Question

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. $

score 233 · Answer 1 · 2020-08-22 07:51:07

233

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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 22 Aug 2020 - 7:51

score 129 · Answer 2 · 2020-09-07 21:36:03

129

Views

Constructing multivariate polynomial from roots

Published on 07 Sep 2020 - 21:36

score 99 · Answer 3 · 2020-09-16 17:31:55

99

Views

Show that in $\mathbb{Z}[x,y]$, $\langle x+y,x-y\rangle\subsetneq\langle x,y\rangle$

Published on 16 Sep 2020 - 17:31

score 415 · Answer 4 · 2020-10-14 07:51:16

415

Views

Multivariate Quadratic Regression For 3+ input variables

Published on 14 Oct 2020 - 7:51

score 65 · Answer 5 · 2020-10-18 04:34:28

65

Views

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Published on 18 Oct 2020 - 4:34

score 105 · Answer 6 · 2026-02-23 11:59:33

105

Views

Help Solving Multivariable Quintic Function

Published on 23 Feb 2026 - 11:59

score 70 · Answer 7 · 2020-10-25 09:31:43

70

Views

What does it mean for two equations to be 'invariant'?

Published on 25 Oct 2020 - 9:31

score 67 · Answer 8 · 2020-11-11 17:04:34

67

Views

Is there a notion of transcendental numbers for polynomials of multiple variables?

Published on 11 Nov 2020 - 17:04

score 75 · Answer 9 · 2020-11-18 00:38:24

75

Views

How does one write the factorization of a general multivariable polynomial?

Published on 18 Nov 2020 - 0:38

score 35 · Answer 10 · 2020-12-02 20:17:40

35

Views

If the real zeroes of real polynomial $p(x,y)$ are disjoint points and curves, is $p(x,y)$ a positive sum of squares?

Published on 02 Dec 2020 - 20:17

score 165 · Answer 11 · 2020-12-30 20:03:50

165

Views

When is a multivariate cubic polynomial mapping $\Bbb{R}^n$ to $\Bbb{R}^n$ both one-to-one and onto?

Published on 30 Dec 2020 - 20:03

score 126 · Answer 12 · 2021-01-04 11:00:02

126

Views

Finding last coefficient of a multivariate polynomial in $GF(2)$ in polynomial time

Published on 04 Jan 2021 - 11:00

score 91 · Answer 13 · 2021-01-09 12:54:03

91

Views

Show $ (2 - b^2c^2) (1 + b^2) \ge (b^2 + c^2)(b + c - 3)^2 $ in some range.

Published on 09 Jan 2021 - 12:54

score 78 · Answer 14 · 2026-02-23 16:57:59

78

Views

Method of Frobenius Confusion

Published on 23 Feb 2026 - 16:57

score 101 · Answer 15 · 2026-02-23 09:02:41

101

Views

The best methods for multivariate polynomial equations over finite fields

Published on 23 Feb 2026 - 9:02

List Question

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. $

Constructing multivariate polynomial from roots

Show that in $\mathbb{Z}[x,y]$, $\langle x+y,x-y\rangle\subsetneq\langle x,y\rangle$

Multivariate Quadratic Regression For 3+ input variables

Irreducible subsets of the affine plane

Help Solving Multivariable Quintic Function

What does it mean for two equations to be 'invariant'?

Is there a notion of transcendental numbers for polynomials of multiple variables?

How does one write the factorization of a general multivariable polynomial?

If the real zeroes of real polynomial $p(x,y)$ are disjoint points and curves, is $p(x,y)$ a positive sum of squares?

When is a multivariate cubic polynomial mapping $\Bbb{R}^n$ to $\Bbb{R}^n$ both one-to-one and onto?

Finding last coefficient of a multivariate polynomial in $GF(2)$ in polynomial time

Show $ (2 - b^2c^2) (1 + b^2) \ge (b^2 + c^2)(b + c - 3)^2 $ in some range.

Method of Frobenius Confusion

The best methods for multivariate polynomial equations over finite fields

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