def _sage_(self):
"""
EXAMPLES:
sage: m = lie('[[1,0,3,3],[12,4,-4,7],[-1,9,8,0],[3,-5,-2,9]]') # optional - lie
sage: m.sage() # optional - lie
[ 1 0 3 3]
[12 4 -4 7]
[-1 9 8 0]
[ 3 -5 -2 9]
"""
t = self.type()
if t == "grp":
raise ValueError, "cannot convert Lie groups to native Sage objects"
elif t == "mat":
import sage.matrix.constructor
return sage.matrix.constructor.matrix(eval(str(self).replace("\n", "").strip()))
elif t == "pol":
import sage.misc.misc
from sage.rings.all import PolynomialRing, QQ
# Figure out the number of variables
s = str(self)
open_bracket = s.find("[")
close_bracket = s.find("]")
nvars = len(s[open_bracket:close_bracket].split(","))
# create the polynomial ring
R = PolynomialRing(QQ, nvars, "x")
x = R.gens()
pol = R(0)
# Split up the polynomials into terms
terms = []
for termgrp in s.split(" - "):
# The first entry in termgrp has
# a negative coefficient
termgrp = "-" + termgrp.strip()
terms += termgrp.split("+")
# Make sure we don't accidentally add a negative
# sign to the first monomial
if s[0] != "-":
terms[0] = terms[0][1:]
# go through all the terms in s
for term in terms:
xpos = term.find("X")
coef = eval(term[:xpos].strip())
exps = eval(term[xpos + 1 :].strip())
monomial = sage.misc.misc.prod(map(lambda i: x[i] ** exps[i], range(nvars)))
pol += coef * monomial
return pol
elif t == "tex":
return repr(self)
elif t == "vid":
return None
else:
return ExpectElement._sage_(self)
def _sage_(self):
"""
EXAMPLES:
sage: m = lie('[[1,0,3,3],[12,4,-4,7],[-1,9,8,0],[3,-5,-2,9]]') # optional - lie
sage: m.sage() # optional - lie
[ 1 0 3 3]
[12 4 -4 7]
[-1 9 8 0]
[ 3 -5 -2 9]
"""
t = self.type()
if t == 'grp':
raise ValueError, "cannot convert Lie groups to native Sage objects"
elif t == 'mat':
import sage.matrix.constructor
return sage.matrix.constructor.matrix( eval( str(self).replace('\n','').strip()) )
elif t == 'pol':
import sage.misc.misc
from sage.rings.all import PolynomialRing, QQ
#Figure out the number of variables
s = str(self)
open_bracket = s.find('[')
close_bracket = s.find(']')
nvars = len(s[open_bracket:close_bracket].split(','))
#create the polynomial ring
R = PolynomialRing(QQ, nvars, 'x')
x = R.gens()
pol = R(0)
#Split up the polynomials into terms
terms = []
for termgrp in s.split(' - '):
#The first entry in termgrp has
#a negative coefficient
termgrp = "-"+termgrp.strip()
terms += termgrp.split('+')
#Make sure we don't accidentally add a negative
#sign to the first monomial
if s[0] != "-":
terms[0] = terms[0][1:]
#go through all the terms in s
for term in terms:
xpos = term.find('X')
coef = eval(term[:xpos].strip())
exps = eval(term[xpos+1:].strip())
monomial = sage.misc.misc.prod(map(lambda i: x[i]**exps[i] , range(nvars)))
pol += coef * monomial
return pol
elif t == 'tex':
return repr(self)
elif t == 'vid':
return None
else:
return ExpectElement._sage_(self)
def _sage_(self):
"""
EXAMPLES::
sage: m = lie('[[1,0,3,3],[12,4,-4,7],[-1,9,8,0],[3,-5,-2,9]]') # optional - lie
sage: m.sage() # optional - lie
[ 1 0 3 3]
[12 4 -4 7]
[-1 9 8 0]
[ 3 -5 -2 9]
"""
t = self.type()
if t == 'grp':
raise ValueError("cannot convert Lie groups to native Sage objects")
elif t == 'mat':
import sage.matrix.constructor
return sage.matrix.constructor.matrix( eval( str(self).replace('\n','').strip()) )
elif t == 'pol':
from sage.rings.all import PolynomialRing, QQ
#Figure out the number of variables
s = str(self)
open_bracket = s.find('[')
close_bracket = s.find(']')
nvars = len(s[open_bracket:close_bracket].split(','))
#create the polynomial ring
R = PolynomialRing(QQ, nvars, 'x')
x = R.gens()
pol = R(0)
#Split up the polynomials into terms
terms = []
for termgrp in s.split(' - '):
#The first entry in termgrp has
#a negative coefficient
termgrp = "-"+termgrp.strip()
terms += termgrp.split('+')
#Make sure we don't accidentally add a negative
#sign to the first monomial
if s[0] != "-":
terms[0] = terms[0][1:]
#go through all the terms in s
for term in terms:
xpos = term.find('X')
coef = eval(term[:xpos].strip())
exps = eval(term[xpos+1:].strip())
monomial = prod([x[i]**exps[i] for i in range(nvars)])
pol += coef * monomial
return pol
elif t == 'tex':
return repr(self)
elif t == 'vid':
return None
else:
return ExpectElement._sage_(self)
def __repr__(self):
"""
EXAMPLES::
sage: gap(2)
2
"""
s = ExpectElement.__repr__(self)
if s.find('must have a value') != -1:
raise RuntimeError, "An error occurred creating an object in %s from:\n'%s'\n%s"%(self.parent().name(), self._create, s)
return s
def __repr__(self):
"""
EXAMPLES::
sage: gap(2)
2
"""
s = ExpectElement.__repr__(self)
if s.find('must have a value') != -1:
raise RuntimeError, "An error occurred creating an object in %s from:\n'%s'\n%s"%(self.parent().name(), self._create, s)
return s
def __init__(self, parent, value, is_name=False, name=None):
"""
Create a Maxima element.
See ``MaximaElement`` for full documentation.
EXAMPLES::
sage: maxima(zeta(7))
zeta(7)
TESTS::
sage: from sage.interfaces.maxima import MaximaElement
sage: loads(dumps(MaximaElement))==MaximaElement
True
sage: a = maxima(5)
sage: type(a)
<class 'sage.interfaces.maxima.MaximaElement'>
sage: loads(dumps(a))==a
True
"""
ExpectElement.__init__(self, parent, value, is_name=False, name=None)
def __init__(self, parent, value, is_name=False, name=None):
"""
Create a Maxima element.
See ``MaximaElement`` for full documentation.
EXAMPLES::
sage: maxima(zeta(7))
zeta(7)
TESTS::
sage: from sage.interfaces.maxima import MaximaElement
sage: loads(dumps(MaximaElement))==MaximaElement
True
sage: a = maxima(5)
sage: type(a)
<class 'sage.interfaces.maxima.MaximaElement'>
sage: loads(dumps(a))==a
True
"""
ExpectElement.__init__(self, parent, value, is_name=False, name=None)
