Question

Suppose $G$ and $G'$ are grobner bases for the ideal $I$. Show that $\overline{f}^{G} = \overline{f}^{G'}$ for $f \in k[x_1, \cdots, x_n]$

score 84 · Answer 1 · 2021-12-13 01:47:26

Suppose $G$ and $G'$ are grobner bases for the ideal $I$. Show that $\overline{f}^{G} = \overline{f}^{G'}$ for $f \in k[x_1, \cdots, x_n]$

score 90 · Answer 2 · 2021-12-20 08:01:03

90

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Differences in theory of Groebner bases when we work over finite fields.

Published on 20 Dec 2021 - 8:01

score 127 · Answer 3 · 2026-03-26 01:28:31

127

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Understanding Graver basis, Grobner basis, and Lawrence lifting

Published on 26 Mar 2026 - 1:28

score 145 · Answer 4 · 2026-03-26 01:28:16

145

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Termination of Buchberger's algorithm for path algebras

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score 38 · Answer 5 · 2026-03-25 08:00:43

38

Views

Number of monomials in the complement of $\langle LT(I) \rangle$.

Published on 25 Mar 2026 - 8:00

score 77 · Answer 6 · 2022-04-06 00:03:44

77

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$G$ is a Grobner basis if and only if $\overline{f}^{G} = 0$

Published on 06 Apr 2022 - 0:03

score 38 · Answer 7 · 2022-04-10 18:04:42

38

Views

Is the induced map $V(I) \longrightarrow V(J)$ is surjective for $I=(xy-1,y^2-z)\subset\Bbb C[x,y,z]$ and $J=I\cap \Bbb C[y,z]$?

Published on 10 Apr 2022 - 18:04

score 399 · Answer 8 · 2022-04-17 20:36:17

399

Views

How to find an ideal of variety?

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score 74 · Answer 9 · 2026-03-25 21:45:04

74

Views

Extension theorem over reals

Published on 25 Mar 2026 - 21:45

score 253 · Answer 10 · 2022-05-10 23:43:22

253

Views

When does the system $x^n-1=y^n-1=x(y-1)^2+y(x-1)^2=0$ have only the trivial solution $(1,1)$ over the prime field of order $p$?

Published on 10 May 2022 - 23:43

score 85 · Answer 11 · 2026-03-25 08:01:32

85

Views

Find (a generating set for) $\mathbb{Q}[x]\cap I$ where $I=\langle x^2-y,y^2-x,x^5-x^2\rangle$ (generate gröbner basis).

Published on 25 Mar 2026 - 8:01

score 326 · Answer 12 · 2026-03-27 16:28:11

326

Views

Example of initial ideal

Published on 27 Mar 2026 - 16:28

score 36 · Answer 13 · 2022-09-25 09:55:34

36

Views

Solve system of polynomial equations based on distance?

Published on 25 Sep 2022 - 9:55

score 157 · Answer 14 · 2026-03-25 23:52:17

157

Views

Algorithm for writing an image of a polynomial in a quotient ring in terms of a given basis of the quotient ring.

Published on 25 Mar 2026 - 23:52

score 111 · Answer 15 · 2026-03-25 08:04:54

111

Views

Determining reduced Groebner basis of $I(V)$ by using Lagrange

Published on 25 Mar 2026 - 8:04

List Question

Suppose $G$ and $G'$ are grobner bases for the ideal $I$. Show that $\overline{f}^{G} = \overline{f}^{G'}$ for $f \in k[x_1, \cdots, x_n]$

Differences in theory of Groebner bases when we work over finite fields.

Understanding Graver basis, Grobner basis, and Lawrence lifting

Termination of Buchberger's algorithm for path algebras

Number of monomials in the complement of $\langle LT(I) \rangle$.

$G$ is a Grobner basis if and only if $\overline{f}^{G} = 0$

Is the induced map $V(I) \longrightarrow V(J)$ is surjective for $I=(xy-1,y^2-z)\subset\Bbb C[x,y,z]$ and $J=I\cap \Bbb C[y,z]$?

How to find an ideal of variety?

Extension theorem over reals

When does the system $x^n-1=y^n-1=x(y-1)^2+y(x-1)^2=0$ have only the trivial solution $(1,1)$ over the prime field of order $p$?

Find (a generating set for) $\mathbb{Q}[x]\cap I$ where $I=\langle x^2-y,y^2-x,x^5-x^2\rangle$ (generate gröbner basis).

Example of initial ideal

Solve system of polynomial equations based on distance?

Algorithm for writing an image of a polynomial in a quotient ring in terms of a given basis of the quotient ring.

Determining reduced Groebner basis of $I(V)$ by using Lagrange

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