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pep cleanup in ore_polynomial_element.pyx
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@fchapoton
fchapoton committed Dec 13, 2022
1 parent bb7ee85 commit bbe553a
Showing 1 changed file with 53 additions and 61 deletions.
114 changes: 53 additions & 61 deletions src/sage/rings/polynomial/ore_polynomial_element.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -300,10 +300,8 @@ cdef class OrePolynomial(AlgebraElement):
To: Ore Polynomial Ring in x over Finite Field in t of size 5^3 twisted by t |--> t^5
"""
if a:
n = self._new_c([a],P,check)
else:
n = self._new_c([],P)
return n
return self._new_c([a], P, check)
return self._new_c([], P)

def __setitem__(self, n, value):
r"""
Expand Down Expand Up @@ -527,9 +525,7 @@ cdef class OrePolynomial(AlgebraElement):
cdef Morphism m = self._parent.twisting_morphism(-self.degree())
if m is None:
return self * a
else:
return self * m(a)
return r
return self * m(a)

def right_monic(self):
r"""
Expand Down Expand Up @@ -578,8 +574,7 @@ cdef class OrePolynomial(AlgebraElement):
a = self.base_ring()(~self.leading_coefficient())
except (ZeroDivisionError, TypeError):
raise NotImplementedError("the leading coefficient is not a unit")
r = a * self
return r
return a * self

cpdef _mod_(self, other):
r"""
Expand Down Expand Up @@ -625,9 +620,8 @@ cdef class OrePolynomial(AlgebraElement):
Traceback (most recent call last):
...
NotImplementedError: the leading coefficient of the divisor is not invertible
"""
q,_ = self.right_quo_rem(right)
q, _ = self.right_quo_rem(right)
return q

cpdef _div_(self, right):
Expand Down Expand Up @@ -918,13 +912,13 @@ cdef class OrePolynomial(AlgebraElement):
V1 = self._parent.zero()
V3 = other
while V3:
Q,R = G._left_quo_rem(V3)
T = U - V1*Q
Q, R = G._left_quo_rem(V3)
T = U - V1 * Q
U = V1
G = V3
V1 = T
V3 = R
V = G - self*U
V = G - self * U
V, _ = V._left_quo_rem(other)
if monic:
lc = ~G.leading_coefficient()
Expand All @@ -934,7 +928,7 @@ cdef class OrePolynomial(AlgebraElement):
G = G * lc
U = U * lc
V = V * lc
return G,U,V
return G, U, V

cdef _left_quo_rem(self, OrePolynomial other):
r"""
Expand Down Expand Up @@ -1137,19 +1131,19 @@ cdef class OrePolynomial(AlgebraElement):
V3 = other
while not V3.is_zero():
Q, R = G._right_quo_rem(V3)
T = U - Q*V1
T = U - Q * V1
U = V1
G = V3
V1 = T
V3 = R
V = G - U*self
V,_ = V._right_quo_rem(other)
V = G - U * self
V, _ = V._right_quo_rem(other)
if monic:
lc = ~G.leading_coefficient()
G = lc * G
U = lc * U
V = lc * V
return G,U,V
return G, U, V

@coerce_binop
def right_gcd(self, other, monic=True):
Expand Down Expand Up @@ -1330,7 +1324,7 @@ cdef class OrePolynomial(AlgebraElement):
cdef OrePolynomial V = <OrePolynomial>self._parent.zero()
while other:
Q, R = self._right_quo_rem(other)
T = U - Q*V
T = U - Q * V
U = V
V = T
self = other
Expand Down Expand Up @@ -1407,7 +1401,7 @@ cdef class OrePolynomial(AlgebraElement):
cdef OrePolynomial V = <OrePolynomial>self._parent.zero()
while other:
Q, R = self._left_quo_rem(other)
T = U - V*Q
T = U - V * Q
U = V
V = T
self = other
Expand Down Expand Up @@ -1460,7 +1454,6 @@ cdef class OrePolynomial(AlgebraElement):
W1, _ = L._left_quo_rem(other)
return L, V1, W1


