Category:ApCoCoA-1:Package slinalg: Difference between revisions

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New page: The basic idea behind this package is to make Bertini usable in/with ApCoCoA. This is the alpha version of the package bertini, which includes the Betini interface to CoCoA. Essentially, ...
 
m Andraschko moved page Category:Package slinalg to Category:ApCoCoA-1:Package slinalg: Clearer page title
 
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The basic idea behind this package is to make Bertini usable in/with ApCoCoA.
This package enables you to calculate Echelon form of a sparse matrix over F2 using two different techniques. The elments of the matrix are represented by the positions of non zero entries.
 
* Calculate Echelon form using a variant of usual Gaussian Eliminaiton. The performance of this method is directly proprotional to the sparsity and depends on the structure of the Matrix.
This is the alpha version of the package bertini, which includes the Betini interface to CoCoA. Essentially, you can call Bertini from with inside CoCoA, using this Package.
* Calculate Echelon form using structured Gaussian Elimimation.  


{{ApCoCoAServer}}
{{ApCoCoAServer}}


'''NUMERICAL ALGEBRAIC GEOMETRY:'''
[[Category:ApCoCoA-1 Manual]]
 
Numerical algebraic geometry is the study based on homotopy continuation method and algebraic geometry. It has same relation to algebraic geomertry, as Numerical Linear Algebra to linear algebra. In Numerical Algebraic Geometry we can fine isolated solutions. For positive dimensional systems, we can find out numerical irreducible deocmpostions.
 
'''Bertini:''' Software for Numerical Algebraic Geometry
 
Bertini is a software desgined for computations in Numerical Algebric Geometry, particularly, for solving polynomial systems numerically using homotopy continuation method available at [http://www.nd.edu/~sommese/bertini/]. Its a general-purpose solver, written in C, that was created for research about polynomial continuation. The Key Features of Bertini are:
 
* Finds isolated solutions using total-degree start systems, multihomogeneous-degree start systems, and also user defined homotopies.
* Implements parameter continuation for families of systems, such as the inverse kinematics of six-revolute serial-link arms, or the forward kinematics of Stewart-Gough parallel-link robots.
* Adaptive multiprecision implemented for finding isolated solutions and for the numerical irreducible decomposition.
* Treats positive-dimensional solutions by computing witness sets.
* Has automatic differentiation which preserves the straightline quality of an input system.
* Uses homogenization to accurately compute solutions at infinity.
* Provides a fractional power-series endgame to accurately compute singular roots.
* Allows for subfunctions.
* Allows for witness set manipulation via both sampling and membership testing.
* Accepts square or nonsquare systems.
 
 
 
[[Category:ApCoCoA_Manual]]

Latest revision as of 15:18, 2 October 2020

This package enables you to calculate Echelon form of a sparse matrix over F2 using two different techniques. The elments of the matrix are represented by the positions of non zero entries.

  • Calculate Echelon form using a variant of usual Gaussian Eliminaiton. The performance of this method is directly proprotional to the sparsity and depends on the structure of the Matrix.
  • Calculate Echelon form using structured Gaussian Elimimation.

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

Pages in category "ApCoCoA-1:Package slinalg"

The following 2 pages are in this category, out of 2 total.

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