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minor details in doc and code of algebras/ #40325

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2 changes: 1 addition & 1 deletion src/sage/algebras/affine_nil_temperley_lieb.py
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Original file line number Diff line number Diff line change
Expand Up @@ -221,7 +221,7 @@ def has_no_braid_relation(self, w, i) -> bool:

sage: A = AffineNilTemperleyLiebTypeA(5)
sage: W = A.weyl_group()
sage: s=W.simple_reflections()
sage: s = W.simple_reflections()
sage: A.has_no_braid_relation(s[2]*s[1]*s[0]*s[4]*s[3],0)
False
sage: A.has_no_braid_relation(s[2]*s[1]*s[0]*s[4]*s[3],2)
Expand Down
39 changes: 18 additions & 21 deletions src/sage/algebras/free_algebra_element.py
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Original file line number Diff line number Diff line change
Expand Up @@ -18,8 +18,7 @@
sage: (x*y)^3
x*y*x*y*x*y
"""

#*****************************************************************************
# ***************************************************************************
# Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu>
#
# Distributed under the terms of the GNU General Public License (GPL)
Expand All @@ -31,8 +30,8 @@
# See the GNU General Public License for more details; the full text
# is available at:
#
# http://www.gnu.org/licenses/
#*****************************************************************************
# https://www.gnu.org/licenses/
# ***************************************************************************

from sage.misc.repr import repr_lincomb
from sage.monoids.free_monoid_element import FreeMonoidElement
Expand All @@ -56,7 +55,7 @@
sage: y * x < x * y
False
"""
def __init__(self, A, x):
def __init__(self, A, x) -> None:
"""
Create the element ``x`` of the FreeAlgebra ``A``.

Expand All @@ -68,7 +67,7 @@
"""
if isinstance(x, FreeAlgebraElement):
# We should have an input for when we know we don't need to
# convert the keys/values
# convert the keys/values
x = x._monomial_coefficients
R = A.base_ring()
if isinstance(x, AlgebraElement): # and x.parent() == A.base_ring():
Expand Down Expand Up @@ -131,7 +130,7 @@
7
sage: (2*x+y).subs({x:1,y:z})
2 + z
sage: f=x+3*y+z
sage: f = x+3*y+z
sage: f(1,2,1/2)
15/2
sage: f(1,2)
Expand All @@ -157,7 +156,8 @@
pass
return None

x = [extract_from(kwds,(p.gen(i),p.variable_name(i))) for i in range(p.ngens())]
x = [extract_from(kwds, (p.gen(i), p.variable_name(i)))

Check warning on line 159 in src/sage/algebras/free_algebra_element.py

View check run for this annotation

Codecov / codecov/patch

src/sage/algebras/free_algebra_element.py#L159 

Added line #L159 was not covered by tests
for i in range(p.ngens())]
elif isinstance(x[0], tuple):
x = x[0]

Expand All @@ -169,18 +169,19 @@
result = None
for m, c in self._monomial_coefficients.items():
if result is None:
result = c*m(x)
result = c * m(x)
else:
result += c*m(x)
result += c * m(x)

if result is None:
return self.parent().zero()
return result

def _mul_(self, y):
"""
Return the product of ``self`` and ``y`` (another free algebra
element with the same parent).
Return the product of ``self`` and ``y``.

This is another free algebra element with the same parent.

EXAMPLES::

Expand All @@ -192,16 +193,16 @@
z_elt = {}
for mx, cx in self:
for my, cy in y:
key = mx*my
key = mx * my
if key in z_elt:
z_elt[key] += cx*cy
z_elt[key] += cx * cy
else:
z_elt[key] = cx*cy
z_elt[key] = cx * cy
if not z_elt[key]:
del z_elt[key]
return A._from_dict(z_elt)

def is_unit(self):
def is_unit(self) -> bool:
r"""
Return ``True`` if ``self`` is invertible.

Expand Down Expand Up @@ -274,10 +275,6 @@
return scalar * Factorization([(self, 1)])
return super()._acted_upon_(scalar, self_on_left)

# For backward compatibility
# _lmul_ = _acted_upon_
# _rmul_ = _acted_upon_

def _im_gens_(self, codomain, im_gens, base_map):
"""
Apply a morphism defined by its values on the generators.
Expand All @@ -304,7 +301,7 @@
return codomain.sum(base_map(c) * m(*im_gens)
for m, c in self._monomial_coefficients.items())

def variables(self):
def variables(self) -> list:
"""
Return the variables used in ``self``.