@coerce_binop
def left_lcm(self, other, monic=True):
r"""
Expand Down Expand Up @@ -1648,14 +1641,14 @@ cdef class OrePolynomial(AlgebraElement):
if y.find("-") == 0:
y = y[1:]
if not atomic_repr and n > 0 and (y.find("+") != -1 or y.find("-") != -1):
x = "(%s)"%x
x = "(%s)" % x
if n > 1:
var = "*%s^%s"%(name,n)
elif n==1:
var = "*%s"%name
var = "*%s^%s" % (name, n)
elif n == 1:
var = "*%s" % name
else:
var = ""
s += "%s%s"%(x,var)
s += "%s%s" % (x, var)
s = s.replace(" + -", " - ")
s = re.sub(r' 1(\.0+)?\*', ' ', s)
s = re.sub(r' -1(\.0+)?\*', ' -', s)
Expand Down Expand Up @@ -1693,16 +1686,16 @@ cdef class OrePolynomial(AlgebraElement):
x = self[n]
x = y = x._latex_()
if x != '0':
if n != m-1:
if n != m - 1:
s += " + "
if y.find("-") == 0:
y = y[1:]
if not atomic_repr and n > 0 and (y.find("+") != -1 or y.find("-") != -1):
x = "\\left(%s\\right)"%x
x = "\\left(%s\\right)" % x
if n > 1:
var = "|%s^{%s}"%(name,n)
elif n==1:
var = "|%s"%name
var = "|%s^{%s}" % (name, n)
elif n == 1:
var = "|%s" % name
else:
var = ""
s += "%s %s" % (x, var)
Expand Down Expand Up @@ -1798,7 +1791,7 @@ cdef class OrePolynomial(AlgebraElement):
if n == 0 or self.degree() < 0:
return self
if n > 0:
return self._parent(n*[self.base_ring().zero()] + self.list(), check=False)
return self._parent(n * [self.base_ring().zero()] + self.list(), check=False)
if n < 0:
if n > self.degree():
return self._parent([])
Expand Down Expand Up @@ -2097,7 +2090,7 @@ cdef class OrePolynomial(AlgebraElement):
sage: a.exponents()
[0, 2, 4]
"""
return [i for i in range(self.degree()+1) if bool(self[i])]
return [i for i in range(self.degree() + 1) if bool(self[i])]

def prec(self):
r"""
Expand Down Expand Up @@ -2157,9 +2150,8 @@ cdef class OrePolynomial(AlgebraElement):
raise ValueError("n must be at least 0")
if len(v) < n:
z = self._parent.base_ring().zero()
return v + [z]*(n - len(v))
else:
return v[:int(n)]
return v + [z] * (n - len(v))
return v[:int(n)]

def variable_name(self):
r"""
Expand Down Expand Up @@ -2195,14 +2187,15 @@ cdef void lmul_gen(list A, Morphism m, d):
"""
if m is None:
A.append(A[-1])
for j in range(len(A)-2, 0, -1):
A[j] = d(A[j]) + A[j-1]
for j in range(len(A) - 2, 0, -1):
A[j] = d(A[j]) + A[j - 1]
else:
A.append(m(A[-1]))
for j in range(len(A)-2, 0, -1):
A[j] = d(A[j]) + m(A[j-1])
for j in range(len(A) - 2, 0, -1):
A[j] = d(A[j]) + m(A[j - 1])
A[0] = d(A[0])


cdef class OrePolynomial_generic_dense(OrePolynomial):
r"""
Generic implementation of dense Ore polynomial supporting any valid base
Expand Down Expand Up @@ -2317,8 +2310,8 @@ cdef class OrePolynomial_generic_dense(OrePolynomial):
This is an internal method. Use :meth:`__hash__` instead.
"""
#todo - come up with a way to create hashes of zero that
# that do not incorrectly indicate that the element is 0.
# todo - come up with a way to create hashes of zero that
# that do not incorrectly indicate that the element is 0.
cdef long result = 0
cdef long result_mon
cdef long c_hash
Expand Down Expand Up @@ -2577,11 +2570,11 @@ cdef class OrePolynomial_generic_dense(OrePolynomial):
cdef Py_ssize_t dx = len(x), dy = len(y)
cdef RingElement c
if dx > dy:
r = self._new_c([x[i] - y[i] for i from 0 <= i < dy] + x[dy:], self._parent, 0)
r = self._new_c([x[i] - y[i] for i in range(dy)] + x[dy:], self._parent, 0)
elif dx < dy:
r = self._new_c([x[i] - y[i] for i from 0 <= i < dx] + [ -c for c in y[dx:] ], self._parent, 0)
r = self._new_c([x[i] - y[i] for i in range(dx)] + [-c for c in y[dx:]], self._parent, 0)
else:
r = self._new_c([x[i] - y[i] for i from 0 <= i < dx], self._parent, 1)
r = self._new_c([x[i] - y[i] for i in range(dx)], self._parent, 1)
return r

