Merge sagemath#32717

src/sage/coding/code_bounds.py

@@ -177,7 +177,8 @@
 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, sqrt
+from sage.functions.all import log
+from sage.misc.functional import sqrt
 from .delsarte_bounds import (delsarte_bound_hamming_space,
                               delsarte_bound_additive_hamming_space)
 

src/sage/coding/guruswami_sudan/gs_decoder.py

@@ -31,7 +31,8 @@
 from sage.coding.guruswami_sudan.utils import (johnson_radius,
                                                gilt,
                                                solve_degree2_to_integer_range)
-from sage.functions.other import floor, sqrt
+from sage.functions.other import floor
+from sage.misc.functional import sqrt
 
 def n_k_params(C, n_k):
     r"""

src/sage/coding/guruswami_sudan/utils.py

@@ -19,7 +19,8 @@
 #*****************************************************************************
 
 
-from sage.functions.other import floor, sqrt
+from sage.functions.other import floor
+from sage.misc.functional import sqrt
 from sage.rings.integer_ring import ZZ
 from sage.rings.integer import Integer
 

src/sage/coding/linear_code.py

@@ -837,7 +837,7 @@ def chinen_polynomial(self):
         - Chinen, K. "An abundance of invariant polynomials satisfying the
           Riemann hypothesis", April 2007 preprint.
         """
-        from sage.functions.all import sqrt
+        from sage.misc.functional import sqrt
         C = self
         n = C.length()
         RT = PolynomialRing(QQ,2,"Ts")

src/sage/combinat/binary_recurrence_sequences.py

@@ -67,7 +67,7 @@
 from sage.rings.integer import Integer
 from sage.arith.all import lcm, next_prime, is_prime, next_prime_power, legendre_symbol
 from sage.functions.log import log
-from sage.functions.other import sqrt
+from sage.misc.functional import sqrt
 
 
 class BinaryRecurrenceSequence(SageObject):

src/sage/combinat/parallelogram_polyomino.py

@@ -39,7 +39,7 @@
 from sage.combinat.combinat import catalan_number
 from sage.combinat.combinatorial_map import combinatorial_map
 from sage.functions.trig import cos, sin
-from sage.functions.other import sqrt
+from sage.misc.functional import sqrt
 
 from sage.plot.graphics import Graphics
 from sage.plot.line import line

src/sage/combinat/posets/poset_examples.py

@@ -1924,7 +1924,8 @@ def _random_lattice(n, p):
         meet for `e, m` for all `m \in M`. We do that by keeping
         track of meet matrix and list of maximal elements.
     """
-    from sage.functions.other import floor, sqrt
+    from sage.functions.other import floor
+    from sage.misc.functional import sqrt
     from sage.misc.prandom import random
 
     n = n-1

src/sage/combinat/root_system/plot.py

@@ -1574,7 +1574,7 @@ def barycentric_projection_matrix(n, angle=0):
 
     """
     from sage.matrix.constructor import matrix
-    from sage.functions.other import sqrt
+    from sage.misc.functional import sqrt
     n = ZZ(n)
     if n == 0:
         return matrix(QQ, 0, 1)

src/sage/combinat/symmetric_group_representations.py

@@ -29,7 +29,7 @@
 # ****************************************************************************
 
 from sage.symbolic.ring import SR
-from sage.functions.all import sqrt
+from sage.misc.functional import sqrt
 from sage.combinat.partition import Partition, Partitions
 from sage.combinat.permutation import Permutation, Permutations, from_cycles
 from sage.combinat.tableau import StandardTableaux, Tableau

src/sage/combinat/words/word_generators.py

@@ -574,7 +574,8 @@ def FibonacciWord(self, alphabet=(0, 1), construction_method="recursive"):
             return w
 
