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)
def _coerce_map_from_(self, R):
r"""
There is a coercion from anything that has a coercion into the reals.
The way Sage works is that everything that should be
comparable with infinity can be coerced into the infinity
ring, so if you ever compare with infinity the comparison is
done there. If you don't have a coercion then you will get
undesirable answers from the fallback comparison (likely
memory location).
EXAMPLES::
sage: InfinityRing.has_coerce_map_from(int) # indirect doctest
True
sage: InfinityRing.has_coerce_map_from(AA)
True
sage: InfinityRing.has_coerce_map_from(RDF)
True
sage: InfinityRing.has_coerce_map_from(RIF)
True
As explained above, comparison works by coercing to the
infinity ring::
sage: cm = get_coercion_model()
sage: cm.explain(AA(3), oo, operator.lt)
Coercion on left operand via
Coercion map:
From: Algebraic Real Field
To: The Infinity Ring
Arithmetic performed after coercions.
Result lives in The Infinity Ring
The Infinity Ring
The symbolic ring does not coerce to the infinity ring, so
symbolic comparisons with infinities all happen in the
symbolic ring::
sage: SR.has_coerce_map_from(InfinityRing)
True
sage: InfinityRing.has_coerce_map_from(SR)
False
Complex numbers do not coerce into the infinity ring (what
would `i \infty` coerce to?). This is fine since they can not
be compared, so we do not have to enforce consistency when
comparing with infinity either::
sage: InfinityRing.has_coerce_map_from(CDF)
False
sage: InfinityRing.has_coerce_map_from(CC)
False
sage: CC(0, oo) < CC(1) # does not coerce to infinity ring
True
"""
from sage.rings.real_mpfr import mpfr_prec_min, RealField
if RealField(mpfr_prec_min()).has_coerce_map_from(R):
return True
from sage.rings.real_mpfi import RealIntervalField_class
if isinstance(R, RealIntervalField_class):
return True
try:
from sage.rings.real_arb import RealBallField
if isinstance(R, RealBallField):
return True
except ImportError:
pass
return False
def _coerce_map_from_(self, R):
r"""
There is a coercion from anything that has a coercion into the reals.
The way Sage works is that everything that should be
comparable with infinity can be coerced into the infinity
ring, so if you ever compare with infinity the comparison is
done there. If you don't have a coercion then you will get
undesirable answers from the fallback comparison (likely
memory location).
EXAMPLES::
sage: InfinityRing.has_coerce_map_from(int) # indirect doctest
True
sage: InfinityRing.has_coerce_map_from(AA)
True
sage: InfinityRing.has_coerce_map_from(RDF)
True
sage: InfinityRing.has_coerce_map_from(RIF)
True
As explained above, comparison works by coercing to the
infinity ring::
sage: cm = get_coercion_model()
sage: cm.explain(AA(3), oo, operator.lt)
Coercion on left operand via
Conversion map:
From: Algebraic Real Field
To: The Infinity Ring
Arithmetic performed after coercions.
Result lives in The Infinity Ring
The Infinity Ring
The symbolic ring does not coerce to the infinity ring, so
symbolic comparisons with infinities all happen in the
symbolic ring::
sage: SR.has_coerce_map_from(InfinityRing)
True
sage: InfinityRing.has_coerce_map_from(SR)
False
Complex numbers do not coerce into the infinity ring (what
would `i \infty` coerce to?). This is fine since they can not
be compared, so we do not have to enforce consistency when
comparing with infinity either::
sage: InfinityRing.has_coerce_map_from(CDF)
False
sage: InfinityRing.has_coerce_map_from(CC)
False
sage: CC(0, oo) < CC(1) # does not coerce to infinity ring
True
"""
from sage.rings.real_mpfr import mpfr_prec_min, RealField
if RealField(mpfr_prec_min()).has_coerce_map_from(R):
return True
from sage.rings.real_mpfi import RealIntervalField_class
if isinstance(R, RealIntervalField_class):
return True
return False