The table below shows the results of computing
160,000 instances of the intersection (5.11), recording the number having
a given number of real points, and sorting this by the simple Schubert data.
The data is a sequence of 4 2's and 4 3's, up to reversal and cyclic
permutations, there are 8 such sequences.
Observe that the apparent lower bound on the number of real solutions depends
on the sequence, which is a measure of the configuration of the conditions.
This reinforces the observation
made in Section 3.i concerning the subtle
dependence of the number of real solutions on the configuration of the
conditions.
Other calculations we have done reinforce this observation.
Data | Number of Real Solutions | ||||||
0 | 2 | 4 | 6 | 8 | 10 | 12 | |
22223333 | 0 | 0 | 0 | 0 | 0 | 0 | 20000 |
22332233 | 0 | 0 | 136 | 1533 | 7045 | 5261 | 6025 |
22233233 | 0 | 0 | 67 | 3015 | 6683 | 4822 | 5413 |
22322333 | 0 | 0 | 9 | 1677 | 3835 | 6247 | 8232 |
22323323 | 0 | 0 | 303 | 2090 | 6014 | 7690 | 3903 |
22232333 | 0 | 195 | 1476 | 1776 | 3628 | 4546 | 8379 |
22323233 | 0 | 37 | 1944 | 4367 | 6160 | 4634 | 2858 |
23232323 | 251 | 929 | 5740 | 3168 | 5420 | 2828 | 1662 |