         elif construction_method == "function":
-            from sage.functions.other import sqrt, floor
+            from sage.functions.other import floor
+            from sage.misc.functional import sqrt
             phi = (1 + sqrt(5))/2 # the golden ratio
             f = lambda n:a if floor((n+2)*phi) - floor((n+1)*phi) == 2 else b
             return W(f)

src/sage/crypto/lwe.py

@@ -92,7 +92,8 @@
 """
 
 from sage.functions.log import log
-from sage.functions.other import sqrt, floor, ceil
+from sage.functions.other import floor, ceil
+from sage.misc.functional import sqrt
 from sage.misc.functional import cyclotomic_polynomial, round
 from sage.misc.randstate import set_random_seed
 from sage.misc.prandom import randint

src/sage/dynamics/arithmetic_dynamics/endPN_automorphism_group.py

@@ -23,7 +23,7 @@
 
 from copy import copy, deepcopy
 from sage.combinat.subset import Subsets
-from sage.functions.all import sqrt
+from sage.misc.functional import sqrt
 from itertools import permutations, combinations, product
 from sage.matrix.constructor import matrix
 from sage.structure.element import is_Matrix

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -59,7 +59,7 @@ class initialization directly.
 from sage.categories.number_fields import NumberFields
 from sage.categories.homset import End
 from sage.dynamics.arithmetic_dynamics.generic_ds import DynamicalSystem
-from sage.functions.all import sqrt
+from sage.misc.functional import sqrt
 from sage.functions.other import ceil
 from sage.libs.pari.all import PariError
 from sage.matrix.constructor import matrix, identity_matrix

src/sage/dynamics/arithmetic_dynamics/wehlerK3.py

@@ -29,7 +29,7 @@
 from sage.calculus.functions import jacobian
 from sage.categories.fields import Fields
 from sage.categories.number_fields import NumberFields
-from sage.functions.all import sqrt
+from sage.misc.functional import sqrt
 from sage.misc.cachefunc import cached_method
 from sage.misc.mrange import xmrange
 from sage.rings.all import CommutativeRing

src/sage/functions/bessel.py

@@ -210,7 +210,7 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.functions.other import sqrt
+from sage.misc.functional import sqrt
 from sage.functions.log import exp
 from sage.functions.hyperbolic import sinh, cosh
 from sage.functions.trig import sin, cos

src/sage/functions/error.py

@@ -44,7 +44,8 @@
 from sage.symbolic.function import BuiltinFunction
 from sage.libs.mpmath import utils as mpmath_utils
 from sage.symbolic.expression import Expression
-from sage.functions.all import sqrt, exp
+from sage.functions.all import exp
+from sage.misc.functional import sqrt
 from sage.symbolic.constants import pi
 from sage.rings.rational import Rational
 from sage.rings.infinity import unsigned_infinity

src/sage/functions/orthogonal_polys.py

@@ -1824,7 +1824,7 @@ def eval_recursive(self, n, m, x, **kwds):
             sage: gen_legendre_Q(2,2,x).subs(x=2).expand()
             9/2*I*pi - 9/2*log(3) + 14/3
         """
-        from sage.functions.all import sqrt
+        from sage.misc.functional import sqrt
         if m == n + 1 or n == 0:
             if m.mod(2).is_zero():
                 denom = (1 - x**2)**(m/2)

src/sage/functions/other.py

@@ -19,9 +19,13 @@
              'gamma_inc_lower', 'psi', 'beta'), deprecation=24411)
 
 from sage.symbolic.function import GinacFunction, BuiltinFunction
-from sage.symbolic.expression import Expression, register_symbol, symbol_table, I
+from sage.symbolic.expression import Expression, register_symbol, symbol_table
 from sage.symbolic.ring import SR
-from sage.rings.all import Integer, Rational, RealField, ZZ, ComplexField
+from sage.rings.integer import Integer
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational import Rational
+from sage.rings.complex_mpfr import ComplexField
+from sage.rings.real_mpfr import RealField
 from sage.misc.latex import latex
 from sage.structure.element import Element
 import math
@@ -35,7 +39,7 @@
 
 from sage.arith.all import binomial as arith_binomial
 
-one_half = SR.one() / SR(2)
+from sage.misc.functional import sqrt
 
 
 class Function_abs(GinacFunction):
@@ -752,156 +756,6 @@ def _eval_(self, x):
 frac = Function_frac()
 
