gh-35776: cylint: no more xrange in matroids
    
<!-- Please provide a concise, informative and self-explanatory title.
-->
<!-- Don't put issue numbers in the title. Put it in the Description
below. -->
<!-- For example, instead of "Fixes #12345", use "Add a new method to
multiply two integers" -->

### 📚 Description

getting rid of the uses of `xrange` in matroids

also changing a few C-style loops into python-style loops

<!-- Describe your changes here in detail. -->
<!-- Why is this change required? What problem does it solve? -->
<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes #12345". -->
<!-- If your change requires a documentation PR, please link it
appropriately. -->

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. It should be `[x]` not `[x
]`. -->

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- #12345: short description why this is a dependency
- #34567: ...
-->

<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
    
URL: #35776
Reported by: Frédéric Chapoton
Reviewer(s): Matthias Köppe

Author: Release Manager

src/sage/matroids/basis_exchange_matroid.pyx

@@ -176,7 +176,7 @@ cdef class BasisExchangeMatroid(Matroid):
             self._E = groundset
         self._idx = {}
         cdef long i
-        for i in xrange(self._groundset_size):
+        for i in range(self._groundset_size):
             self._idx[self._E[i]] = i
 
         if basis is not None:
@@ -219,7 +219,7 @@ cdef class BasisExchangeMatroid(Matroid):
         self._groundset = frozenset(E)
 
         self._idx = {}
-        for i in xrange(self._groundset_size):
+        for i in range(self._groundset_size):
             self._idx[self._E[i]] = i
 
         if self._weak_partition_var:
@@ -1090,7 +1090,7 @@ cdef class BasisExchangeMatroid(Matroid):
         bitset_free(loops)
         bitset_free(loop)
         bitset_free(active_rows)
-        for i in xrange(self.full_rank()):
+        for i in range(self.full_rank()):
             bitset_free(comp[i])
         sig_free(comp)
         return res
@@ -1267,16 +1267,16 @@ cdef class BasisExchangeMatroid(Matroid):
         flats = <bitset_t*>sig_malloc((self.full_rank() + 1) * sizeof(bitset_t))
         todo = <bitset_t*>sig_malloc((self.full_rank() + 1) * sizeof(bitset_t))
 
-        for i in xrange(self.full_rank() + 1):
+        for i in range(self.full_rank() + 1):
             bitset_init(flats[i], self._bitset_size)
             bitset_init(todo[i], self._bitset_size)
-        f_vec = [0 for i in xrange(self.full_rank() + 1)]
+        f_vec = [0 for i in range(self.full_rank() + 1)]
         i = 0
         bitset_clear(todo[0])
         self.__closure(flats[0], todo[0])
         bitset_complement(todo[0], flats[0])
         self._f_vector_rec(f_vec, flats, todo, 0, 0)
-        for i in xrange(self.full_rank() + 1):
+        for i in range(self.full_rank() + 1):
             bitset_free(flats[i])
             bitset_free(todo[i])
         sig_free(flats)
@@ -1340,7 +1340,7 @@ cdef class BasisExchangeMatroid(Matroid):
         flats = <bitset_t*>sig_malloc((r + 1) * sizeof(bitset_t))
         todo = <bitset_t*>sig_malloc((r + 1) * sizeof(bitset_t))
 
-        for i in xrange(r + 1):
+        for i in range(r + 1):
             bitset_init(flats[i], self._bitset_size)
             bitset_init(todo[i], self._bitset_size)
         Rflats = SetSystem(self._E)
@@ -1349,7 +1349,7 @@ cdef class BasisExchangeMatroid(Matroid):
         self.__closure(flats[0], todo[0])
         bitset_complement(todo[0], flats[0])
         self._flats_rec(Rflats, r, flats, todo, 0, 0)
-        for i in xrange(r + 1):
+        for i in range(r + 1):
             bitset_free(flats[i])
             bitset_free(todo[i])
         sig_free(flats)
@@ -1415,7 +1415,7 @@ cdef class BasisExchangeMatroid(Matroid):
         coflats = <bitset_t*>sig_malloc((r + 1) * sizeof(bitset_t))
         todo = <bitset_t*>sig_malloc((r + 1) * sizeof(bitset_t))
 
