公猪
发表于 2025-3-25 06:03:25
https://doi.org/10.1007/978-1-4020-4362-8jective, this can be made through the computation of the Hilbert polynomial; if it is affine, consider a completion of the affine variety; the completion may have larger dimension than the affine variety, but in this case it may have irreducible components contained in the hyperplane at infinity. Th
peptic-ulcer
发表于 2025-3-25 09:22:23
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inquisitive
发表于 2025-3-25 12:57:20
https://doi.org/10.1007/978-1-4020-4362-8ioned in the title. It is shown how these matrices can be built from a finite number of small matrices. It is reported how these small matrices, of which the largest is a 25 by 25 matrix, were found using computer algebra systems.
ECG769
发表于 2025-3-25 16:07:18
https://doi.org/10.1007/978-1-4020-4362-8per nucleus of an arbitrary configuration of nuclei and electrons. Such a lower bound provides a theoretical explanation of why the electrons do not simply collapse into the nuclei. The existence of a lower bound for the energy was originally proved by Dyson and Lenard in . Lieb and Thirring [4,3
慎重
发表于 2025-3-25 23:48:22
https://doi.org/10.1007/978-1-4020-4362-8 implemented a program DEMS for computing the Liapunov function and Liapunov constants. This function and these constants are used in the study of stability criteria, differentiation between center and focus and the construction of limit cycles. The solutions of the problems concerning the investiga
敬礼
发表于 2025-3-26 00:29:10
https://doi.org/10.1007/978-1-4020-4362-8c solution of the equation is determined, a surprising bifurcation phenomenon is discovered via computer graphics. This “computer-discovered” bifurcation, in turn, leads to further mathematical analysis and deeper geometric understanding of the solution. Indeed, this is a simple example of an elemen
夹克怕包裹
发表于 2025-3-26 04:59:19
https://doi.org/10.1007/978-1-4020-4362-8s not to carry out a direct symbolic algebraic manipulation of formulae characterizing this bifurcation (direction, stability and amplitudes of bifurcating periodic orbits, ...). It is planned to develop a recursive algorithm well suited to symbolic computation implementation, which is based upon th
脖子
发表于 2025-3-26 11:34:16
https://doi.org/10.1007/978-1-4020-4362-8puter algebra system REDUCE and numerical methods for polynomial roots location. The stability analysis is performed by the Fourier method and polynomial root location is based on the Routh algorithm. Several practical examples show the usefulness of the programs described.
文字
发表于 2025-3-26 16:06:31
John E. Cooper,Margaret E. Coopereful in factorization of large integers. For many applications it is important to be able to recognize when two quadratic forms are equivalent, so it is useful to be able to reduce these quadratic forms to a canonical representation..For applications in factorization, the quadratic forms used have l
antipsychotic
发表于 2025-3-26 20:14:18
https://doi.org/10.1007/978-94-011-9574-4w how we obtained new unexpected results trough computer algebra experiments. This was the direct result of computing in the ring of polynomials modulo the cyclotomic polynomial, instead of computing with roots of unity.