Trac #32413: Remove unnecessary uses of SR and symbolic functions in …

…sage.categories, sage.coding

`git grep -E '[.](symbolic|calculus|functions).*import' src/sage/coding`
reveals a number of calls to the symbolic calculus subsystem of Sage
that can be avoided, similar to what is done in #32411

URL: https://trac.sagemath.org/32413
Reported by: mkoeppe
Ticket author(s): Frédéric Chapoton
Reviewer(s): Matthias Koeppe

src/sage/categories/coalgebras_with_basis.py

@@ -196,13 +196,13 @@ def coproduct_iterated(self, n=1):
                 return self
             if n == 1:
                 return self.coproduct()
-            from sage.functions.all import ceil
             from sage.rings.integer import Integer
 
             # Use coassociativity of `\Delta` to perform many coproducts simultaneously.
             fn = Integer(n - 1) // 2
-            cn = ceil(Integer(n - 1) / 2)
-            split = lambda a,b: tensor([a.coproduct_iterated(fn), b.coproduct_iterated(cn)])
+            cn = Integer(n - 1) // 2 if n % 2 else Integer(n) // 2
+            split = lambda a, b: tensor([a.coproduct_iterated(fn),
+                                         b.coproduct_iterated(cn)])
             return self.coproduct().apply_multilinear_morphism(split)
 
     class Super(SuperModulesCategory):

src/sage/categories/examples/finite_enumerated_sets.py

@@ -1,18 +1,18 @@
 r"""
 Examples of finite enumerated sets
 """
-#*****************************************************************************
+# ****************************************************************************
 #  Copyright (C) 2009 Florent Hivert <[email protected]>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#******************************************************************************
+#                  https://www.gnu.org/licenses/
+# *****************************************************************************
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import IntegerRing
-from sage.functions.other import sqrt
+
 
 class Example(UniqueRepresentation, Parent):
     r"""
@@ -75,8 +75,9 @@ def __init__(self):
             Category of facade finite enumerated sets
             sage: TestSuite(C).run()
         """
-        self._set = [Integer(_) for _ in [1,2,3]]
-        Parent.__init__(self, facade = IntegerRing(), category = FiniteEnumeratedSets())
+        self._set = [Integer(_) for _ in [1, 2, 3]]
+        Parent.__init__(self, facade=IntegerRing(),
+                        category=FiniteEnumeratedSets())
 
     def _repr_(self):
         """
@@ -109,9 +110,10 @@ def __iter__(self):
         """
         return iter(self._set)
 
+
 class IsomorphicObjectOfFiniteEnumeratedSet(UniqueRepresentation, Parent):
 
-    def __init__(self, ambient = Example()):
+    def __init__(self, ambient=Example()):
         """
         TESTS::
 
@@ -123,7 +125,8 @@ def __init__(self, ambient = Example()):
             sage: TestSuite(C).run()
         """
         self._ambient = ambient
-        Parent.__init__(self, facade = IntegerRing(), category = FiniteEnumeratedSets().IsomorphicObjects())
+        Parent.__init__(self, facade=IntegerRing(),
+                        category=FiniteEnumeratedSets().IsomorphicObjects())
 
     def ambient(self):
         """
@@ -156,7 +159,7 @@ def lift(self, x):
             sage: C.lift(9)
             3
         """
-        return sqrt(x)
+        return x.sqrt()
 
     def retract(self, x):
         """

src/sage/categories/examples/graded_connected_hopf_algebras_with_basis.py

@@ -1,16 +1,16 @@
 r"""
 Examples of graded connected Hopf algebras with basis
 """
-#*****************************************************************************
+# ****************************************************************************
 #  Copyright (C) 2015 Jean-Baptiste Priez <[email protected]>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.categories.graded_hopf_algebras_with_basis import GradedHopfAlgebrasWithBasis
 from sage.combinat.free_module import CombinatorialFreeModule
-from sage.functions.other import binomial
+from sage.arith.misc import binomial
 from sage.misc.cachefunc import cached_method
 from sage.sets.non_negative_integers import NonNegativeIntegers
 

src/sage/categories/finite_dimensional_lie_algebras_with_basis.py

@@ -1120,7 +1120,7 @@ def chevalley_eilenberg_complex(self, M=None, dual=False, sparse=True, ncpus=Non
                                           " (the trivial module)")
 
             from itertools import combinations
-            from sage.functions.other import binomial
+            from sage.arith.misc import binomial
             from sage.matrix.matrix_space import MatrixSpace
             R = self.base_ring()
             zero = R.zero()

src/sage/categories/lie_conformal_algebras.py

@@ -282,7 +282,7 @@ def _test_jacobi(self, **options):
             tester = self._tester(**options)
             S = tester.some_elements()
             from sage.misc.misc import some_tuples
-            from sage.functions.other import binomial
+            from sage.arith.misc import binomial
             pz = tester._instance.zero()
             for x,y,z in some_tuples(S, 3, tester._max_runs):
                 brxy = x.bracket(y)