Expand Down
6 changes: 3 additions & 3 deletions src/sage/algebras/fusion_rings/fusion_double.py
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Original file line number Diff line number Diff line change
Expand Up @@ -286,7 +286,7 @@ def s_ijconj(self, i, j, unitary=False, base_coercion=True):

EXAMPLES::

sage: P=FusionDouble(CyclicPermutationGroup(3),prefix='p',inject_variables=True)
sage: P = FusionDouble(CyclicPermutationGroup(3),prefix='p',inject_variables=True)
sage: P.s_ij(p1,p3)
zeta3
sage: P.s_ijconj(p1,p3)
Expand Down Expand Up @@ -695,7 +695,7 @@ def product_on_basis(self, a, b):

EXAMPLES::

sage: Q=FusionDouble(SymmetricGroup(3),prefix='q',inject_variables=True)
sage: Q = FusionDouble(SymmetricGroup(3),prefix='q',inject_variables=True)
sage: q3*q4
q1 + q2 + q5 + q6 + q7
sage: Q._names
Expand Down Expand Up @@ -820,7 +820,7 @@ def twist(self, reduced=True):

EXAMPLES::

sage: Q=FusionDouble(CyclicPermutationGroup(3))
sage: Q = FusionDouble(CyclicPermutationGroup(3))
sage: [x.twist() for x in Q.basis()]
[0, 0, 0, 0, 2/3, 4/3, 0, 4/3, 2/3]
sage: [x.ribbon() for x in Q.basis()]
Expand Down
62 changes: 31 additions & 31 deletions src/sage/algebras/iwahori_hecke_algebra.py
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Original file line number Diff line number Diff line change
Expand Up @@ -233,7 +233,7 @@ class IwahoriHeckeAlgebra(Parent, UniqueRepresentation):

sage: R.<q> = LaurentPolynomialRing(ZZ)
sage: H = IwahoriHeckeAlgebra('A3', q^2)
sage: T=H.T(); Cp=H.Cp(); C=H.C()
sage: T = H.T(); Cp = H.Cp(); C = H.C()
sage: C(T[1])
q*C[1] + q^2
sage: elt = Cp(T[1,2,1]); elt
Expand All @@ -245,7 +245,7 @@ class IwahoriHeckeAlgebra(Parent, UniqueRepresentation):

sage: R.<q> = LaurentPolynomialRing(ZZ)
sage: H = IwahoriHeckeAlgebra('A3', q, -q^-1)
sage: T=H.T(); Cp=H.Cp(); C=H.C()
sage: T = H.T(); Cp = H.Cp(); C = H.C()
sage: C(T[1])
C[1] + q
sage: elt = Cp(T[1,2,1]); elt
Expand All @@ -256,7 +256,7 @@ class IwahoriHeckeAlgebra(Parent, UniqueRepresentation):
In the group algebra, so that `(T_r-1)(T_r+1) = 0`::

sage: H = IwahoriHeckeAlgebra('A3', 1)
sage: T=H.T(); Cp=H.Cp(); C=H.C()
sage: T = H.T(); Cp = H.Cp(); C = H.C()
sage: C(T[1])
C[1] + 1
sage: Cp(T[1,2,1])
Expand All @@ -270,7 +270,7 @@ class IwahoriHeckeAlgebra(Parent, UniqueRepresentation):

sage: R.<q>=LaurentPolynomialRing(ZZ)
sage: H = IwahoriHeckeAlgebra('A3', q)
sage: C=H.C()
sage: C = H.C()
Traceback (most recent call last):
...
ValueError: the Kazhdan-Lusztig bases are defined only when -q_1*q_2 is a square
Expand All @@ -279,7 +279,7 @@ class IwahoriHeckeAlgebra(Parent, UniqueRepresentation):

