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test_script.py
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from sage.all import *
import zonotopal_algebra.poly_utils as poly_utils
from zonotopal_algebra import ZonotopalAlgebra
def main():
check_internal_D_space(p401_cols, "xy")
simple_cols = [
[1, 0],
[0, 1],
[1, 1]
]
A2_root_system_cols = [
[1, -1, 0],
[1, 0, -1],
[0, 1, -1]
]
p401_cols = [
[1, 0],
[0, 1],
[1, 1],
[1, 0],
[0, 1]
]
A3_root_system_cols = [
[1, -1, 0, 0],
[1, 0, -1, 0],
[0, 1, -1, 0],
[1, 0, 0, -1],
[0, 1, 0, -1],
[0, 0, 1, -1]
]
external_A3_root_system_cols = [
[1, -1, 0, 0],
[1, 0, -1, 0],
[0, 1, -1, 0],
[1, 0, 0, -1],
[0, 1, 0, -1],
[0, 0, 1, -1],
[1, 0, 0, -1],
[0, 1, 0, -1],
[0, 0, 1, -1]
]
large_matroid_cols = [
[1, -1, 0, 0],
[1, 0, -1, 0],
[0, 1, -1, 0],
[1, 0, 0, -1],
[0, 1, 0, -1],
[0, 0, 1, -1],
[1, 1, 1, 1],
[1, 1, 1, 2],
[1, 1, 1, 1],
[2, 1, 3, -2],
[2, 1, 3, -2]
]
def check_central_D_space(cols, varNames):
X = Matrix(QQ, cols).transpose()
Z = ZonotopalAlgebra(X, variant="central", varNames=varNames)
print("Z =", Z)
print()
print("Central P-space basis:")
P_basis = Z.P_space_basis()
for B in P_basis:
print("%s: %s" % (tuple(B), P_basis[B].factor()))
print()
print("Central D-space basis:")
D_basis = Z.D_space_basis()
for B in D_basis:
print("%s: %s" % (tuple(B), D_basis[B].factor()))
print()
print("Central I-ideal generators:")
I_gens = Z.I_ideal_gens()
for p in I_gens:
print(p.factor())
print()
print("Central J-ideal generators:")
J_gens = Z.J_ideal_gens()
for p in J_gens:
print(p.factor())
print()
print("P-D duality check:")
for B1 in P_basis:
p = P_basis[B1]
for B2 in D_basis:
d = D_basis[B2]
print(poly_utils.diff_bilinear_form(p, d),)
print()
print()
print("D = ker(J) check:")
for d in D_basis.values():
for j in J_gens:
print( poly_utils.poly_deriv(j, d),)
print()
def check_internal_D_space(cols, varNames):
X = Matrix(QQ, cols).transpose()
Z1 = ZonotopalAlgebra(X, variant="central", varNames=varNames)
Z2 = ZonotopalAlgebra(X, variant="internal", varNames=varNames)
print("Z2 =", Z2)
print()
print("Internal P-space basis:")
P_basis = Z2.P_space_basis()
for B in P_basis:
print("%s: %s" % (tuple(B), P_basis[B].factor()))
print()
print("Internal D-space basis:")
# central_D_basis = Z1.D_space_basis()
# D_basis = {B: central_D_basis[B] for B in Z2._internal_bases()}
D_basis = Z2.D_space_basis()
for B in D_basis:
print("%s: %s" % (tuple(B), D_basis[B].factor()))
print()
print("Internal I-ideal generators:")
I_gens = Z2.I_ideal_gens()
for p in I_gens:
print(p.factor())
print()
print("Internal J-ideal generators:")
J_gens = Z2.J_ideal_gens()
for p in J_gens:
print(p.factor())
print()
print("P-D duality check:")
for B1 in P_basis:
p = P_basis[B1]
for B2 in D_basis:
d = D_basis[B2]
print(poly_utils.diff_bilinear_form(p, d),)
print()
print()
print("D = ker(J) check:")
for d in D_basis.values():
for j in J_gens:
print(poly_utils.poly_deriv(j, d),)
print()
def check_external_D_space(cols, varNames):
X = Matrix(QQ, cols).transpose()
Z = ZonotopalAlgebra(X, variant="external", varNames=varNames)
print("Z =", Z)
print()
print("External P-space basis:")
P_basis = Z.P_space_basis()
for B in P_basis:
print("%s: %s" % (tuple(B), P_basis[B].factor()))
print()
print("External D-space basis:")
D_basis = Z.D_space_basis()
for B in D_basis:
print("%s: %s" % (tuple(B), D_basis[B].factor()))
print()
print("External I-ideal generators:")
I_gens = Z.I_ideal_gens()
for p in I_gens:
print(p.factor())
print()
print("External J-ideal generators:")
J_gens = Z.J_ideal_gens()
for p in J_gens:
print(p.factor())
print()
print("P-D duality check:")
for B1 in P_basis:
p = P_basis[B1]
for B2 in D_basis:
d = D_basis[B2]
print(poly_utils.diff_bilinear_form(p, d),)
print()
print()
print("D = ker(J) check:")
for d in D_basis.values():
for j in J_gens:
print(poly_utils.poly_deriv(j, d),)
print
# def main():
# cols1 = [
# [1, -1, 0, 0],
# [1, 0, -1, 0],
# [0, 1, -1, 0],
# [1, 0, 0, -1],
# [0, 1, 0, -1],
# [0, 0, 1, -1]
# ]
# X1 = Matrix(QQ, cols1).transpose()
#
# Z1 = ZonotopalAlgebra(X1, variant="internal")
# P1 = Z1.polynomial_ring()
# x0, x1, x2, x3 = P1.gens()
# print("Z1 =", Z1)
# p = (x1 - 2*x2 + x3)
# print("Polynomial:", p)
# print("In P-space basis:", Z1.P_space()(p))
# cols2 = [
# [1, 0],
# [0, 1],
# [1, 1],
# [1, 0],
# [0, 1]
# ]
# cols3 = [
# [0, 0, 1],
# [0, 1, 0],
# [1, 0, 1],
# [1, 0, 0],
# [1, 1, 0]
# ]
# X3 = Matrix(QQ, cols3).transpose()
#
# Z3 = ZonotopalAlgebra(X3, variant="internal")
# print("Z3 =", Z3)
# print("Internal bases:")
# print(list(Z3._internal_bases()))
# print("Hyperplanes")
# print(list(Z3._ordered_matroid().hyperplanes()))
# gens = Z3.I_ideal_gens()
# for g in gens:
# print factor(g)
if __name__ == "__main__":
main()