gh-35879: various cython-lint fixes in algebras,arith,calculus,categories
    
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### 📚 Description

fixes some cython-lint warnings in the modified files, in the folders
`algebras, arith, calculus, categories`

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URL: #35879
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe

Author: Release Manager

src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx

@@ -164,7 +164,6 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
         """
         cdef list L = []
         cdef FreeAlgebra_letterplace P = self._parent
-        cdef int ngens = P.__ngens
         if P._base._repr_option('element_is_atomic'):
             for E, c in zip(self._poly.exponents(), self._poly.coefficients()):
                 monstr = P.exponents_to_string(E)
@@ -239,7 +238,6 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
         """
         cdef list L = []
         cdef FreeAlgebra_letterplace P = self._parent
-        cdef int ngens = P.__ngens
         from sage.misc.latex import latex
         if P._base._repr_option('element_is_atomic'):
             for E, c in zip(self._poly.exponents(), self._poly.coefficients()):

src/sage/algebras/letterplace/free_algebra_letterplace.pyx

@@ -594,7 +594,7 @@ cdef class FreeAlgebra_letterplace(Algebra):
         cdef list tmp
         for i from 0<=i<nblocks:
             base = i*ngens
-            tmp = [(j,E[base+j]) for j in range(ngens) if E[base+j]]
+            tmp = [(j, E[base+j]) for j in range(ngens) if E[base+j]]
             if not tmp:
                 continue
             var_ind, exp = tmp[0]
@@ -627,7 +627,7 @@ cdef class FreeAlgebra_letterplace(Algebra):
         cdef list names = self.latex_variable_names()
         for i from 0<=i<nblocks:
             base = i*ngens
-            tmp = [(j,E[base+j]) for j in range(ngens) if E[base+j]]
+            tmp = [(j, E[base+j]) for j in range(ngens) if E[base+j]]
             if not tmp:
                 continue
             var_ind, exp = tmp[0]

src/sage/algebras/octonion_algebra.pyx

@@ -389,7 +389,6 @@ cdef class Octonion_generic(AlgebraElement):
             0
         """
         cdef int i
-        a, b, c = self._parent._params
         cdef tuple table = self._parent._mult_table
         ret = self.vec.get_unsafe(0) ** 2
         for i in range(1, 8):
@@ -782,13 +781,13 @@ class OctonionAlgebra(UniqueRepresentation, Parent):
         g = a * b * c
         self._mult_table = (
           ((0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1)),
-          ((1, 1), (0, a), (3,-1), (2,-a), (5,-1), (4,-a), (7, 1), (6, a)),
-          ((2, 1), (3, 1), (0, b), (1, b), (6,-1), (7,-1), (4,-b), (5,-b)),
-          ((3, 1), (2, a), (1,-b), (0,-d), (7,-1), (6,-a), (5, b), (4, d)),
+          ((1, 1), (0, a), (3, -1), (2, -a), (5, -1), (4, -a), (7, 1), (6, a)),
+          ((2, 1), (3, 1), (0, b), (1, b), (6, -1), (7, -1), (4, -b), (5, -b)),
+          ((3, 1), (2, a), (1, -b), (0, -d), (7, -1), (6, -a), (5, b), (4, d)),
           ((4, 1), (5, 1), (6, 1), (7, 1), (0, c), (1, c), (2, c), (3, c)),
-          ((5, 1), (4, a), (7, 1), (6, a), (1,-c), (0,-e), (3,-c), (2,-e)),
-          ((6, 1), (7,-1), (4, b), (5,-b), (2,-c), (3, c), (0,-f), (1, f)),
-          ((7, 1), (6,-a), (5, b), (4,-d), (3,-c), (2, e), (1,-f), (0, g)),
+          ((5, 1), (4, a), (7, 1), (6, a), (1, -c), (0, -e), (3, -c), (2, -e)),
+          ((6, 1), (7, -1), (4, b), (5, -b), (2, -c), (3, c), (0, -f), (1, f)),
+          ((7, 1), (6, -a), (5, b), (4, -d), (3, -c), (2, e), (1, -f), (0, g)),
         )
 
     def _test_alternative(self, **options):

src/sage/algebras/quatalg/quaternion_algebra_element.pxd

@@ -8,15 +8,15 @@ from sage.categories.morphism cimport Morphism
 
 cdef class QuaternionAlgebraElement_abstract(AlgebraElement):
     cpdef bint is_constant(self)
-    cdef _do_print(self, x,y,z,w)
+    cdef _do_print(self, x, y, z, w)
     cpdef conjugate(self)
     cpdef reduced_norm(self)
     cpdef reduced_trace(self)
 
 cdef class QuaternionAlgebraElement_generic(QuaternionAlgebraElement_abstract):
     cdef object x, y, z, w
-        # we will assume that our element has the representation
-        # x + yi + zj + wk, where i^2 = a, j^2 = b
+    # we will assume that our element has the representation
+    # x + yi + zj + wk, where i^2 = a, j^2 = b
 
