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Fix bug in SkewPolynomialRing when twisting morphism is trivial #40697

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Merged
merged 4 commits into from
Sep 21, 2025
Merged

Fix bug in SkewPolynomialRing when twisting morphism is trivial #40697

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8a1cb27
special cases when _morphism is None
Aug 26, 2025
3d01554
Merge branch 'develop' into skew_poly_mul
xcaruso Aug 27, 2025
8fceda5
Merge branch 'develop' into skew_poly_mul
Sep 11, 2025
d0a839e
Merge branch 'skew_poly_mul' of github.com:xcaruso/sage into skew_pol…
Sep 11, 2025
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35 changes: 20 additions & 15 deletions src/sage/rings/polynomial/ore_function_field.py
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Original file line number Diff line number Diff line change
Expand Up @@ -299,16 +299,16 @@ def _repr_(self) -> str:
sage: T.<d> = OrePolynomialRing(R, der)
sage: T.fraction_field() # needs sage.rings.function_field
Ore Function Field in d over Fraction Field of Univariate Polynomial Ring in t over Rational Field twisted by d/dt

TESTS::

sage: k = GF(7)
sage: S.<x> = SkewPolynomialRing(k, polcast=False)
sage: S.fraction_field()
Ore Function Field in x over Finite Field of size 7 untwisted
"""
s = "Ore Function Field in %s over %s twisted by " % (self.variable_name(), self.base_ring())
morphism = self.twisting_morphism()
derivation = self.twisting_derivation()
if derivation is None:
s += morphism._repr_short()
else:
if morphism is not None:
s += "%s and " % morphism._repr_short()
s += derivation._repr_()
s = "Ore Function Field in %s over %s " % (self.variable_name(), self.base_ring())
s += self._ring._repr_twist()
return s

def _latex_(self):
Expand All @@ -331,15 +331,20 @@ def _latex_(self):
sage: L = T.fraction_field()
sage: latex(L) # indirect doctest
\mathrm{Frac}(\Bold{Q}[t])\left(\delta ; \frac{d}{dt} \right)

TESTS::

sage: k = GF(7)
sage: S.<x> = SkewPolynomialRing(k, polcast=False)
sage: K = S.fraction_field()
sage: latex(K) # indirect doctest
\Bold{F}_{7}\left(x\right)
"""
from sage.misc.latex import latex
s = "%s\\left(%s" % (latex(self.base_ring()), self.latex_variable_names()[0])
sep = ";"
if self.twisting_morphism() is not None:
s += sep + latex(self.twisting_morphism())
sep = ","
if self.twisting_derivation() is not None:
s += sep + latex(self.twisting_derivation())
twist = self._ring._latex_twist()
if twist != "":
s += ";" + twist
return s + "\\right)"

def change_var(self, var):
Expand Down
123 changes: 94 additions & 29 deletions src/sage/rings/polynomial/skew_polynomial_element.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -371,7 +371,8 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):
cdef RingElement a = eval_pt
for c in coefficients:
ret += c * a
a = sigma(a)
if sigma is not None:
a = sigma(a)
return ret

def conjugate(self, n):
Expand Down Expand Up @@ -417,7 +418,16 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):
sage: v = u.conjugate(-1)
sage: u*y == y*v
True

TESTS::

sage: k = GF(7)
sage: S.<x> = SkewPolynomialRing(k, polcast=False)
sage: x.conjugate(1)
x
"""
if self._parent._morphism is None:
return self
r = self._new_c([self._parent.twisting_morphism(n)(x) for x in self.list()],
self._parent, 0)
return r
Expand Down Expand Up @@ -537,6 +547,13 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):

sage: S(0)*a, (S(0)*a).list()
(0, [])

::

sage: k = GF(7)
sage: S.<x> = SkewPolynomialRing(k, polcast=False)
sage: x * x
x^2
"""
cdef list x = (<SkewPolynomial_generic_dense>self)._coeffs
cdef list y = (<SkewPolynomial_generic_dense>right)._coeffs
Expand All @@ -552,13 +569,22 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):
r = self._new_c([c*a for a in y], parent, 0)
return r
cdef list coeffs = []
for k from 0 <= k <= dx+dy:
start = 0 if k <= dy else k-dy
end = k if k <= dx else dx
sum = x[start] * parent.twisting_morphism(start)(y[k-start])
for i from start < i <= end:
sum += x[i] * parent.twisting_morphism(i)(y[k-i])
coeffs.append(sum)
if parent._morphism is None:
for k from 0 <= k <= dx+dy:
start = 0 if k <= dy else k-dy
end = k if k <= dx else dx
sum = x[start] * y[k-start]
for i from start < i <= end:
sum += x[i] * y[k-i]
coeffs.append(sum)
else:
for k from 0 <= k <= dx+dy:
start = 0 if k <= dy else k-dy
end = k if k <= dx else dx
sum = x[start] * parent.twisting_morphism(start)(y[k-start])
for i from start < i <= end:
sum += x[i] * parent.twisting_morphism(i)(y[k-i])
coeffs.append(sum)
r = self._new_c(coeffs, parent, 0)
return r

