On Tue, Aug 13, 2019, at 8:32 AM, Fredrik Johansson wrote:
> On Tuesday, August 13, 2019 at 8:59:23 AM UTC+2, Aaron Meurer wrote:On
> Mon, Aug 12, 2019 at 8:39 PM Ondřej Čertík <ond...@certik.us> wrote:
> > >
> > >
> > >
> > > On Mon, Aug 12, 2019, at 7:47 PM, Aaron Meurer wrote:
> > > > A possible middle ground would be to print the definition as a SymPy
> > > > expression. The docstrings in the ODE module use the ODE module to
> > > > pretty print the general solution
> > > > https://docs.sympy.org/latest/modules/solvers/ode.html (unfortunately,
> > > > using the ASCII pretty printer, we could potentially use Unicode if we
> > > > fix https://github.com/sympy/sympy/issues/15700.
> > > >
> > > > It doesn't apply to every function. Some formulas aren't expressible
> > > > in SymPy. I think a good middle ground would be to show the LaTeX, so
> > > > that it looks nice in the HTML, but also pretty print the formula in a
> > > > doctest so that it is readable in plain text (and also you get the
> > > > SymPy code for the definition formula). The only downside is that the
> > > > information becomes duplicated.
> > > >
> > > > Another idea, I don't know how hard it would be, or how confusing the
> > > > output would be to people reading the page, would be to have a special
> > > > pretty print function that shows the pprint() output in the docstring
> > > > itself, but the Sphinx build would replace that with a LaTeX
> > > > representation.
> > >
> > > We can port all missing features from Fungrim into SymPy, so that we can
> > > use SymPy itself to represent any math. There are a few things that can't
> > > be represented by SymPy naturally:
> > >
> > > * such as "x+x".
> > > * order of terms "x*y" vs "y*x", the same with "x+y" vs "y+x"
> > >
> > > That is a fundamental design choice, needed for performance (even more so
> > > in SymEngine). Besides those, I don't know if there is some other
> > > obstacle to represent all the things from Fulgrim. When looking at the
> > > formulas that we need to represent, I don't think we ever need things
> > > like "x+x", but it would be useful to preserve the order of terms.
> > >
> > > I don't know if there are other semantic differences between SymPy
> and Fungrim. Fredrik, do you know if there are other issues?
> Apart from specific objects and functions that don't have definitions
> yet, nothing major as far as I know. There are probably differences in
> special values and the like; for example, log(0) is zoo in SymPy but it
> is (tentatively) -Infinity in Fungrim.
>
> Here are some concrete limitations of the Fungrim formula language for
> writing semantic math right now:
>
> * No formalization of variable-length tuples, variable-size matrices etc
> * No formalization of functions (as mathematical objects, as opposed to
> just their defining expressions) and function spaces
> * No formalization of formal variables (e.g. x as a formal generator of
> R[x], as opposed to a variable x representing an unknown value)
> * No formalization of abstract algebraic structures
> * The constructions for defining bound variables are not yet fully
> defined / consistent / unambiguous, making fully automatic semantic
> parsing problematic
So for SymPy documentation, I am now thinking we should just use SymPy to
represent all the equations (and add all missing functionality that's needed to
do that), I think that can be more readable than LaTeX (what do you think
Jason?), and we can still write tooling to convert it to nice equations online.
> > Not all function definitions can be represented in SymPy. For instance
> > the Meijer G-function is defined by a path integral
> > (https://docs.sympy.org/latest/modules/functions/special.html#sympy.functions.special.hyper.meijerg),
> >
> > and there's no way to make an Integral object in SymPy that is over a
> > path L. I don't know if the G-function is in fungrim. Fungrim seems to
> > be lacking a search functionality.
>
> You can search the git repository, and
> http://fungrim.org/definitions.html currently has a list of symbols
> (though not every implemented symbol has been defined there yet).
>
> Indeed, the Meijer G-function does not have a symbol yet. Paths and
> integrals over paths are also on the todo list!
>
> > At any rate, this all seems out of scope for Lauren's project. I think
> > we should decide on something that we can do now for our docstring
> > standard. If we later decide that something like fungrim can replace
> > it, and we have the tooling written, we can change the standard.
>
> +1
>
> However, there is some potential for collaboration already, related to
> this issue. One of the (many) reasons for creating Fungrim was that I
> find it cumbersome to put a lot of math in the documentation for mpmath
> and Arb; putting in links to Fungrim is an alternative. Here is an
> example: I recently put the Coulomb wave functions in Arb, and on
>
> http://arblib.org/acb_hypgeom.html#coulomb-wave-functions
>
> I just link to the page in Fungrim instead of giving all the formulas
> in the Arb documentation. In the source code
>
> https://github.com/fredrik-johansson/arb/blob/master/acb_hypgeom/coulomb.c
> https://github.com/fredrik-johansson/arb/blob/master/acb_hypgeom/coulomb_jet.c
>
> I put in comments referencing the formula in Fungrim that is used in each
> case.
>
> What I would like to do is to replace more of the existing
> formula-heavy documentation in mpmath and Arb with Fungrim links, as
> soon the content exists in Fungrim. Perhaps this would make sense for
> the SymPy documentation too.
A few suggestions:
* You should enable https on the website and use https in the source code.
* how do you generate the text math, e.g., the second line in:
/* http://fungrim.org/entry/07a654/ */
/* F''/2 = q F, q = (2eta/z + l(l+1)/z^2 - 1)/2 */
the website itself might be able to give such text in many cases.
Ondrej
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