gh-38104: `sage.coding`: Update `# needs`
    
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- Cherry-picked from #35095.

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### ⌛ Dependencies

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URL: #38104
Reported by: Matthias Köppe
Reviewer(s): David Coudert, Kwankyu Lee, Matthias Köppe

Author: Release Manager

src/sage/coding/abstract_code.py

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.modules sage.rings.finite_rings
+# sage.doctest: needs sage.modules sage.rings.finite_rings
 r"""
 Codes
 

src/sage/coding/ag_code.py

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings sage.schemes
+# sage.doctest: needs sage.rings.finite_rings sage.schemes
 """
 AG codes
 

src/sage/coding/ag_code_decoders.pyx

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.rings.finite_rings sage.schemes
+# sage.doctest: needs sage.rings.finite_rings sage.schemes
 r"""
 Decoders for AG codes
 

src/sage/coding/bch_code.py

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.modules sage.rings.finite_rings
+# sage.doctest: needs sage.modules sage.rings.finite_rings
 r"""
 BCH code
 

src/sage/coding/binary_code.pyx

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.modules sage.rings.finite_rings
+# sage.doctest: needs sage.modules sage.rings.finite_rings
 r"""
 Optimized low-level binary code representation
 
@@ -899,6 +899,7 @@ cdef class BinaryCode:
 
         EXAMPLES::
 
+            sage: # needs sage.graphs
             sage: import sage.coding.binary_code
             sage: from sage.coding.binary_code import *
             sage: M = Matrix(GF(2), [[1,1,1,1]])
@@ -3977,6 +3978,7 @@ cdef class BinaryCodeClassifier:
 
         MORE EXAMPLES::
 
+            sage: # needs sage.groups
             sage: soc_iter = codes.databases.self_orthogonal_binary_codes(12, 6, 4)
             sage: L = list(soc_iter)
             sage: for n in range(13):

src/sage/coding/channel.py

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.modules sage.rings.finite_rings
+# sage.doctest: needs sage.modules sage.rings.finite_rings
 r"""
 Channels
 

src/sage/coding/code_bounds.py

@@ -199,6 +199,7 @@ def _check_n_q_d(n, q, d, field_based=True):
 
     TESTS::
 
+        sage: # needs sage.libs.pari
         sage: from sage.coding.code_bounds import _check_n_q_d
         sage: _check_n_q_d(20, 16, 5)
         True
@@ -251,26 +252,26 @@ def codesize_upper_bound(n, d, q, algorithm=None):
 
     EXAMPLES::
 
-        sage: codes.bounds.codesize_upper_bound(10,3,2)
+        sage: codes.bounds.codesize_upper_bound(10, 3, 2)
         93
-        sage: codes.bounds.codesize_upper_bound(24,8,2,algorithm="LP")
+        sage: codes.bounds.codesize_upper_bound(24, 8, 2, algorithm="LP")               # needs sage.numerical.mip
         4096
-        sage: codes.bounds.codesize_upper_bound(10,3,2,algorithm="gap")  # optional - gap_package_guava
+        sage: codes.bounds.codesize_upper_bound(10, 3, 2, algorithm="gap")      # optional - gap_package_guava
         85
-        sage: codes.bounds.codesize_upper_bound(11,3,4,algorithm=None)
+        sage: codes.bounds.codesize_upper_bound(11, 3, 4, algorithm=None)               # needs sage.symbolic
         123361
-        sage: codes.bounds.codesize_upper_bound(11,3,4,algorithm="gap")  # optional - gap_package_guava
+        sage: codes.bounds.codesize_upper_bound(11, 3, 4, algorithm="gap")      # optional - gap_package_guava
         123361
-        sage: codes.bounds.codesize_upper_bound(11,3,4,algorithm="LP")
+        sage: codes.bounds.codesize_upper_bound(11, 3, 4, algorithm="LP")               # needs sage.numerical.mip
         109226
 
     TESTS:
 
     Make sure :issue:`22961` is fixed::
 
-        sage: codes.bounds.codesize_upper_bound(19,10,2)
+        sage: codes.bounds.codesize_upper_bound(19, 10, 2)
         20
-        sage: codes.bounds.codesize_upper_bound(19,10,2,algorithm="gap") # optional - gap_package_guava
+        sage: codes.bounds.codesize_upper_bound(19, 10, 2, algorithm="gap")     # optional - gap_package_guava
         20
 
