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Systems of polynomial equations are one of the most universal mathematical objects. Almost all problems of cryptographic analysis can be reduced to solving systems of polynomial equations ...
Systems of polynomial equations are one of the most universal mathematical objects. Almost all problems of cryptographic analysis can be reduced to solving systems of polynomial equations ...
The program CRACK is a computer algebra package written in REDUCE for the solution of over- determined systems of algebraic, ordinary or partial differential equations with at most polynomial non ...
$| for which |$F_*^e T$| are free |$T$|-modules (e.g., polynomial rings and power series rings with |$F$|-finite coefficient rings,) and also all complete regular rings (cf. [8, Proposition 5.3]). These rings ...
, the presentation matrix will indeed have corank $$r$$. In what follows it will be useful to know the Betti numbers of all truncations of a module (without needing to determine them explicitly). Lemma 2.1. Let ...
. A polynomial |$f(a_0,a_{1},\ldots )$| is isobaric of weight |$g$| if all the monomials appearing in |$f$| have weight |$g$|. Of course, every polynomial |$f(a_0,\ldots ,a_n)$| decomposes in a unique way ...
possible, and it implies the existence of low-rank factorizations of positive semidefinite bivariate matrix polynomials and representations of biforms as sums of few squares. We determine the number ...
absolutely irreducible polynomial f¯∈Fq[x,y]. Or it could mean that we are considering the affine/projective curve defined by a given more general system of equations over Fq. In all cases, we will ignore ...
Hilbert series is |$H_{n}=\frac {1}{1-2t+2t^{n}-t^{n+1}}$|, so they are all infinite dimensional. Moreover, growth could be polynomial (but nonlinear) for the potential of degree 4, and is always ...
Abstract We study the asymptotic behavior of the Castelnuovo–Mumford regularity along chains of graded ideals in increasingly larger polynomial rings that are invariant under the action of symmetric ...
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