On Dec 13, 2007 5:28 PM, didier deshommes <[EMAIL PROTECTED]> wrote:
>
> William,
> Would you mind making this a blog post? This is a great reference of
> how interfaces work in Sage.
Great idea! Done:
http://sagemath.blogspot.com/
>
> didier
>
> 2007/12/13, William Stein <[EMAIL PROTECTED]>:
>
> > I figured out a clean way to have this sort of notation work in
> > Mathematica etc. rom Sage when
> > I was hiking with my wife in Sedona to Vultee Arch a couple years ago.
> > Basically when you do say
> > s = mathematica(nu)
> > Sage converts nu into a Mathematica-readable string by calling
> > nu._mathematica_init_():
> >
> > sage: nu = sqrt(2) + I*sin(3)
> > sage: nu._mathematica_init_()
> > '(Sqrt[2]) + ((I) * (Sin[3]))'
> >
> > Note that _mathematica_init_ on the nu in the above example calls
> > other _mathematica_init_'s,
> > e.g., sqrt(2) has a mathematica_init_ method that calls that
> > _mathematica_init_ method for 2, etc.
> > Mathematica itself is not used at all yet. Incidentally, just like
> > you can latex expressions, e.g.,
> >
> > sage: latex(nu)
> > {i \cdot \sin \left( 3 \right)} + \sqrt{ 2 }
> >
> > for inclusion in a paper or something, you can also mathematica them
> > as above, to share
> > with mathematica users...
> >
> > Anyway Sage sends this string to mathematica:
> >
> > 'sage0 := (Sqrt[2]) + ((I) * (Sin[3]))'
> >
> > Mathematica evaluates it and Sage creates a Python wrapper object,
> > which knows the variable
> > name 'sage0':
> >
> > sage: s = mathematica(nu)
> > sage: s.name( )
> > 'sage0'
> > sage: type(s)
> > <class 'sage.interfaces.mathematica.MathematicaElement'>
> > sage: s
> > Sqrt[2] + I*Sin[3]
> >
> > Now there is a running instance of mathematica, and it has an object
> > defined in it
> > called sage0, which is equal to our nu:
> >
> > sage: mathematica.eval('sage0')
> > Sqrt[2] + I Sin[3]
> >
> >
> > You can even play around with that copy of Mathematica more directly
> > from the command
> > line (or with %mathematica in a cell in the Sage notebook):
> >
> > sage: %mathematica
> >
> > --> Switching to Mathematica <--
> >
> > ''
> > mathematica: sage0
> > Sqrt[2] + I*Sin[3]
> > mathematica: Sqrt[sage0]
> > Sqrt[Sqrt[2] + I*Sin[3]]
> > mathematica: N[sage0]
> > 1.4142135623730951 + 0.1411200080598672*I
> >
> > [[Note this is like the Mathematica command line but better since it
> > has readline support, etc.]]
> >
> > mathematica: %sage
> > --> Exiting back to SAGE <--
> >
> > Finally, if you want to call a function and give the version
> > of nu that is in Mathematica as an argument, you just call
> > the function on it using Pythonic notation:
> >
> > sage: s.Sqrt()
> > Sqrt[Sqrt[2] + I*Sin[3]]
> > sage: s.N()
> > 1.4142135623730951 + 0.1411200080598672*I
> >
> > What happens here is that say s.Sqrt creates a Python class that
> > wraps the Mathematica function Sqrt with argument s not yet evaluated,
> > so even this works:
> >
> > sage: s.Sqrt?
> > Docstring:
> > Sqrt[z] or Sqrt[z] gives the square root of z.
> >
> > When we did s.Sqrt? Sage queries Mathematica for how Sqrt works.
> >
> > Everything above applies equally to the Maple, Matlab, Maxima, PARI,
> > Singular, etc., interfaces. There is *much* that can be done to make
> > the Mathematica interface in particular even more cool. Ideas appreciated!
> >
> > By the way, it snowed very nicely on the hike, and my wife and I had a
> > great time.
> >
> > -- William
> >
> > >
> >
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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