>
> Hello,
>
> I'm currently preparing an article that involves GrĂśbner basis
> computation and then finding the representation of some polynomial in
> terms of that GrĂśbner basis. Doing this in FriCAS, is, of course, easy,
> but I was unable to find that such an extended reduction is already
> implemented in FriCAS.
>
> What about the following?
>
> https://github.com/hemmecke/fricas/commit/1ea2f36f0a2bf8dd251cbb0fb6ab810b734d2c88.patch
>
Looks good. However, comment:
-- Reduce the non-leading terms of x (which is assumed to be non-zero).
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
looks strange: I see no check preventing zero and no mathematical
reason for zero (AFAICS one use 'reduce' to get representation of ideal
members, in such case polynomial part of x is 0). Probably
'tailReduce' needs quick exit for 0.
> The new domain can be used like this.
>
> (1) -> Z ==> Integer
> (2) -> vl := [x,y,z]
>
> (2) [x, y, z]
> (3) -> E ==> DirectProduct(3, NNI)
> (4) -> P ==> GeneralDistributedMultivariatePolynomial(vl, Z, E)
> (5) -> G: List P := [x^5-x^4*y^3+2*z, y^4-z^3]
>
> 5 4 3 4 3
> (5) [x - x y + 2 z, y - z ]
> (6) -> p: P := x^7
>
> 7
> (6) x
> (7) -> z := reduce(p, G)$ExtendedPolynomialReduction(Z, E, P)
>
> (7)
> 4 6 2 3 2 4
> [poly = - x y z + 2 x z + 2 x y z + 2 y z ,
> 2 3 6 4 5 4 3 2
> repr = [- x - x y - y , - x y - x y z + 2 y z], mult = - 1]
> (8) -> z.mult * p - (z.poly + z.repr.1 * G.1 + z.repr.2 * G.2)
>
> (8) 0
>
> May I commit?
OK (after you look at the issue).
--
Waldek Hebisch
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