Ralf Hemmecke <[EMAIL PROTECTED]> writes:
> To me the problem is bad design.
>
> halfExtendedSubResultantGcd1 and
> halfExtendedSubResultantGcd2 could well have returned the same type
> Record(gcd: P, coef: P). By the name of the function it would have been
> clear how to interpret the coef entry.
Although I didn't look close enough, I think that might be worth it.
> In fact, I would rather have liked that both functions simply return a
> multivalue or a Cross(P, P), but unfortunately, that does not work in
> panAxiom.
>
> If you look closely, then
>
> g := if mdeg p < mdeg ts_v
> then gcd halfExtendedSubResultantGcd2(ts_v,p)$P
> else gcd halfExtendedSubResultantGcd1(p,ts_v)$P
> would then have been a shorter version of the "if" including the
> following "g:=gcd(n,d)". But I guess that does not yet work in SPAD.
No. But at least we could write:
hesrg := if mdeg p < mdeg ts_v
then halfExtendedSubResultantGcd2(ts_v,p)$P
else halfExtendedSubResultantGcd1(p,ts_v)$P
g := gcd(hesrg.coef, hesrg.gcd)
(n, d) := ((hesrg.coef exquo g)::P, (hesrg.gcd exquo g)::P)
or:
g := gcd(n := hesrg.coef, d := hesrg.gcd)
(n, d) := ((n exquo g)::P, (d exquo g)::P)
but I think the latter is only for me...
Both looks nicer to me than
if mdeg(p) < mdeg(ts_v) then
hesrg: Record (gcd : P, coef2 : P) :=
halfExtendedSubResultantGcd2(ts_v,p)$P
d: P := hesrg.gcd; n: P := hesrg.coef2
else
hesrg: Record (gcd : P, coef1 : P) :=
halfExtendedSubResultantGcd1(p,ts_v)$P
d: P := hesrg.gcd; n: P := hesrg.coef1
g := gcd(n,d)
(n, d) := ((n exquo g)::P, (d exquo g)::P)
-------------------------------------------------------------------------------
It seems that the following three definitions are the only ones where the
result type encodes the name of the operation a second time:
newpoly.spad.pamphlet:77: halfExtendedSubResultantGcd1: ($, $) ->
Record(gcd: $, coef1: $)
newpoly.spad.pamphlet:87: halfExtendedResultant1: ($, $) ->
Record(resultant: R, coef1: $)
prs.spad.pamphlet:143: semiSubResultantGcdEuclidean1: (polR,
polR)->Record(coef1: polR, gcd: polR)
I think we should consider renaming them. However, in my opinion, newpoly
should go away anyway and be merged into the other polynomial domains properly:
it says that it is a post facto extension in spirit, but SPAD doesn't have
"extend"...
It seems that the main usage of NewSparseUnivariatePolynomial is in
NewSparseMultivariatePolynomial. Are the operations it exports useless
elsewhere?
I guess we should ask Marc at the workshop...
Martin
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