Hi Viny,
The following works for me:
def mmatosage(mma_list):
# Convert the mathematica object to a string
string = repr(mma_list)
# Convert mathematica-style {} to python style []
string = string.replace('{','[').replace('}',']')
# Replace mathematica's crazy exponent notation with the standard
# one e.g. 6.05*^3 ==> 6.05e3
string = string.replace('*^', 'e')
# Delete new lines (both \n and \r\n appear sporadically)
string = string.replace('\n', ' ').replace('\r', ' ')
sage_stuff = sage_eval(string,locals = {'E':E,'x':x,'y':y})
return sage_stuff
sage: var('E')
sage: var('x')
sage: var('y')
sage: mma_list = mathematica("{((1 + E^x^2)*x)/(1 + E^x^2 +
2*E^x^2*x^2), ((-1 + E^y^2)*y)/(-1 + E^y^2 + 2*E^y^2*y^2)}")
sage: arr = mmatosage(mma_list)
sage: print arr
[(E^(x^2) + 1)*x/(2*E^(x^2)*x^2 + E^(x^2) + 1), (E^(y^2) - 1)*y/(2*E^
(y^2)*y^2 + E^(y^2) - 1)]
sage: print "1st element:", arr[0]
1st element: (E^(x^2) + 1)*x/(2*E^(x^2)*x^2 + E^(x^2) + 1)
This seems to do what you want. It seems to be the best way to import
symbolics from mathematica. I hope that Sage will eventually do the
var() and locals={} bits automatically when you call mma_list.sage(),
but in the meantime we can do it the dirty way.
I'd be happy to help out with the implementation of this method, but
I've only ever hacked together my code, and so don't really know
anything about how to contribute.
Cheers,
Felix
On Aug 15, 8:45 pm, Viny <hje...@hotmail.com> wrote:
> Hello everybody!
>
> Thanks for your help.
> I'm realizing that i'm definitely really bad in sage, perhaps i'll be
> best in another life!!lol!
> This is a piece of a code for changing a symbolic mathematica list
> expression to a sage list expression:
>
> def mmatosage(mma_list):
> # Convert the mathematica object to a string
> string = repr(mma_list)
> # Convert mathematica-style {} to python style []
> string = string.replace('{','[').replace('}',']')
> # Replace mathematica's crazy exponent notation with the standard
> one
> string = string.replace('^', '**')
> # Delete new lines (both \n and \r\n appear sporadically)
> string = string.replace('\n', ' ').replace('\r', ' ')
> sage_stuff = sage_eval(string,locals =
> {'E':'E','x':'x','y':'y'},preparse=False,)
> return sage_stuff
>
> I get the folowing error when I apply it to this mathematica
> expression {((1 + E^x^2)*x)/(1 + E^x^2 + 2*E^x^2*x^2),
> ((-1 + E^y^2)*y)/(-1 + E^y^2 + 2*E^y^2*y^2)}
>
> ---> 41 sage_stuff = sage_eval(string,locals =
> {'E':'E','x':'x','y':'y'},preparse=False)
> 42 return sage_stuff
>
> /usr/local/src/sage-4.0.2/local/lib/python2.5/site-packages/sage/misc/
> sage_eval.pyc in sage_eval(source, locals, cmds, preparse)
> 197 return locals['_sage_eval_returnval_']
> 198 else:
> --> 199 return eval(source, sage.all.__dict__, locals)
> 200
> 201
>
> /usr/local/src/sage-4.0.2/local/lib/python2.5/site-packages/sage/
> all.pyc in <module>()
>
> TypeError: unsupported operand type(s) for ** or pow(): 'str' and
> 'int'
>
> I have any idea.
>
> Thankx for your help!
>
> On 15 août, 03:09, Marshall Hampton <hampto...@gmail.com> wrote:
>
>
>
> > Oh right, sorry. I always do that and then remember after the syntax
> > error...
>
> > On Aug 14, 6:35 pm, William Stein <wst...@gmail.com> wrote:
>
> > > On Fri, Aug 14, 2009 at 4:32 PM, Marshall Hampton<hampto...@gmail.com>
> > > wrote:
>
> > > > You probably have to pass in the "dx" as a local variable, i.e. do
> > > > something like
>
> > > > sage_stuff = sage_eval(expr, locals = {'dx' = 'dx'})
>
> > > It's {'dx':'dx'} or something like that. Definitely not 'dx' = 'dx'.
>
> > > > where expr is your mathematica expression.
>
> > > > -Marshall Hampton
>
> > > > On Aug 14, 1:49 pm, Viny <hje...@hotmail.com> wrote:
> > > >> Thanks for your help Felix, with your ideas i made progresses. But the
> > > >> problem isn't fixe yet. Since i have some symbolic variable such 'dx'
> > > >> in my expressions, the
> > > >> code's line --> 500 return eval(string, {'I': numpy.complex(0,1)})
> > > >> generate this folowing error
> > > >> NameError: name 'dx' is not defined
> > > >> Even when i put in the begining of my function var ("dx"), the problem
> > > >> stay.