Expand All @@ -576,6 +602,13 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):
sage: modulus = x^3 + t*x^2 + (t+3)*x - 2
sage: a.left_power_mod(100,modulus) # indirect doctest
(4*t^2 + t + 1)*x^2 + (t^2 + 4*t + 1)*x + 3*t^2 + 3*t

::

sage: k = GF(7)
sage: S.<x> = SkewPolynomialRing(k, polcast=False)
sage: x.left_power_mod(100, x^2 + x + 1) # indirect doctest
x
"""
cdef list x = self._coeffs
cdef list y = right._coeffs
Expand All @@ -585,19 +618,34 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):
if d2 == -1:
self._coeffs = [ ]
elif d1 >= 0:
for k from d1 < k <= d1+d2:
start = 0 if k <= d2 else k-d2
sum = x[start] * parent.twisting_morphism(start)(y[k-start])
for i from start < i <= d1:
sum += x[i] * parent.twisting_morphism(i)(y[k-i])
x.append(sum)
for k from d1 >= k >= 0:
start = 0 if k <= d2 else k-d2
end = k if k <= d1 else d1
sum = x[start] * parent.twisting_morphism(start)(y[k-start])
for i from start < i <= end:
sum += x[i] * parent.twisting_morphism(i)(y[k-i])
x[k] = sum
if parent._morphism is None:
for k from d1 < k <= d1+d2:
start = 0 if k <= d2 else k-d2
sum = x[start] * y[k-start]
for i from start < i <= d1:
sum += x[i] * y[k-i]
x.append(sum)
for k from d1 >= k >= 0:
start = 0 if k <= d2 else k-d2
end = k if k <= d1 else d1
sum = x[start] * y[k-start]
for i from start < i <= end:
sum += x[i] * y[k-i]
x[k] = sum
else:
for k from d1 < k <= d1+d2:
start = 0 if k <= d2 else k-d2
sum = x[start] * parent.twisting_morphism(start)(y[k-start])
for i from start < i <= d1:
sum += x[i] * parent.twisting_morphism(i)(y[k-i])
x.append(sum)
for k from d1 >= k >= 0:
start = 0 if k <= d2 else k-d2
end = k if k <= d1 else d1
sum = x[start] * parent.twisting_morphism(start)(y[k-start])
for i from start < i <= end:
sum += x[i] * parent.twisting_morphism(i)(y[k-i])
x[k] = sum

cdef void _inplace_pow(self, Py_ssize_t n) noexcept:
r"""
Expand Down Expand Up @@ -644,12 +692,17 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):
cdef list q = [ ]
parent = self._parent
for i from da-db >= i >= 0:
try:
c = parent.twisting_morphism(-db)(inv*a[i+db])
if parent._morphism is None:
c = inv * a[i+db]
for j from 0 <= j < db:
a[i+j] -= b[j] * parent.twisting_morphism(j)(c)
except Exception:
raise NotImplementedError("inversion of the twisting morphism %s" % parent.twisting_morphism())
a[i+j] -= b[j] * c
else:
try:
c = parent.twisting_morphism(-db)(inv*a[i+db])
for j from 0 <= j < db:
a[i+j] -= b[j] * parent.twisting_morphism(j)(c)
except Exception:
raise NotImplementedError("inversion of the twisting morphism %s" % parent.twisting_morphism())
q.append(c)
q.reverse()
return (self._new_c(q, parent), self._new_c(a[:db], parent, 1))
Expand All @@ -658,6 +711,13 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):
r"""
Return the quotient and remainder of the right euclidean
division of ``self`` by ``other`` (C implementation).

TESTS::

sage: k = GF(7)
sage: S.<x> = SkewPolynomialRing(k, polcast=False)
sage: (x^3).right_quo_rem(x^2 + x + 1)
(x + 6, 1)
"""
sig_check()
cdef list a = list(self._coeffs)
Expand All @@ -675,9 +735,14 @@ cdef class SkewPolynomial_generic_dense(OrePolynomial_generic_dense):
cdef list q = [ ]
parent = self._parent
for i from da-db >= i >= 0:
c = parent.twisting_morphism(i)(inv) * a[i+db]
for j from 0 <= j < db:
a[i+j] -= c * parent.twisting_morphism(i)(b[j])
if parent._morphism is None:
c = inv * a[i+db]
for j from 0 <= j < db:
a[i+j] -= c * b[j]
else:
c = parent.twisting_morphism(i)(inv) * a[i+db]
for j from 0 <= j < db:
a[i+j] -= c * parent.twisting_morphism(i)(b[j])
q.append(c)
q.reverse()
return (self._new_c(q, parent), self._new_c(a[:db], parent, 1))
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