Trac #32794: sage.functions.log.log: Move to sage.misc.functional

`sage.functions` is the home for symbolic functions; this package will
not be included in the distribution package '''sagemath-standard-no-
symbolics''' (#32601), nor in smaller distributions such as '''sagemath-
polyhedra''' (#32432).

`sage.functions.log.log` is not a symbolic function but only wrapper def
that either delegates to a symbolic function or calls a method. We move
it to `sage.misc.functional` so that non-symbolic uses of it do not pull
in symbolics; and change these imports.

There is already a function `log` in `sage.misc.functional`, deprecated
since #19444 (Sage 8.1).  We replace it.

We keep a non-deprecated import of `log` in `sage.functions.log` for
symbolic uses.

Similar to what was done in #32717 for `sqrt`.

URL: https://trac.sagemath.org/32794
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Dima Pasechnik

src/sage/coding/code_bounds.py

@@ -177,8 +177,7 @@
 from sage.rings.all import QQ, RR, ZZ, RDF
 from sage.arith.misc import is_prime_power
 from sage.arith.all import binomial
-from sage.functions.all import log
-from sage.misc.functional import sqrt
+from sage.misc.functional import sqrt, log
 from .delsarte_bounds import (delsarte_bound_hamming_space,
                               delsarte_bound_additive_hamming_space)
 
@@ -582,9 +581,9 @@ def entropy(x, q=2):
 
         sage: codes.bounds.entropy(0, 2)
         0
-        sage: codes.bounds.entropy(1/5,4).factor()
+        sage: codes.bounds.entropy(1/5,4).factor()    # optional - sage.symbolic
         1/10*(log(3) - 4*log(4/5) - log(1/5))/log(2)
-        sage: codes.bounds.entropy(1, 3)
+        sage: codes.bounds.entropy(1, 3)              # optional - sage.symbolic
         log(2)/log(3)
 
     Check that values not within the limits are properly handled::

src/sage/coding/kasami_codes.pyx

@@ -322,7 +322,7 @@ class KasamiCode(AbstractLinearCode):
             sage: C.minimum_distance()
             3
         """
-        from sage.functions.log import log
+        from sage.misc.functional import log
 
         m = log(self._s, 2)
         F = GF(self._s)

src/sage/combinat/words/finite_word.py

@@ -1496,7 +1496,7 @@ def topological_entropy(self, n):
         if n == 0:
             return 1
         pn = self.number_of_factors(n)
-        from sage.functions.all import log
+        from sage.functions.log import log
         return log(pn, base=d)/n
 
     def rauzy_graph(self, n):

src/sage/functions/log.py

@@ -21,6 +21,8 @@
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 
+from sage.misc.functional import log as log
+
 
 class Function_exp(GinacFunction):
     r"""
@@ -274,187 +276,6 @@ def __init__(self):
 logb = Function_log2()
 
