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Make the key polynomials know their degree #35115

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Mar 26, 2023
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Make the key polynomials know their degree #35115

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18 changes: 18 additions & 0 deletions src/sage/combinat/key_polynomial.py
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Original file line number Diff line number Diff line change
Expand Up @@ -29,6 +29,7 @@
# ****************************************************************************

from sage.categories.graded_algebras_with_basis import GradedAlgebrasWithBasis
from sage.misc.cachefunc import cached_method
from sage.combinat.integer_vector import IntegerVectors
from sage.combinat.free_module import CombinatorialFreeModule
from sage.combinat.permutation import Permutation
Expand Down Expand Up @@ -558,6 +559,7 @@ def __getitem__(self, c):
c = C(c)
return self._monomial(c)

@cached_method
def one_basis(self):
r"""
Return the basis element indexing the identity.
Expand All @@ -576,6 +578,22 @@ def one_basis(self):
return self._indices([0] * self._k)
return self._indices([])

def degree_on_basis(self, alpha):
"""
Return the degree of the basis element indexed by ``alpha``.

EXAMPLES::

sage: k = KeyPolynomials(QQ)
sage: k.degree_on_basis([2,1,0,2])
5

sage: k = KeyPolynomials(QQ, 5)
sage: k.degree_on_basis([2,1,0,2,0])
5
"""
return ZZ(sum(alpha))

def polynomial_ring(self):
r"""
Return the polynomial ring associated to ``self``.
Expand Down