Ralf Hemmecke <[EMAIL PROTECTED]> writes:
> > Well, I think that only "morally" equal functions should share names.
> > Although
> > this is very vague indeed. I'd expect that two functions of the same name,
> > one
> > taking a list of variables and a list of exponents which together specify a
> > monomial (and which I personally consider bad practice already, but anyway),
> > and the other taking a monomial in the form of IndexedExponents should yield
> > the *same* result.
>
> Oh, I am sorry. I would also ban
>
> coefficient: (%, List Var, List NNI) -> % (*1)
Me too.
> and instead change
>
> coefficient: (%, IndexedExponents Var) -> Coef (*2)
>
> to return %.
This is exported by AbelianMonoidRing, and I think it's OK to have it. At
least, it's consistent with Polynomial Integer:
(35) -> coefficient(x^2+y+y*z, monomial(1,z)$IndexedExponents(Symbol))
(35) 0
Type: NonNegativeInteger
> But I am not totally convinced. Having two lists in the argument is bad. I'd
> rather prefer something like
>
> coefficient: (%, List Cross(Var, NNI)) -> %
>
> Here the return type % is fine.
I'd rather prefer
coefficient: (%, Monomial) -> ???
which is what I did in (35) above.
Only, the return type is not totally clear. Maybe the signature in
AbelianMonoidRing should export both
coefficient: (%, Monomial) -> %
and
coefficient: (%, Monomial) -> Coeff
> Also (*2) is not totally optimal. Suppose you power series contains x
> and y and you give IndexedExponents that only involve x. The return type
> should then be % instead of Coef.
Well, currently it seems that there are two kinds of coefficient functions:
1) eg in POLYCAT:
coefficient: (%,List VarSet,List NonNegativeInteger) -> %
++ coefficient(p, lv, ln) views the polynomial p as a polynomial
++ in the variables of lv and returns the coefficient of the term
++ \spad{lv**ln}, i.e. \spad{prod(lv_i ** ln_i)}.
2) in AbelianMonoidRing, where the exponents of variables that are not given
are implicitely assumed as zero.
so:
(39) -> coefficient(x^2+y+y*z, monomial(1,z)$IS)
(39) 0
Type: NonNegativeInteger
(40) -> coefficient(x^2+y+y*z, z, 1)
(40) y
Type: Polynomial(Integer)
I think we should consider to remove or rename one of them. I'm not completely
sure which one, though.
Now that I see the pattern, I think I'll provide both for TS, for the moment.
Proper design takes too long.
Martin
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