>
> > > >> Thanks again
>
> > > >> On 14 août, 04:04, thelamecamel <thelameca...@gmail.com> wrote:
>
> > > >> > Hi Viny,
>
> > > >> > Sage's mathematica support at present seems to be geared towards
> > > >> > sending data to mathematica and printing the results to the screen,
> > > >> > rather than getting mathematica's results back into sage for data
> > > >> > manipulation. So the going may be a little rough.
>
> > > >> > Sage can convert its own arrays into mathematica's notation, e.g.
> > > >> > Jason's example
> > > >> > sage: b=mathematica([1,2,3])
> > > >> > will create a mathematica variable representing the array {1,2,3},
> > > >> > accessible from sage. I'm not sure whether you can send mathematica
> > > >> > more complicated things such as functions in this fashion.
>
> > > >> > Once you've got your variables into mathematica, you perform
> > > >> > mathematica functions on them like so:
> > > >> > sage: x = mathematica(1)
> > > >> > sage: mathematica.eval('myfunc[x_,y_]:=x+y')
> > > >> > sage: x.myfunc(2)
> > > >> > 3
>
> > > >> > It's hard to get your mathematica results back into sage for use. As
> > > >> > Jason noted below, mathematica arrays with {} don't get converted
> > > >> > back
> > > >> > into sage arrays with []. There is a ticket related to the array
> > > >> > problem <http://trac.sagemath.org/sage_trac/ticket/4948>, but there
> > > >> > seems to be no progress on it.
>
> > > >> > I gave up and rolled my own mathematica list to numpy array
> > > >> > conversion
> > > >> > - you might find it useful. I believe that using eval() is frowned
> > > >> > upon for security reasons. If you want sage arrays rather than numpy
> > > >> > arrays, then use sage_eval() (which is considerably slower for large
> > > >> > arrays) and strip out the numpy stuff. Comments on the below code
> > > >> > are
> > > >> > welcome.
>
> > > >> > import numpy
> > > >> > import re
> > > >> > def mma_to_numpy(mma_arr):
> > > >> > """Convert mathematica array to numpy array."""
> > > >> > # Convert the mathematica object to a string
> > > >> > string = repr(mma_arr)
> > > >> > # Convert mathematica-style {} to python style []
> > > >> > string = string.replace('{','[').replace('}',']')
> > > >> > # Replace mathematica's crazy exponent notation with the standard
> > > >> > one
> > > >> > string = string.replace('*^', 'e')
> > > >> > # Delete new lines (both \n and \r\n appear sporadically)
> > > >> > string = string.replace('\n', ' ').replace('\r', ' ')
> > > >> > # Detect characters that should not be in an array
> > > >> > if re.findall(r'[a-df-zA-HJ-Z]+', string) != []:
> > > >> > raise TypeError, "Mathematica returns non-array: %s" % string
> > > >> > # Read the string into numpy, interpreting I as j
> > > >> > return eval(string, {'I': numpy.complex(0,1)})
>
> > > >> > You use it as such:
> > > >> > sage: b = mathematica([1.5,2.+3.j,3])
> > > >> > sage: b
> > > >> > {1.5, 2. + 3.*I, 3}
> > > >> > sage: numpy.array(mma_to_numpy(b), dtype='D')
> > > >> > array([ 1.5+0.j, 2.0+3.j, 3.0+0.j])
>
> > > >> > Hope that this helps - there isn't much documentation on this stuff.
>
> > > >> > Cheers,
> > > >> > Felix
>
> > > >> > On Aug 13, 8:26 pm, Viny <hje...@hotmail.com> wrote:
>
> > > >> > > On 13 août, 10:47, Viny <hje...@hotmail.com> wrote:
>
> > > >> > > > Hi,
>
> > > >> > > > I have a problem of memory into maxima when it performs a
> > > >> > > > symbolic
> > > >> > > > expression of an hessian matrix. This symbolic expression of the
> > > >> > > > hessian seems to be too big. My sage program is written using
> > > >> > > > python.
> > > >> > > > And i want to compute the hessian matrix with mathematica 6.0 in
> > > >> > > > my
> > > >> > > > sage file.
> > > >> > > > I need to compute symbolic expresstion of the gradient and the
> > > >> > > > hessian
> > > >> > > > with mathematica and after compute the mathématica LinearSolve
> > > >> > > > function to solve hessian^-1*grad.
> > > >> > > > How to make this interface in my .sage?
> > > >> > > > Please help me!!!
>
> > > >> > > > I have mathematica 6.0 and sage4.0.2 in my linux 64bit system.
>
> > > >> > > This is an example of the function to compute the gradient in
> > > >> > > my .sage, but it doesn't work.
> > > >> > > def grad(f,v):
> > > >> > > return mathematica ( f ).D( [ ' v ',1] )
> > > >> > > The result is {0,0} . I have another problem of format, i don't
> > > >> > > know
> > > >> > > the command to change { } in () in the mathematica result {0,0}
>
> > > --
> > > William Stein
> > > Associate Professor of Mathematics
> > > University of Washingtonhttp://wstein.org
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