B. Buchberger. Ein Algorithmus zum Au#nden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal. Dissertation, Universit at Innsbruck, 1965 Home/Search Document Not in Database Summary Related Articles Check |
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Numerical Analysis in the Twentieth Century - Brezinski, Wuytack (2001) (Correct)
....of these packages. maple was conceived in November 1980 and soon became very popular. Nowadays, symbolic computing is often coupled with numerical algorithms for a better eciency. Computer algebra systems are based on deep mathematics such as Gr obner bases, introduced in 1965 by Bruno Buchberger [40] and integration in nite terms, due to Joseph Liouville (1809 1882) 177, pp. 351 422] 1965: The fast Fourier transform Let f n = f(nT=N) be the values of a given function f at equidistant points. The discrete Fourier transform of f is the function f whose values at the points k = k=T are ....
B. Buchberger, Ein Algorithmus zum Aunden der Basiselemente des Restklassenringes nach einem Nulldimensionalen Polynomideal, Doctoral Dissertation, Mathematische Institut, Universitat Innsbruck, Austria, 1965.
Flatness Properties of Entire Functions Over.. - Apel, Stückrad.. (2001) (Correct)
.... A subset F I of non zero polynomials belonging to I is called a Gr obner basis of I (with respect to ) if the leading terms of the elements of F generate lt(I) Let D I : T n lt(I) The residue classes of the elements of D I modulo I form a K vector space basis of the quotient ring R=I (cf. [BB1], BW] CLO] The theory of Gr obner bases can be generalized to ideals generated by polynomials in the ring E of entire functions. Each entire function g 2 E can be uniquely represented as an in nite sum g = P u2T c u u, c u 2 K . In analogy to the polynomial case g is called irreducible ....
B. Buchberger, Ein Algorithmus zum Aunden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Ph.D. Thesis, Univ. Innsbruck, 1965.
A new efficient algorithm for computing Gröbner basis (F 4 ) - Faugere (2000) (Correct)
....2.1 Sketch of the algorithm It is well known than during the execution of the Buchberger algorithm, one as a lot of choices: select a critical pair in the list of critical pairs. choose one reductor among a list of reductors when reducing a polynomial by a list of polynomials. Buchberger[5] proves that these degree of freedom are not important for the correctness of the algorithm, but everyone know that these choices are crucials for the total time computation ( 1] For instance, consider the case where all the input polynomials have the same leading monomial. In that case, all ....
B. Buchberger. Ein Algorithmus zum Aunden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Innsbruck, 1965.
A Computer Algebra Approach to Orthonormal Wavelets - Chyzak, Paule, Scherzer, al. (2000) (Correct)
....X ( 1) k h 1 k k l = 0; l = 0; N 1) 3) where h k = 0 for k 1 N or k N . 3 Closed form representation of lter coe cients Gr obner bases are the obvious tools to use for solving systems of polynomial equations symbolically. After their original introduction by B. Buchberger [Buc65] to answer ideal theoretic questions, the solving of algebraic systems was soon realized to be one of their natural domains of application [Buc70] We illustrate the Gr obner bases method for N = 2. In this case we are interested in all common roots of the ve polynomials in the four variables h 1 ....
B. Buchberger. Ein Algorithmus zum Aunden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Philosophische Fakultat an der LeopoldFranzens -Universitat, Innsbruck, Austria, 1965. 5
Computing Gröbner Bases and Syzygies Using Second Syzygies - de Jong (2000) (Correct)
....of f and g: S(f; g) lcm(L(f) L(g) L(f) f lcm(L(f) L(g) L(g) g: This is only de ned if L(f) x i and L(f) x i with the same i. In this case we say that L(f) and L(g) lie in the same summand. If this is not the case, we formally put S(f; g) 0. Theorem 1. 1 (Buchberger, [1]) The set G = ff 1 ; f s g is a Gr obner basis for (f 1 ; f s ) if and only if for all pairs i 6= j the remainder on division, or normal form, NF(S(f i ; f j )jG) of S(f i ; f j ) by G is zero. Therefore, to show that a certain set ff 1 ; f s g is a Gr obner basis we have ....
Buchberger, B. (1965) Ein Algorithmus zum Aunden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Dissertation Innsbruck (1965.)
Zhuang-Zi: A New Algorithm for Solving Multivariate.. - Ding, Gower, Schmidt (2006) (1 citation) (Correct)
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B. Buchberger. Ein Algorithmus zum Au#nden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal. Dissertation, Universit at Innsbruck, 1965
Incorporating Decision Procedures in Implicit Induction - Armando, Rusinowitch.. (Correct)
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B. Buchberger. Ein Algorithmus zum Aunden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Philosophische Fakultat an der Leopold-Franzens-Universitat, Insbruck, Austria, 1965.
De Nugis Groebnerialium 2: Applying Macaulay's Trick in order to.. - Mora (2002) (Correct)
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B. Buchberger (1965). Ein Algorithmus zum Aunden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Ph. D. Thesis, Innsbruck. 11
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