gh-36036: Fix E721 warnings for .pyx files
    
Fix E721 warnings for .pyx files

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pycodestyle reports: "E721 do not compare types, for exact checks use
`is` / `is not`, for instance checks use `isinstance()`." So replace
`type(x) == str` with `isinstance(x, str)`, replace `type(x) != type(y)`
with `type(x) is not type(y)`, etc. This is a followup to #36032 which
dealt with .py files.

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URL: #36036
Reported by: John H. Palmieri
Reviewer(s): John H. Palmieri, Matthias Köppe

Author: Release Manager

src/sage/dynamics/complex_dynamics/mandel_julia_helper.pyx

@@ -739,7 +739,7 @@ cpdef polynomial_mandelbrot(f, parameter=None, double x_center=0,
     # Take the given base color and create a list of evenly spaced
     # colors between the given base color and white. The number of
     # colors in the list depends on the variable color_num.
-    if type(base_color) == Color:
+    if isinstance(base_color, Color):
         # Convert Color to RGB list
         base_color = [int(k*255) for k in base_color]
     color_list = []
@@ -973,7 +973,7 @@ cpdef general_julia(f, double x_center=0, double y_center=0, image_width=4,
     # Take the given base color and create a list of evenly spaced
     # colors between the given base color and white. The number of
     # colors in the list depends on the variable color_num.
-    if type(base_color) == Color:
+    if isinstance(base_color, Color):
         # Convert Color to RGB list
         base_color = [int(k*255) for k in base_color]
     color_list = []

src/sage/libs/coxeter3/coxeter.pyx

@@ -86,8 +86,10 @@ cdef class String:
             sage: all([tb > ta1, tb >= ta1, tb >= tb])                 # optional - coxeter3
             True
         """
-        if type(other) != type(self):
-            return False
+        if type(other) is not type(self):
+            if op in (Py_LT, Py_LE, Py_GT, Py_GE):
+                return NotImplemented
+            return op == Py_NE
 
         s = repr(self)
         o = repr(other)
@@ -199,8 +201,10 @@ cdef class Type:
             sage: all([tb > ta1, tb >= ta1, tb >= tb])                 # optional - coxeter3
             True
         """
-        if type(other) != type(self):
-            return False
+        if type(other) is not type(self):
+            if op in (Py_LT, Py_LE, Py_GT, Py_GE):
+                return NotImplemented
+            return op == Py_NE
 
         s = repr(self)
         o = repr(other)
@@ -363,8 +367,10 @@ cdef class CoxGroup(SageObject):
             sage: B4 >= A5                                                              # optional - coxeter3
             True
         """
-        if type(other) != type(self):
-            return False
+        if type(other) is not type(self):
+            if op in (Py_LT, Py_LE, Py_GT, Py_GE):
+                return NotImplemented
+            return op == Py_NE
 
         s_t = self.type()
         o_t = other.type()
@@ -839,8 +845,10 @@ cdef class CoxGroupElement:
             sage: w1 != v1                                        # optional - coxeter3
             True
         """
-        if type(other) != type(self):
-            return False
+        if type(other) is not type(self):
+            if op in (Py_LT, Py_LE, Py_GT, Py_GE):
+                return NotImplemented
+            return op == Py_NE
 
         s_p = self.parent_group()
         o_p = other.parent_group()

src/sage/matrix/action.pyx

@@ -268,7 +268,7 @@ cdef class MatrixMatrixAction(MatrixMulAction):
                 B = B.dense_matrix()
             else:
                 A = A.dense_matrix()
-        assert type(A) == type(B), (type(A), type(B))
+        assert type(A) is type(B), (type(A), type(B))
         prod = A._matrix_times_matrix_(B)
         if A._subdivisions is not None or B._subdivisions is not None:
             Asubs = A.subdivisions()

src/sage/matroids/extension.pyx

@@ -484,7 +484,7 @@ cdef class MatroidExtensions(LinearSubclasses):
         """
         if M.full_rank() == 0:
             pass
-        if type(M) == BasisMatroid:
+        if isinstance(M, BasisMatroid):
             BM = M
         else:
             BM = BasisMatroid(M)