 
-def log(*args, **kwds):
-    """
-    Return the logarithm of the first argument to the base of
-    the second argument which if missing defaults to ``e``.
-
-    It calls the ``log`` method of the first argument when computing
-    the logarithm, thus allowing the use of logarithm on any object
-    containing a ``log`` method. In other words, ``log`` works
-    on more than just real numbers.
-
-    EXAMPLES::
-
-        sage: log(e^2)
-        2
-
-    To change the base of the logarithm, add a second parameter::
-
-        sage: log(1000,10)
-        3
-
-    The synonym ``ln`` can only take one argument::
-
-        sage: ln(RDF(10))
-        2.302585092994046
-        sage: ln(2.718)
-        0.999896315728952
-        sage: ln(2.0)
-        0.693147180559945
-        sage: ln(float(-1))
-        3.141592653589793j
-        sage: ln(complex(-1))
-        3.141592653589793j
-
-    You can use
-    :class:`RDF<sage.rings.real_double.RealDoubleField_class>`,
-    :class:`~sage.rings.real_mpfr.RealField` or ``n`` to get a
-    numerical real approximation::
-
-        sage: log(1024, 2)
-        10
-        sage: RDF(log(1024, 2))
-        10.0
-        sage: log(10, 4)
-        1/2*log(10)/log(2)
-        sage: RDF(log(10, 4))
-        1.6609640474436813
-        sage: log(10, 2)
-        log(10)/log(2)
-        sage: n(log(10, 2))
-        3.32192809488736
-        sage: log(10, e)
-        log(10)
-        sage: n(log(10, e))
-        2.30258509299405
-
-    The log function works for negative numbers, complex
-    numbers, and symbolic numbers too, picking the branch
-    with angle between `-\\pi` and `\\pi`::
-
-        sage: log(-1+0*I)
-        I*pi
-        sage: log(CC(-1))
-        3.14159265358979*I
-        sage: log(-1.0)
-        3.14159265358979*I
-
-    Small integer powers are factored out immediately::
-
-        sage: log(4)
-        2*log(2)
-        sage: log(1000000000)
-        9*log(10)
-        sage: log(8) - 3*log(2)
-        0
-        sage: bool(log(8) == 3*log(2))
-        True
-
-    The ``hold`` parameter can be used to prevent automatic evaluation::
-
-        sage: log(-1,hold=True)
-        log(-1)
-        sage: log(-1)
-        I*pi
-        sage: I.log(hold=True)
-        log(I)
-        sage: I.log(hold=True).simplify()
-        1/2*I*pi
-
-    For input zero, the following behavior occurs::
-
-        sage: log(0)
-        -Infinity
-        sage: log(CC(0))
-        -infinity
-        sage: log(0.0)
-        -infinity
-
-    The log function also works in finite fields as long as the
-    argument lies in the multiplicative group generated by the base::
-
-        sage: F = GF(13); g = F.multiplicative_generator(); g
-        2
-        sage: a = F(8)
-        sage: log(a,g); g^log(a,g)
-        3
-        8
-        sage: log(a,3)
-        Traceback (most recent call last):
-        ...
-        ValueError: no logarithm of 8 found to base 3 modulo 13
-        sage: log(F(9), 3)
-        2
-
-    The log function also works for p-adics (see documentation for
-    p-adics for more information)::
-
-        sage: R = Zp(5); R
-        5-adic Ring with capped relative precision 20
-        sage: a = R(16); a
-        1 + 3*5 + O(5^20)
-        sage: log(a)
-        3*5 + 3*5^2 + 3*5^4 + 3*5^5 + 3*5^6 + 4*5^7 + 2*5^8 + 5^9 +
-        5^11 + 2*5^12 + 5^13 + 3*5^15 + 2*5^16 + 4*5^17 + 3*5^18 +
-        3*5^19 + O(5^20)
-
-
-    TESTS:
-
-    Check if :trac:`10136` is fixed::
-
-        sage: ln(x).operator() is ln
-        True
-        sage: log(x).operator() is ln
-        True
-
-        sage: log(1000, 10)
-        3
-        sage: log(3,-1)
-        -I*log(3)/pi
-        sage: log(int(8),2)
-        3
-        sage: log(8,int(2))
-        3
-        sage: log(8,2)
-        3
-        sage: log(1/8,2)
-        -3
-        sage: log(1/8,1/2)
-        3
-        sage: log(8,1/2)
-        -3
-
-        sage: log(1000, 10, base=5)
-        Traceback (most recent call last):
-        ...
-        TypeError: Symbolic function log takes at most 2 arguments (3 given)
-
-    Check if :trac:`29164` is fixed::
-
-        sage: log(0, 2)
-        -Infinity
-    """
-    base = kwds.pop('base', None)
-    if base:
-        args = args + (base,)
-    if not args:
-        raise TypeError("Symbolic function log takes at least 1 arguments (0 given)")
-    if len(args) == 1:
-        return ln(args[0], **kwds)
-    if len(args) > 2:
-        raise TypeError("Symbolic function log takes at most 2 arguments (%s given)" % (len(args) + 1 - (base is not None)))
-    try:
-        return args[0].log(args[1])
-    except ValueError as ex:
-        if ex.args[0].startswith("no logarithm"):
-            raise
-        return logb(args[0], args[1])
-    except (AttributeError, TypeError):
-        return logb(args[0], args[1])
-
-
 class Function_polylog(GinacFunction):
     def __init__(self):
         r"""

src/sage/graphs/generators/distance_regular.pyx

@@ -1865,7 +1865,7 @@ def is_classical_parameters_graph(list array):
         sage: is_classical_parameters_graph([27, 10, 1, 1, 10, 27])
         False
     """
-    from sage.functions.log import log
+    from sage.misc.functional import log
     from sage.rings.integer_ring import ZZ
     from sage.arith.misc import is_prime_power
     from sage.combinat.q_analogues import q_binomial
@@ -2099,8 +2099,7 @@ def graph_with_classical_parameters(int d, int b, alpha_in, beta_in, int gamma):
         Generalised hexagon of order (2, 8): Graph on 819 vertices
     """
     from sage.rings.rational import Rational
-    from sage.functions.log import log
-    from sage.misc.functional import sqrt
+    from sage.misc.functional import sqrt, log
     from sage.graphs.generators.families import JohnsonGraph, HammingGraph
     from sage.graphs.generators.classical_geometries import \
         UnitaryDualPolarGraph, OrthogonalDualPolarGraph, SymplecticDualPolarGraph
@@ -2383,7 +2382,7 @@ def is_near_polygon(array):
     """
     from sage.arith.misc import is_prime_power
     from sage.combinat.q_analogues import q_binomial
-    from sage.functions.log import log
+    from sage.misc.functional import log
 
     if len(array) % 2 != 0:
         return False

src/sage/matrix/operation_table.py

@@ -540,8 +540,8 @@ def _name_maker(self, names):
             ...
             ValueError: element names must be a list, or one of the keywords: 'letters', 'digits', 'elements'
         """
-        from sage.functions.log import log
-        name_list=[]
+        from sage.misc.functional import log
+        name_list = []
         if names == 'digits':
             if self._n == 0 or self._n == 1:
                 width = 1

src/sage/misc/dev_tools.py

@@ -493,7 +493,7 @@ def import_statements(*objects, **kwds):
     :trac:`23779`)::
 
         sage: import_statements('log')
-        from sage.functions.log import log
+        from sage.misc.functional import log
 
     .. NOTE::