gh-36507: Fix implicit noexcept warnings
    
We have about 7k different occurrences of this warning (about 59k with
multiplicities).

It turns out to be easy to fix automatically, which we do. There's only
one mistake and one doctest error to fix after the automatic step.

We also fix a few warnings in regards of `nogil` should appear at the
end.

Finally, we disable `legacy_implicit_noexcept` option which is no longer
necessary.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36507
Reported by: Gonzalo Tornaría
Reviewer(s): Matthias Köppe

Author: Release Manager

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)
-    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff)
+    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff) noexcept
+    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff) noexcept
 
 cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
     pass

src/sage/algebras/clifford_algebra_element.pyx

@@ -64,7 +64,7 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
         """
         return repr_from_monomials(self.list(), self._parent._latex_term, True)
 
-    cdef _mul_(self, other):
+    cdef _mul_(self, other) noexcept:
         """
         Return ``self`` multiplied by ``other``.
 
@@ -175,7 +175,7 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
 
         return self.__class__(self.parent(), d)
 
-    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff):
+    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff) noexcept:
         r"""
         Multiply ``self * term`` with the ``term`` having support ``supp``
         and coefficient ``coeff``.
@@ -223,7 +223,7 @@ cdef class CliffordAlgebraElement(IndexedFreeModuleElement):
 
         return type(self)(self._parent, {supp: coeff}) * self
 
-    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff):
+    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff) noexcept:
         r"""
         Multiply ``term * self`` with the ``term`` having support ``supp``
         and coefficient ``coeff``.
@@ -399,7 +399,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
     """
     An element of an exterior algebra.
     """
-    cdef _mul_(self, other):
+    cdef _mul_(self, other) noexcept:
         """
         Return ``self`` multiplied by ``other``.
 
@@ -519,7 +519,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
 
         return self.__class__(P, d)
 
-    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff):
+    cdef CliffordAlgebraElement _mul_self_term(self, FrozenBitset supp, coeff) noexcept:
         r"""
         Multiply ``self * term`` with the ``term`` having support ``supp``
         and coefficient ``coeff``.
@@ -609,7 +609,7 @@ cdef class ExteriorAlgebraElement(CliffordAlgebraElement):
                 del d[k]
         return type(self)(self._parent, d)
 
-    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff):
+    cdef CliffordAlgebraElement _mul_term_self(self, FrozenBitset supp, coeff) noexcept:
         r"""
         Multiply ``term * self`` with the ``term`` having support ``supp``
         and coefficient ``coeff``.
@@ -938,7 +938,7 @@ cdef class CohomologyRAAGElement(CliffordAlgebraElement):
 
         :class:`~sage.groups.raag.CohomologyRAAG`
     """
-    cdef _mul_(self, other):
+    cdef _mul_(self, other) noexcept:
         """
         Return ``self`` multiplied by ``other``.
 

src/sage/algebras/exterior_algebra_groebner.pxd

@@ -7,8 +7,8 @@ from sage.algebras.clifford_algebra_element cimport CliffordAlgebraElement
 from sage.structure.parent cimport Parent
 from sage.structure.element cimport MonoidElement
 
-cdef long degree(FrozenBitset X)
-cdef CliffordAlgebraElement build_monomial(Parent E, FrozenBitset supp)
+cdef long degree(FrozenBitset X) noexcept
+cdef CliffordAlgebraElement build_monomial(Parent E, FrozenBitset supp) noexcept
 
 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)
-    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)
+    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 bint build_S_poly(self, GBElement f, GBElement 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)
+    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
 
-    cpdef CliffordAlgebraElement reduce(self, CliffordAlgebraElement f)
+    cpdef CliffordAlgebraElement reduce(self, CliffordAlgebraElement f) noexcept
     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)
-    cdef FrozenBitset int_to_bitset(self, Integer n)
+    cdef Integer bitset_to_int(self, FrozenBitset X) noexcept
+    cdef FrozenBitset int_to_bitset(self, Integer n) noexcept
 
 cdef class GroebnerStrategyNegLex(GroebnerStrategy):
     pass

src/sage/algebras/exterior_algebra_groebner.pyx

@@ -29,14 +29,14 @@ from sage.structure.richcmp cimport richcmp, rich_to_bool
 from sage.data_structures.blas_dict cimport iaxpy
 from copy import copy
 
