sagemathgh-37667: Fix noexcept clauses (sagemath#37560)

    
In sagemath#36507 I added a lot of `noexcept` clauses guided by a warning which
is not quite right (see
cython/cython#5999 (comment)).

A new warning in 3.0.9 shows the mistake (incorrectly added `noexcept`
clauses). This broke some doctests (sagemath#37560) and a workaround was
implemented for 10.3 (sagemath#37583) since we were too close to release.

This PR now does the proper fix, removing all the incorrect `noexcept`,
and also adding a few missing `noexcept`.

Note: if one tries this PR with cython <= 3.0.8 it seems it's wrong in
the sense that it will show 40k more warnings after the PR. These are
*incorrect* warnings.

If one uses cython 3.0.9 each of these 40k lines give a correct warning
before this PR and an incorrect warnings after the PR, and there is no
way to avoid 40k warnings.

To confirm this PR is a good one, one needs to use cython 3.0.9 +
cython/cython#6087 or wait for cython 3.0.10. In
this case, the warnings are correct and one will get 40k warnings before
the PR and no warning after the PR.

The last commit reverts the workaround from sagemath#37583 so we don't silence
these warnings on `cython()` now that we have our own code right.

@vbraun: this is "almost trivial" but touches too many files. Could we
merge it in beta0 to avoid conflicts? I did this "kind of" automatically
and I've been testing it for two weeks in almost all my builds. The
changes made should not affect behaviour at all in the legacy mode we
are using cython.

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
    
URL: sagemath#37667
Reported by: Gonzalo Tornaría
Reviewer(s): Gonzalo Tornaría, Matthias Köppe

src/sage/algebras/clifford_algebra_element.pxd

@@ -5,8 +5,8 @@ from sage.modules.with_basis.indexed_element cimport IndexedFreeModuleElement
 from sage.data_structures.bitset cimport FrozenBitset
 
 cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
-    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff) noexcept
-    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff) noexcept
+    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff)
+    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff)
 
 cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
     pass

src/sage/algebras/clifford_algebra_element.pyx

@@ -65,7 +65,7 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
         """
         return repr_from_monomials(self.list(), self._parent._latex_term, True)
 
-    cdef _mul_(self, other) noexcept:
+    cdef _mul_(self, other):
         """
         Return ``self`` multiplied by ``other``.
 
@@ -176,7 +176,7 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
 
         return self.__class__(self.parent(), d)
 
-    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff) noexcept:
+    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff):
         r"""
         Multiply ``self * term`` with the ``term`` having support ``supp``
         and coefficient ``coeff``.
@@ -224,7 +224,7 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
 
         return type(self)(self._parent, {supp: coeff}) * self
 
-    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff) noexcept:
+    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff):
         r"""
         Multiply ``term * self`` with the ``term`` having support ``supp``
         and coefficient ``coeff``.
@@ -400,7 +400,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
     """
     An element of an exterior algebra.
     """
-    cdef _mul_(self, other) noexcept:
+    cdef _mul_(self, other):
         """
         Return ``self`` multiplied by ``other``.
 
@@ -520,7 +520,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
 
         return self.__class__(P, d)
 
-    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff) noexcept:
+    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff):
         r"""
         Multiply ``self * term`` with the ``term`` having support ``supp``
         and coefficient ``coeff``.
@@ -610,7 +610,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
                 del d[k]
         return type(self)(self._parent, d)
 
-    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff) noexcept:
+    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff):
         r"""
         Multiply ``term * self`` with the ``term`` having support ``supp``
         and coefficient ``coeff``.
@@ -939,7 +939,7 @@ cdef class CohomologyRAAGElement(CliffordAlgebraElement):
 
         :class:`~sage.groups.raag.CohomologyRAAG`
     """
-    cdef _mul_(self, other) noexcept:
+    cdef _mul_(self, other):
         """
         Return ``self`` multiplied by ``other``.
 

src/sage/algebras/exterior_algebra_groebner.pxd

@@ -8,7 +8,7 @@ from sage.structure.parent cimport Parent
 from sage.structure.element cimport MonoidElement
 
 cdef long degree(FrozenBitset X) noexcept
-cdef CliffordAlgebraElement build_monomial(Parent E, FrozenBitset supp) noexcept
+cdef CliffordAlgebraElement build_monomial(Parent E, FrozenBitset supp)
 
 cdef class GBElement:
     cdef CliffordAlgebraElement elt
@@ -24,25 +24,25 @@ cdef class GroebnerStrategy:
     cdef Integer rank
     cdef public tuple groebner_basis
 