 
-def _do_sqrt(x, prec=None, extend=True, all=False):
-        r"""
-        Used internally to compute the square root of x.
-
-        INPUT:
-
-        -  ``x`` - a number
-
-        -  ``prec`` - None (default) or a positive integer
-           (bits of precision) If not None, then compute the square root
-           numerically to prec bits of precision.
-
-        -  ``extend`` - bool (default: True); this is a place
-           holder, and is always ignored since in the symbolic ring everything
-           has a square root.
-
-        -  ``extend`` - bool (default: True); whether to extend
-           the base ring to find roots. The extend parameter is ignored if
-           prec is a positive integer.
-
-        -  ``all`` - bool (default: False); whether to return
-           a list of all the square roots of x.
-
-
-        EXAMPLES::
-
-            sage: from sage.functions.other import _do_sqrt
-            sage: _do_sqrt(3)
-            sqrt(3)
-            sage: _do_sqrt(3,prec=10)
-            1.7
-            sage: _do_sqrt(3,prec=100)
-            1.7320508075688772935274463415
-            sage: _do_sqrt(3,all=True)
-            [sqrt(3), -sqrt(3)]
-
-        Note that the extend parameter is ignored in the symbolic ring::
-
-            sage: _do_sqrt(3,extend=False)
-            sqrt(3)
-        """
-        if prec:
-            if x >= 0:
-                 return RealField(prec)(x).sqrt(all=all)
-            else:
-                 return ComplexField(prec)(x).sqrt(all=all)
-        if x == -1:
-            z = I
-        else:
-            z = SR(x) ** one_half
-
-        if all:
-            if z:
-                return [z, -z]
-            else:
-                return [z]
-        return z
-
-def sqrt(x, *args, **kwds):
-        r"""
-        INPUT:
-
-        -  ``x`` - a number
-
-        -  ``prec`` - integer (default: None): if None, returns
-           an exact square root; otherwise returns a numerical square root if
-           necessary, to the given bits of precision.
-
-        -  ``extend`` - bool (default: True); this is a place
-           holder, and is always ignored or passed to the sqrt function for x,
-           since in the symbolic ring everything has a square root.
-
-        -  ``all`` - bool (default: False); if True, return all
-           square roots of self, instead of just one.
-
-        EXAMPLES::
-
-            sage: sqrt(-1)
-            I
-            sage: sqrt(2)
-            sqrt(2)
-            sage: sqrt(2)^2
-            2
-            sage: sqrt(4)
-            2
-            sage: sqrt(4,all=True)
-            [2, -2]
-            sage: sqrt(x^2)
-            sqrt(x^2)
-
-        For a non-symbolic square root, there are a few options.
-        The best is to numerically approximate afterward::
-
-            sage: sqrt(2).n()
-            1.41421356237310
-            sage: sqrt(2).n(prec=100)
-            1.4142135623730950488016887242
-
-        Or one can input a numerical type.
-
-            sage: sqrt(2.)
-            1.41421356237310
-            sage: sqrt(2.000000000000000000000000)
-            1.41421356237309504880169
-            sage: sqrt(4.0)
-            2.00000000000000
-
-        To prevent automatic evaluation, one can use the ``hold`` parameter
-        after coercing to the symbolic ring::
-
-            sage: sqrt(SR(4),hold=True)
-            sqrt(4)
-            sage: sqrt(4,hold=True)
-            Traceback (most recent call last):
-            ...
-            TypeError: ..._do_sqrt() got an unexpected keyword argument 'hold'
-
-        This illustrates that the bug reported in :trac:`6171` has been fixed::
-
-            sage: a = 1.1
-            sage: a.sqrt(prec=100)  # this is supposed to fail
-            Traceback (most recent call last):
-            ...
-            TypeError: ...sqrt() got an unexpected keyword argument 'prec'
-            sage: sqrt(a, prec=100)
-            1.0488088481701515469914535137
-            sage: sqrt(4.00, prec=250)
-            2.0000000000000000000000000000000000000000000000000000000000000000000000000
-
-        One can use numpy input as well::
-
-            sage: import numpy
-            sage: a = numpy.arange(2,5)
-            sage: sqrt(a)
-            array([1.41421356, 1.73205081, 2.        ])
-        """
-        if isinstance(x, float):
-            return math.sqrt(x)
-        elif type(x).__module__ == 'numpy':
-            from numpy import sqrt
-            return sqrt(x)
-        try:
-            return x.sqrt(*args, **kwds)
-        # The following includes TypeError to catch cases where sqrt
-        # is called with a "prec" keyword, for example, but the sqrt
-        # method for x doesn't accept such a keyword.
-        except (AttributeError, TypeError):
-            pass
-        return _do_sqrt(x, *args, **kwds)
-
 # register sqrt in pynac symbol_table for conversion back from other systems
 register_symbol(sqrt, dict(mathematica='Sqrt'))
 symbol_table['functions']['sqrt'] = sqrt

