Merge branch 'u/mkoeppe/replace______is_sr__by_isinstance______sage_r…

…ings_abc_symbolicring__to_handle_symbolic_subrings' of git://trac.sagemath.org/sage into t/32601/modularization_of_sagelib__break_out_a_separate_package_sagemath_standard_no_symbolics

src/sage/combinat/q_analogues.py

@@ -172,7 +172,8 @@ def q_binomial(n, k, q=None, algorithm='auto'):
       uses the naive algorithm. When both ``n`` and ``k`` are big, one
       uses the cyclotomic algorithm.
 
-    - If ``q`` is in the symbolic ring, one uses the cyclotomic algorithm.
+    - If ``q`` is in the symbolic ring (or a symbolic subring), one uses
+      the cyclotomic algorithm.
 
     - Otherwise one uses the naive algorithm, unless ``q`` is a root of
       unity, then one uses the cyclotomic algorithm.
@@ -248,7 +249,7 @@ def q_binomial(n, k, q=None, algorithm='auto'):
     This also works for variables in the symbolic ring::
 
         sage: z = var('z')
-        sage: factor(q_binomial(4,2,z))
+        sage: factor(q_binomial(4, 2, z))
         (z^2 + z + 1)*(z^2 + 1)
 
     This also works for complex roots of unity::
@@ -346,8 +347,8 @@ def q_binomial(n, k, q=None, algorithm='auto'):
         elif is_polynomial:
             algorithm = 'cyclotomic'
         else:
-            from sage.symbolic.ring import SR
-            if R is SR:
+            import sage.rings.abc
+            if isinstance(R, sage.rings.abc.SymbolicRing):
                 algorithm = 'cyclotomic'
             else:
                 algorithm = 'naive'

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -106,7 +106,6 @@ class initialization directly.
 from sage.parallel.ncpus import ncpus
 from sage.parallel.use_fork import p_iter_fork
 from sage.dynamics.arithmetic_dynamics.projective_ds_helper import (_fast_possible_periods,_all_periodic_points)
-lazy_import("sage.symbolic.ring", "SR")
 from itertools import count, product
 from .endPN_automorphism_group import (
     automorphism_group_QQ_CRT,
@@ -423,8 +422,8 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
         if len(polys) != domain.ambient_space().coordinate_ring().ngens():
             raise ValueError('Number of polys does not match dimension of {}'.format(domain))
         R = domain.base_ring()
-        if R is SR:
-            raise TypeError("Symbolic Ring cannot be the base ring")
+        if isinstance(R, sage.rings.abc.SymbolicRing):
+            raise TypeError("the base ring cannot be the Symbolic Ring or a symbolic subring")
 
         if is_ProductProjectiveSpaces(domain):
             splitpolys = domain._factors(polys)

src/sage/functions/other.py

@@ -20,7 +20,7 @@
 
 from sage.symbolic.function import GinacFunction, BuiltinFunction
 from sage.symbolic.expression import Expression, register_symbol, symbol_table
-from sage.symbolic.ring import SR
+from sage.symbolic.ring import SR, SymbolicRing
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational import Rational
@@ -179,6 +179,15 @@ def _eval_floor_ceil(self, x, method, bits=0, **kwds):
         Traceback (most recent call last):
         ...
         ValueError: Calling ceil() on infinity or NaN
+
+    Test that elements of symbolic subrings work in the same way as
+    elements of ``SR``, :trac:`32724`::
+
+        sage: SCR = SR.subring(no_variables=True)
+        sage: floor(log(2^(3/2)) / log(2) + 1/2)
+        2
+        sage: floor(SCR(log(2^(-3/2)) / log(2) + 1/2))
+        -1
     """
     # First, some obvious things...
     try:
@@ -215,8 +224,8 @@ def _eval_floor_ceil(self, x, method, bits=0, **kwds):
     from sage.rings.all import RealIntervalField
 
     # Might it be needed to simplify x? This only applies for
-    # elements of SR.
-    need_to_simplify = (s_parent(x) is SR)
+    # elements of SR (or its subrings)
+    need_to_simplify = isinstance(s_parent(x), SymbolicRing)
 
     # An integer which is close to x. We use this to increase precision
     # by subtracting this guess before converting to an interval field.

