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restart
--path = {"./M2-NSC/M2/Macaulay2/packages"} | path
---------- This had a problem with Keywords
path = {"/Users/sottile/papers/completed/LR/NoKey/packages"} | path
-- This file studies the effect on the performance (or not) of changing
-- the order of the Schubert conditions in a Schubert problem.
-- It involves the Schubert problem 1^2*2^2*3^2 = 10 on G(2,8)
-- Executive summary: It is problematic
recursionLimit=10000
needsPackage "NumericalSchubertCalculus";
setVerboseLevel 0
setRandomSeed 0
-- Consider this ordering of the conditions:
setRandomSeed 0
SchPblm = {
({3}, id_(CC^8)),
({3}, random(CC^8,CC^8)),
({2}, random(CC^8,CC^8)),
({2}, random(CC^8,CC^8)),
({1}, random(CC^8,CC^8)),
({1}, random(CC^8,CC^8))
};
time S = solveSchubertProblem(SchPblm, 2,8);
print(#S)
-- This other order works, as do most with {3} among the first two conditions
--
setRandomSeed 0
SchPblm = {
({3}, id_(CC^8)),
({2}, random(CC^8,CC^8)),
({2}, random(CC^8,CC^8)),
({3}, random(CC^8,CC^8)),
({1}, random(CC^8,CC^8)),
({1}, random(CC^8,CC^8))
};
time S = solveSchubertProblem(SchPblm, 2,8);
print(#S)
--v
-- This one also works, too (but look below)
--
setRandomSeed 0
SchPblm = {
({2}, id_(CC^8)),
({2}, random(CC^8,CC^8)),
({1}, random(CC^8,CC^8)),
({1}, random(CC^8,CC^8)),
({3}, random(CC^8,CC^8)),
({3}, random(CC^8,CC^8))
};
time S = solveSchubertProblem(SchPblm, 2,8);
print(#S)
--
----- The same problem, but with the conditions in the other order does not run very well
setRandomSeed 0 -- ,3,4,5,6,7,8,9,12,13 stdio:25:10:(3): error: assertion failed
setRandomSeed 1 -- ,2,10,11 stdio:15:10:(3): error: zgesvd did not converge
setRandomSeed 13
SchPblm = {
({1}, id_(CC^8)),
({1}, random(CC^8,CC^8)),
({2}, random(CC^8,CC^8)),
({2}, random(CC^8,CC^8)),
({3}, random(CC^8,CC^8)),
({3}, random(CC^8,CC^8))
};
time S = solveSchubertProblem(SchPblm, 2,8);
print(#S)
--
-- This also does not work
--
-- setRandomSeed 0,1,2,3 error: a solution does not fit the expected pattern (numerical error occurred)
setRandomSeed 3
SchPblm = {
({2}, id_(CC^8)),
({2}, random(CC^8,CC^8)),
({3}, random(CC^8,CC^8)),
({3}, random(CC^8,CC^8)),
({1}, random(CC^8,CC^8)),
({1}, random(CC^8,CC^8))
};
time S = solveSchubertProblem(SchPblm, 2,8);
print(#S)
--
-- As shown above swapping the order of the last four, from 3311 to 1133 makes it work
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