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Some small reviewer changes.
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@tscrim
tscrim committed Dec 7, 2022
1 parent fe84785 commit 9fde881
Showing 1 changed file with 40 additions and 40 deletions.
80 changes: 40 additions & 40 deletions src/sage/algebras/commutative_dga.py
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Original file line number Diff line number Diff line change
Expand Up @@ -174,7 +174,7 @@ def __classcall__(cls, A, im_gens):
sage: d1 is d2
True
Check that #34818 is solved::
Check that :trac:`34818` is solved::
sage: A.<a,b,x,u> = GradedCommutativeAlgebra(QQ,degrees=(2,2,3,3))
sage: A = A.quotient(A.ideal([a*u,b*u,x*u]))
Expand All @@ -187,13 +187,12 @@ def __classcall__(cls, A, im_gens):
sage: A.cdg_algebra({x:a*b,a:u,u:a^2})
Traceback (most recent call last):
...
ValueError: The differential does not preserve the ideal
ValueError: the differential does not preserve the ideal
"""
if isinstance(im_gens, (list, tuple)):
im_gens = {A.gen(i): x for i, x in enumerate(im_gens)}

im_gens = {A(a): A(im_gens[a]) for a in im_gens}
im_gens = {A.gen(i): A(x) for i, x in enumerate(im_gens)}
else:
im_gens = {A(a): A(im_gens[a]) for a in im_gens}

R = A.cover_ring()
I = A.defining_ideal()
Expand All @@ -206,8 +205,9 @@ def __classcall__(cls, A, im_gens):
def image_monomial(exponent):
i = 0
cexp = list(exponent)
while i < len(cexp):
if cexp[i] == 0:
ell = len(cexp)
while i < ell:
if not cexp[i]:
i +=1
continue
a = A.gen(i)
Expand All @@ -216,27 +216,27 @@ def image_monomial(exponent):
except KeyError:
da = A.zero()
cexp[i] -= 1
b = prod([A.gen(j)**cexp[j] for j in range(len(cexp))])
b = A.prod(A.gen(j) ** cexp[j] for j in range(len(cexp)))
db = image_monomial(cexp)
im = da * b + (-1)**A._degrees[i]*a*db
return(A(im))
im = da * b + (-1)**A._degrees[i] * a * db
return A(im)
return A.zero()

for g in I.gens():
d = g.dict()
res = A(sum([d[ex]*image_monomial(ex) for ex in d]))
res = A.sum(d[ex] * image_monomial(ex) for ex in d)
if not res.is_zero():
raise ValueError("The differential does not preserve the ideal")
raise ValueError("the differential does not preserve the ideal")

for i in im_gens:
x = im_gens[i]
if (not x.is_zero()
and (not x.is_homogeneous()
or total_degree(x.degree())
!= total_degree(i.degree()) + 1)):
raise ValueError("The given dictionary does not determine a degree 1 map")
raise ValueError("the given dictionary does not determine a degree 1 map")

im_gens = tuple(im_gens.get(x, A.zero()) for x in A.gens())
im_gens = tuple([im_gens.get(x, A.zero()) for x in A.gens()])
return super(Differential, cls).__classcall__(cls, A, im_gens)

def __init__(self, A, im_gens):
Expand Down Expand Up @@ -269,14 +269,14 @@ def __init__(self, A, im_gens):
sage: A.cdg_algebra({a:b, b:c})
Traceback (most recent call last):
...
ValueError: The given dictionary does not determine a valid differential
ValueError: the given dictionary does not determine a valid differential
"""
self._dic_ = {A.gen(i): x for i, x in enumerate(im_gens)}
Morphism.__init__(self, Hom(A, A, category=Modules(A.base_ring())))

for i in A.gens():
if not self(self(i)).is_zero():
raise ValueError("The given dictionary does not determine a valid differential")
raise ValueError("the given dictionary does not determine a valid differential")

def _call_(self, x):
r"""
Expand Down Expand Up @@ -626,7 +626,7 @@ def __init__(self, A, im_gens):
if y != 0:
diff_deg.append(y.degree() - x.degree())
if len(set(diff_deg)) > 1:
raise ValueError("The differential does not have a well-defined degree")
raise ValueError("the differential does not have a well-defined degree")
self._degree_of_differential = diff_deg[0]

@cached_method
Expand Down Expand Up @@ -967,7 +967,7 @@ def __classcall__(cls, base, names=None, degrees=None, R=None, I=None, category=
"""
if names is None:
if degrees is None:
raise ValueError("You must specify names or degrees")
raise ValueError("you must specify names or degrees")
else:
n = len(degrees)
names = tuple('x{}'.format(i) for i in range(n))
Expand Down Expand Up @@ -1229,7 +1229,7 @@ def quotient(self, I, check=True):
[x^2*z, y^2*z, z*t]
"""
if check and any(not i.is_homogeneous() for i in I.gens()):
raise ValueError("The ideal must be homogeneous")
raise ValueError("the ideal must be homogeneous")
NCR = self.cover_ring()
gens1 = list(self.defining_ideal().gens())
gens2 = [i.lift() for i in I.gens()]
Expand Down Expand Up @@ -1473,10 +1473,10 @@ def degree(self, total=False):
sage: A(0).degree()
Traceback (most recent call last):
...
ValueError: The zero element does not have a well-defined degree
ValueError: the zero element does not have a well-defined degree
"""
if self.is_zero():
raise ValueError("The zero element does not have a well-defined degree")
raise ValueError("the zero element does not have a well-defined degree")
exps = self.lift().dict().keys()
degrees = self.parent()._degrees
n = self.parent().ngens()
Expand Down Expand Up @@ -1607,7 +1607,7 @@ def basis_coefficients(self, total=False):
sage: (t + x).basis_coefficients()
Traceback (most recent call last):
...
ValueError: This element is not homogeneous
ValueError: this element is not homogeneous
sage: B.<c,d> = GradedCommutativeAlgebra(QQ, degrees=((2,0), (0,4)))
sage: B.basis(4)
Expand All @@ -1617,10 +1617,10 @@ def basis_coefficients(self, total=False):
sage: (c^2 - 1/2 * d).basis_coefficients()
Traceback (most recent call last):
...
ValueError: This element is not homogeneous
ValueError: this element is not homogeneous
"""
if not self.is_homogeneous(total):
raise ValueError('This element is not homogeneous')
raise ValueError('this element is not homogeneous')

