66,063 research outputs found
The computational complexity of the Chow form
We present a bounded probability algorithm for the computation of the Chow
forms of the equidimensional components of an algebraic variety. Its complexity
is polynomial in the length and in the geometric degree of the input equation
system defining the variety. In particular, it provides an alternative
algorithm for the equidimensional decomposition of a variety.
As an application we obtain an algorithm for the computation of a subclass of
sparse resultants, whose complexity is polynomial in the dimension and the
volume of the input set of exponents. As a further application, we derive an
algorithm for the computation of the (unique) solution of a generic
over-determined equation system.Comment: 60 pages, Latex2
Representation theory and projective geometry
We give an elementary introduction to our papers relating the geometry of
rational homogeneous varieties to representation theory. We also describe
related work and recent progress.Comment: 37 pages with picture
Algorithmic Algebraic Geometry and Flux Vacua
We develop a new and efficient method to systematically analyse four
dimensional effective supergravities which descend from flux compactifications.
The issue of finding vacua of such systems, both supersymmetric and
non-supersymmetric, is mapped into a problem in computational algebraic
geometry. Using recent developments in computer algebra, the problem can then
be rapidly dealt with in a completely algorithmic fashion. Two main results are
(1) a procedure for calculating constraints which the flux parameters must
satisfy in these models if any given type of vacuum is to exist; (2) a stepwise
process for finding all of the isolated vacua of such systems and their
physical properties. We illustrate our discussion with several concrete
examples, some of which have eluded conventional methods so far.Comment: 41 pages, 4 figure
Elimination for generic sparse polynomial systems
We present a new probabilistic symbolic algorithm that, given a variety
defined in an n-dimensional affine space by a generic sparse system with fixed
supports, computes the Zariski closure of its projection to an l-dimensional
coordinate affine space with l < n. The complexity of the algorithm depends
polynomially on combinatorial invariants associated to the supports.Comment: 22 page
Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators
This paper investigates the conditions in the design parameter space for the
existence and distribution of the cusp locus for planar parallel manipulators.
Cusp points make possible non-singular assembly-mode changing motion, which
increases the maximum singularity-free workspace. An accurate algorithm for the
determination is proposed amending some imprecisions done by previous existing
algorithms. This is combined with methods of Cylindric Algebraic Decomposition,
Gr\"obner bases and Discriminant Varieties in order to partition the parameter
space into cells with constant number of cusp points. These algorithms will
allow us to classify a family of degenerate 3-RPR manipulators.Comment: ASME Journal of Mechanisms and Robotics (2012) 1-1
- …