Coverage for local/lib/python2.7/site-packages/sage/symbolic/maxima_wrapper.py : 100%

"Access to Maxima methods" 

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

# Sage: Open Source Mathematical Software 

# Copyright (C) 2010 Burcin Erocal <burcin@erocal.org> 

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

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

# http://www.gnu.org/licenses/ 

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

from sage.structure.sage_object import SageObject 

from sage.interfaces.maxima import MaximaFunctionElement 

from sage.docs.instancedoc import instancedoc 

@instancedoc 

class MaximaFunctionElementWrapper(MaximaFunctionElement): 

def __call__(self, *args, **kwds): 

""" 

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

EXAMPLES:: 

sage: t = sin(x)^2 + cos(x)^2; t 

cos(x)^2 + sin(x)^2 

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

1 

sage: parent(res) 

Symbolic Ring 

""" 

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

**kwds).sage() 

class MaximaWrapper(SageObject): 

def __init__(self, exp): 

""" 

Wrapper around Sage expressions to give access to Maxima methods. 

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

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

methods also work as expected. 

EXAMPLES:: 

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

log(sqrt(2) + 1) + log(sqrt(2) - 1) 

sage: u = t.maxima_methods(); u 

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

sage: type(u) 

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

sage: u.logcontract() 

log((sqrt(2) + 1)*(sqrt(2) - 1)) 

sage: u.logcontract().parent() 

Symbolic Ring 

TESTS: 

Test tab completions:: 

sage: import sagenb.misc.support as s 

sage: u = t.maxima_methods() 

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

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

""" 

self._exp = exp 

self._maxima_exp = None 

def __getattr__(self, s): 

""" 

Direct attempts to get attributes of this wrapper to the corresponding 

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

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

EXAMPLES:: 

sage: t = sin(x)^2 + cos(x)^2; t 

cos(x)^2 + sin(x)^2 

sage: u = t.maxima_methods() 

sage: import sagenb.misc.support as s 

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

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

sage: type(u.airy_ai) 

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

sage: u.airy_ai() 

airy_ai(cos(x)^2 + sin(x)^2) 

""" 

if self._maxima_exp is None: 

self._maxima_exp = self._exp._maxima_() 

if s[0] == '_': 

return getattr(self._maxima_exp, s) 

if s == 'trait_names': # SageNB backward compatibility 

return self._maxima_()._tab_completion 

else: 

# add a wrapper function which converts the result back to 

# a Sage expression 

return MaximaFunctionElementWrapper(self._maxima_exp, s) 

def sage(self): 

""" 

Return the Sage expression this wrapper corresponds to. 

EXAMPLES:: 

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

log(sqrt(2) + 1) + log(sqrt(2) - 1) 

sage: u = t.maxima_methods().sage() 

sage: u is t 

True 

""" 

return self._exp 

def _symbolic_(self, parent): 

""" 

EXAMPLES:: 

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

log(sqrt(2) + 1) + log(sqrt(2) - 1) 

sage: u = t.maxima_methods() 

sage: u._symbolic_(SR) is t 

True 

sage: SR(u) is t # indirect doctest 

True 

""" 

return parent(self._exp) 

def __reduce__(self): 

""" 

EXAMPLES:: 

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

log(sqrt(2) + 1) + log(sqrt(2) - 1) 

sage: u = t.maxima_methods(); u 

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

sage: loads(dumps(u)) 

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

""" 

return (MaximaWrapper, (self._exp,)) 

def _repr_(self): 

""" 

EXAMPLES:: 

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

log(sqrt(2) + 1) + log(sqrt(2) - 1) 

sage: u = t.maxima_methods(); u 

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

sage: u._repr_() 

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

""" 

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