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Apr 2, 2025
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typing annotation in Chow ring ideal #39799

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70 changes: 36 additions & 34 deletions src/sage/matroids/chow_ring_ideal.py
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Original file line number Diff line number Diff line change
Expand Up @@ -15,12 +15,13 @@
# https://www.gnu.org/licenses/
# ****************************************************************************

from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
from itertools import product

from sage.combinat.posets.posets import Poset
from sage.matroids.utilities import cmp_elements_key
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
from sage.rings.polynomial.multi_polynomial_sequence import PolynomialSequence
from sage.combinat.posets.posets import Poset
from itertools import product
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing


class ChowRingIdeal(MPolynomialIdeal):
Expand All @@ -37,7 +38,7 @@ def matroid(self):
"""
return self._matroid

def _lattice_flats(self):
def _lattice_flats(self) -> tuple:
r"""
Return the ranks and chains of lattice of flats of the matroid.

Expand Down Expand Up @@ -65,7 +66,7 @@ def _lattice_flats(self):
chains = lattice_flats.chains() # Only chains
return (ranks, chains)

def flats_to_generator_dict(self):
def flats_to_generator_dict(self) -> dict:
r"""
Return the corresponding generators of flats/groundset elements of
Chow ring ideal.
Expand Down Expand Up @@ -146,7 +147,7 @@ class ChowRingIdeal_nonaug(ChowRingIdeal):
Chow ring ideal of Fano: Binary matroid of rank 3 on 7 elements,
type (3, 0) - non augmented
"""
def __init__(self, M, R):
def __init__(self, M, R) -> None:
r"""
Initialize ``self``.

Expand All @@ -167,7 +168,7 @@ def __init__(self, M, R):
self._flats_generator = dict(zip(flats, gens))
MPolynomialIdeal.__init__(self, poly_ring, self._gens_constructor(poly_ring))

def _gens_constructor(self, poly_ring):
def _gens_constructor(self, poly_ring) -> list:
r"""
Return the generators of ``self``.

Expand Down Expand Up @@ -215,7 +216,7 @@ def _gens_constructor(self, poly_ring):
J = list(atoms_gen.values()) # Linear generators
return I + J

def _repr_(self):
def _repr_(self) -> str:
r"""
Return a string representation of ``self``.

Expand All @@ -228,7 +229,7 @@ def _repr_(self):
"""
return "Chow ring ideal of {} - non augmented".format(self._matroid)

def _latex_(self):
def _latex_(self) -> str:
r"""
Return a LaTeX representation of ``self``.

Expand Down Expand Up @@ -289,7 +290,7 @@ def groebner_basis(self, algorithm='', *args, **kwargs):
term += flats_gen[G]
for G in lattice_flats.order_ideal([F]):
if G != F:
gb.append(flats_gen[G]*(term) ** (ranks[F] - ranks[G]))
gb.append(flats_gen[G] * (term) ** (ranks[F] - ranks[G]))

gb.append(term ** ranks[F])

Expand Down Expand Up @@ -420,7 +421,7 @@ class AugmentedChowRingIdeal_fy(ChowRingIdeal):
Augmented Chow ring ideal of Wheel(3): Regular matroid of rank 3 on 6
elements with 16 bases of Feitchner-Yuzvinsky presentation
"""
def __init__(self, M, R):
def __init__(self, M, R) -> None:
r"""
Initialize ``self``.

Expand Down Expand Up @@ -450,7 +451,7 @@ def __init__(self, M, R):
self._flats_containing[x].append(F)
MPolynomialIdeal.__init__(self, poly_ring, self._gens_constructor(poly_ring))

def _gens_constructor(self, poly_ring):
def _gens_constructor(self, poly_ring) -> list:
r"""
Return the generators of ``self``.

Expand Down Expand Up @@ -488,12 +489,13 @@ def _gens_constructor(self, poly_ring):
A4*B, A3*B, A2*B, A1*B, A0*B]
"""
E = list(self._matroid.groundset())
Q = []
L = []
lattice_flats = Poset((self._flats, lambda x, y: x <= y))
antichains = lattice_flats.antichains().elements_of_depth_iterator(2)
for F, G in antichains:
Q.append(self._flats_generator[F] * self._flats_generator[G]) # Quadratic generators

# Quadratic generators
Q = [self._flats_generator[F] * self._flats_generator[G]
for F, G in antichains]

for x in E:
term = poly_ring.zero()
Expand All @@ -508,7 +510,7 @@ def _gens_constructor(self, poly_ring):
L.append(term1)
return Q + L

def _repr_(self):
def _repr_(self) -> str:
r"""
EXAMPLES::

Expand All @@ -519,7 +521,7 @@ def _repr_(self):
"""
return "Augmented Chow ring ideal of {} of Feitchner-Yuzvinsky presentation".format(self._matroid)

def _latex_(self):
def _latex_(self) -> str:
r"""
Return a LaTeX representation of ``self``.