     Meaningless parameters are rejected::
@@ -308,18 +309,18 @@ def dimension_upper_bound(n, d, q, algorithm=None):
 
     EXAMPLES::
 
-        sage: codes.bounds.dimension_upper_bound(10,3,2)
+        sage: codes.bounds.dimension_upper_bound(10,3,2)                                # needs sage.libs.pari sage.symbolic
         6
-        sage: codes.bounds.dimension_upper_bound(30,15,4)
+        sage: codes.bounds.dimension_upper_bound(30,15,4)                               # needs sage.libs.pari sage.symbolic
         13
-        sage: codes.bounds.dimension_upper_bound(30,15,4,algorithm="LP")
+        sage: codes.bounds.dimension_upper_bound(30,15,4,algorithm="LP")                # needs sage.libs.pari sage.numerical.mip
         12
 
     TESTS:
 
     Meaningless code parameters are rejected::
 
-        sage: codes.bounds.dimension_upper_bound(13,3,6)
+        sage: codes.bounds.dimension_upper_bound(13,3,6)                                # needs sage.libs.pari
         Traceback (most recent call last):
         ...
         ValueError: The alphabet size does not make sense for a code over a field
@@ -421,23 +422,23 @@ def griesmer_upper_bound(n,q,d,algorithm=None):
 
     The bound is reached for the ternary Golay codes::
 
-        sage: codes.bounds.griesmer_upper_bound(12,3,6)
+        sage: codes.bounds.griesmer_upper_bound(12,3,6)                                 # needs sage.libs.pari
         729
-        sage: codes.bounds.griesmer_upper_bound(11,3,5)
+        sage: codes.bounds.griesmer_upper_bound(11,3,5)                                 # needs sage.libs.pari
         729
 
     ::
 
-        sage: codes.bounds.griesmer_upper_bound(10,2,3)
+        sage: codes.bounds.griesmer_upper_bound(10,2,3)                                 # needs sage.libs.pari
         128
-        sage: codes.bounds.griesmer_upper_bound(10,2,3,algorithm="gap")  # optional - gap_package_guava
+        sage: codes.bounds.griesmer_upper_bound(10,2,3,algorithm="gap")         # optional - gap_package_guava, needs sage.libs.pari
         128
 
     TESTS::
 
-        sage: codes.bounds.griesmer_upper_bound(11,3,6)
+        sage: codes.bounds.griesmer_upper_bound(11,3,6)                                 # needs sage.libs.pari
         243
-        sage: codes.bounds.griesmer_upper_bound(11,3,6)
+        sage: codes.bounds.griesmer_upper_bound(11,3,6)                                 # needs sage.libs.pari
         243
     """
     _check_n_q_d(n, q, d)
@@ -448,7 +449,7 @@ def griesmer_upper_bound(n,q,d,algorithm=None):
     else:
         # To compute the bound, we keep summing up the terms on the RHS
         # until we start violating the inequality.
-        from sage.functions.other import ceil
+        from sage.arith.misc import integer_ceil as ceil
         den = 1
         s = 0
         k = 0
@@ -570,7 +571,7 @@ def gv_info_rate(n, delta, q):
 
     EXAMPLES::
 
-        sage: RDF(codes.bounds.gv_info_rate(100,1/4,3))  # abs tol 1e-15
+        sage: RDF(codes.bounds.gv_info_rate(100,1/4,3))  # abs tol 1e-15                # needs sage.libs.pari sage.symbolic
         0.36704992608261894
     """
     q = ZZ(q)
@@ -592,9 +593,9 @@ def entropy(x, q=2):
 
         sage: codes.bounds.entropy(0, 2)
         0
-        sage: codes.bounds.entropy(1/5,4).factor()    # optional - sage.symbolic
+        sage: codes.bounds.entropy(1/5,4).factor()                                      # needs sage.symbolic
         1/10*(log(3) - 4*log(4/5) - log(1/5))/log(2)
-        sage: codes.bounds.entropy(1, 3)              # optional - sage.symbolic
+        sage: codes.bounds.entropy(1, 3)                                                # needs sage.symbolic
         log(2)/log(3)
 
     Check that values not within the limits are properly handled::
@@ -641,8 +642,9 @@ def entropy_inverse(x, q=2):
 
     EXAMPLES::
 
+        sage: # needs sage.symbolic
         sage: from sage.coding.code_bounds import entropy_inverse
-        sage: entropy_inverse(0.1)
+        sage: entropy_inverse(0.1)                                                      # needs scipy
         0.012986862055...
         sage: entropy_inverse(1)
         1/2
@@ -678,10 +680,11 @@ def gv_bound_asymp(delta, q):
 
