def _an_element_(self):
r"""
Return an element of this symbolic subring.
OUTPUT:
A symbolic expression.
TESTS::
sage: from sage.symbolic.subring import SymbolicSubring
sage: SymbolicSubring(rejecting_variables=('r',)).an_element()
some_variable
sage: _.parent()
Symbolic Subring rejecting the variable r
sage: SymbolicSubring(rejecting_variables=('some_variable',)).an_element()
some_some_variable
sage: _.parent()
Symbolic Subring rejecting the variable some_variable
sage: SymbolicSubring(rejecting_variables=('some_some_variable',)).an_element()
some_variable
sage: _.parent()
Symbolic Subring rejecting the variable some_some_variable
sage: SymbolicSubring(rejecting_variables=('some_variable','some_some_variable')).an_element()
some_some_some_variable
sage: _.parent()
Symbolic Subring rejecting the variables some_some_variable, some_variable
"""
v = SR.an_element()
while not self.has_valid_variable(v):
v = SR('some_' + str(v))
return self(v)
def create_key_and_extra_args(self,
accepting_variables=None,
rejecting_variables=None,
no_variables=False,
**kwds):
r"""
Given the arguments and keyword, create a key that uniquely
determines this object.
See :class:`SymbolicSubringFactory` for details.
TESTS::
sage: from sage.symbolic.subring import SymbolicSubring
sage: SymbolicSubring.create_key_and_extra_args()
Traceback (most recent call last):
...
ValueError: Cannot create a symbolic subring since nothing is specified.
sage: SymbolicSubring.create_key_and_extra_args(
....: accepting_variables=('a',), rejecting_variables=('r',))
Traceback (most recent call last):
...
ValueError: Cannot create a symbolic subring since input is ambiguous.
sage: SymbolicSubring.create_key_and_extra_args(
....: accepting_variables=('a',), no_variables=True)
Traceback (most recent call last):
...
ValueError: Cannot create a symbolic subring since input is ambiguous.
sage: SymbolicSubring.create_key_and_extra_args(
....: rejecting_variables=('r',), no_variables=True)
Traceback (most recent call last):
...
ValueError: Cannot create a symbolic subring since input is ambiguous.
"""
if accepting_variables is None and \
rejecting_variables is None and \
not no_variables:
raise ValueError('Cannot create a symbolic subring '
'since nothing is specified.')
if accepting_variables is not None and rejecting_variables is not None or \
rejecting_variables is not None and no_variables or \
no_variables and accepting_variables is not None:
raise ValueError('Cannot create a symbolic subring '
'since input is ambiguous.')
if accepting_variables is not None:
vars = tuple(accepting_variables)
if vars:
cls = SymbolicSubringAcceptingVars
else:
cls = SymbolicConstantsSubring
elif rejecting_variables is not None:
vars = tuple(rejecting_variables)
cls = SymbolicSubringRejectingVars
elif no_variables:
vars = tuple()
cls = SymbolicConstantsSubring
vars = tuple(sorted(iter(SR(v) for v in vars), key=str))
return (cls, vars), kwds
def _an_element_(self):
r"""
Return an element of this symbolic subring.
OUTPUT:
A symbolic expression.
TESTS::
sage: from sage.symbolic.subring import SymbolicSubring
sage: SymbolicSubring(rejecting_variables=('r',)).an_element()
some_variable
sage: _.parent()
Symbolic Subring rejecting the variable r
sage: SymbolicSubring(rejecting_variables=('some_variable',)).an_element()
some_some_variable
sage: _.parent()
Symbolic Subring rejecting the variable some_variable
sage: SymbolicSubring(rejecting_variables=('some_some_variable',)).an_element()
some_variable
sage: _.parent()
Symbolic Subring rejecting the variable some_some_variable
sage: SymbolicSubring(rejecting_variables=('some_variable','some_some_variable')).an_element()
some_some_some_variable
sage: _.parent()
Symbolic Subring rejecting the variables some_some_variable, some_variable
"""
v = SR.an_element()
while not self.has_valid_variable(v):
v = SR('some_' + str(v))
return self(v)
def _an_element_(self):
r"""
Return an element of this symbolic subring.
OUTPUT:
A symbolic expression.
TESTS::
sage: from sage.symbolic.subring import SymbolicSubring
sage: SymbolicSubring(no_variables=True).an_element()
I*pi*e
sage: _.parent()
Symbolic Constants Subring
"""
return self(SR('I') * SR('pi') * SR('e'))
def has_valid_variable(self, variable):
r"""
Return whether the given ``variable`` is valid in this subring.
