Re: [fricas-devel] addition of ExtendedPolynomialReduction
Now thinking about the "reductum(0)=0" assumption. I can easily remove it from my code (see below). tailReduce(x: X, basis: List X): X == empty? basis => x p: R := polynomial x -- We iterate over the non-leading terms of polynomial(x). r: R := 0 v: V := representation x m: C := multiplier x -- We keep the representation part attached to p and hand it -- over to denominatorFreeTopReduce. Thus we get the representation -- from the reduced polynomial. while not zero? p repeat r := r + leadingMonomial p p := reductum p x := denominatorFreeTopReduce([p, v, 1], basis) v := representation x p := polynomial x m := multiplier(x) * m r := multiplier(x) * r [r, v, m] and compare with https://github.com/fricas/fricas/commit/a4c3af045560d631f06c68ca542676b84cd227d2#diff-ebde1584f365f97c30d05da63bb4ba4bR117 Waldek, would you prefer this new code in another commit? (I think I should have done that rewrite before. Sorry.) I just had a quick check. I modified GeneralDistributedMultivariatePolynomial in such a way that it gives an error on reductum(0). Then my test code does not even reach reduce$ExtendedPolynomialReduction, because groebner stops with the reductum(0) error. Ralf -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] addition of ExtendedPolynomialReduction
>> 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. Indeed that comment looks strange. I've removed it and also added the zero test. However, the code was not wrong, because the loop in tailReduce runs with the condition zero?(p). There was only a "leadingMonomial(0)" and "reductum(0)". But both of them yield 0 according to the specification in FiniteAbelianMonoidRing http://fricas.github.io/api/AbelianMonoidRing.html#l-abelian-monoid-ring-reductum Oh... I just now see that for leadingMonomial the specification is not so explicit, but at least the implementation of PolynomialRing is fine. http://fricas.github.io/api/AbelianMonoidRing.html#l-abelian-monoid-ring-leading-monomial https://github.com/hemmecke/fricas/blob/master-hemmecke/src/algebra/poly.spad#L348 but at least the implementation of PolynomialRing is fine. Actually, I don't think that code should rely on leadingMonomial(0)=0 or reductum(0)=0. Waldek, what's your opinion on that? Ralf -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] addition of ExtendedPolynomialReduction
> > 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] > > 54 3 43 >(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 36 4 54 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 -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] addition of ExtendedPolynomialReduction
Hello, I'm currently preparing an article that involves Gröbner basis computation and then finding the representation of some polynomial in terms of that Gröbner 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 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] 54 3 43 (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 36 4 54 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? Ralf -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
