Hi Ralf,
On 02/02/2015 03:39 PM, Ralf Hemmecke wrote:
I do not want to wait. One trick is to have a general function
which takes needed operations as parameters. So one can
have something like:
IntegrateSols(F, L) : Exports == Implementation where
F : Join(Field, CharacteristicZero, RetractableTo Integer,
RetractableTo Fraction Integer)
L : UnivariateSkewPolynomialCategory(F)
U ==> Union(F, "failed")
SF ==> (L, F) -> Record(particular : U, basis : List F)
Exports ==> with
integrate_sols : (L, L, L -> L, SF) -> Union(L, List(L))
++ integrate_sols(op, D, adjoint, rat_solve) ...
or put extra requirements on L like
L : UnivariateSkewPolynomialCategory(F) with
adjoint : % -> % (*)
D : () -> %
Actually, either way is fine, but I would somehow prefer the second
variant. The bad thing is anyway that if (as in (*)) only the name of
the function is listed, i.e., without its axioms, then it's pretty
unclear what the exact requirements of L are. So instead of listing just
the function signatures, it should be similar to the introduction of
DifferentialRing.
https://github.com/fricas/fricas/blob/master/src/algebra//catdef.spad#L269
Thanks for your comments. I've included the function descriptions along
with the signatures.
Another point, is the return type of integrate_sols. Isn't it a bit
unhandy to go for Union(L, List L)?
Wouldn't List(L) or Union(L, Record(ltilde: L, r: L)) be better? Or
maybe Record(ltilde: L, r: Union(L, failed))?
I don't know, actually. Union(L, List(L)) seemed to best fit the
description of the function as mentioned in the paper.
However, Union(L, Record(ltilde: L, r: L)) also seems good as it offers
extra information about what the 2 elements actually mean in the latter
case. So, I've changed the return type to it.
Ralf
Thanks,
Abhinav.
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