def solve(problems):
"""
Runs the Littlewood-Richardson homotopies on the problems.
"""
from phcpy.schubert import littlewood_richardson_homotopies as lrhom
(k, n) = (4, 8) # in G(4,8)
for (brackets, count) in problems:
print(brackets, '=', count)
(rc, flags, pols, sols) = lrhom(n, k, brackets)
assert(len(sols) == count)
def test_basic(prc='d'):
"""
Performs a basic test on the Littlewood-Richardson homotopies.
"""
from phcpy.schubert import littlewood_richardson_homotopies as lrhom
brk = [[2, 4, 6], [2, 4, 6], [2, 4, 6]]
print('basic test with brackets', brk)
(roco, flags, fsys, sols) = lrhom(6, 3, brk, precision=prc)
print('the root count :', roco)
print('the flags :', flags)
print('the solutions :')
for sol in sols:
print(sol)
verify(fsys, sols)
print('number of solutions :', len(sols))
def test_basic(prc='d'):
"""
Performs a basic test on the Littlewood-Richardson homotopies.
"""
from phcpy.schubert import littlewood_richardson_homotopies as lrhom
brk = [[2, 4, 6], [2, 4, 6], [2, 4, 6]]
print('basic test with brackets', brk)
(roco, flags, fsys, sols) = lrhom(6, 3, brk, precision=prc)
print('the root count :', roco)
print('the flags :', flags)
print('the solutions :')
for sol in sols:
print(sol)
verify(fsys, sols)
print('number of solutions :', len(sols))
def test_p1(prc='d'):
"""
First big problem in G(4,8).
"""
from phcpy.schubert import littlewood_richardson_homotopies as lrhom
brk = [[3, 6, 7, 8], [3, 6, 7, 8], [3, 6, 7, 8], [3, 6, 7, 8], \
[3, 6, 7, 8], [3, 6, 7, 8], [3, 6, 7, 8], [4, 6, 7, 8], \
[4, 6, 7, 8]]
print('basic test with brackets', brk)
(roco, flags, fsys, sols) = lrhom(8, 4, brk, precision=prc)
print('the root count :', roco)
print('the flags :', flags)
print('the solutions :')
for sol in sols:
print(sol)
verify(fsys, sols)
print('number of solutions :', len(sols))
def test_p1(prc='d'):
"""
First big problem in G(4,8).
"""
from phcpy.schubert import littlewood_richardson_homotopies as lrhom
brk = [[3, 6, 7, 8], [3, 6, 7, 8], [3, 6, 7, 8], [3, 6, 7, 8], \
[3, 6, 7, 8], [3, 6, 7, 8], [3, 6, 7, 8], [4, 6, 7, 8], \
[4, 6, 7, 8]]
print('basic test with brackets', brk)
(roco, flags, fsys, sols) = lrhom(8, 4, brk, precision=prc)
print('the root count :', roco)
print('the flags :', flags)
print('the solutions :')
for sol in sols:
print(sol)
verify(fsys, sols)
print('number of solutions :', len(sols))
