Thanks Waldek!
I am currently preparing a proper patch. I decided to try a few
approaches, so it won't be before tonight...
Martin
Am Dienstag, 10. Juli 2018 17:30:18 UTC+2 schrieb Waldek Hebisch:
>
> Martin R wrote:
> >
> > Dear all,
> >
> > as you may know, I am trying to improve the accessibility of FriCAS from
> > sage, since some people (including myself) value FriCAS strengths.
> >
> > I wanted to add functionality to translate FriCAS' sums and products
> into
> > sage's, but ran into a stupid problem.
> >
> > Basically, I use the unparsed InputForm to obtain an expression tree
> from
> > FriCAS EXPR. Consider now:
> >
> > (52) -> f := guess([reduce(*, [reduce(+, [1/k for k in 1..m], 0) for m
> in
> > 1..n], 1) for n in 0..10]).1
> >
> > p - 1
> > n - 1 11
> > ++-++ --+ 1
> > (52) | | > ------- + 1
> > | | --+ s + 2
> > p = 0 s = 0 10
> > 11 10
> > Type:
> > Expression(Integer)
> > (53) -> f::INFORM
> >
> > (53)
> > (%defprod (+ (%defsum (/ 1 (+ %LW 2)) %LW (*01000s 10) 0 (+ %LX -
> 1)) 1)
> > %LX (*01000p 11) 0 (+ n - 1))
> > Type:
> > InputForm
> >
> > As you can see, the summation variables have subscripts. However, the
> > string representation of the InputForm of scripted symbols does not
> allow
> > to reproduce the symbol. In fact, the code in symbol.spad is simply:
> >
> > convert(s : %) : InputForm == convert(s pretend Symbol)$InputForm
> >
> > Would it be possible to change that to something like the following
> > (WARNING: only lightly tested!). Two comments:
> >
> > 1) The scripts are of type OutputForm, but there is no way to get an
> > InputForm from an OutputForm. So the below will not work always, but
> only
> > when the input is reasonable. In fact
> > interpret convert subscript('s, [z^2]) works...
> >
> > 2) There seems to be a problem when the subscript has a value. For
> > example, x := subscript('s, ['x^2]) produces an error about cons'ing
> > InputForm with InputForm. Not sure what's happening there.
> >
> > Best wishes,
> >
> > Martin
> >
> > Code:
> >
> > convert(s: Symbol): InputForm ==
> > not scripted? s => convert(name s)$InputForm
> >
> > ls := scripts s
> > A: List InputForm := [e pretend InputForm for e in ls.sub]
> > B: List InputForm := [e pretend InputForm for e in ls.sup]
> > C: List InputForm := [e pretend InputForm for e in ls.presup]
> > D: List InputForm := [e pretend InputForm for e in ls.presub]
> > E: List InputForm := [e pretend InputForm for e in ls.args]
> > a: InputForm := convert('script)
> > b: InputForm := convert name s
> > c: InputForm := cons(convert('construct), [cons(convert('construct),
> e)
> > for e in [A, B, C, D, E]])
> > convert([a, b, c])
>
> Well, you need coercion from OutputForm to InputForm. Above
> you try 'pretend' but it is very poor coercion. The problem is
> that InputForm is evaluated, at least you would need something
> like Lisp quote. Since we do not have quote, the correct way
> is to walk aroud InputForm and recursively convert them. So
> correct InputForm for OutputForm of 'x^2' is something like
> parsed version of the following
>
> prefix(outputForm('^), [outputForm('x), outputForm(2)])$OutputForm
>
> --
> Waldek Hebisch
>
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