sage: R.<v> = LaurentPolynomialRing(ZZ)
sage: H = IwahoriHeckeAlgebra(['A',2,1], v^2)
sage: T=H.T(); Cp=H.Cp(); C=H.C()
sage: T = H.T(); Cp = H.Cp(); C = H.C()
sage: C(T[1,0,2])
v^3*C[1,0,2] + v^4*C[1,0] + v^4*C[0,2] + v^4*C[1,2]
+ v^5*C[0] + v^5*C[2] + v^5*C[1] + v^6
Expand Down Expand Up @@ -1621,8 +1621,8 @@ def hash_involution_on_basis(self, w):

sage: R.<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra('A3', v**2)
sage: T=H.T()
sage: s=H.coxeter_group().simple_reflection(1)
sage: T = H.T()
sage: s = H.coxeter_group().simple_reflection(1)
sage: T.hash_involution_on_basis(s)
-(v^-2)*T[1]
sage: T[s].hash_involution()
Expand Down Expand Up @@ -1661,8 +1661,8 @@ def goldman_involution_on_basis(self, w):

sage: R.<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra('A3', v**2)
sage: T=H.T()
sage: s=H.coxeter_group().simple_reflection(1)
sage: T = H.T()
sage: s = H.coxeter_group().simple_reflection(1)
sage: T.goldman_involution_on_basis(s)
-T[1] - (1-v^2)
sage: T[s].goldman_involution()
Expand Down Expand Up @@ -1836,8 +1836,8 @@ def to_T_basis(self, w):

EXAMPLES::

sage: H=IwahoriHeckeAlgebra("A3",1); Cp=H.Cp(); C=H.C()
sage: s=H.coxeter_group().simple_reflection(1)
sage: H = IwahoriHeckeAlgebra("A3",1); Cp = H.Cp(); C = H.C()
sage: s = H.coxeter_group().simple_reflection(1)
sage: C.to_T_basis(s)
T[1] - 1
sage: Cp.to_T_basis(s)
Expand Down Expand Up @@ -2032,8 +2032,8 @@ def hash_involution_on_basis(self, w):

sage: R.<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra('A3', v**2)
sage: Cp=H.Cp()
sage: s=H.coxeter_group().simple_reflection(1)
sage: Cp = H.Cp()
sage: s = H.coxeter_group().simple_reflection(1)
sage: Cp.hash_involution_on_basis(s)
-Cp[1] + (v^-1+v)
sage: Cp[s].hash_involution()
Expand Down Expand Up @@ -2130,7 +2130,7 @@ def product_on_basis(self, w1, w2):
sage: # optional - coxeter3
sage: R.<v> = LaurentPolynomialRing(ZZ, 'v')
sage: W = CoxeterGroup('A3', implementation='coxeter3')
sage: H = IwahoriHeckeAlgebra(W, v**2); Cp=H.Cp()
sage: H = IwahoriHeckeAlgebra(W, v**2); Cp = H.Cp()
sage: Cp.product_on_basis(W([1,2,1]), W([3,1]))
(v^-1+v)*Cp[1,2,1,3]
sage: Cp.product_on_basis(W([1,2,1]), W([3,1,2]))
Expand Down Expand Up @@ -2267,7 +2267,7 @@ def _decompose_into_generators(self, u):

sage: R.<v> = LaurentPolynomialRing(ZZ, 'v') # optional - coxeter3
sage: W = CoxeterGroup('A3', implementation='coxeter3') # optional - coxeter3
sage: H = IwahoriHeckeAlgebra(W, v**2); Cp=H.Cp() # optional - coxeter3
sage: H = IwahoriHeckeAlgebra(W, v**2); Cp = H.Cp() # optional - coxeter3

When `u` is itself a generator `s`, the decomposition is trivial::

Expand Down Expand Up @@ -2440,8 +2440,8 @@ def hash_involution_on_basis(self, w):

sage: R.<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra('A3', v**2)
sage: C=H.C()
sage: s=H.coxeter_group().simple_reflection(1)
sage: C = H.C()
sage: s = H.coxeter_group().simple_reflection(1)
sage: C.hash_involution_on_basis(s)
-C[1] - (v^-1+v)
sage: C[s].hash_involution()
Expand Down Expand Up @@ -2473,7 +2473,7 @@ class A(_Basis):

sage: R.<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra('A3', v**2)
sage: A=H.A(); T=H.T()
sage: A = H.A(); T = H.T()
sage: T(A[1])
T[1] + (1/2-1/2*v^2)
sage: T(A[1,2])
Expand Down Expand Up @@ -2526,8 +2526,8 @@ def to_T_basis(self, w):
EXAMPLES::