-    cdef inline GBElement build_elt(self, CliffordAlgebraElement f) noexcept
-    cdef inline GBElement prod_GB_term(self, GBElement f, FrozenBitset t) noexcept
-    cdef inline GBElement prod_term_GB(self, FrozenBitset t, GBElement f) noexcept
+    cdef inline GBElement build_elt(self, CliffordAlgebraElement f)
+    cdef inline GBElement prod_GB_term(self, GBElement f, FrozenBitset t)
+    cdef inline GBElement prod_term_GB(self, FrozenBitset t, GBElement f)
     cdef inline bint build_S_poly(self, GBElement f, GBElement g) noexcept
 
-    cdef inline FrozenBitset leading_support(self, CliffordAlgebraElement f) noexcept
-    cdef inline partial_S_poly_left(self, GBElement f, GBElement g) noexcept
-    cdef inline partial_S_poly_right(self, GBElement f, GBElement g) noexcept
-    cdef set preprocessing(self, list P, list G) noexcept
-    cdef list reduction(self, list P, list G) noexcept
+    cdef inline FrozenBitset leading_support(self, CliffordAlgebraElement f)
+    cdef inline partial_S_poly_left(self, GBElement f, GBElement g)
+    cdef inline partial_S_poly_right(self, GBElement f, GBElement g)
+    cdef set preprocessing(self, list P, list G)
+    cdef list reduction(self, list P, list G)
 
-    cpdef CliffordAlgebraElement reduce(self, CliffordAlgebraElement f) noexcept
+    cpdef CliffordAlgebraElement reduce(self, CliffordAlgebraElement f)
     cdef bint reduce_single(self, CliffordAlgebraElement f, CliffordAlgebraElement g) except -1
     cdef int reduced_gb(self, list G) except -1
 
     # These are the methods that determine the ordering of the monomials.
     # These must be implemented in subclasses. Declare them as "inline" there.
-    cdef Integer bitset_to_int(self, FrozenBitset X) noexcept
-    cdef FrozenBitset int_to_bitset(self, Integer n) noexcept
+    cdef Integer bitset_to_int(self, FrozenBitset X)
+    cdef FrozenBitset int_to_bitset(self, Integer n)
 
 cdef class GroebnerStrategyNegLex(GroebnerStrategy):
     pass

src/sage/algebras/exterior_algebra_groebner.pyx

@@ -37,7 +37,7 @@ cdef inline long degree(FrozenBitset X) noexcept:
     return bitset_len(X._bitset)
 
 
-cdef inline CliffordAlgebraElement build_monomial(Parent E, FrozenBitset supp) noexcept:
+cdef inline CliffordAlgebraElement build_monomial(Parent E, FrozenBitset supp):
     """
     Helper function for the fastest way to build a monomial.
     """
@@ -130,14 +130,14 @@ cdef class GroebnerStrategy:
         else:
             self.side = 2
 
-    cdef inline FrozenBitset leading_support(self, CliffordAlgebraElement f) noexcept:
+    cdef inline FrozenBitset leading_support(self, CliffordAlgebraElement f):
         """
         Return the leading support of the exterior algebra element ``f``.
         """
         cdef dict mc = <dict> f._monomial_coefficients
         return self.int_to_bitset(max(self.bitset_to_int(k) for k in mc))
 
-    cdef inline partial_S_poly_left(self, GBElement f, GBElement g) noexcept:
+    cdef inline partial_S_poly_left(self, GBElement f, GBElement g):
         r"""
         Compute one half of the `S`-polynomial for ``f`` and ``g``.
 
@@ -154,7 +154,7 @@ cdef class GroebnerStrategy:
             ret.elt._monomial_coefficients[k] *= inv
         return ret
 
-    cdef inline partial_S_poly_right(self, GBElement f, GBElement g) noexcept:
+    cdef inline partial_S_poly_right(self, GBElement f, GBElement g):
         r"""
         Compute one half of the `S`-polynomial for ``f`` and ``g``.
 
