322 research outputs found
Order sorted computer algebra and coercions
SIGLEAvailable from British Library Document Supply Centre-DSC:DXN017043 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Generic access to symbolic computing services
Symbolic computation is one of the computational domains that requires large computational
resources. Computer Algebra Systems (CAS), the main tools used for symbolic
computations, are mainly designed to be used as software tools installed on standalone
machines that do not provide the required resources for solving large symbolic computation
problems. In order to support symbolic computations an infrastructure built upon
massively distributed computational environments must be developed.
Building an infrastructure for symbolic computations requires a thorough analysis of
the most important requirements raised by the symbolic computation world and must
be built based on the most suitable architectural styles and technologies. The architecture
that we propose is composed of several main components: the Computer Algebra
System (CAS) Server that exposes the functionality implemented by one or more supporting
CASs through generic interfaces of Grid Services; the Architecture for Grid
Symbolic Services Orchestration (AGSSO) Server that allows seamless composition of
CAS Server capabilities; and client side libraries to assist the users in describing workflows
for symbolic computations directly within the CAS environment. We have also
designed and developed a framework for automatic data management of mathematical
content that relies on OpenMath encoding.
To support the validation and fine tuning of the system we have developed a simulation
platform that mimics the environment on which the architecture is deployed
On barycentric subdivision, with simulations
Consider the barycentric subdivision which cuts a given triangle along its
medians to produce six new triangles. Uniformly choosing one of them and
iterating this procedure gives rise to a Markov chain. We show that almost
surely, the triangles forming this chain become flatter and flatter in the
sense that their isoperimetric values goes to infinity with time. Nevertheless,
if the triangles are renormalized through a similitude to have their longest
edge equal to [0,1]\subset\CC (with 0 also adjacent to the shortest edge),
their aspect does not converge and we identify the limit set of the opposite
vertex with the segment [0,1/2]. In addition we prove that the largest angle
converges to in probability. Our approach is probabilistic and these
results are deduced from the investigation of a limit iterated random function
Markov chain living on the segment [0,1/2]. The stationary distribution of this
limit chain is particularly important in our study. In an appendix we present
related numerical simulations (not included in the version submitted for
publication)
Q(sqrt(-3))-Integral Points on a Mordell Curve
We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4
Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System
Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics
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