     EXAMPLES::
 
-        sage: RDF(codes.bounds.gv_bound_asymp(1/4,2))
+        sage: # needs sage.symbolic
+        sage: RDF(codes.bounds.gv_bound_asymp(1/4,2))                                   # needs sage.libs.pari
         0.18872187554086...
         sage: f = lambda x: codes.bounds.gv_bound_asymp(x,2)
-        sage: plot(f,0,1)
+        sage: plot(f,0,1)                                                               # needs sage.libs.pari sage.plot
         Graphics object consisting of 1 graphics primitive
     """
     return 1 - entropy(delta, q)
@@ -693,10 +696,11 @@ def hamming_bound_asymp(delta, q):
 
     EXAMPLES::
 
-        sage: RDF(codes.bounds.hamming_bound_asymp(1/4,2))
+        sage: # needs sage.symbolic
+        sage: RDF(codes.bounds.hamming_bound_asymp(1/4,2))                              # needs sage.libs.pari
         0.456435556800...
         sage: f = lambda x: codes.bounds.hamming_bound_asymp(x,2)
-        sage: plot(f,0,1)
+        sage: plot(f,0,1)                                                               # needs sage.libs.pari sage.plot
         Graphics object consisting of 1 graphics primitive
     """
     return 1 - entropy(delta / 2, q)
@@ -711,7 +715,7 @@ def singleton_bound_asymp(delta, q):
         sage: codes.bounds.singleton_bound_asymp(1/4,2)
         3/4
         sage: f = lambda x: codes.bounds.singleton_bound_asymp(x,2)
-        sage: plot(f,0,1)
+        sage: plot(f,0,1)                                                               # needs sage.plot
         Graphics object consisting of 1 graphics primitive
     """
     return 1 - delta
@@ -740,7 +744,7 @@ def elias_bound_asymp(delta, q):
 
     EXAMPLES::
 
-        sage: codes.bounds.elias_bound_asymp(1/4,2)
+        sage: codes.bounds.elias_bound_asymp(1/4,2)                                     # needs sage.symbolic
         0.39912396330...
     """
     r = 1 - 1 / q
@@ -755,7 +759,7 @@ def mrrw1_bound_asymp(delta, q):
 
     EXAMPLES::
 
-        sage: codes.bounds.mrrw1_bound_asymp(1/4,2)   # abs tol 4e-16
+        sage: codes.bounds.mrrw1_bound_asymp(1/4,2)   # abs tol 4e-16                   # needs sage.symbolic
         0.3545789026652697
     """
     return RDF(entropy((q-1-delta*(q-2)-2*sqrt((q-1)*delta*(1-delta)))/q,q))

src/sage/coding/code_constructions.py

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.modules sage.rings.finite_rings
+# sage.doctest: needs sage.modules sage.rings.finite_rings
 r"""
 Linear code constructors that do not preserve the structural information
 
@@ -227,47 +227,49 @@ def permutation_action(g, v):
 
     EXAMPLES::
 
+        sage: # needs sage.groups
         sage: V = VectorSpace(GF(3),5)
         sage: v = V([0,1,2,0,1])
-        sage: G = SymmetricGroup(5)                                                     # optional - sage.groups
-        sage: g = G([(1,2,3)])                                                          # optional - sage.groups
-        sage: permutation_action(g,v)                                                   # optional - sage.groups
+        sage: G = SymmetricGroup(5)
+        sage: g = G([(1,2,3)])
+        sage: permutation_action(g,v)
         (1, 2, 0, 0, 1)
-        sage: g = G([()])                                                               # optional - sage.groups
-        sage: permutation_action(g,v)                                                   # optional - sage.groups
+        sage: g = G([()])
+        sage: permutation_action(g,v)
         (0, 1, 2, 0, 1)
-        sage: g = G([(1,2,3,4,5)])                                                      # optional - sage.groups
-        sage: permutation_action(g,v)                                                   # optional - sage.groups
+        sage: g = G([(1,2,3,4,5)])
+        sage: permutation_action(g,v)
         (1, 2, 0, 1, 0)
         sage: L = Sequence([1,2,3,4,5])
-        sage: permutation_action(g,L)                                                   # optional - sage.groups
+        sage: permutation_action(g,L)
         [2, 3, 4, 5, 1]
         sage: MS = MatrixSpace(GF(3),3,7)
         sage: A = MS([[1,0,0,0,1,1,0],[0,1,0,1,0,1,0],[0,0,0,0,0,0,1]])
-        sage: S5 = SymmetricGroup(5)                                                    # optional - sage.groups
-        sage: g = S5([(1,2,3)])                                                         # optional - sage.groups
+        sage: S5 = SymmetricGroup(5)
+        sage: g = S5([(1,2,3)])
         sage: A
         [1 0 0 0 1 1 0]
         [0 1 0 1 0 1 0]
         [0 0 0 0 0 0 1]
-        sage: permutation_action(g,A)                                                   # optional - sage.groups
+        sage: permutation_action(g,A)
         [0 1 0 1 0 1 0]
         [0 0 0 0 0 0 1]
         [1 0 0 0 1 1 0]
 