cpdef _neg_(self):
Expand Down Expand Up @@ -2654,7 +2647,7 @@ cdef class OrePolynomial_generic_dense(OrePolynomial):
This is an helper function.
"""
cdef list BA = [ self.base_ring().zero() ] * (len(self._coeffs) + len(A) - 1)
cdef list BA = [self.base_ring().zero()] * (len(self._coeffs) + len(A) - 1)
cdef Morphism m = self._parent._morphism
cdef d = self._parent._derivation
cdef coeff
Expand Down Expand Up @@ -2713,7 +2706,7 @@ cdef class OrePolynomial_generic_dense(OrePolynomial):
sage: f.degree()
-1
"""
return self._new_c([ s*c for c in self._coeffs ], self._parent, 1)
return self._new_c([s * c for c in self._coeffs], self._parent, 1)

cpdef _mul_(self, other):
r"""
Expand Down Expand Up @@ -2766,19 +2759,19 @@ cdef class OrePolynomial_generic_dense(OrePolynomial):
cdef RingElement s, inv = other.leading_coefficient()
cdef Py_ssize_t nb = len(A) - degB
cdef list L
cdef list quo = [ ]
cdef list quo = []
if not inv.is_unit():
raise ValueError("the leading coefficient of the divisor in not a unit")
inv = inv.inverse_of_unit()
for i in range(nb-1, -1, -1):
s = A[i+degB]
for i in range(nb - 1, -1, -1):
s = A[i + degB]
if s:
s = s * inv
if m is not None:
s = m(s)
L = (<OrePolynomial_generic_dense>other)._mul_list([s])
for j in range(len(L)-1):
A[i+j] -= L[j]
for j in range(len(L) - 1):
A[i + j] -= L[j]
quo.append(s)
quo.reverse()
return self._new_c(quo, self._parent), self._new_c(A[:degB], self._parent, 1)
Expand All @@ -2797,8 +2790,8 @@ cdef class OrePolynomial_generic_dense(OrePolynomial):
cdef d = self._parent._derivation
cdef RingElement s, inv = other.leading_coefficient()
cdef list XnB = (<OrePolynomial_generic_dense>other)._coeffs
cdef list XnBs = [ ]
cdef list quo = [ ]
cdef list XnBs = []
cdef list quo = []
if not inv.is_unit():
raise ValueError("the leading coefficient of the divisor in not a unit")
inv = inv.inverse_of_unit()
Expand All @@ -2807,21 +2800,20 @@ cdef class OrePolynomial_generic_dense(OrePolynomial):
XnB = list(XnB)
lmul_gen(XnB, m, d)
XnBs.append(XnB)
for i in range(nb-1, -1, -1):
s = A[i+degB]
for i in range(nb - 1, -1, -1):
s = A[i + degB]
if s:
if m:
s *= self._parent.twisting_morphism(i)(inv)
else:
s *= inv
XnB = XnBs[i]
for j in range(len(XnB)-1):
for j in range(len(XnB) - 1):
A[j] -= s * XnB[j]
quo.append(s)
quo.reverse()
return self._new_c(quo, self._parent), self._new_c(A[:degB], self._parent, 1)


cpdef list coefficients(self, sparse=True):
r"""
Return the coefficients of the monomials appearing in ``self``.
Expand Down Expand Up @@ -2930,7 +2922,7 @@ cdef class OrePolynomial_generic_dense(OrePolynomial):
X = S.gen() + s
Xi = S.one()
ans = S(self[0])
for i in range(1, self.degree()+1):
for i in range(1, self.degree() + 1):
Xi = X * Xi
ans += self[i] * Xi
return ans
Expand Down Expand Up @@ -3039,7 +3031,7 @@ cdef class OrePolynomialBaseringInjection(Morphism):
"""
assert codomain.base_ring() is domain, \
"the domain of the injection must be the base ring of the Ore polynomial ring"
Morphism.__init__(self, Hom(domain,codomain))
Morphism.__init__(self, Hom(domain, codomain))
self._an_element = codomain.gen()
self._repr_type_str = "Ore Polynomial base injection"
self._new_constant_poly_ = self._an_element._new_constant_poly
Expand Down

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