src/sage/categories/super_lie_conformal_algebras.py

@@ -122,7 +122,7 @@ def _test_jacobi(self, **options):
                 elements.append(s)
             S = elements
             from sage.misc.misc import some_tuples
-            from sage.functions.other import binomial
+            from sage.arith.misc import binomial
             pz = tester._instance.zero()
             for x,y,z in some_tuples(S, 3, tester._max_runs):
                 if x.is_zero() or y.is_zero():

src/sage/coding/channel.py

@@ -44,8 +44,9 @@
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
+from copy import copy
 
 from sage.structure.sage_object import SageObject
 from sage.rings.integer import Integer
@@ -55,8 +56,7 @@
 from sage.misc.abstract_method import abstract_method
 from sage.categories.cartesian_product import cartesian_product
 from sage.modules.free_module import VectorSpace
-from sage.functions.other import binomial
-from copy import copy
+from sage.arith.misc import binomial
 
 
 def random_error_vector(n, F, error_positions):

src/sage/coding/codecan/autgroup_can_label.pyx

@@ -101,7 +101,7 @@ and to the action of the symmetric group only::
 
 from sage.coding.codecan.codecan import PartitionRefinementLinearCode
 from sage.combinat.permutation import Permutation
-from sage.functions.other import factorial
+from sage.arith.misc import factorial
 
 
 def _cyclic_shift(n, p):

src/sage/coding/grs_code.py

@@ -47,6 +47,7 @@
 # (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
+from copy import copy
 
 from sage.categories.cartesian_product import cartesian_product
 
@@ -63,14 +64,14 @@
 from sage.misc.functional import symbolic_sum
 from sage.misc.misc_c import prod
 
-from copy import copy
-from sage.functions.other import binomial, floor
+from sage.functions.other import binomial
 from sage.symbolic.ring import SR
 
 from .linear_code import AbstractLinearCode
 from .encoder import Encoder
 from .decoder import Decoder, DecodingError
 
+
 class GeneralizedReedSolomonCode(AbstractLinearCode):
     r"""
     Representation of a (Generalized) Reed-Solomon code.
@@ -1563,7 +1564,7 @@ def _partial_xgcd(self, a, b, PolRing):
             sage: D._partial_xgcd(a, b, P)
             (10*x^2 + 3*x + 5, 1)
         """
-        stop = floor(self.code().dimension() + self.code().length()) // 2
+        stop = (self.code().dimension() + self.code().length()) // 2
         s = PolRing.one()
         prev_s = PolRing.zero()
 

src/sage/coding/guruswami_sudan/interpolation.py

@@ -7,19 +7,19 @@
 - David Lucas, ported the original implementation in Sage
 """
 
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2015 David Lucas <[email protected]>
 #                     2015 Johan S. R. Nielsen <[email protected]>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 
-from sage.functions.other import ceil, binomial
+from sage.arith.misc import binomial
 from sage.matrix.constructor import matrix
 from sage.misc.misc_c import prod
 
@@ -68,7 +68,7 @@ def _monomial_list(maxdeg, l, wy):
     EXAMPLES::
 
         sage: from sage.coding.guruswami_sudan.interpolation import _monomial_list
-        sage: _monomial_list(8, 1, 3)
+        sage: list(_monomial_list(8, 1, 3))
         [(0, 0),
          (1, 0),
          (2, 0),
@@ -83,11 +83,10 @@ def _monomial_list(maxdeg, l, wy):
          (3, 1),
          (4, 1)]
     """
-    monomials = []
-    for y in range(0, l+1):
-        for x in range(0,  ceil(maxdeg - y*wy)):
-            monomials.append((x, y))
-    return monomials
+    for y in range(l + 1):
+        for x in range(maxdeg - y * wy):
+            yield (x, y)
+
 
 def _interpolation_matrix_given_monomials(points, s, monomials):
     r"""
@@ -216,10 +215,11 @@ def _interpolation_matrix_problem(points, tau, parameters, wy):
         )
     """
     s, l = parameters[0], parameters[1]
-    monomials = _monomial_list(_interpolation_max_weighted_deg(len(points), tau, s), l, wy)
+    monomials = list(_monomial_list(_interpolation_max_weighted_deg(len(points), tau, s), l, wy))
     M = _interpolation_matrix_given_monomials(points, s, monomials)
     return (M, monomials)
 
+
 def gs_interpolation_linalg(points, tau, parameters, wy):
     r"""
     Compute an interpolation polynomial Q(x,y) for the Guruswami-Sudan algorithm

src/sage/coding/reed_muller_code.py

@@ -15,19 +15,21 @@
     - :class:`ReedMullerVectorEncoder`, an encoder with a vectorial message space (for both the two code classes)
     - :class:`ReedMullerPolynomialEncoder`, an encoder with a polynomial message space (for both the code classes)
 """
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2016 Parthasarathi Panda <[email protected]>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from operator import mul
+from functools import reduce
+
 from sage.matrix.constructor import matrix
-from sage.functions.other import binomial
+from sage.arith.misc import binomial
 from sage.coding.linear_code import AbstractLinearCode, LinearCodeSyndromeDecoder
 from sage.coding.encoder import Encoder
 from sage.combinat.subset import Subsets
@@ -38,7 +40,6 @@
 from sage.modules.free_module_element import vector
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.misc.cachefunc import cached_method
-from functools import reduce
 
 
 def _binomial_sum(n, k):