INPUT:
- ``variable`` -- a symbolic variable.
OUTPUT:
A boolean.
EXAMPLES::
sage: from sage.symbolic.subring import SymbolicSubring
sage: S = SymbolicSubring(rejecting_variables=('r',))
sage: S.has_valid_variable('a')
True
sage: S.has_valid_variable('r')
False
sage: S.has_valid_variable('x')
True
"""
return SR(variable) not in self._vars_
def _coerce_map_from_(self, P):
r"""
Return whether ``P`` coerces into this symbolic subring.
INPUT:
- ``P`` -- a parent.
OUTPUT:
A boolean or ``None``.
TESTS::
sage: from sage.symbolic.subring import GenericSymbolicSubring
sage: GenericSymbolicSubring(vars=tuple()).has_coerce_map_from(SR) # indirect doctest # not tested see #19231
False
::
sage: from sage.symbolic.subring import SymbolicSubring
sage: C = SymbolicSubring(no_variables=True)
sage: C.has_coerce_map_from(ZZ) # indirect doctest
True
sage: C.has_coerce_map_from(QQ) # indirect doctest
True
sage: C.has_coerce_map_from(RR) # indirect doctest
True
sage: C.has_coerce_map_from(RIF) # indirect doctest
True
sage: C.has_coerce_map_from(CC) # indirect doctest
True
sage: C.has_coerce_map_from(CIF) # indirect doctest
True
sage: C.has_coerce_map_from(AA) # indirect doctest
True
sage: C.has_coerce_map_from(QQbar) # indirect doctest
True
sage: C.has_coerce_map_from(SR) # indirect doctest
False
"""
if P == SR:
# Workaround; can be deleted once #19231 is fixed
return False
from sage.rings.real_mpfr import mpfr_prec_min
from sage.rings.all import (ComplexField, RLF, CLF, AA, QQbar,
InfinityRing)
from sage.rings.real_mpfi import is_RealIntervalField
from sage.rings.complex_interval_field import is_ComplexIntervalField
if isinstance(P, type):
return SR._coerce_map_from_(P)
elif RLF.has_coerce_map_from(P) or \
CLF.has_coerce_map_from(P) or \
AA.has_coerce_map_from(P) or \
QQbar.has_coerce_map_from(P):
return True
elif (P is InfinityRing or is_RealIntervalField(P)
or is_ComplexIntervalField(P)):
return True
elif ComplexField(mpfr_prec_min()).has_coerce_map_from(P):
return P not in (RLF, CLF, AA, QQbar)
def _coerce_map_from_(self, P):
r"""
Return whether ``P`` coerces into this symbolic subring.
INPUT:
- ``P`` -- a parent.
OUTPUT:
A boolean or ``None``.
TESTS::
sage: from sage.symbolic.subring import GenericSymbolicSubring
sage: GenericSymbolicSubring(vars=tuple()).has_coerce_map_from(SR) # indirect doctest # not tested see #19231
False
::
sage: from sage.symbolic.subring import SymbolicSubring
sage: C = SymbolicSubring(no_variables=True)
sage: C.has_coerce_map_from(ZZ) # indirect doctest
True
sage: C.has_coerce_map_from(QQ) # indirect doctest
True
sage: C.has_coerce_map_from(RR) # indirect doctest
True
sage: C.has_coerce_map_from(RIF) # indirect doctest
True
sage: C.has_coerce_map_from(CC) # indirect doctest
True
sage: C.has_coerce_map_from(CIF) # indirect doctest
True
sage: C.has_coerce_map_from(AA) # indirect doctest
True
sage: C.has_coerce_map_from(QQbar) # indirect doctest
True
sage: C.has_coerce_map_from(SR) # indirect doctest
False
"""
if P == SR:
# Workaround; can be deleted once #19231 is fixed
return False
from sage.rings.real_mpfr import mpfr_prec_min
from sage.rings.all import (ComplexField,
RLF, CLF, AA, QQbar, InfinityRing)
from sage.rings.real_mpfi import is_RealIntervalField
from sage.rings.complex_interval_field import is_ComplexIntervalField
if isinstance(P, type):
return SR._coerce_map_from_(P)
elif RLF.has_coerce_map_from(P) or \
CLF.has_coerce_map_from(P) or \
AA.has_coerce_map_from(P) or \
QQbar.has_coerce_map_from(P):
return True
elif (P is InfinityRing or
is_RealIntervalField(P) or is_ComplexIntervalField(P)):
return True
elif ComplexField(mpfr_prec_min()).has_coerce_map_from(P):
return P not in (RLF, CLF, AA, QQbar)
