def __init__(self, parent, im_gen, base_morphism):
"""
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: f = K.hom(1/x); f
Morphism of function fields defined by x |--> 1/x
sage: isinstance(f, sage.rings.function_field.maps.FunctionFieldMorphism)
True
"""
RingHomomorphism.__init__(self, parent)
self._im_gen = im_gen
self._base_morphism = base_morphism
def __init__(self, parent, im_gen, base_morphism):
"""
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: f = K.hom(1/x); f
Morphism of function fields defined by x |--> 1/x
sage: isinstance(f, sage.rings.function_field.maps.FunctionFieldMorphism)
True
"""
RingHomomorphism.__init__(self, parent)
self._im_gen = im_gen
self._base_morphism = base_morphism
def __init__(self, parent, im_gen, base_morphism):
"""
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: f = K.hom(1/x); f
Function Field endomorphism of Rational function field in x over Rational Field
Defn: x |--> 1/x
sage: isinstance(f, sage.rings.function_field.maps.FunctionFieldMorphism)
True
"""
RingHomomorphism.__init__(self, parent)
self._im_gen = im_gen
self._base_morphism = base_morphism
def __init__(self, parent, im_gen, base_morphism):
"""
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: f = K.hom(1/x); f
Function Field endomorphism of Rational function field in x over Rational Field
Defn: x |--> 1/x
sage: isinstance(f, sage.rings.function_field.maps.FunctionFieldMorphism)
True
"""
RingHomomorphism.__init__(self, parent)
self._im_gen = im_gen
self._base_morphism = base_morphism
def __init__(self, parent, im_gen, base_morphism):
"""
Initialize.
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: f = K.hom(1/x); f
Function Field endomorphism of Rational function field in x over Rational Field
Defn: x |--> 1/x
sage: TestSuite(f).run(skip="_test_category")
"""
RingHomomorphism.__init__(self, parent)
self._im_gen = im_gen
self._base_morphism = base_morphism
def __init__(self, domain, codomain, ringembed):
r"""
Initialize this morphism.
TESTS::
sage: k.<a> = GF(5^3)
sage: S.<x> = SkewPolynomialRing(k, k.frobenius_endomorphism())
sage: K = S.fraction_field()
sage: Z = K.center()
sage: iota = K.coerce_map_from(Z)
sage: TestSuite(iota).run(skip=['_test_category'])
"""
RingHomomorphism.__init__(self, Hom(domain, codomain))
self._codomain = codomain
self._ringembed = ringembed
self._section = SectionOreFunctionCenterInjection(self)
def __init__(self, domain, codomain, embed, order):
r"""
Initialize this morphism.
EXAMPLES::
sage: k.<a> = GF(5^3)
sage: S.<x> = SkewPolynomialRing(k, k.frobenius_endomorphism())
sage: Z = S.center()
sage: S.convert_map_from(Z) # indirect doctest
Embedding of the center of Ore Polynomial Ring in x over Finite Field in a of size 5^3 twisted by a |--> a^5 into this ring
"""
RingHomomorphism.__init__(self, Hom(domain, codomain))
self._embed = embed
self._order = order
self._codomain = codomain
self._section = SectionSkewPolynomialCenterInjection(self)
def __init__(self, parent, abs_hom):
r"""
EXAMPLES::
sage: K.<a, b> = NumberField( [x^3 + 2, x^2 + x + 1] )
sage: f = K.hom(-a*b - a, K); f
Relative number field endomorphism of Number Field in a with defining polynomial x^3 + 2 over its base field
Defn: a |--> (-b - 1)*a
b |--> b
sage: type(f)
<class 'sage.rings.number_field.homset.RelativeNumberFieldHomset_with_category.element_class'>
"""
RingHomomorphism.__init__(self, parent)
self._abs_hom = abs_hom
K = abs_hom.domain()
from_K, to_K = K.structure()
self._from_K = from_K
self._to_K = to_K
def __init__(self, parent, abs_hom):
r"""
EXAMPLES::
sage: K.<a, b> = NumberField( [x^3 + 2, x^2 + x + 1] )
sage: f = K.hom(-a*b - a, K); f
Relative number field endomorphism of Number Field in a with defining polynomial x^3 + 2 over its base field
Defn: a |--> (-b - 1)*a
b |--> b
sage: type(f)
<class 'sage.rings.number_field.morphism.RelativeNumberFieldHomomorphism_from_abs'>
"""
RingHomomorphism.__init__(self, parent)
self.__abs_hom = abs_hom
K = abs_hom.domain()
from_K, to_K = K.structure()
self.__K = K
self.__from_K = from_K
self.__to_K = to_K