src/sage/functions/special.py

@@ -165,7 +165,8 @@
 from sage.symbolic.constants import pi
 from sage.symbolic.function import BuiltinFunction
 from sage.libs.mpmath import utils as mpmath_utils
-from sage.functions.all import sqrt, sin, cot, exp
+from sage.functions.all import sin, cot, exp
+from sage.misc.functional import sqrt
 from sage.symbolic.constants import I
 
 

src/sage/geometry/hyperbolic_space/hyperbolic_coercion.py

@@ -25,7 +25,8 @@
 from sage.modules.free_module_element import vector
 from sage.rings.integer import Integer
 from sage.rings.infinity import infinity
-from sage.functions.other import real, imag, sqrt
+from sage.functions.other import real, imag
+from sage.misc.functional import sqrt
 from sage.misc.lazy_import import lazy_import
 lazy_import('sage.misc.call', 'attrcall')
 

src/sage/geometry/hyperbolic_space/hyperbolic_geodesic.py

@@ -93,7 +93,8 @@
 from sage.symbolic.constants import pi
 from sage.modules.free_module_element import vector
 from sage.matrix.constructor import matrix
-from sage.functions.other import real, imag, sqrt
+from sage.functions.other import real, imag
+from sage.misc.functional import sqrt
 from sage.functions.trig import arccos
 from sage.functions.log import exp
 from sage.functions.hyperbolic import sinh, cosh, arcsinh

src/sage/geometry/hyperbolic_space/hyperbolic_isometry.py

@@ -51,7 +51,8 @@
 from sage.rings.infinity import infinity
 from sage.misc.latex import latex
 from sage.rings.real_double import RDF
-from sage.functions.other import imag, sqrt
+from sage.functions.other import imag
+from sage.misc.functional import sqrt
 from sage.functions.all import arccosh, sign
 
 from sage.geometry.hyperbolic_space.hyperbolic_constants import EPSILON

src/sage/geometry/hyperbolic_space/hyperbolic_model.py

@@ -81,7 +81,8 @@
 from sage.structure.parent import Parent
 from sage.misc.bindable_class import BindableClass
 from sage.misc.lazy_import import lazy_import
-from sage.functions.other import imag, real, sqrt
+from sage.functions.other import imag, real
+from sage.misc.functional import sqrt
 from sage.functions.all import arccosh
 from sage.rings.all import CC
 from sage.rings.real_double import RDF