@@ -171,7 +171,7 @@ cdef class GroebnerStrategy:
             ret.elt._monomial_coefficients[k] *= inv
         return ret
 
-    cdef inline GBElement build_elt(self, CliffordAlgebraElement f) noexcept:
+    cdef inline GBElement build_elt(self, CliffordAlgebraElement f):
         """
         Convert ``f`` into a ``GBElement``.
         """
@@ -181,7 +181,7 @@ cdef class GroebnerStrategy:
         cdef Integer r = <Integer> max(self.bitset_to_int(k) for k in mc)
         return GBElement(f, self.int_to_bitset(r), r)
 
-    cdef inline GBElement prod_GB_term(self, GBElement f, FrozenBitset t) noexcept:
+    cdef inline GBElement prod_GB_term(self, GBElement f, FrozenBitset t):
         """
         Return the GBElement corresponding to ``f * t``.
 
@@ -193,7 +193,7 @@ cdef class GroebnerStrategy:
         cdef FrozenBitset ls = <FrozenBitset> f.ls._union(t)
         return GBElement(<CliffordAlgebraElement> ret, ls, self.bitset_to_int(ls))
 
-    cdef inline GBElement prod_term_GB(self, FrozenBitset t, GBElement f) noexcept:
+    cdef inline GBElement prod_term_GB(self, FrozenBitset t, GBElement f):
         """
         Return the GBElement corresponding to ``t * f``.
 
@@ -220,7 +220,7 @@ cdef class GroebnerStrategy:
 
         return (<FrozenBitset> f.ls.intersection(g.ls)).isempty()
 
-    cdef inline set preprocessing(self, list P, list G) noexcept:
+    cdef inline set preprocessing(self, list P, list G):
         """
         Perform the preprocessing step.
         """
@@ -266,7 +266,7 @@ cdef class GroebnerStrategy:
                     break
         return L
 
-    cdef inline list reduction(self, list P, list G) noexcept:
+    cdef inline list reduction(self, list P, list G):
         """
         Perform the reduction of ``P`` mod ``G`` in ``E``.
         """
@@ -451,7 +451,7 @@ cdef class GroebnerStrategy:
         cdef list G = [self.build_elt(f) for f in self.groebner_basis]
         self.reduced_gb(G)
 
-    cpdef CliffordAlgebraElement reduce(self, CliffordAlgebraElement f) noexcept:
+    cpdef CliffordAlgebraElement reduce(self, CliffordAlgebraElement f):
         """
         Reduce ``f`` modulo the ideal with Gröbner basis ``G``.
 
@@ -533,10 +533,10 @@ cdef class GroebnerStrategy:
                 iaxpy(-coeff, gp._monomial_coefficients, f._monomial_coefficients)
         return was_reduced
 
-    cdef Integer bitset_to_int(self, FrozenBitset X) noexcept:
+    cdef Integer bitset_to_int(self, FrozenBitset X):
         raise NotImplementedError
 
-    cdef FrozenBitset int_to_bitset(self, Integer n) noexcept:
+    cdef FrozenBitset int_to_bitset(self, Integer n):
         raise NotImplementedError
 
     def sorted_monomials(self, as_dict=False):
@@ -615,7 +615,7 @@ cdef class GroebnerStrategyNegLex(GroebnerStrategy):
     """
     Gröbner basis strategy implementing neglex ordering.
     """
-    cdef inline Integer bitset_to_int(self, FrozenBitset X) noexcept:
+    cdef inline Integer bitset_to_int(self, FrozenBitset X):
         """
         Convert ``X`` to an :class:`Integer`.
         """
@@ -626,7 +626,7 @@ cdef class GroebnerStrategyNegLex(GroebnerStrategy):
             elt = bitset_next(X._bitset, elt + 1)
         return ret
 
-    cdef inline FrozenBitset int_to_bitset(self, Integer n) noexcept:
+    cdef inline FrozenBitset int_to_bitset(self, Integer n):
         """
         Convert a nonnegative integer ``n`` to a :class:`FrozenBitset`.
         """
@@ -646,7 +646,7 @@ cdef class GroebnerStrategyDegRevLex(GroebnerStrategy):
     """
     Gröbner basis strategy implementing degree revlex ordering.
     """
-    cdef inline Integer bitset_to_int(self, FrozenBitset X) noexcept:
+    cdef inline Integer bitset_to_int(self, FrozenBitset X):
         """
         Convert ``X`` to an :class:`Integer`.
         """
@@ -665,7 +665,7 @@ cdef class GroebnerStrategyDegRevLex(GroebnerStrategy):
             elt = bitset_next(X._bitset, elt + 1)
         return Integer(sum(n.binomial(i) for i in range(deg+1)) - t - 1)
 
