)⁵ (135)²,(J₁)⁶
m,p     5,2 6,2 7,2     5,3    4,3     5,3        6,3
d       6   15   36       6    16      32         61
Number checked 10,000 2821 504 10,160 2002     400        294

Schubert data	(J₂)⁵	(J₂)⁶	(J₂)⁷	(J₃)⁵	(J₂)⁶	(135)⁵	(135)²,(J₁)⁶
m,p	5,2	6,2	7,2	5,3	4,3	5,3	6,3
d	6	15	36	6	16	32	61
Number checked	10,000	2821	504	10,160	2002	400	294