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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | )abbrev category NTSCAT NormalizedTriangularSetCategory
++ Author: Marc Moreno Maza
++ Date Created: 10/07/1998
++ Date Last Updated: 12/12/1998
++ References :
++ SALSA Solvers for Algebraic Systems and Applications
++ Kalk91 Three contributions to elimination theory
++ Kalk98 Algorithmic properties of polynomial rings
++ Aubr96 Triangular Sets for Solving Polynomial Systems:
++ Aubr99 On the Theories of Triangular Sets
++ Aubr99a Triangular Sets for Solving Polynomial Systems:
++ Laza91 A new method for solving algebraic systems of positive dimension
++ Maza95 Polynomial Gcd Computations over Towers of Algebraic Extensions
++ Maza97 Calculs de pgcd au-dessus des tours d'extensions simples et
++ resolution des systemes d'equations algebriques
++ Maza98 A new algorithm for computing triangular decomposition of
++ algebraic varieties
++ Maza00 On Triangular Decompositions of Algebraic Varieties
++ Description:
++ The category of normalized triangular sets. A triangular
++ set ts is said normalized if for every algebraic
++ variable v of ts the polynomial select(ts,v)
++ is normalized w.r.t. every polynomial in collectUnder(ts,v).
++ A polynomial p is said normalized w.r.t. a non-constant
++ polynomial q if p is constant or degree(p,mdeg(q)) = 0
++ and init(p) is normalized w.r.t. q. One of the important
++ features of normalized triangular sets is that they are regular sets.
NormalizedTriangularSetCategory(R,E,V,P) : Category == SIG where
R : GcdDomain
E : OrderedAbelianMonoidSup
V : OrderedSet
P : RecursivePolynomialCategory(R,E,V)
SIG ==> RegularTriangularSetCategory(R,E,V,P)
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