Expand Down Expand Up @@ -554,11 +556,12 @@ def groebner_basis(self, algorithm='', *args, **kwargs):
gb = [] # reduced groebner basis with two eliminated cases
E = list(self._matroid.groundset())
poly_ring = self.ring()
reln = lambda x,y: x <= y
lattice_flats = Poset((self._flats, reln))

lattice_flats = Poset((self._flats, lambda x, y: x <= y))
antichains = lattice_flats.antichains().elements_of_depth_iterator(2)
for F, G in antichains:
gb.append(self._flats_generator[F] * self._flats_generator[G]) # non-nested flats
# non-nested flats
gb.append(self._flats_generator[F] * self._flats_generator[G])
for i in E:
term = poly_ring.zero()
for H in self._flats_containing[i]:
Expand All @@ -575,7 +578,7 @@ def groebner_basis(self, algorithm='', *args, **kwargs):
order_ideal_modified = lattice_flats.order_ideal([F])
order_ideal_modified.remove(F)
for G in order_ideal_modified: # nested flats
gb.append(self._flats_generator[G]*term1**(self._matroid.rank(F) - self._matroid.rank(G)))
gb.append(self._flats_generator[G] * term1**(self._matroid.rank(F) - self._matroid.rank(G)))

return PolynomialSequence(poly_ring, [gb])

Expand Down Expand Up @@ -611,10 +614,9 @@ def normal_basis(self, algorithm='', *args, **kwargs):
monomial_basis.append(R.one())
else:
k = len(subset)
max_powers = []
max_powers.append(ranks[subset[0]])
for i in range(1, k):
max_powers.append(ranks[subset[i]] - ranks[subset[i-1]])
max_powers = [ranks[subset[0]]]
max_powers.extend(ranks[subset[i]] - ranks[subset[i - 1]]
for i in range(1, k))
ranges = [range(1, p) for p in max_powers]
ranges[0] = range(1, max_powers[0] + 1)
for combination in product(*(r for r in ranges)):
Expand Down Expand Up @@ -674,7 +676,7 @@ class AugmentedChowRingIdeal_atom_free(ChowRingIdeal):
Augmented Chow ring ideal of Wheel(3): Regular matroid of rank 3 on 6
elements with 16 bases in the atom-free presentation
"""
def __init__(self, M, R):
def __init__(self, M, R) -> None:
r"""
Initialize ``self``.

Expand All @@ -695,7 +697,7 @@ def __init__(self, M, R):
self._flats_generator = dict(zip(self._flats, gens))
MPolynomialIdeal.__init__(self, poly_ring, self._gens_constructor(poly_ring))

def _gens_constructor(self, poly_ring):
def _gens_constructor(self, poly_ring) -> list:
r"""
Return the generators of ``self``.

Expand All @@ -714,8 +716,7 @@ def _gens_constructor(self, poly_ring):
for F in self._flats:
for x in F:
flats_containing[x].append(F)
reln = lambda x,y: x <= y
lattice_flats = Poset((self._flats, reln))
lattice_flats = Poset((self._flats, lambda x, y: x <= y))
antichains = lattice_flats.antichains().elements_of_depth_iterator(2)
for F, G in antichains:
Q.append(self._flats_generator[F] * self._flats_generator[G])
Expand All @@ -727,11 +728,12 @@ def _gens_constructor(self, poly_ring):
if term**2 not in Q:
Q.append(term**2)

if F not in flats_containing[x]: # generators for every set of flats not containing element
Q.append(self._flats_generator[F]*term)
if F not in flats_containing[x]:
# generators for every set of flats not containing element
Q.append(self._flats_generator[F] * term)
return Q

def _repr_(self):
def _repr_(self) -> str:
r"""
EXAMPLES::

Expand All @@ -742,7 +744,7 @@ def _repr_(self):
"""
return "Augmented Chow ring ideal of {} in the atom-free presentation".format(self._matroid)

def _latex_(self):
def _latex_(self) -> str:
r"""
Return the LaTeX output of the ring and generators of ``self``.

Expand Down
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