basis = self.parent().basis(self.degree(total))
lift = self.lift()
Expand Down Expand Up @@ -1752,7 +1752,7 @@ def quotient(self, I, check=True):
[x^2*z, y^2*z, z*t]
"""
if check and any(not i.is_homogeneous() for i in I.gens()):
raise ValueError("The ideal must be homogeneous")
raise ValueError("the ideal must be homogeneous")
NCR = self.cover_ring()
gens1 = list(self.defining_ideal().gens())
gens2 = [i.lift() for i in I.gens()]
Expand Down Expand Up @@ -1906,26 +1906,26 @@ def degree(self, total=False):
sage: (a**2*b + c).degree()
Traceback (most recent call last):
...
ValueError: This element is not homogeneous
ValueError: this element is not homogeneous
sage: (a**2*b + c).degree(total=True)
3
sage: A(0).degree()
Traceback (most recent call last):
...
ValueError: The zero element does not have a well-defined degree
ValueError: the zero element does not have a well-defined degree
"""
if total:
return GCAlgebra.Element.degree(self)
if self.is_zero():
raise ValueError("The zero element does not have a well-defined degree")
raise ValueError("the zero element does not have a well-defined degree")
degrees = self.parent()._degrees_multi
n = self.parent().ngens()
exps = self.lift().dict().keys()
l = [sum(exp[i] * degrees[i] for i in range(n)) for exp in exps]
if len(set(l)) == 1:
return l[0]
else:
raise ValueError('This element is not homogeneous')
raise ValueError('this element is not homogeneous')


###########################################################
Expand Down Expand Up @@ -2021,15 +2021,15 @@ def __init__(self, A, differential):
sage: A.cdg_algebra({a: a*b*c})
Traceback (most recent call last):
...
ValueError: The given dictionary does not determine a degree 1 map
ValueError: the given dictionary does not determine a degree 1 map
The differential composed with itself must be zero::
sage: A.<a,b,c> = GradedCommutativeAlgebra(QQ, degrees=(1,2,3))
sage: A.cdg_algebra({a:b, b:c})
Traceback (most recent call last):
...
ValueError: The given dictionary does not determine a valid differential
ValueError: the given dictionary does not determine a valid differential
"""
cat = Algebras(A.base()).Graded() & ChainComplexes(A.base())
GCAlgebra.__init__(self, A.base(), names=A._names,
Expand Down Expand Up @@ -2114,17 +2114,17 @@ def quotient(self, I, check=True):
sage: B.quotient(B.ideal(y*x))
Traceback (most recent call last):
...
ValueError: The differential does not preserve the ideal
ValueError: the differential does not preserve the ideal
sage: B.quotient(B.ideal(x))
Traceback (most recent call last):
...
ValueError: The differential does not preserve the ideal
ValueError: the differential does not preserve the ideal
"""
J = self.ideal(I)
AQ = GCAlgebra.quotient(self, J, check)
for g in I.gens():
if not AQ(g.differential()).is_zero():
raise ValueError("The differential does not preserve the ideal")
raise ValueError("the differential does not preserve the ideal")
dic = {AQ(a): AQ(a.differential()) for a in self.gens()}
return AQ.cdg_algebra(dic)

Expand Down Expand Up @@ -2909,10 +2909,10 @@ def is_coboundary(self):
sage: (x*z+y**2).is_coboundary()
Traceback (most recent call last):
...
ValueError: This element is not homogeneous
ValueError: this element is not homogeneous
"""
if not self.is_homogeneous():
raise ValueError('This element is not homogeneous')
raise ValueError('this element is not homogeneous')
# To avoid taking the degree of 0, we special-case it.
if self.is_zero():
return True
Expand Down Expand Up @@ -2955,7 +2955,7 @@ def is_cohomologous_to(self, other):
return self.is_coboundary()
if (not isinstance(other, DifferentialGCAlgebra.Element)
or self.parent() is not other.parent()):
raise ValueError('The element {} does not lie in this DGA'
raise ValueError('the element {} does not lie in this DGA'
.format(other))
if (self - other).is_homogeneous():
return (self - other).is_coboundary()
Expand Down Expand Up @@ -3099,7 +3099,7 @@ def __init__(self, A, differential):
sage: B = A.cdg_algebra(differential={x:y, t:z}) # bad
Traceback (most recent call last):
...
ValueError: The differential does not have a well-defined degree
ValueError: the differential does not have a well-defined degree
"""
cat = Algebras(A.base()).Graded() & ChainComplexes(A.base())
GCAlgebra_multigraded.__init__(self, A.base(), names=A._names,
Expand Down Expand Up @@ -3452,7 +3452,7 @@ def GradedCommutativeAlgebra(ring, names=None, degrees=None, max_degree=None,
sage: GradedCommutativeAlgebra(QQ)
Traceback (most recent call last):
...
ValueError: You must specify names or degrees
ValueError: you must specify names or degrees
"""
if max_degree:
from .finite_gca import FiniteGCAlgebra
Expand Down

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