def _coerce_map_from_(self, S):
"""
This is called implicitly by arithmetic methods.
EXAMPLES::
sage: k = GF(7)
sage: e = k(6)
sage: e * 2 # indirect doctest
5
sage: 12 % 7
5
sage: ZZ.residue_field(7).hom(GF(7))(1) # See trac 11319
1
sage: K.<w> = QuadraticField(337) # See trac 11319
sage: pp = K.ideal(13).factor()[0][0]
sage: RF13 = K.residue_field(pp)
sage: RF13.hom([GF(13)(1)])
Ring morphism:
From: Residue field of Fractional ideal (w + 18)
To: Finite Field of size 13
Defn: 1 |--> 1
Check that :trac:`19573` is resolved::
sage: Integers(9).hom(GF(3))
Natural morphism:
From: Ring of integers modulo 9
To: Finite Field of size 3
sage: Integers(9).hom(GF(5))
Traceback (most recent call last):
...
TypeError: natural coercion morphism from Ring of integers modulo 9 to Finite Field of size 5 not defined
There is no coercion from a `p`-adic ring to its residue field::
sage: GF(3).has_coerce_map_from(Zp(3))
False
"""
if S is int:
return integer_mod.Int_to_IntegerMod(self)
elif S is ZZ:
return integer_mod.Integer_to_IntegerMod(self)
elif isinstance(S, IntegerModRing_generic):
from .residue_field import ResidueField_generic
if (S.characteristic() % self.characteristic() == 0 and
(not isinstance(S, ResidueField_generic) or
S.degree() == 1)):
try:
return integer_mod.IntegerMod_to_IntegerMod(S, self)
except TypeError:
pass
to_ZZ = ZZ._internal_coerce_map_from(S)
if to_ZZ is not None:
return integer_mod.Integer_to_IntegerMod(self) * to_ZZ
def _coerce_map_from_(self, S):
"""
This is called implicitly by arithmetic methods.
EXAMPLES::
sage: k = GF(7)
sage: e = k(6)
sage: e * 2 # indirect doctest
5
sage: 12 % 7
5
sage: ZZ.residue_field(7).hom(GF(7))(1) # See trac 11319
1
sage: K.<w> = QuadraticField(337) # See trac 11319
sage: pp = K.ideal(13).factor()[0][0]
sage: RF13 = K.residue_field(pp)
sage: RF13.hom([GF(13)(1)])
Ring morphism:
From: Residue field of Fractional ideal (w - 18)
To: Finite Field of size 13
Defn: 1 |--> 1
"""
if S is int:
return integer_mod.Int_to_IntegerMod(self)
elif S is ZZ:
return integer_mod.Integer_to_IntegerMod(self)
elif isinstance(S, IntegerModRing_generic):
from sage.rings.residue_field import ResidueField_generic
if S.characteristic() == self.characteristic() and \
(not isinstance(S, ResidueField_generic) or S.degree() == 1):
try:
return integer_mod.IntegerMod_to_IntegerMod(S, self)
except TypeError:
pass
to_ZZ = ZZ._internal_coerce_map_from(S)
if to_ZZ is not None:
return integer_mod.Integer_to_IntegerMod(self) * to_ZZ