-cdef inline long degree(FrozenBitset X):
+cdef inline long degree(FrozenBitset X) noexcept:
     """
     Compute the degree of ``X``.
     """
     return bitset_len(X._bitset)
 
 
-cdef inline CliffordAlgebraElement build_monomial(Parent E, FrozenBitset supp):
+cdef inline CliffordAlgebraElement build_monomial(Parent E, FrozenBitset supp) noexcept:
     """
     Helper function for the fastest way to build a monomial.
     """
@@ -129,14 +129,14 @@ cdef class GroebnerStrategy:
         else:
             self.side = 2
 
-    cdef inline FrozenBitset leading_support(self, CliffordAlgebraElement f):
+    cdef inline FrozenBitset leading_support(self, CliffordAlgebraElement f) noexcept:
         """
         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):
+    cdef inline partial_S_poly_left(self, GBElement f, GBElement g) noexcept:
         r"""
         Compute one half of the `S`-polynomial for ``f`` and ``g``.
 
@@ -153,7 +153,7 @@ cdef class GroebnerStrategy:
             ret.elt._monomial_coefficients[k] *= inv
         return ret
 
-    cdef inline partial_S_poly_right(self, GBElement f, GBElement g):
+    cdef inline partial_S_poly_right(self, GBElement f, GBElement g) noexcept:
         r"""
         Compute one half of the `S`-polynomial for ``f`` and ``g``.
 
@@ -170,7 +170,7 @@ cdef class GroebnerStrategy:
             ret.elt._monomial_coefficients[k] *= inv
         return ret
 
-    cdef inline GBElement build_elt(self, CliffordAlgebraElement f):
+    cdef inline GBElement build_elt(self, CliffordAlgebraElement f) noexcept:
         """
         Convert ``f`` into a ``GBElement``.
         """
@@ -180,7 +180,7 @@ 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):
+    cdef inline GBElement prod_GB_term(self, GBElement f, FrozenBitset t) noexcept:
         """
         Return the GBElement corresponding to ``f * t``.
 
@@ -192,7 +192,7 @@ 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):
+    cdef inline GBElement prod_term_GB(self, FrozenBitset t, GBElement f) noexcept:
         """
         Return the GBElement corresponding to ``t * f``.
 
@@ -204,7 +204,7 @@ cdef class GroebnerStrategy:
         cdef FrozenBitset ls = <FrozenBitset> f.ls._union(t)
         return GBElement(<CliffordAlgebraElement> ret, ls, self.bitset_to_int(ls))
 
-    cdef inline bint build_S_poly(self, GBElement f, GBElement g):
+    cdef inline bint build_S_poly(self, GBElement f, GBElement g) noexcept:
         r"""
         Check to see if we should build the `S`-polynomial.
 
@@ -219,7 +219,7 @@ cdef class GroebnerStrategy:
 
         return (<FrozenBitset> f.ls.intersection(g.ls)).isempty()
 
-    cdef inline set preprocessing(self, list P, list G):
+    cdef inline set preprocessing(self, list P, list G) noexcept:
         """
         Perform the preprocessing step.
         """
@@ -265,7 +265,7 @@ cdef class GroebnerStrategy:
                     break
         return L
 
-    cdef inline list reduction(self, list P, list G):
+    cdef inline list reduction(self, list P, list G) noexcept:
         """
         Perform the reduction of ``P`` mod ``G`` in ``E``.
         """
@@ -450,7 +450,7 @@ 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):
+    cpdef CliffordAlgebraElement reduce(self, CliffordAlgebraElement f) noexcept:
         """
         Reduce ``f`` modulo the ideal with Gröbner basis ``G``.
 
