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Added 'algorithm' parameter to all groebner_basis() methods
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@25shriya
25shriya committed Sep 18, 2024
1 parent 91a757a commit 12c0d5f
Showing 1 changed file with 123 additions and 113 deletions.
236 changes: 123 additions & 113 deletions src/sage/matroids/chow_ring_ideal.py
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Original file line number Diff line number Diff line change
Expand Up @@ -202,7 +202,7 @@ def _repr_(self):
"""
return "Chow ring ideal of {}".format(self._matroid)

def groebner_basis(self):
def groebner_basis(self, algorithm='constructed'):
r"""
Returns the Groebner basis of the Chow ring ideal.
Return type - ``PolynomialSequence``.
Expand All @@ -228,66 +228,69 @@ def groebner_basis(self):
sage: ch.groebner_basis().is_groebner()
True
"""

flats = list(self._flats_generator)
gb = list()
R = self.ring()
if frozenset() in flats:
flats.remove(frozenset()) #Non-empty proper flats needed

ranks = {F:self._matroid.rank(F) for F in flats}

flats_gen = self._flats_generator
subsets = []
# Generate all subsets of flats using combinations
for r in range(len(flats) + 1): # r is the size of the subset
subsets.extend(list(subset) for subset in combinations(flats, r))

for subset in subsets:
flag = True
sorted_list = sorted(subset, key=len)
for i in range (len(sorted_list)): #Checking whether the subset is a chain
if (i != 0) & (len(sorted_list[i]) == len(sorted_list[i-1])):
flag = False
break

if flag is False:
term = R.one()
for x in subset:
term *= flats_gen[x]
gb.append(term)

else:
if subset == []:
for F in flats:
term = R.zero()
for G in flats:
if G >= F:
term += flats_gen[G]
gb.append((term)**(ranks[F]))

if algorithm == 'constructed':
flats = list(self._flats_generator)
gb = list()
R = self.ring()
if frozenset() in flats:
flats.remove(frozenset()) #Non-empty proper flats needed

ranks = {F:self._matroid.rank(F) for F in flats}

flats_gen = self._flats_generator
subsets = []
# Generate all subsets of flats using combinations
for r in range(len(flats) + 1): # r is the size of the subset
subsets.extend(list(subset) for subset in combinations(flats, r))

for subset in subsets:
flag = True
sorted_list = sorted(subset, key=len)
for i in range (len(sorted_list)): #Checking whether the subset is a chain
if (i != 0) & (len(sorted_list[i]) == len(sorted_list[i-1])):
flag = False
break

if flag is False:
term = R.one()
for x in subset:
term *= flats_gen[x]
gb.append(term)

else:
for j in range(len(subset)):
for k in range(j+1, len(subset)): #Checking if every element in the chain is maximal
if (sorted_list[j] != sorted_list[k]) & (sorted_list[j].issubset(sorted_list[k])):
flag = False
break

if flag is True:
if subset == []:
for F in flats:
if F > reduce(lambda a, b: a.union(b), sorted_list):
term = R.one()
for x in subset:
term *= flats_gen[x]
term1 = R.zero()
for G in flats:
if G >= F:
term1 += flats_gen[G]
if term1 != R.zero():
gb.append(term*(term1**(ranks[F] - ranks[sorted_list[len(subset) - 1]])))

g_basis = PolynomialSequence(R, [gb])
return g_basis
term = R.zero()
for G in flats:
if G >= F:
term += flats_gen[G]
gb.append((term)**(ranks[F]))

else:
for j in range(len(subset)):
for k in range(j+1, len(subset)): #Checking if every element in the chain is maximal
if (sorted_list[j] != sorted_list[k]) & (sorted_list[j].issubset(sorted_list[k])):
flag = False
break

if flag is True:
for F in flats:
if F > reduce(lambda a, b: a.union(b), sorted_list):
term = R.one()
for x in subset:
term *= flats_gen[x]
term1 = R.zero()
for G in flats:
if G >= F:
term1 += flats_gen[G]
if term1 != R.zero():
gb.append(term*(term1**(ranks[F] - ranks[sorted_list[len(subset) - 1]])))

g_basis = PolynomialSequence(R, [gb])
return g_basis

elif algorithm == 'generic':
super().groebner_basis()


class AugmentedChowRingIdeal_fy(ChowRingIdeal):
Expand Down Expand Up @@ -440,7 +443,7 @@ def _repr_(self):
"""
return "Augmented Chow ring ideal of {} of Feitchner-Yuzvinsky presentation".format(self._matroid)

