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1
Computer Algebra in Scientific Computing CASC’99: ... - Strona 85
The following theorem shows how to use Gröbner bases to effectively compute a Gröbner basis of the kth elimination ideal Ik. Theorem 7. Let I be an ideal of Kai, ..., xn] and let G be a Gröbner basis of I with respect to a k-elimination order for k ...
Victor G. Ganzha, Ernst W. Mayr, Evgenii Vorozhtsov,
2012
2
A First Course in Computational Algebraic Geometry - Strona 75
We wish to find generators of the kth elimination ideal Ik:InK[Xk+1,...,/\Cnj. Elements of the ideal Ik are said to be obtained from f1, . . . , f, by eliminating X1,...,Xk. Definition 2.33 A monomial ordering > on K [x1, . . . ,x,,] is called an elimination ...
Wolfram Decker, Gerhard Pfister,
2013
3
A Primer of Algebraic Geometry: Constructive Computational ...
Using this language, we see that eliminating xi,...,xjt means finding nonzero polynomials in the k-th elimination ideal Ik- The next theorem expresses that if deg( aHP[) = d (or dimV(J) = d in case k is algebraically closed), then the elimination of ...
Huishi Li, Freddy Van Oystaeyen,
2000
4
Value Distribution Theory Related to Number Theory - Strona 50
In the definition of the affine algebraic variety Z, if the ideal IK is not assumed prime, then we obtain an affine algebraic set Z. The set Z is a finite union of its irreducible components (affine algebraic varieties) . Let Z be an affine variety, defined ...
Pei-Chu Hu, Chung-Chun Yang,
2006
5
Formal Algorithmic Elimination for PDEs - Strona 205
3.1.1), in order to determine the intersection of I with the subalgebra generated by the relevant jet variables in U. Since the vanishing ideal IK{U} (S) is finitely generated as a radical differential ideal, we construct in this way a generating set for ...
6
Lie Groups: An Approach Through Invariants and Representations
We know that such relations are the intersection of the linear span of the given monomials with the determinantal ideal Ik (cf. §6.2). Now the span of the multilinear monomials 117:1 x,,-,,- is the span of the double tableaux with n boxes in which ...
7
Featured Reviews in Mathematical Reviews 1997-1999: With ...
The restrictions of all polynomials from Jk on this transversal span an ideal Ik in the local ring R of analytic germs (T, a) —> C, and this ideal is of a finite codimension Hk = dime R/Ik < oo in R, because the intersection T C\Zk . = {a} is isolated.
Donald G. Babbitt, Jane E. Kister,
2000
8
Perspectives of Systems Informatics: 7th International ... - Strona 249
(2) Next, we prove that the dimensions of the prime ideals from the minimal decomposition of a polynomial ideal Ik+n+1 after a P-solvable loop sequence of length k + n + 1 are less or equal than the dimensions of prime ideals from the minimal ...
Amir Pnueli, Irina Virbitskaite, Andrei Voronkov,
2010
9
Diophantine Approximation on Linear Algebraic Groups: ... - Strona 237
Assume that P, ..., P. have been constructed for some integer k with r < k < s and that the corresponding ideal Ik has the required properties. Let p1, ..., p, be the associated prime ideals of Ik. Since they all have rank k < s, none of these prime ...
10
Representations and Invariants of the Classical Groups - Strona 262
The SFT gives generators for the ideal Ik.m.n and the decompositions of Ik.m.n and Aff(X>V*,m,,,) as modules for GL(A) x GL{m). Theorem 5.2.15 (SFT for GL(/j)) Assume n < min(k, m). (1) The set of all minors of size (n + 1) x (n + 1) is a minimal ...
Roe Goodman, Nolan R. Wallach,
1998
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