5,150 reputation
1934
bio website mpi-sws.org
location Kaiserslautern, Germany
age 33
visits member for 2 years, 8 months
seen 23 mins ago

PhD student at MPI-SWS.


Feb
28
comment Given S is non-empty and sup(S)=inf(S), prove that the set S has only one element.
A minor thing: What if $S = \varnothing$?
Feb
20
comment Knuth-Bendix completion algorithm: word problem
I'm not quite sure what you mean be "see certain structures". Are you asking how Knuth-Bendix is implemented, or do you want to know how to find the complete set of normal forms?
Feb
9
comment Buchberger's criterion to show Grobner basis for linear forms
Yes, that's the idea here.
Feb
9
comment Buchberger's criterion to show Grobner basis for linear forms
Right, scratch the "strictly". If its support is contained, you can reduce by $g$, yielding $E$ (and if you do it right, you can reduce in such a way the the leading coefficient of $D$ is reduced to zero), thereby getting a polynomial that is smaller according to the monomial ordering. By properties of the reduction, $E \in L$ again, so you can repeat the process. Because of well-foundedness, this can only happen finitely many times. What would the normal form look like, when it's in $L$?
Feb
9
comment Buchberger's criterion to show Grobner basis for linear forms
Didn't you want to show this for $k \neq l$? Anyway, if $k = l$, you have found a critical pair. Since $L$ is an ideal, certainly $D := x_l A -x_k B \in L$. By definition of $S$, there's some $g \in S$ whose support is strictly contained in that of $D$. What can you deduce from this?
Feb
9
comment Buchberger's criterion to show Grobner basis for linear forms
Note that A and B are elements of $S$, and they have different leading coefficients. Let's assume that $l<k$. So, first reduce with $A$ as long as possible. Can you then prove that the remainder is divisible by $B$?
Feb
8
revised Is this expression positive or negative
Not a question about formal languages; retagged.
Jan
31
reviewed Approve suggested edit on Binomial Theorem Practical Problem
Jan
31
reviewed Approve suggested edit on Continuous mapping between topological spaces
Dec
30
reviewed Reject suggested edit on Order of elements in abelian groups
Dec
7
comment Why $\langle I, J\rangle =R$ for distinct prime ideals $I$, $J$ of a principal ideal domain $R$?
You need the extra side condition $I,J \neq 0$!
Dec
6
reviewed Reviewed find the extremal of a function
Dec
6
comment find the extremal of a function
I'm sorry, but I find this answer completely incomprehensible.
Dec
6
reviewed Looks OK Show that if a, b and c are integers with c|ab then c|(a,c)(b,c)
Dec
6
reviewed No Action Needed Show that if $a$ and $b$ are positive integers then there are divisors $c$ of $a$ and $d$ of $b$ with $(c, d) = 1$ and $cd = [a, b]$
Dec
6
reviewed Close Find the value of $\cos(2\pi /5)$ using radicals
Nov
28
awarded  Fanatic
Nov
27
comment Show that the field $L = \mathbb F_3[X]/\langle X^5 - X + 1\rangle$ consists of $243$ elements and that $[X][f] = [1]$ for some $[f] \in L$.
Some hints: First of all, it helps to consider $L$ as an $\mathbb F_3$-vectorspace, and note that $243 = 3^5$. Now, if $K$ is a finite field with $k$ elements, an $n$-dimemsional $K$-vectorspace has $k^n$ elements... To show that $L$ is a field, you should be able to use the following well-known theorem: Let $R$ be a ring and $I$ a maximal ideal. Then $R/I$ is a field.
Nov
26
reviewed Close Show that $M$ is a right $R^{0}$-module
Nov
25
reviewed Leave Open Minimal difference between classical and intuitionistic sequent calculus