src/sage/geometry/polyhedron/parent.py

@@ -15,6 +15,7 @@
 from sage.modules.free_module import FreeModule, is_FreeModule
 from sage.misc.cachefunc import cached_method, cached_function
 from sage.misc.lazy_import import lazy_import
+import sage.rings.abc
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.rings.real_double import RDF
@@ -113,6 +114,13 @@ def Polyhedra(ambient_space_or_base_ring=None, ambient_dim=None, backend=None, *
         ...
         ValueError: the 'polymake' backend for polyhedron cannot be used with Algebraic Real Field
 
+        sage: Polyhedra(QQ, 2, backend='normaliz')   # optional - pynormaliz
+        Polyhedra in QQ^2
+        sage: Polyhedra(SR, 2, backend='normaliz')   # optional - pynormaliz  # optional - sage.symbolic
+        Polyhedra in (Symbolic Ring)^2
+        sage: SCR = SR.subring(no_variables=True)                             # optional - sage.symbolic
+        sage: Polyhedra(SCR, 2, backend='normaliz')  # optional - pynormaliz  # optional - sage.symbolic
+        Polyhedra in (Symbolic Constants Subring)^2
     """
     if ambient_space_or_base_ring is not None:
         if ambient_space_or_base_ring in Rings():
@@ -161,7 +169,7 @@ def Polyhedra(ambient_space_or_base_ring=None, ambient_dim=None, backend=None, *
         return Polyhedra_QQ_normaliz(base_ring, ambient_dim, backend)
     elif backend == 'normaliz' and base_ring is ZZ:
         return Polyhedra_ZZ_normaliz(base_ring, ambient_dim, backend)
-    elif backend == 'normaliz' and (base_ring is SR or base_ring.is_exact()):
+    elif backend == 'normaliz' and (isinstance(base_ring, sage.rings.abc.SymbolicRing) or base_ring.is_exact()):
         return Polyhedra_normaliz(base_ring, ambient_dim, backend)
     elif backend == 'cdd' and base_ring in (ZZ, QQ):
         return Polyhedra_QQ_cdd(QQ, ambient_dim, backend)

src/sage/manifolds/differentiable/scalarfield_algebra.py

@@ -32,7 +32,7 @@ class `C^k` over a topological field `K` (in
 #******************************************************************************
 
 from sage.rings.infinity import infinity
-from sage.symbolic.ring import SR
+from sage.symbolic.ring import SymbolicRing
 from sage.manifolds.scalarfield_algebra import ScalarFieldAlgebra
 from sage.manifolds.differentiable.scalarfield import DiffScalarField
 
@@ -406,6 +406,10 @@ def _coerce_map_from_(self, other):
             sage: CM = M.scalar_field_algebra()
             sage: CM._coerce_map_from_(SR)
             True
+            sage: SCR = SR.subring(no_variables=True); SCR
+            Symbolic Constants Subring
+            sage: CM._coerce_map_from_(SCR)
+            True
             sage: CM._coerce_map_from_(X.function_ring())
             True
             sage: U = M.open_subset('U', coord_def={X: x>0})
@@ -418,7 +422,7 @@ def _coerce_map_from_(self, other):
         """
         from sage.manifolds.chart_func import ChartFunctionRing
 
-        if other is SR:
+        if isinstance(other, SymbolicRing):
             return True  # coercion from the base ring (multiplication by the
                          # algebra unit, i.e. self.one())
                          # cf. ScalarField._lmul_() for the implementation of

src/sage/manifolds/scalarfield_algebra.py

@@ -36,7 +36,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.categories.commutative_algebras import CommutativeAlgebras
 from sage.categories.topological_spaces import TopologicalSpaces
-from sage.symbolic.ring import SR
+from sage.symbolic.ring import SymbolicRing, SR
 from sage.manifolds.scalarfield import ScalarField
 
 class ScalarFieldAlgebra(UniqueRepresentation, Parent):
@@ -509,6 +509,10 @@ def _coerce_map_from_(self, other):
             sage: CM = M.scalar_field_algebra()
             sage: CM._coerce_map_from_(SR)
             True
+            sage: SCR = SR.subring(no_variables=True); SCR
+            Symbolic Constants Subring
+            sage: CM._coerce_map_from_(SCR)
+            True
             sage: CM._coerce_map_from_(X.function_ring())
             True
             sage: U = M.open_subset('U', coord_def={X: x>0})
@@ -520,7 +524,7 @@ def _coerce_map_from_(self, other):
 
