By Evelyne Hubert (auth.), Franz Winkler, Ulrich Langer (eds.)

This booklet constitutes the completely refereed post-proceedings of the second one overseas convention on Symbolic and Numerical clinical Computation, SNSC 2001, held in Hagenberg, Austria, in September 2001.

The 19 revised complete papers provided have been rigorously chosen in the course of rounds of reviewing and development. The papers are equipped in topical sections on symbolics and numerics of differential equations, symbolics and numerics in algebra and geometry, and purposes in physics and engineering.

**Read or Download Symbolic and Numerical Scientific Computation: Second International Conference, SNSC 2001, Hagenberg, Austria, September 12–14, 2001. Revised Papers PDF**

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**Additional resources for Symbolic and Numerical Scientific Computation: Second International Conference, SNSC 2001, Hagenberg, Austria, September 12–14, 2001. Revised Papers**

**Example text**

We examine these three cases separately. 3. 4, g ∈ (Fx ) + I(B). By induction hypothesis on I0 we thus obtain F ⊂ (Fˆ ∪ Fˇ ) + (g) + (B) ⊂ (Fˆ ) + I(B) (3) If deg(g, x) > 0, let hg = init(g) = lcoeﬀ(g, x). 2 (Fˆ ) + I(B) = (Fˆ \ Fx ) + (Fx ) + I(B) = (Fˆ \ Fx ) + (Fx ) + I(B) : h∞ ∩ (Fˆ \ Fx ) + (Fx ) + I(B) + (hg ) g . 6, B g is a regular chain and ((Fx ) + I(B)) : h∞ g = I(B g). 2, Fˇ ⊂ I(C) ⊂ I(B). Thus F ⊂ (Fˆ ∪ Fˇ ) + (B) + (hg ) ⊂ (Fˆ ) + I(B) + (hg ) . (6) S is the set deprived from the tuple {(Fˆ , Fˇ , C)}.

A node is given by a 3-tuple (Fˆ , Fˇ , C). A son of a node (Fˆ , Fˇ , C) is an element of the constructed sets S0 , S1 , S2 or S2 . A leaf is an element (∅, ∗, ∗). Triangulation-Decomposition Algorithms I: Polynomial Systems 33 For convenience, we shall introduce a dummy variable x0 that we assume to ¯ = X ∪ {x0 }. We extend each be lower than all the variables of X. We write X ˆ ˇ ˆ ˇ ¯ ≤y ] and 3-tuple (F , F , C) to a 4-tuple (F , F , C, y) where y is such that C ⊂ K[X ˆ ¯ E ∩ K[X≤y ] = ∅. The root is now (F, ∅, ∅, x0 ).

3 A Sub-algorithm of the Split The relatively-prime algorithm presented is a sub-algorithm of split. 2 when dealing with non squarefree polynomials. Its role is to compute an irredundant decomposition of the saturation of a characterisable ideal by a polynomial. The call of split to relativelyprime requires in fact to compute saturations of ideals of K[X][x] of the type I(C) + (c) : lcoeﬀ(c, x)∞ as it is possible that deg(c, x) = 0. 8. Krelatively-prime Input: – – – – K[X][x] a ring of polynomials.