-    cdef inline FrozenBitset int_to_bitset(self, Integer n) noexcept:
+    cdef inline FrozenBitset int_to_bitset(self, Integer n):
         """
         Convert a nonnegative integer ``n`` to a :class:`FrozenBitset`.
         """
@@ -687,7 +687,7 @@ cdef class GroebnerStrategyDegLex(GroebnerStrategy):
     """
     Gröbner basis strategy implementing degree lex ordering.
     """
-    cdef inline Integer bitset_to_int(self, FrozenBitset X) noexcept:
+    cdef inline Integer bitset_to_int(self, FrozenBitset X):
         """
         Convert ``X`` to an :class:`Integer`.
         """
@@ -706,7 +706,7 @@ cdef class GroebnerStrategyDegLex(GroebnerStrategy):
             elt = bitset_next(X._bitset, elt + 1)
         return Integer(sum(n.binomial(i) for i in range(deg+1)) - t - 1)
 
-    cdef inline FrozenBitset int_to_bitset(self, Integer n) noexcept:
+    cdef inline FrozenBitset int_to_bitset(self, Integer n):
         """
         Convert a nonnegative integer ``n`` to a :class:`FrozenBitset`.
         """

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_element.pxd

@@ -6,4 +6,4 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
     cdef Matrix __matrix
     cdef FiniteDimensionalAlgebraElement __inverse
 
-cpdef FiniteDimensionalAlgebraElement unpickle_FiniteDimensionalAlgebraElement(A, vec, mat) noexcept
+cpdef FiniteDimensionalAlgebraElement unpickle_FiniteDimensionalAlgebraElement(A, vec, mat)

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_element.pyx

@@ -20,7 +20,7 @@ from sage.rings.integer import Integer
 
 from cpython.object cimport PyObject_RichCompare as richcmp
 
-cpdef FiniteDimensionalAlgebraElement unpickle_FiniteDimensionalAlgebraElement(A, vec, mat) noexcept:
+cpdef FiniteDimensionalAlgebraElement unpickle_FiniteDimensionalAlgebraElement(A, vec, mat):
     """
     Helper for unpickling of finite dimensional algebra elements.
 
@@ -365,7 +365,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         return self._vector.ncols()
 
     # (Rich) comparison
-    cpdef _richcmp_(self, right, int op) noexcept:
+    cpdef _richcmp_(self, right, int op):
         """
         EXAMPLES::
 
@@ -400,7 +400,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         """
         return richcmp(self._vector, <FiniteDimensionalAlgebraElement>right._vector, op)
 
-    cpdef _add_(self, other) noexcept:
+    cpdef _add_(self, other):
         """
         EXAMPLES::
 
@@ -411,7 +411,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         """
         return self._parent.element_class(self._parent, self._vector + <FiniteDimensionalAlgebraElement>other._vector)
 
-    cpdef _sub_(self, other) noexcept:
+    cpdef _sub_(self, other):
         """
         EXAMPLES::
 
@@ -422,7 +422,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         """
         return self._parent.element_class(self._parent, self._vector - <FiniteDimensionalAlgebraElement>other._vector)
 
-    cpdef _mul_(self, other) noexcept:
+    cpdef _mul_(self, other):
         """
         EXAMPLES::
 
@@ -434,7 +434,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         """
         return self._parent.element_class(self._parent, self._vector * <FiniteDimensionalAlgebraElement>(other)._matrix)
 
-    cpdef _lmul_(self, Element other) noexcept:
+    cpdef _lmul_(self, Element other):
         """
         TESTS::
 
@@ -450,7 +450,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
                             .format(self.parent(), other.parent()))
         return self._parent.element_class(self._parent, self._vector * other)
 
-    cpdef _rmul_(self, Element other) noexcept:
+    cpdef _rmul_(self, Element other):
         """
         TESTS::
 

src/sage/algebras/fusion_rings/fast_parallel_fmats_methods.pxd

@@ -1,4 +1,4 @@
-cdef _fmat(fvars, Nk_ij, one, a, b, c, d, x, y) noexcept
-cpdef _backward_subs(factory, bint flatten=*) noexcept
-cpdef executor(tuple params) noexcept
-cpdef _solve_for_linear_terms(factory, list eqns=*) noexcept
+cdef _fmat(fvars, Nk_ij, one, a, b, c, d, x, y)
+cpdef _backward_subs(factory, bint flatten=*)
+cpdef executor(tuple params)
+cpdef _solve_for_linear_terms(factory, list eqns=*)