         """
         from .chart_func import ChartFunctionRing
-        if other is SR:
+        if isinstance(other, SymbolicRing):
             return True  # coercion from the base ring (multiplication by the
                          # algebra unit, i.e. self.one())
                          # cf. ScalarField._lmul_() for the implementation of

src/sage/matrix/matrix2.pyx

@@ -14288,7 +14288,6 @@ cdef class Matrix(Matrix1):
         code. The boolean ``semi`` argument exists only to change
         "greater than zero" into "greater than or equal to zero."
         """
-        from sage.symbolic.ring import SR
         from sage.rings.real_lazy import RLF,CLF
 
         R = self.base_ring()
@@ -14297,7 +14296,7 @@ cdef class Matrix(Matrix1):
                 R.has_coerce_map_from(RLF) or
                 CLF.has_coerce_map_from(R) or
                 R.has_coerce_map_from(CLF) or
-                R is SR):
+                isinstance(R, sage.rings.abc.SymbolicRing)):
             # This is necessary to avoid "going through the motions"
             # with e.g. a one-by-one identity matrix over the finite
             # field of order 5^2, which might otherwise look positive-
@@ -16904,16 +16903,23 @@ cdef class Matrix(Matrix1):
             ValueError: The base ring of the matrix is neither symbolic nor
             exact.
 
+        Symbolic subrings are fine::
+
+            sage: SCR = SR.subring(no_variables=True); SCR
+            Symbolic Constants Subring
+            sage: K = Cone([(1,2,3), (4,5,6)])
+            sage: L = identity_matrix(SCR, 3)
+            sage: L.is_positive_operator_on(K)
+            True
         """
-        from sage.symbolic.ring import SR
         import sage.geometry.abc
 
         if K2 is None:
             K2 = K1
         if not (isinstance(K1, sage.geometry.abc.ConvexRationalPolyhedralCone)
                 and isinstance(K2, sage.geometry.abc.ConvexRationalPolyhedralCone)):
             raise TypeError('K1 and K2 must be cones.')
-        if not self.base_ring().is_exact() and not self.base_ring() is SR:
+        if not self.base_ring().is_exact() and not isinstance(self.base_ring(), sage.rings.abc.SymbolicRing):
             msg = 'The base ring of the matrix is neither symbolic nor exact.'
             raise ValueError(msg)
 
@@ -17048,13 +17054,20 @@ cdef class Matrix(Matrix1):
             ValueError: The base ring of the matrix is neither symbolic nor
             exact.
 
+        Symbolic subrings are fine::
+
+            sage: SCR = SR.subring(no_variables=True); SCR
+            Symbolic Constants Subring
+            sage: K = Cone([(1,2,3), (4,5,6)])
+            sage: L = identity_matrix(SCR, 3)
+            sage: L.is_cross_positive_on(K)
+            True
         """
-        from sage.symbolic.ring import SR
         import sage.geometry.abc
 
         if not isinstance(K, sage.geometry.abc.ConvexRationalPolyhedralCone):
             raise TypeError('K must be a cone.')
-        if not self.base_ring().is_exact() and not self.base_ring() is SR:
+        if not self.base_ring().is_exact() and not isinstance(self.base_ring(), sage.rings.abc.SymbolicRing):
             msg = 'The base ring of the matrix is neither symbolic nor exact.'
             raise ValueError(msg)
 
@@ -17302,6 +17315,15 @@ cdef class Matrix(Matrix1):
             ValueError: The base ring of the matrix is neither symbolic nor
             exact.
 
+        Symbolic subrings are fine::
+
+            sage: SCR = SR.subring(no_variables=True); SCR
+            Symbolic Constants Subring
+            sage: K = Cone([(1,2,3), (4,5,6)])
+            sage: L = identity_matrix(SCR, 3)
+            sage: L.is_lyapunov_like_on(K)
+            True
+
         A matrix is Lyapunov-like on a cone if and only if both the
         matrix and its negation are cross-positive on the cone::
 
@@ -17314,14 +17336,12 @@ cdef class Matrix(Matrix1):
             ....:             (-L).is_cross_positive_on(K))  # long time
             sage: actual == expected                         # long time
             True
-
         """
-        from sage.symbolic.ring import SR
         import sage.geometry.abc
 
         if not isinstance(K, sage.geometry.abc.ConvexRationalPolyhedralCone):
             raise TypeError('K must be a cone.')
-        if not self.base_ring().is_exact() and not self.base_ring() is SR:
+        if not self.base_ring().is_exact() and not isinstance(self.base_ring(), sage.rings.abc.SymbolicRing):
             msg = 'The base ring of the matrix is neither symbolic nor exact.'
             raise ValueError(msg)
 

src/sage/repl/ipython_kernel/interact.py

@@ -41,8 +41,7 @@
 from .widgets import EvalText, SageColorPicker
 from .widgets_sagenb import input_grid
 from sage.structure.element import parent
-from sage.misc.lazy_import import lazy_import
-lazy_import("sage.symbolic.ring", "SR")
+import sage.rings.abc
 from sage.plot.colors import Color
 from sage.structure.element import Matrix
 