-        for i in xrange(r + 1):
+        for i in range(r + 1):
             bitset_init(coflats[i], self._bitset_size)
             bitset_init(todo[i], self._bitset_size)
         Rcoflats = SetSystem(self._E)
@@ -1424,7 +1424,7 @@ cdef class BasisExchangeMatroid(Matroid):
         self.__coclosure(coflats[0], todo[0])
         bitset_complement(todo[0], coflats[0])
         self._coflats_rec(Rcoflats, r, coflats, todo, 0, 0)
-        for i in xrange(r + 1):
+        for i in range(r + 1):
             bitset_free(coflats[i])
             bitset_free(todo[i])
         sig_free(coflats)
@@ -1462,28 +1462,28 @@ cdef class BasisExchangeMatroid(Matroid):
         flats = <bitset_t*>sig_malloc((k + 1) * sizeof(bitset_t))
         todo = <bitset_t*>sig_malloc((k + 1) * sizeof(bitset_t))
 
-        for i in xrange(k + 1):
+        for i in range(k + 1):
             bitset_init(flats[i], self._bitset_size)
             bitset_init(todo[i], self._bitset_size)
-        f_inc = [[0 for e in range(self._groundset_size + 1)] for i in xrange(k + 1)]
+        f_inc = [[0 for e in range(self._groundset_size + 1)] for i in range(k + 1)]
         i = 0
         bitset_clear(todo[0])
         self.__closure(flats[0], todo[0])
         bitset_complement(todo[0], flats[0])
         self._flat_element_inv_rec(f_inc, k, flats, todo, 0, 0)
-        for i in xrange(k + 1):
+        for i in range(k + 1):
             bitset_free(flats[i])
             bitset_free(todo[i])
         sig_free(flats)
         sig_free(todo)
         fie = {}
         for e in range(self._groundset_size):
-            t = tuple([f_inc[i][e] for i in xrange(k + 1)])
+            t = tuple([f_inc[i][e] for i in range(k + 1)])
             if t in fie:
                 fie[t].add(self._E[e])
             else:
                 fie[t] = set([self._E[e]])
-        f_vec = tuple([f_inc[i][self._groundset_size] for i in xrange(k + 1)])
+        f_vec = tuple([f_inc[i][self._groundset_size] for i in range(k + 1)])
         return fie, f_vec
 
     cdef _flat_element_inv_rec(self, object f_inc, long R, bitset_t* flats, bitset_t* todo, long elt, long i):
@@ -1806,7 +1806,7 @@ cdef class BasisExchangeMatroid(Matroid):
             if self.__is_independent(self._input):
                 bitset_copy(self._input2, self._current_basis)
                 e = bitset_first(self._current_basis)
-                for e in xrange(self._groundset_size):
+                for e in range(self._groundset_size):
                     if not bitset_in(self._current_basis, e):
                         self.__fundamental_circuit(self._output, e)
                         if e > bitset_first(self._output):
@@ -1854,7 +1854,7 @@ cdef class BasisExchangeMatroid(Matroid):
             if self.__is_independent(self._input):
                 bitset_copy(self._input2, self._current_basis)
                 e = bitset_first(self._current_basis)
-                for e in xrange(self._groundset_size):
+                for e in range(self._groundset_size):
                     if not bitset_in(self._current_basis, e):
                         self.__fundamental_circuit(self._output, e)
                         if e > bitset_first(self._output):
@@ -2162,7 +2162,7 @@ cdef class BasisExchangeMatroid(Matroid):
         Bitpacked version of ``is_isomorphism``.
         """
         cdef long i
-        morph = [other._idx[morphism[self._E[i]]] for i in xrange(len(self))]
+        morph = [other._idx[morphism[self._E[i]]] for i in range(len(self))]
         bitset_clear(self._input)
         bitset_set_first_n(self._input, self._matroid_rank)
         repeat = True
@@ -2226,15 +2226,15 @@ cdef class BasisExchangeMatroid(Matroid):
         if self.full_rank() != other.full_rank():
             return None
         if self.full_rank() == 0 or self.full_corank() == 0:
-            return {self.groundset_list()[i]: other.groundset_list()[i] for i in xrange(len(self))}
+            return {self.groundset_list()[i]: other.groundset_list()[i] for i in range(len(self))}
 
