Question

Is there a reason why the $S$-polynomial is defined in this way?

score 1.1k · Answer 1 · 2012-11-12 07:57:16

1.1k

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Is there a reason why the $S$-polynomial is defined in this way?

Published on 12 Nov 2012 - 7:57

score 658 · Answer 2 · 2026-03-25 19:11:43

658

Views

Dimension of a certain quotient ring of $\mathbb{C}[x_0,\ldots,x_{m-1}]$.

Published on 25 Mar 2026 - 19:11

score 114 · Answer 3 · 2013-01-28 15:22:04

114

Views

Is there an ideal decomposition that counts the number of monomial generators?

Published on 28 Jan 2013 - 15:22

score 297 · Answer 4 · 2013-01-31 19:52:54

297

Views

Basis of matrices with a variable

Published on 31 Jan 2013 - 19:52

score 287 · Answer 5 · 2013-03-09 17:52:38

287

Views

Reduced Gröbner Basis for $u:=X^2+2XYZ$ and $v:=XY+2Y^2Z-1$

Published on 09 Mar 2013 - 17:52

score 299 · Answer 6 · 2013-03-13 19:24:38

299

Views

Gröbner Basis for Ideal $J$

Published on 13 Mar 2013 - 19:24

score 234 · Answer 7 · 2026-03-25 14:25:10

234

Views

Prove: A basis $G$ is a Grobner basis of an ideal $\iff$ for every element $S$ in a homogeneous basis for the syzygies $S(G)$ we have $S.G \to_{G}0. $

Published on 25 Mar 2026 - 14:25

score 169 · Answer 8 · 2020-09-02 18:57:23

169

Views

Alternative Gröbner Basis Packages

Published on 02 Sep 2020 - 18:57

score 73 · Answer 9 · 2020-09-14 17:53:22

73

Views

Characterise the set of solutions of a nonlinear system of equations

Published on 14 Sep 2020 - 17:53

score 799 · Answer 10 · 2020-09-16 02:10:08

799

Views

Minimal Gröbner bases have the same leading terms

Published on 16 Sep 2020 - 2:10

score 71 · Answer 11 · 2026-03-25 22:26:49

71

Views

Let $P$ be prime and $Q\subset P$. How feasible is the computation of a Gröbner basis of a min prime over $Q$ compared to the computation for $P$?

Published on 25 Mar 2026 - 22:26

score 472 · Answer 12 · 2026-03-26 12:58:13

472

Views

Is a minimal Gröbner Basis a minimal system of generators?

Published on 26 Mar 2026 - 12:58

score 78 · Answer 13 · 2020-10-20 10:31:23

78

Views

Unexpected result for Groebner basis

Published on 20 Oct 2020 - 10:31

score 219 · Answer 14 · 2020-11-12 20:18:28

219

Views

Biggest circle under a polynomial curve

Published on 12 Nov 2020 - 20:18

score 38 · Answer 15 · 2020-11-24 11:03:19

38

Views

$f_m:=x^m+x^{-m^2},m\in\mathbb{Z}$ is not a $\mathbb{Q}$ basis for $\mathbb{Q}[x,x^{-1}]$

Published on 24 Nov 2020 - 11:03

List Question

Is there a reason why the $S$-polynomial is defined in this way?

Dimension of a certain quotient ring of $\mathbb{C}[x_0,\ldots,x_{m-1}]$.

Is there an ideal decomposition that counts the number of monomial generators?

Basis of matrices with a variable

Reduced Gröbner Basis for $u:=X^2+2XYZ$ and $v:=XY+2Y^2Z-1$

Gröbner Basis for Ideal $J$

Prove: A basis $G$ is a Grobner basis of an ideal $\iff$ for every element $S$ in a homogeneous basis for the syzygies $S(G)$ we have $S.G \to_{G}0. $

Alternative Gröbner Basis Packages

Characterise the set of solutions of a nonlinear system of equations

Minimal Gröbner bases have the same leading terms

Let $P$ be prime and $Q\subset P$. How feasible is the computation of a Gröbner basis of a min prime over $Q$ compared to the computation for $P$?

Is a minimal Gröbner Basis a minimal system of generators?

Unexpected result for Groebner basis

Biggest circle under a polynomial curve

$f_m:=x^m+x^{-m^2},m\in\mathbb{Z}$ is not a $\mathbb{Q}$ basis for $\mathbb{Q}[x,x^{-1}]$

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