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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/symbolic/maxima_wrapper.py
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###############################################################################

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#   Sage: Open Source Mathematical Software

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#       Copyright (C) 2010 Burcin Erocal <[email protected]>

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#  Distributed under the terms of the GNU General Public License (GPL),

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#  version 2 or any later version.  The full text of the GPL is available at:

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#                  http://www.gnu.org/licenses/

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###############################################################################

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from sage.structure.sage_object import SageObject

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from sage.interfaces.maxima import MaximaFunctionElement

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class MaximaFunctionElementWrapper(MaximaFunctionElement):

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    def __call__(self, *args, **kwds):

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        """

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        Returns a Sage expression instead of a Maxima pexpect interface element.

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        EXAMPLES::

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            sage: t = sin(x)^2 + cos(x)^2; t

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            sin(x)^2 + cos(x)^2

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            sage: res = t.maxima_methods().trigsimp(); res

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            1

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            sage: type(res)

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            <type 'sage.symbolic.expression.Expression'>

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        """

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        return super(MaximaFunctionElementWrapper, self).__call__(*args,

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                **kwds).sage()

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class MaximaWrapper(SageObject):

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    def __init__(self, exp):

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        """

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        Wrapper around Sage expressions to give access to Maxima methods.

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        We convert the given expression to Maxima and convert the return value

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        back to a Sage expression. Tab completion and help strings of Maxima

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        methods also work as expected.

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        EXAMPLES::

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            sage: t = log(sqrt(2) - 1) + log(sqrt(2) + 1); t

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            log(sqrt(2) - 1) + log(sqrt(2) + 1)

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            sage: u = t.maxima_methods(); u

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            MaximaWrapper(log(sqrt(2) - 1) + log(sqrt(2) + 1))

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            sage: type(u)

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            <class 'sage.symbolic.maxima_wrapper.MaximaWrapper'>

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            sage: u.logcontract()

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            log((sqrt(2) - 1)*(sqrt(2) + 1))

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            sage: u.logcontract().parent()

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            Symbolic Ring

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        TESTS:

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        Test tab completions::

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            sage: import sagenb.misc.support as s

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            sage: u = t.maxima_methods()

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            sage: s.completions('u.elliptic_',globals(),system='python')

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            ['u.elliptic_e', 'u.elliptic_ec', 'u.elliptic_eu', 'u.elliptic_f', 'u.elliptic_kc', 'u.elliptic_pi']

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        """

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        self._exp = exp

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        self._maxima_exp = None

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    def __getattr__(self, s):

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        """

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        Direct attempts to get attributes of this wrapper to the corresponding

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        Maxima expression. This allows tab completion to work as expected.

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        We wrap the function calls in order to convert results back to Sage.

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        EXAMPLES::

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            sage: t = sin(x)^2 + cos(x)^2; t

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            sin(x)^2 + cos(x)^2

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            sage: u = t.maxima_methods()

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            sage: import sagenb.misc.support as s

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            sage: s.completions('u.airy_',globals(),system='python')

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            ['u.airy_ai', 'u.airy_bi', 'u.airy_dai', 'u.airy_dbi']

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            sage: type(u.airy_ai)

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            <class 'sage.symbolic.maxima_wrapper.MaximaFunctionElementWrapper'>

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            sage: u.airy_ai()

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            airy_ai(sin(x)^2 + cos(x)^2)

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        """

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        if self._maxima_exp is None:

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            self._maxima_exp = self._exp._maxima_()

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        if s == 'trait_names' or s[:1] == '_':

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            return getattr(self._maxima_exp, s)

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        else:

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            # add a wrapper function which converts the result back to

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            # a Sage expression

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            return MaximaFunctionElementWrapper(self._maxima_exp, s)

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    def sage(self):

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        """

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        Return the Sage expression this wrapper corresponds to.

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        EXAMPLES::

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            sage: t = log(sqrt(2) - 1) + log(sqrt(2) + 1); t

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            log(sqrt(2) - 1) + log(sqrt(2) + 1)

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            sage: u = t.maxima_methods().sage()

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            sage: u is t

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            True

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        """

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        return self._exp

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    def _symbolic_(self, parent):

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        """

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        EXAMPLES::

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            sage: t = log(sqrt(2) - 1) + log(sqrt(2) + 1); t

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            log(sqrt(2) - 1) + log(sqrt(2) + 1)

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            sage: u = t.maxima_methods()

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            sage: SR(u) is t # indirect doctest

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            True

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        """

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        return parent(self._exp)

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    def __reduce__(self):

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        """

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        EXAMPLES::

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            sage: t = log(sqrt(2) - 1) + log(sqrt(2) + 1); t

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            log(sqrt(2) - 1) + log(sqrt(2) + 1)

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            sage: u = t.maxima_methods(); u

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            MaximaWrapper(log(sqrt(2) - 1) + log(sqrt(2) + 1))

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            sage: loads(dumps(u))

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            MaximaWrapper(log(sqrt(2) - 1) + log(sqrt(2) + 1))

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        """

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        return (MaximaWrapper, (self._exp,))

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    def _repr_(self):

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        """

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        EXAMPLES::

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            sage: t = log(sqrt(2) - 1) + log(sqrt(2) + 1); t

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            log(sqrt(2) - 1) + log(sqrt(2) + 1)

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            sage: u = t.maxima_methods(); u

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            MaximaWrapper(log(sqrt(2) - 1) + log(sqrt(2) + 1))

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            sage: u._repr_()

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            'MaximaWrapper(log(sqrt(2) - 1) + log(sqrt(2) + 1))'

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        """

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        return "MaximaWrapper(%s)"%(self._exp)

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