         if self._weak_invariant() != other._weak_invariant():
             return None
         PS = self._weak_partition()
         PO = other._weak_partition()
         if len(PS) == len(self) and len(PO) == len(other):
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PS[i])] = min(PO[i])
             if self.__is_isomorphism(other, morphism):
                 return morphism
@@ -2247,7 +2247,7 @@ cdef class BasisExchangeMatroid(Matroid):
         PO = other._strong_partition()
         if len(PS) == len(self) and len(PO) == len(other):
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PS[i])] = min(PO[i])
             if self.__is_isomorphism(other, morphism):
                 return morphism
@@ -2258,7 +2258,7 @@ cdef class BasisExchangeMatroid(Matroid):
             PHS = self._heuristic_partition()
             PHO = other._heuristic_partition()
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PHS[i])] = min(PHO[i])
             if self.__is_isomorphism(other, morphism):
                 return morphism
@@ -2327,7 +2327,7 @@ cdef class BasisExchangeMatroid(Matroid):
         PO = other._weak_partition()
         if len(PS) == len(self) and len(PO) == len(other):
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PS[i])] = min(PO[i])
             return self.__is_isomorphism(other, morphism)
 
@@ -2337,15 +2337,15 @@ cdef class BasisExchangeMatroid(Matroid):
         PO = other._strong_partition()
         if len(PS) == len(self) and len(PO) == len(other):
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PS[i])] = min(PO[i])
             return self.__is_isomorphism(other, morphism)
 
         if self._heuristic_invariant() == other._heuristic_invariant():
             PHS = self._heuristic_partition()
             PHO = other._heuristic_partition()
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PHS[i])] = min(PHO[i])
             if self.__is_isomorphism(other, morphism):
                 return True

src/sage/matroids/basis_matroid.pyx

@@ -178,7 +178,7 @@ cdef class BasisMatroid(BasisExchangeMatroid):
             bitset_init(self._bb, bc)
             bitset_set_first_n(self._bb, bc)
             NB = M.nonbases()
-            for i in xrange(len(NB)):
+            for i in range(len(NB)):
                 bitset_discard(self._bb, set_to_index(NB._subsets[i]))
 
             bitset_init(self._b, (<BasisExchangeMatroid>M)._bitset_size)
@@ -364,7 +364,7 @@ cdef class BasisMatroid(BasisExchangeMatroid):
         cdef BasisMatroid D
         D = BasisMatroid(groundset=self._E, rank=self.full_corank())
         N = binom[self._groundset_size][self._matroid_rank]
-        for i in xrange(N):
+        for i in range(N):
             if not bitset_in(self._bb, i):
                 bitset_discard(D._bb, N - i - 1)
         D.reset_current_basis()
@@ -684,16 +684,16 @@ cdef class BasisMatroid(BasisExchangeMatroid):
         cdef long i, j
         cdef list bc
         cdef dict bi
-        bc = [0 for i in xrange(len(self))]
-        for i in xrange(binom[self._groundset_size][self._matroid_rank]):
+        bc = [0 for i in range(len(self))]
+        for i in range(binom[self._groundset_size][self._matroid_rank]):
             if not bitset_in(self._bb, i):
                 index_to_set(self._b, i, self._matroid_rank, self._groundset_size)
                 j = bitset_first(self._b)
                 while j >= 0:
                     bc[j] += 1
                     j = bitset_next(self._b, j + 1)
         bi = {}
-        for e in xrange(len(self)):
+        for e in range(len(self)):
             if bc[e] in bi:
                 bi[bc[e]].append(e)
             else:
@@ -902,7 +902,7 @@ cdef class BasisMatroid(BasisExchangeMatroid):
         bitset_complement(bb_comp, self._bb)
 
         bitset_init(b2, max(len(self), 1))
-        morph = [(<BasisMatroid>other)._idx[morphism[self._E[i]]] for i in xrange(len(self))]
+        morph = [(<BasisMatroid>other)._idx[morphism[self._E[i]]] for i in range(len(self))]
         i = bitset_first(bb_comp)
         while i != -1:
             index_to_set(self._b, i, self._matroid_rank, self._groundset_size)
@@ -993,7 +993,7 @@ cdef class BasisMatroid(BasisExchangeMatroid):
         if self.full_rank() != other.full_rank():
             return None
         if self.full_rank() == 0:
-            return {self.groundset_list()[i]: other.groundset_list()[i] for i in xrange(len(self))}
+            return {self.groundset_list()[i]: other.groundset_list()[i] for i in range(len(self))}
         if self.bases_count() != other.bases_count():
             return None
 