 cdef class QuaternionAlgebraElement_number_field(QuaternionAlgebraElement_abstract):
     cdef fmpz_poly_t x, y, z, w, a, b, modulus

src/sage/arith/functions.pxd

@@ -1,4 +1,3 @@
 cpdef LCM_list(v)
 
 cdef LCM_generic(itr, ret)
-

src/sage/arith/multi_modular.pxd

@@ -2,12 +2,12 @@ from sage.ext.mod_int cimport *
 from sage.libs.gmp.types cimport mpz_t
 
 cdef class MultiModularBasis_base():
-    cdef int      n
+    cdef int n
     cdef mod_int* moduli
-    cdef mpz_t*   partial_products
-    cdef mod_int* C # precomputed values for CRT
-    cdef mpz_t    product
-    cdef mpz_t    half_product
+    cdef mpz_t* partial_products
+    cdef mod_int* C  # precomputed values for CRT
+    cdef mpz_t product
+    cdef mpz_t half_product
     cdef unsigned long _l_bound
     cdef unsigned long _u_bound
     cdef unsigned long _num_primes

src/sage/arith/multi_modular.pyx

@@ -194,7 +194,6 @@ cdef class MultiModularBasis_base():
           the allowed interval; we will not return a prime in
           known_primes.
         """
-        cdef Py_ssize_t i
         cdef mod_int p
         while True:
             if len(known_primes) >= self._num_primes:
@@ -372,11 +371,10 @@ cdef class MultiModularBasis_base():
             return self.n
 
         # find new prime moduli
-        cdef int i
         new_moduli = []
         new_partial_products = []
-        cdef Integer M # keeps current height
-        cdef mod_int p # keeps current prime moduli
+        cdef Integer M  # keeps current height
+        cdef mod_int p  # keeps current prime moduli
 
         if self.n == 0:
             M = smallInteger(1)
@@ -633,7 +631,6 @@ cdef class MultiModularBasis_base():
             if mpz_cmp(z[j], self.half_product) > 0:
                 mpz_sub(z[j], z[j], self.product)
 
-
         cdef Integer zz
         zz = PY_NEW(Integer)
         mpz_set(zz.value, self.half_product)

src/sage/calculus/interpolation.pyx

@@ -92,7 +92,7 @@ cdef class Spline:
         ...
         ValueError: Order of derivative must be 1 or 2.
     """
-    def __init__(self, v=[]):
+    def __init__(self, v=None):
         """
         EXAMPLES::
 
@@ -101,7 +101,7 @@ cdef class Spline:
             sage: type(S)
             <class 'sage.calculus.interpolation.Spline'>
         """
-        self.v = list(v)
+        self.v = [] if v is None else list(v)
         self.started = 0
 
     def __dealloc__(self):
@@ -136,7 +136,7 @@ cdef class Spline:
             self.v[i] = xy
         else:
             for j from len(self.v) <= j <= i:
-                self.v.append((0,0))
+                self.v.append((0, 0))
             self.v[i] = xy
         self.stop_interp()
 

src/sage/calculus/interpolators.pyx

@@ -29,6 +29,7 @@ cimport numpy as np
 from math import pi
 cdef double TWOPI = 2*pi
 
+
 def polygon_spline(pts):
     """
     Creates a polygon from a set of complex or `(x,y)` points. The polygon
@@ -61,6 +62,7 @@ def polygon_spline(pts):
     """
     return PSpline(pts)
 
+
 cdef class PSpline:
     """
     A ``CCSpline`` object contains a polygon interpolation of a figure
@@ -160,6 +162,7 @@ cdef class PSpline:
         pt2 = self.pts[(int(t1) + 1) % self.N]
         return (pt2 - pt1) * self.N / TWOPI
 
+
 def complex_cubic_spline(pts):
     """
     Creates a cubic spline interpolated figure from a set of complex or
@@ -192,6 +195,7 @@ def complex_cubic_spline(pts):
     """
     return CCSpline(pts)
 
+
 cdef class CCSpline:
     """
     A ``CCSpline`` object contains a cubic interpolation of a figure
@@ -209,7 +213,7 @@ cdef class CCSpline:
         (0.9549296...-0.9549296...j)
     """
     cdef int N
-    cdef np.ndarray avec,bvec,cvec,dvec
+    cdef np.ndarray avec, bvec, cvec, dvec
 
     #standard cubic interpolation method
     def __init__(self, pts):
@@ -222,7 +226,7 @@ cdef class CCSpline:
         if isinstance(pts[0], tuple):
             pts = np.array(
                 [complex(pt[0], pt[1]) for pt in pts], dtype=np.complex128)
-        cdef int N, i, k
+        cdef int N, i
         N = len(pts)
         yvec = np.zeros(N, dtype=np.complex128)
         for i in range(N):

src/sage/calculus/ode.pxd

@@ -1,6 +1,4 @@
 cdef class ode_system:
    cdef int  c_j(self,double , double *, double *,double *)
 
-
    cdef int c_f(self,double t, double* , double* )
-