src/sage/matroids/lean_matrix.pyx

@@ -396,7 +396,7 @@ cdef class LeanMatrix:
         cdef long i
         cdef LeanMatrix A
         if isinstance(left, LeanMatrix):
-            if type(left) == type(right):
+            if type(left) is type(right):
                 return (<LeanMatrix>left)._matrix_times_matrix_(right)
             else:
                 return NotImplemented
@@ -457,7 +457,7 @@ cdef class LeanMatrix:
             return NotImplemented
         if not isinstance(left, LeanMatrix) or not isinstance(right, LeanMatrix):
             return NotImplemented
-        if type(left) != type(right):
+        if type(left) is not type(right):
             return NotImplemented
         if op == Py_EQ:
             res = True

src/sage/matroids/linear_matroid.pyx

@@ -4451,7 +4451,7 @@ cdef class TernaryMatroid(LinearMatroid):
         """
         if certificate:
             return self._is_isomorphic(other), self._isomorphism(other)
-        if type(other) == TernaryMatroid:
+        if isinstance(other, TernaryMatroid):
             return self.is_field_isomorphic(other)
         else:
             return LinearMatroid._is_isomorphic(self, other)
@@ -6152,7 +6152,7 @@ cdef class RegularMatroid(LinearMatroid):
         """
         if certificate:
             return self._is_isomorphic(other), self._isomorphism(other)
-        if type(other) == RegularMatroid:
+        if isinstance(other, RegularMatroid):
             return self.is_field_isomorphic(other)
         else:
             return LinearMatroid._is_isomorphic(self, other)

src/sage/numerical/backends/generic_backend.pyx

@@ -423,7 +423,7 @@ cdef class GenericBackend:
             sage: p.add_linear_constraint([(0, 3), (1, 2)], None, 6) # optional - Nonexistent_LP_solver
             sage: p.remove_constraints([0, 1])                       # optional - Nonexistent_LP_solver
         """
-        if type(constraints) == int: self.remove_constraint(constraints)
+        if isinstance(constraints, int): self.remove_constraint(constraints)
 
         cdef int last = self.nrows() + 1
 

src/sage/rings/integer.pyx

@@ -2852,12 +2852,12 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
         except (ValueError, TypeError):
             pass
 
-        if type(m) == Integer and type(self) == Integer:
+        if isinstance(m, Integer):
             elog = self.exact_log(m)
             if elog == -sage.rings.infinity.infinity or m**elog == self:
                 return elog
 
-        if (type(m) == Rational and type(self) == Integer
+        if (isinstance(m, Rational)
                 and m.numer() == 1):
             elog = -self.exact_log(m.denom())
             if m**elog == self:

src/sage/rings/number_field/totallyreal.pyx

@@ -292,7 +292,7 @@ def enumerate_totallyreal_fields_prim(n, B, a = [], verbose=0, return_seqs=False
     f_out[n_int] = 1
 
     if keep_fields:
-        if type(keep_fields) == bool:
+        if isinstance(keep_fields, bool):
             keepB = pari(int(math.floor(B*math.log(B))))
         else:
             keepB = pari(keep_fields)
@@ -337,7 +337,7 @@ def enumerate_totallyreal_fields_prim(n, B, a = [], verbose=0, return_seqs=False
     if verbose:
         verb_int = 1
         saveout = sys.stdout
-        if type(verbose) == str:
+        if isinstance(verbose, str):
             fsock = open(verbose, 'w')
             sys.stdout = fsock
         # Else, print to screen
@@ -458,7 +458,7 @@ def enumerate_totallyreal_fields_prim(n, B, a = [], verbose=0, return_seqs=False
         print("Polynomials with nfdisc <= B:", counts[3])
         for i from 0 <= i < lenS:
             print(S[i])
-        if type(verbose) == str:
+        if isinstance(verbose, str):
             fsock.close()
         sys.stdout = saveout
 

src/sage/structure/category_object.pyx

@@ -188,7 +188,7 @@ cdef class CategoryObject(SageObject):
         if self._category is None:
             self._init_category_(category)
             return
-        if not (type(category) == tuple or type(category) == list):
+        if not isinstance(category, (tuple, list)):
             category = [category]
         self._category = self._category.join([self._category]+list(category))