Skip to content

Commit

Permalink
some suggestions done
Browse files Browse the repository at this point in the history
  • Loading branch information
@fchapoton
fchapoton committed Nov 11, 2024
1 parent e5f20fd commit 582bc6d
Show file tree
Hide file tree
Showing 2 changed files with 48 additions and 23 deletions.
6 changes: 5 additions & 1 deletion src/doc/en/reference/references/index.rst
View file
Original file line number Diff line number Diff line change
Expand Up @@ -3207,6 +3207,10 @@ REFERENCES:
The Electronic Journal of Combinatorics 11 (2004), #R77.
http://www.combinatorics.org/Volume_11/PDF/v11i1r77.pdf
.. [HaHo2017] Nate Harman and Sam Hopkins,
*Quantum integer-valued polynomials*,
J. Alg. Comb. 2017, :doi:`10.1007/s10801-016-0717-3`
.. [Hai1989] M.D. Haiman, *On mixed insertion, symmetry, and shifted
Young tableaux*. Journal of Combinatorial Theory, Series
A Volume 50, Number 2 (1989), pp. 196-225.
Expand All @@ -3220,7 +3224,7 @@ REFERENCES:
http://www-math.mit.edu/~hajiagha/pp11.ps
.. [Han1960] Haim Hanani,
On quadruple systems,
*On quadruple systems*,
pages 145--157, vol. 12,
Canadian Journal of Mathematics,
1960
Expand Down
65 changes: 43 additions & 22 deletions src/sage/rings/polynomial/q_integer_valued_polynomials.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -4,19 +4,16 @@
AUTHORS:
- Frédéric Chapoton (2024-03): Initial version
REFERENCES:
.. [HaHo2017] Nate Harman and Sam Hopkins, *Quantum integer-valued
polynomials*, J. Alg. Comb. 2017, :doi:`10.1007/s10801-016-0717-3`
"""
# ***************************************************************************
# ****************************************************************************
# Copyright (C) 2024 Frédéric Chapoton <chapoton-math-unistra-fr>
#
# Distributed under the terms of the GNU General Public License (GPL)
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
# https://www.gnu.org/licenses/
# ***************************************************************************
# ****************************************************************************
from sage.arith.misc import binomial
from sage.categories.algebras import Algebras
from sage.categories.realizations import Category_realization_of_parent
Expand Down Expand Up @@ -159,6 +156,7 @@ def __init__(self, R) -> None:
raise TypeError(msg)
laurent = LaurentPolynomialRing(R, 'q')
self._ground_ring = R
self._q = laurent.gen()
cat = Algebras(laurent).Commutative().WithBasis()
Parent.__init__(self, base=laurent, category=cat.WithRealizations())

Expand Down Expand Up @@ -262,6 +260,18 @@ def one_basis(self):
"""
return self.basis().keys()(0)

def q(self):
"""
Return the variable `q`.
EXAMPLES::
sage: A = QuantumValuedPolynomialRing(QQ).S()
sage: A.q()
q
"""
return self.realization_of()._q

def degree_on_basis(self, m):
r"""
Return the degree of the basis element indexed by ``m``.
Expand Down Expand Up @@ -299,6 +309,16 @@ def from_polynomial(self, p):
B[1]
sage: A.from_polynomial((B[2]+2*B[3]).polynomial())
B[2] + 2*B[3]
TESTS::
sage: A = QuantumValuedPolynomialRing(QQ).B()
sage: q = polygen(QQ,'q')
sage: x = polygen(q.parent(),'x')
sage: A.from_polynomial(x**2/(q+1)+1)
Traceback (most recent call last):
...
ValueError: not a polynomial with integer values : 1/(q + 1) is not a Laurent polynomial
"""
B = self.basis()
poly = self._poly
Expand Down Expand Up @@ -511,7 +531,7 @@ def product_on_basis(self, n1, n2):
j = ZZ(n2)
if j < i:
j, i = i, j
q = self.base_ring().gen()
q = self.q()
return self._from_dict({i + j - k: (-1)**k
* q_binomial(i, k)
* q_binomial(i + j - k, i)
Expand Down Expand Up @@ -539,7 +559,7 @@ def _from_binomial_basis(self, i):
"""
i = ZZ(i)
R = self.base_ring()
q = self.base_ring().gen()
q = self.q()
return self._from_dict({k: R((-1)**(i - k) * q_binomial(i, k))
* q**(-i**2 + binomial(i - k, 2))
for k in range(i + 1)})
Expand All @@ -563,11 +583,13 @@ def from_h_vector(self, hv):
"""
B = self.basis()
ring = self.base_ring()
q = ring.gen()
q = self.q()
d = len(hv) - 1
m = matrix(ring, d + 1, d + 1,
lambda j, i: (-1)**(d - j) * q_binomial(d - i, d - j, q) *
q**(-d * (d - i) + binomial(d - j, 2)))
[(-1)**(d - j) * q_binomial(d - i, d - j, q) *
q**(-d * (d - i) + binomial(d - j, 2))
for j in range(d + 1)
for i in range(d + 1)])
v = vector(ring, [hv[i] for i in range(d + 1)])
return sum(ring(c) * B[i] for i, c in enumerate(m * v))

Expand Down Expand Up @@ -599,7 +621,7 @@ def _element_constructor_(self, x):
R = self.base_ring()
# coercion via base ring
x = R(x)
if x == 0:
if not x:
return self.element_class(self, {})
return self.from_base_ring_from_one_basis(x)

Expand Down Expand Up @@ -717,7 +739,6 @@ def _poly(self, i):
return q_binomial_x(i, i)

class Element(CombinatorialFreeModule.Element):

def umbra(self):
"""
Return the Bernoulli umbra.
Expand Down Expand Up @@ -776,7 +797,7 @@ def variable_shift(self, k=1):
return self

A = self.parent()
q = A.base_ring().gen()
q = A.q()

def on_basis(n):
return {A._indices(j): q**(k * j)
Expand Down Expand Up @@ -827,7 +848,7 @@ def h_vector(self):
"""
d = max(self.support())
ring = self.parent().base_ring()
q = ring.gen()
q = self.parent().q()

def fn(j, i):
return ((-1)**(d - j) *
Expand Down Expand Up @@ -951,7 +972,7 @@ def product_on_basis(self, n1, n2):
if j < i:
j, i = i, j

q = self.base_ring().gen()
q = self.q()
return self._from_dict({i + j - k:
q_binomial(i, k)
* q_binomial(i + j - k, i)
Expand All @@ -978,7 +999,7 @@ def _from_shifted_basis(self, i):
"""
i = ZZ(i)
R = self.base_ring()
q = self.base_ring().gen()
q = self.q()
return self._from_dict({k: R(q_binomial(i, k))
* q**(k**2)
for k in range(i + 1)})
Expand Down Expand Up @@ -1007,7 +1028,7 @@ def _element_constructor_(self, x):
R = self.base_ring()
# coercion via base ring
x = R(x)
if x == 0:
if not x:
return self.element_class(self, {})
return self.from_base_ring_from_one_basis(x)

Expand Down Expand Up @@ -1155,7 +1176,7 @@ def variable_shift(self, k=1):
return self

A = self.parent()
q = A.base_ring().gen()
q = A.q()

def on_basis(n):
return {A._indices(j): q**((k + j - n) * j)
Expand Down

0 comments on commit 582bc6d

Please sign in to comment.