59 research outputs found
Automatically Discovering Hidden Transformation Chaining Constraints
Model transformations operate on models conforming to precisely defined
metamodels. Consequently, it often seems relatively easy to chain them: the
output of a transformation may be given as input to a second one if metamodels
match. However, this simple rule has some obvious limitations. For instance, a
transformation may only use a subset of a metamodel. Therefore, chaining
transformations appropriately requires more information. We present here an
approach that automatically discovers more detailed information about actual
chaining constraints by statically analyzing transformations. The objective is
to provide developers who decide to chain transformations with more data on
which to base their choices. This approach has been successfully applied to the
case of a library of endogenous transformations. They all have the same source
and target metamodel but have some hidden chaining constraints. In such a case,
the simple metamodel matching rule given above does not provide any useful
information
On hyperbolic fixed points in ultrametric dynamics
Let K be a complete ultrametric field. We give lower and upper bounds for the
size of linearization discs for power series over K near hyperbolic fixed
points. These estimates are maximal in the sense that there exist examples
where these estimates give the exact size of the corresponding linearization
disc. In particular, at repelling fixed points, the linearization disc is equal
to the maximal disc on which the power series is injective.Comment: http://www.springerlink.com/content/?k=doi%3a%2810.1134%2fS2070046610030052%2
Linearization in ultrametric dynamics in fields of characteristic zero - equal characteristic case
Let be a complete ultrametric field of charactersitic zero whose
corresponding residue field is also of charactersitic zero. We give
lower and upper bounds for the size of linearization disks for power series
over near an indifferent fixed point. These estimates are maximal in the
sense that there exist exemples where these estimates give the exact size of
the corresponding linearization disc. Similar estimates in the remaning cases,
i.e. the cases in which is either a -adic field or a field of prime
characteristic, were obtained in various papers on the -adic case
(Ben-Menahem:1988,Thiran/EtAL:1989,Pettigrew/Roberts/Vivaldi:2001,Khrennikov:2001)
later generalized in (Lindahl:2009 arXiv:0910.3312), and in (Lindahl:2004
http://iopscience.iop.org/0951-7715/17/3/001/,Lindahl:2010Contemp. Math)
concerning the prime characteristic case
Computing the -th Term of a -Holonomic Sequence
International audienceIn 1977, Strassen invented a famous baby-step / giant-step algorithm that computes the factorial in arithmetic complexity quasi-linear in . In 1988, the Chudnovsky brothers generalized Strassen’s algorithm to the computation of the -th term of any holonomic sequence in the same arithmetic complexity. We design -analogues of these algorithms. We first extend Strassen’s algorithm to the computation of the -factorial of , then Chudnovskys' algorithm to the computation of the -th term of any -holonomic sequence. Both algorithms work in arithmetic complexity quasi-linear in~. We describe various algorithmic consequences, including the acceleration of polynomial and rational solving of linear -differential equations, and the fast evaluation of large classes of polynomials, including a family recently considered by Nogneng and Schost
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