@@ -210,6 +209,14 @@ def widget_from_tuple(cls, abbrev, *args, **kwds):
             Dropdown(index=1, options={'one': 1, 'two': 2, 'three': 3}, value=2)
             sage: sage_interactive.widget_from_tuple( (sqrt(2), pi) )
             FloatSlider(value=2.277903107981444, max=3.141592653589793, min=1.4142135623730951)
+
+        TESTS:
+
+        Symbolic subrings::
+
+            sage: SCR = SR.subring(no_variables=True)
+            sage: sage_interactive.widget_from_tuple( (SCR(sqrt(2)), SCR(pi)) )
+            FloatSlider(value=2.277903107981444, max=3.141592653589793, min=1.4142135623730951)
         """
         # Support (description, abbrev)
         if len(abbrev) == 2 and isinstance(abbrev[0], str):
@@ -224,7 +231,7 @@ def widget_from_tuple(cls, abbrev, *args, **kwds):
         # Numerically evaluate symbolic expressions
 
         def n(x):
-            if parent(x) is SR:
+            if isinstance(parent(x), sage.rings.abc.SymbolicRing):
                 return x.numerical_approx()
             else:
                 return x

src/sage/repl/ipython_kernel/widgets_sagenb.py

@@ -42,9 +42,7 @@
 from sage.structure.all import parent
 from sage.arith.srange import srange
 from sage.plot.colors import Color
-from sage.misc.lazy_import import lazy_import
-lazy_import("sage.symbolic.ring", "SR")
-from sage.rings.all import RR
+import sage.rings.abc
 
 
 from .widgets import HTMLText as text_control
@@ -235,6 +233,14 @@ def slider(vmin, vmax=None, step_size=None, default=None, label=None, display_va
         True
         sage: slider(5, display_value=False).readout
         False
+
+    Symbolic subrings work like ``SR``::
+
+        sage: SCR = SR.subring(no_variables=True)
+        sage: w = slider(SCR(e), SCR(pi)); w
+        TransformFloatSlider(value=2.718281828459045, max=3.141592653589793, min=2.718281828459045)
+        sage: parent(w.get_interact_value())
+        Real Field with 53 bits of precision
     """
     kwds = {"readout": display_value}
     if label:
@@ -272,7 +278,8 @@ def err(v):
     p = parent(sum(x for x in (vmin, vmax, step_size) if x is not None))
 
     # Change SR to RR
-    if p is SR:
+    if isinstance(p, sage.rings.abc.SymbolicRing):
+        from sage.rings.real_mpfr import RR
         p = RR
 
     # Convert all inputs to the common parent

src/sage/rings/continued_fraction.py

@@ -207,6 +207,7 @@
 
 from sage.structure.sage_object import SageObject
 from sage.structure.richcmp import richcmp_method, rich_to_bool
+import sage.rings.abc
 from .integer import Integer
 from .integer_ring import ZZ
 from .infinity import Infinity
@@ -2601,6 +2602,12 @@ def continued_fraction(x, value=None):
 
         sage: continued_fraction(1.575709393346379)
         [1; 1, 1, 2, 1, 4, 18, 1, 5, 2, 25037802, 7, 1, 3, 1, 28, 1, 8, 2]
+
+    Constants in symbolic subrings work like constants in ``SR``::
+
+        sage: SCR = SR.subring(no_variables=True)
+        sage: continued_fraction(SCR(pi))
+        [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, ...]
     """
 
     if isinstance(x, ContinuedFraction_base):
@@ -2675,10 +2682,9 @@ def continued_fraction(x, value=None):
     if x.parent().is_exact():
         return ContinuedFraction_real(x)
 
-    # we treat separately the symbolic ring that holds all constants and
-    # which is not exact
-    from sage.symbolic.ring import SR
-    if x.parent() == SR:
+    # We treat the Symbolic Ring and its subrings separately.  They hold all constants and
+    # are not exact.
+    if isinstance(x.parent(), sage.rings.abc.SymbolicRing):
         return ContinuedFraction_real(x)
 
     return continued_fraction(continued_fraction_list(x))