Ran at 10.15 on Wednesdays in 1West 2.7: Now finished.
Cylindrical Algebraic Decomposition via Triangular Decomposition
The aim of this seminar series is to understand this paper, and related topics.
- Cylindrical Algebraic Decomposition via Triangular Decomposition by Chen,C., Moreno Maza,M., Xia,B. & Yang,L.. Also in Proc. ISSAC 2009.
- On the Theories of Triangular Sets by Aubry,P., Lazard,D. & Moreno Maza,M. J. Symbolic Comp. 28(1999) pp. 105-124.
- Triangular Sets for Solving Polynomial Systems:
A Comparison of Four Methods by Aubry,P. & Moreno Maza,M.
J. Symbolic Comp. 28(1999) pp. 125-154.
- Comprehensive Triangular Decomposition by Chen,C., Golubitsky,O., Lemaire,F., Moreno Maza,M. & Pan,W.,
Proc. Computer Algebra and Symbolic Computing 2007
(eds. V.G. Ganzha, E.W. Mayr & E.V. Vorozhtsov), Springer Lecture Notes in
Computer Science 4770, Springer-Verlag, 2007, pp. 73-101.
- Bounds on numbers of vectors of multiplicities for polynomials which are easy to compute by Grigoriev,D.Yu. & Vorobjov,N.N.,Jr., Proc. ISSAC 2000 (ed. C. Traverso), ACM, New York, 2000, pp. 137-146. The paper referred to on 22.9.2009: Theorem 3 refers to parametric factorization of polynomials.
- Ali Ayad's thesis (in French), supervised by Grigoriev.
- Incomplete draft of my new book especially chapter 3.3.
- Maple's 'help' on Regular Chains Really quite mathematically good, as one might expect from the ultimate authors.
We have concluded with two research questions.
- 18.8.2009: introduction to the problem, why non-linear is different. Concept of a triangular set. Some motivating examples.
- 25.8.2009: some terminology: V(T), the variety of T, W(T), the regular zeros of T. Z(P,Q), the zeros of P outside (the zeros of) Q. W(T)=Z(T,init(T)).
- 1.9.2009: no seminar: university closed.
- 8.9.2009: further discussion of the example
- 15.9.2009: no seminar: university Open Day
- 22.9.2009: initial discussion of Comprehensive Triangular Decomposition
- 29.9.2009: further seminar: plan for what to do in the future
- Various intermediate seminars, which JHD forgot to record
- 28.10.2009: Marc Moreno Maza gave the seminar remotely: his slides are
- 4.11.2009: concluding seminar, led by JHD.
- For the purposes of
the Bradford/Davenport/Phisanbut agenda,
is a full CAD necessary, or can we stop earlier in the chain indicated in
- This agenda (unlike many others) is agnostic with respect to variable orderings. Hence can we use
the ideas of Dolzmann et al.
to choose the 'best' orderings (and what exactly would 'best' be?)?