def groebner_basis(self):
def groebner_basis(self, algorithm='constructed'):
r"""
Returns the Groebner basis of the augmented Chow ring ideal.
Return type - ``PolynomialSequence``.
Expand All @@ -455,38 +458,41 @@ def groebner_basis(self):
sage: ch.defining_ideal().basis_is_groebner()
True
"""
gb = []
E = list(self._matroid.groundset())
poly_ring = self.ring()
for F in self._flats:
for G in self._flats:
if not (F < G or G < F): #Non-nested flats
gb.append(self._flats_generator[F]*self._flats_generator[G])
for i in E:
term = poly_ring.zero()
term1 = poly_ring.zero()
for H in self._flats:
if i in H:
term += self._flats_generator[H]
if H > G:
term1 += self._flats_generator[H]
if term != poly_ring.zero():
gb.append(self._flats_generator[i] + term) #5.7
if term1 != poly_ring.zero():
gb.append(term1**(self._matroid.rank(G)) + 1) #5.6

if i in G: #if element in flat
if algorithm == 'constructed':
gb = []
E = list(self._matroid.groundset())
poly_ring = self.ring()
for F in self._flats:
for G in self._flats:
if not (F < G or G < F): #Non-nested flats
gb.append(self._flats_generator[F]*self._flats_generator[G])
for i in E:
term = poly_ring.zero()
term1 = poly_ring.zero()
for H in self._flats:
if i in H:
term += self._flats_generator[H]
if H > G:
term1 += self._flats_generator[H]
if term != poly_ring.zero():
gb.append(self._flats_generator[i] + term) #5.7
if term1 != poly_ring.zero():
gb.append(self._flats_generator[i]*((term1)**self._matroid.rank(G)))

elif not i in G: #if element not in flat
gb.append(self._flats_generator[i]*self._flats_generator[F])

elif G < F: #nested flats
gb.append(self._flats_generator[G]*term1**(self._matroid.rank(F)-self._matroid.rank(G)))

g_basis = PolynomialSequence(poly_ring, [gb])
return g_basis
gb.append(term1**(self._matroid.rank(G)) + 1) #5.6

if i in G: #if element in flat
if term1 != poly_ring.zero():
gb.append(self._flats_generator[i]*((term1)**self._matroid.rank(G)))

elif not i in G: #if element not in flat
gb.append(self._flats_generator[i]*self._flats_generator[F])

elif G < F: #nested flats
gb.append(self._flats_generator[G]*term1**(self._matroid.rank(F)-self._matroid.rank(G)))

g_basis = PolynomialSequence(poly_ring, [gb])
return g_basis
elif algorithm == 'generic':
super().groebner_basis()

class AugmentedChowRingIdeal_atom_free(ChowRingIdeal):
r"""
Expand Down Expand Up @@ -633,7 +639,7 @@ def _repr_(self):
"""
return "Augmented Chow ring ideal of {} of atom-free presentation".format(self._matroid)

def groebner_basis(self):
def groebner_basis(self, algorithm='constructed'):
"""
Returns the Groebner basis of the augmented Chow ring ideal.
Return type - ``PolynomialSequence``.
Expand All @@ -651,27 +657,31 @@ def groebner_basis(self):
sage: ch.defining_ideal().basis_is_groebner()
True
"""
gb = []
flats = [X for i in range(1, self._matroid.rank())
for X in self._matroid.flats(i)]
poly_ring = self.ring()
if frozenset() in flats: #Non empty proper flats
flats.remove(frozenset())
for F in flats:
for G in flats:
if not (F > G or G > F): #Non nested flats
gb.append(self._flats_generator[F]*self._flats_generator[G])
elif F < G: #Nested flats
term = poly_ring.zero()
for H in flats:
if H < F:
term += self._flats_generator[H]
if term != poly_ring.zero():
gb.append(self._flats_generator[F]*(term**self._matroid.rank(G))*
(term**(self._matroid.rank(G)-self._matroid.rank(F))))

g_basis = PolynomialSequence(poly_ring, [gb])
return g_basis
if algorithm == 'constructed':
gb = []
flats = [X for i in range(1, self._matroid.rank())
for X in self._matroid.flats(i)]
poly_ring = self.ring()
if frozenset() in flats: #Non empty proper flats
flats.remove(frozenset())
for F in flats:
for G in flats:
if not (F > G or G > F): #Non nested flats
gb.append(self._flats_generator[F]*self._flats_generator[G])
elif F < G: #Nested flats
term = poly_ring.zero()
for H in flats:
if H < F:
term += self._flats_generator[H]
if term != poly_ring.zero():
gb.append(self._flats_generator[F]*(term**self._matroid.rank(G))*
(term**(self._matroid.rank(G)-self._matroid.rank(F))))

g_basis = PolynomialSequence(poly_ring, [gb])
return g_basis

elif algorithm == 'generic':
super().groebner_basis()



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