@@ -1003,7 +1003,7 @@ cdef class BasisMatroid(BasisExchangeMatroid):
         PO = other._bases_partition()
         if len(PS) == len(self) and len(PO) == len(other):
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PS[i])] = min(PO[i])
             if self._is_relaxation(other, morphism):
                 return morphism
@@ -1016,7 +1016,7 @@ cdef class BasisMatroid(BasisExchangeMatroid):
         PO = other._bases_partition2()
         if len(PS) == len(self) and len(PO) == len(other):
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PS[i])] = min(PO[i])
             if self._is_relaxation(other, morphism):
                 return morphism
@@ -1027,7 +1027,7 @@ cdef class BasisMatroid(BasisExchangeMatroid):
             PHS = self._bases_partition3()
             PHO = other._bases_partition3()
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PHS[i])] = min(PHO[i])
             if self._is_relaxation(other, morphism):
                 return morphism
@@ -1085,7 +1085,7 @@ cdef class BasisMatroid(BasisExchangeMatroid):
         PO = other._bases_partition()
         if len(PS) == len(self) and len(PO) == len(other):
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PS[i])] = min(PO[i])
             return self._is_relaxation(other, morphism)
 
@@ -1095,15 +1095,15 @@ cdef class BasisMatroid(BasisExchangeMatroid):
         PO = other._bases_partition2()
         if len(PS) == len(self) and len(PO) == len(other):
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PS[i])] = min(PO[i])
             return self._is_relaxation(other, morphism)
 
         if self._bases_invariant3() == other._bases_invariant3():
             PHS = self._bases_partition3()
             PHO = other._bases_partition3()
             morphism = {}
-            for i in xrange(len(self)):
+            for i in range(len(self)):
                 morphism[min(PHS[i])] = min(PHO[i])
             if self._is_relaxation(other, morphism):
                 return True
@@ -1246,7 +1246,7 @@ cdef  binom_init(long N, long K):
     if binom[0][0] != 1:
         binom[0][0] = 1
         binom[0][1] = 0
-        for n in xrange(1, 2955):
+        for n in range(1, 2955):
             bin = 1
             k = 0
             while bin < 2 ** 32 and k <= 32 and k <= n:

src/sage/matroids/extension.pyx

@@ -340,8 +340,8 @@ cdef class LinearSubclasses:
 
         self._planes_on_line = [[] for l in range(self._hyperlines_count)]
         self._lines_on_plane = [[] for l in range(self._hyperplanes_count)]
-        for l in xrange(self._hyperlines_count):
-            for h in xrange(self._hyperplanes_count):
+        for l in range(self._hyperlines_count):
+            for h in range(self._hyperplanes_count):
                 if self._hyperplanes[h] >= self._hyperlines[l]:
                     self._lines_on_plane[h].append(l)
                     self._planes_on_line[l].append(h)
@@ -353,10 +353,10 @@ cdef class LinearSubclasses:
 
         if line_length is not None:
             self._line_length = line_length
-            self._mandatory_lines = [l for l in xrange(self._hyperlines_count) if len(self._planes_on_line[l]) >= line_length]
+            self._mandatory_lines = [l for l in range(self._hyperlines_count) if len(self._planes_on_line[l]) >= line_length]
 
         if subsets is not None:
-            for p in xrange(self._hyperplanes_count):
+            for p in range(self._hyperplanes_count):
                 H = self._hyperplanes[p]
                 for S in subsets:
                     if frozenset(S).issubset(H):
@@ -370,7 +370,7 @@ cdef class LinearSubclasses:
             if len(E) != len(E2) or len(F) != 1:
                 raise ValueError("LinearSubclasses: the ground set of the splice matroid is not of the form E + e-f")
 
-            for p in xrange(self._hyperplanes_count):
+            for p in range(self._hyperplanes_count):
                 X = self._hyperplanes[p] - F
                 if splice._rank(X) == splice.full_rank() - 1:
                     if splice._rank(X | F2) == splice.full_rank() - 1:
@@ -490,7 +490,7 @@ cdef class MatroidExtensions(LinearSubclasses):
             BM = BasisMatroid(M)
         LinearSubclasses.__init__(self, BM, line_length=line_length, subsets=subsets, splice=splice)
         self._BX = BM._extension(e, [])
-        self._BH = [BM._extension(e, [self._hyperplanes[i]]) for i in xrange(len(self._hyperplanes))]
+        self._BH = [BM._extension(e, [self._hyperplanes[i]]) for i in range(len(self._hyperplanes))]
         if orderly:
             self._orderly = True