     It also works on lists and is a "left action"::
 
+        sage: # needs sage.groups
         sage: v = [0,1,2,0,1]
-        sage: G = SymmetricGroup(5)                                                     # optional - sage.groups
-        sage: g = G([(1,2,3)])                                                          # optional - sage.groups
-        sage: gv = permutation_action(g,v); gv                                          # optional - sage.groups
+        sage: G = SymmetricGroup(5)
+        sage: g = G([(1,2,3)])
+        sage: gv = permutation_action(g,v); gv
         [1, 2, 0, 0, 1]
-        sage: permutation_action(g,v) == g(v)                                           # optional - sage.groups
+        sage: permutation_action(g,v) == g(v)
         True
-        sage: h = G([(3,4)])                                                            # optional - sage.groups
-        sage: gv = permutation_action(g,v)                                              # optional - sage.groups
-        sage: hgv = permutation_action(h,gv)                                            # optional - sage.groups
-        sage: hgv == permutation_action(h*g,v)                                          # optional - sage.groups
+        sage: h = G([(3,4)])
+        sage: gv = permutation_action(g,v)
+        sage: hgv = permutation_action(h,gv)
+        sage: hgv == permutation_action(h*g,v)
         True
 
     AUTHORS:
@@ -729,15 +731,15 @@ def ToricCode(P,F):
          sage: C = codes.ToricCode([[0,0],[1,0],[2,0],[0,1],[1,1]], GF(7))
          sage: C
          [36, 5] linear code over GF(7)
-         sage: C.minimum_distance()
+         sage: C.minimum_distance()                                                     # needs sage.groups
          24
          sage: C.minimum_distance(algorithm="guava")  # optional - gap_package_guava
          ...24
          sage: C = codes.ToricCode([[-2,-2],[-1,-2],[-1,-1],[-1,0],
          ....:                      [0,-1],[0,0],[0,1],[1,-1],[1,0]], GF(5))
          sage: C
          [16, 9] linear code over GF(5)
-         sage: C.minimum_distance()
+         sage: C.minimum_distance()                                                     # needs sage.groups
          6
          sage: C.minimum_distance(algorithm="guava")  # optional - gap_package_guava
          6
@@ -786,9 +788,9 @@ def WalshCode(m):
         [8, 3] linear code over GF(2)
         sage: C.spectrum()
         [1, 0, 0, 0, 7, 0, 0, 0, 0]
-        sage: C.minimum_distance()
+        sage: C.minimum_distance()                                                      # needs sage.libs.gap
         4
-        sage: C.minimum_distance(algorithm='gap')  # check d=2^(m-1)
+        sage: C.minimum_distance(algorithm='gap')  # check d=2^(m-1)                    # needs sage.libs.gap
         4
 
     REFERENCES:

src/sage/coding/codecan/codecan.pyx

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.pari
 r"""
 Canonical forms and automorphism group computation for linear codes over finite fields
 

src/sage/coding/cyclic_code.py

@@ -1,4 +1,4 @@
-# sage.doctest: optional - sage.modules sage.rings.finite_rings
+# sage.doctest: needs sage.modules sage.rings.finite_rings
 r"""
 Cyclic code
 
@@ -977,7 +977,7 @@ def message_space(self):
             sage: g = x ** 3 + x + 1
             sage: C = codes.CyclicCode(generator_pol=g, length=n)
             sage: E = codes.encoders.CyclicCodePolynomialEncoder(C)
-            sage: E.message_space()
+            sage: E.message_space()                                                     # needs sage.libs.ntl
             Univariate Polynomial Ring in x over Finite Field of size 2 (using GF2X)
         """
         return self._polynomial_ring