def _sympy_(self):
r"""
Return an instance of a subclass of SymPy ``Set`` corresponding to ``self``.
EXAMPLES::
sage: predicate(x, y, z) = sqrt(x^2 + y^2 + z^2) < 12; predicate
(x, y, z) |--> sqrt(x^2 + y^2 + z^2) < 12
sage: SmallTriples = ConditionSet(ZZ^3, predicate); SmallTriples
{ (x, y, z) ∈ Ambient free module of rank 3 over the principal
ideal domain Integer Ring : sqrt(x^2 + y^2 + z^2) < 12 }
sage: ST = SmallTriples._sympy_(); ST
ConditionSet((x, y, z), sqrt(x**2 + y**2 + z**2) < 12,
ProductSet(Integers, Integers, Integers))
sage: (1, 3, 5) in ST
True
sage: (5, 7, 9) in ST
False
sage: Interval = ConditionSet(RR, x >= -7, x <= 4, vars=[x]); Interval
{ x ∈ Real Field with 53 bits of precision : x >= -7, x <= 4 }
sage: Interval._sympy_()
ConditionSet(x, (x >= -7) & (x <= 4), SageSet(Real Field with 53 bits of precision))
If a predicate is not symbolic, we fall back to creating a wrapper::
sage: Evens = ConditionSet(ZZ, is_even); Evens
{ x ∈ Integer Ring : <function is_even at 0x...>(x) }
sage: Evens._sympy_()
SageSet({ x ∈ Integer Ring : <function is_even at 0x...>(x) })
"""
from sage.interfaces.sympy import sympy_init
sympy_init()
import sympy
args = self.arguments()
single_arg = len(args) == 1
if single_arg:
args = args[0]
try:
conditions = [
self._call_predicate(predicate, args)
for predicate in self._predicates
]
sym = tuple(x._sympy_() for x in self.arguments())
if single_arg:
sym = sym[0]
result = sympy.ConditionSet(
sym,
sympy.And(*[condition._sympy_() for condition in conditions]),
base_set=self._universe._sympy_())
result._sage_object = self
return result
except TypeError:
# Fall back to creating a wrapper
return super()._sympy_()
def _sympy_(self):
r"""
Return the SymPy set ``Naturals``.
EXAMPLES::
sage: PositiveIntegers()._sympy_()
Naturals
"""
from sympy import Naturals
from sage.interfaces.sympy import sympy_init
sympy_init()
return Naturals
def _sympy_(self):
r"""
Return the SymPy set ``Rationals``.
EXAMPLES::
sage: QQ._sympy_()
Rationals
"""
from sympy import Rationals
from sage.interfaces.sympy import sympy_init
sympy_init()
return Rationals
def _sympy_(self):
r"""
Return the SymPy set ``Naturals0``.
EXAMPLES::
sage: NN = NonNegativeIntegers()
sage: NN._sympy_()
Naturals0
"""
from sympy import Naturals0
from sage.interfaces.sympy import sympy_init
sympy_init()
return Naturals0
def _start(self):
"""
Start up the Mathics interpreter and sets the initial prompt and options.
This is called the first time the Mathics interface is actually used.
EXAMPLES::
sage: mathics._start() # optional - mathics
sage: type(mathics._session) # optional - mathics
<class 'mathics.session.MathicsSession'>
"""
if not self._session:
from mathics.session import MathicsSession
self._session = MathicsSession()
from sage.interfaces.sympy import sympy_init
sympy_init()
from sympy import Symbol
from sympy.core.relational import Relational
Symbol._sage_ = _mathics_sympysage_symbol