示例#1
0
    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)
示例#2
0
文件: subring.py 项目: ProgVal/sage
    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)
示例#3
0
文件: infinity.py 项目: yarv/sage
    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
示例#4
0
文件: infinity.py 项目: Etn40ff/sage
    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