sage: R.<v> = LaurentPolynomialRing(QQ)
sage: H = IwahoriHeckeAlgebra('A3', v**2); A=H.A(); T=H.T()
sage: s=H.coxeter_group().simple_reflection(1)
sage: H = IwahoriHeckeAlgebra('A3', v**2); A = H.A(); T = H.T()
sage: s = H.coxeter_group().simple_reflection(1)
sage: A.to_T_basis(s)
T[1] + (1/2-1/2*v^2)
sage: T(A[1,2])
Expand All @@ -2550,8 +2550,8 @@ def goldman_involution_on_basis(self, w):

sage: R.<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra('A3', v**2)
sage: A=H.A()
sage: s=H.coxeter_group().simple_reflection(1)
sage: A = H.A()
sage: s = H.coxeter_group().simple_reflection(1)
sage: A.goldman_involution_on_basis(s)
-A[1]
sage: A[1,2].goldman_involution()
Expand Down Expand Up @@ -2593,7 +2593,7 @@ class B(_Basis):

sage: R.<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra('A3', v**2)
sage: A=H.A(); T=H.T(); Cp=H.Cp()
sage: A = H.A(); T = H.T(); Cp = H.Cp()
sage: T(A[1])
T[1] + (1/2-1/2*v^2)
sage: T(A[1,2])
Expand Down Expand Up @@ -2659,8 +2659,8 @@ def to_T_basis(self, w):
EXAMPLES::

sage: R.<v> = LaurentPolynomialRing(QQ)
sage: H = IwahoriHeckeAlgebra('A3', v**2); B=H.B(); T=H.T()
sage: s=H.coxeter_group().simple_reflection(1)
sage: H = IwahoriHeckeAlgebra('A3', v**2); B = H.B(); T = H.T()
sage: s = H.coxeter_group().simple_reflection(1)
sage: B.to_T_basis(s)
T[1] + (1/2-1/2*v^2)
sage: T(B[1,2])
Expand All @@ -2687,8 +2687,8 @@ def goldman_involution_on_basis(self, w):

sage: R.<v> = LaurentPolynomialRing(QQ, 'v')
sage: H = IwahoriHeckeAlgebra('A3', v**2)
sage: B=H.B()
sage: s=H.coxeter_group().simple_reflection(1)
sage: B = H.B()
sage: s = H.coxeter_group().simple_reflection(1)
sage: B.goldman_involution_on_basis(s)
-B[1]
sage: B[1,2].goldman_involution()
Expand Down Expand Up @@ -2822,8 +2822,8 @@ def _bar_on_coefficients(self, c):
EXAMPLES::

sage: R.<q>=LaurentPolynomialRing(ZZ)
sage: H=IwahoriHeckeAlgebra("A3",q^2)
sage: GH=H._generic_iwahori_hecke_algebra
sage: H = IwahoriHeckeAlgebra("A3",q^2)
sage: GH = H._generic_iwahori_hecke_algebra
sage: GH._bar_on_coefficients(GH.u_inv)
u
sage: GH._bar_on_coefficients(GH.v_inv)
Expand Down Expand Up @@ -2871,8 +2871,8 @@ def specialize_to(self, new_hecke):
EXAMPLES::

sage: R.<a,b>=LaurentPolynomialRing(ZZ,2)
sage: H=IwahoriHeckeAlgebra("A3",a^2,-b^2)
sage: GH=H._generic_iwahori_hecke_algebra
sage: H = IwahoriHeckeAlgebra("A3",a^2,-b^2)
sage: GH = H._generic_iwahori_hecke_algebra
sage: GH.T()(GH.C()[1])
(v^-1)*T[1] + (-u*v^-1)
sage: ( GH.T()(GH.C()[1]) ).specialize_to(H)
Expand Down
2 changes: 1 addition & 1 deletion src/sage/algebras/steenrod/steenrod_algebra.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2966,7 +2966,7 @@ def top_class(self):

TESTS::

sage: A=SteenrodAlgebra(2, profile=(3,2,1), basis='pst')
sage: A = SteenrodAlgebra(2, profile=(3,2,1), basis='pst')
sage: A.top_class().parent() is A
True
"""
Expand Down
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