Commutative Algebra, Singularities and Computer Algebra: by Ciprian S. Borcea (auth.), Jürgen Herzog, Victor Vuletescu

By Ciprian S. Borcea (auth.), Jürgen Herzog, Victor Vuletescu (eds.)

Commutative Algebra, Singularities and laptop Algebra provides present tendencies in commutative algebra, algebraic combinatorics, singularity idea and machine algebra, and highlights the interplay among those disciplines. Contributions by means of prime overseas mathematicians completely speak about issues in: modules concept, integrally closed beliefs and determinantal beliefs, singularities in projective areas and Castelnuovo-Mumford regularity, Groebner and SAGBI foundation, and using the pc programs Bergman, CoCoA and SINGULAR.

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Extra info for Commutative Algebra, Singularities and Computer Algebra: Proceedings of the NATO Advanced Research Workshop on Commutative Algebra, Singularities and Computer Algebra Sinaia, Romania 17–22 September 2002

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2. 6. is said to be shellabfe if it is pure and tal order, say F"F2 , ... ,Fe , so that the followi ng if its facets can be given a to condition holds: for all i and j with I :S j < i :S e there exist v E F; \ F j and an index k, I :S k < i, such that Fi \ Fk = {v} . 6.. Shellability is a strong property, very well suited for inductive arguments. Suppose that F] , .. ; denote the smallest simplicial complex containing F" ... ; the smallest simplicial complex containing Fj n F; for all j < i. e.

Is G-KRS. 6. ,) = k. 6. ) - k boxes in the bitableau with the corresponding 0 entries. 6. 1 . 9. Let I" ... ,t, be positive integers and set I = It I . l" and gj = y,(t,,, . , t,). If char K = 0 or char K > min(/i' m - I; , n- Ii) Jar all i, lhen I is in-KR5 and in(I) is generated, as a K-vector space, by the monomials M with r,(M) '" gJor all i. 9 is satisfactory if one only wants to determine the initial ideal of the product It1.. 11" but it does not tell us how to find a Grabner basis. e.

S; i j + 1 for all i, (b) if ( = (+1 then 'j;::: 'i+1' Property (a) is clear since the algorithm chooses £j+l ~ i j. If £i = £i+l then the pivot position of the (j + I)tb deletion step lies left of (or above) the pivot position of the ith deletion step. Now it is easy to see that the element pushed out by the (i + I)th step is not larger than that pushed oul by the ith step. KRS gives a correspondence between standard bitableaux and two-line arrays with properties (a) and (b). It is bijective since it has an inverse.

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