@@ -515,10 +515,10 @@ cdef class GroebnerStrategy:
                 iaxpy(-coeff, gp._monomial_coefficients, f._monomial_coefficients)
         return was_reduced
 
-    cdef Integer bitset_to_int(self, FrozenBitset X):
+    cdef Integer bitset_to_int(self, FrozenBitset X) noexcept:
         raise NotImplementedError
 
-    cdef FrozenBitset int_to_bitset(self, Integer n):
+    cdef FrozenBitset int_to_bitset(self, Integer n) noexcept:
         raise NotImplementedError
 
     def sorted_monomials(self, as_dict=False):
@@ -597,7 +597,7 @@ cdef class GroebnerStrategyNegLex(GroebnerStrategy):
     """
     Gröbner basis strategy implementing neglex ordering.
     """
-    cdef inline Integer bitset_to_int(self, FrozenBitset X):
+    cdef inline Integer bitset_to_int(self, FrozenBitset X) noexcept:
         """
         Convert ``X`` to an :class:`Integer`.
         """
@@ -608,7 +608,7 @@ cdef class GroebnerStrategyNegLex(GroebnerStrategy):
             elt = bitset_next(X._bitset, elt + 1)
         return ret
 
-    cdef inline FrozenBitset int_to_bitset(self, Integer n):
+    cdef inline FrozenBitset int_to_bitset(self, Integer n) noexcept:
         """
         Convert a nonnegative integer ``n`` to a :class:`FrozenBitset`.
         """
@@ -628,7 +628,7 @@ cdef class GroebnerStrategyDegRevLex(GroebnerStrategy):
     """
     Gröbner basis strategy implementing degree revlex ordering.
     """
-    cdef inline Integer bitset_to_int(self, FrozenBitset X):
+    cdef inline Integer bitset_to_int(self, FrozenBitset X) noexcept:
         """
         Convert ``X`` to an :class:`Integer`.
         """
@@ -647,7 +647,7 @@ 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):
+    cdef inline FrozenBitset int_to_bitset(self, Integer n) noexcept:
         """
         Convert a nonnegative integer ``n`` to a :class:`FrozenBitset`.
         """
@@ -669,7 +669,7 @@ cdef class GroebnerStrategyDegLex(GroebnerStrategy):
     """
     Gröbner basis strategy implementing degree lex ordering.
     """
-    cdef inline Integer bitset_to_int(self, FrozenBitset X):
+    cdef inline Integer bitset_to_int(self, FrozenBitset X) noexcept:
         """
         Convert ``X`` to an :class:`Integer`.
         """
@@ -688,7 +688,7 @@ 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):
+    cdef inline FrozenBitset int_to_bitset(self, Integer n) noexcept:
         """
         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)
+cpdef FiniteDimensionalAlgebraElement unpickle_FiniteDimensionalAlgebraElement(A, vec, mat) noexcept

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):
+cpdef FiniteDimensionalAlgebraElement unpickle_FiniteDimensionalAlgebraElement(A, vec, mat) noexcept:
     """
     Helper for unpickling of finite dimensional algebra elements.
 
@@ -341,7 +341,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         return self._vector.ncols()
 
     # (Rich) comparison
-    cpdef _richcmp_(self, right, int op):
+    cpdef _richcmp_(self, right, int op) noexcept:
         """
         EXAMPLES::
 
@@ -373,7 +373,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         """
         return richcmp(self._vector, <FiniteDimensionalAlgebraElement>right._vector, op)
 
-    cpdef _add_(self, other):
+    cpdef _add_(self, other) noexcept:
         """
         EXAMPLES::
 
@@ -383,7 +383,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         """
         return self._parent.element_class(self._parent, self._vector + <FiniteDimensionalAlgebraElement>other._vector)
 
-    cpdef _sub_(self, other):
+    cpdef _sub_(self, other) noexcept:
         """
         EXAMPLES::
 
@@ -393,7 +393,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         """
         return self._parent.element_class(self._parent, self._vector - <FiniteDimensionalAlgebraElement>other._vector)
 
-    cpdef _mul_(self, other):
+    cpdef _mul_(self, other) noexcept:
         """
         EXAMPLES::
 
@@ -403,7 +403,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
         """
         return self._parent.element_class(self._parent, self._vector * <FiniteDimensionalAlgebraElement>(other)._matrix)
 
-    cpdef _lmul_(self, Element other):
+    cpdef _lmul_(self, Element other) noexcept:
         """
         TESTS::
 
@@ -417,7 +417,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
                             .format(self.parent(), other.parent()))
         return self._parent.element_class(self._parent, self._vector * other)
 
-    cpdef _rmul_(self, Element other):
+    cpdef _rmul_(self, Element other) noexcept:
         """
         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)
-cpdef _backward_subs(factory, bint flatten=*)
-cpdef executor(tuple params)
-cpdef _solve_for_linear_terms(factory, list eqns=*)
+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