Exemple #1
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    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
Exemple #2
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    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
Exemple #3
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    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
Exemple #4
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    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
Exemple #5
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    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)
Exemple #7
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    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)
Exemple #8
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    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
Exemple #9
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    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