Difference between revisions of "ApCoCoA-1:PGBC.ParallelGBC"
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| − | Computes a Gröbner Bases over a prime field using the degree reverse lexicographic term ordering in parallel. | + | <command> |
| − | + | <title>PGBC.ParallelGBC</title> | |
| − | + | <short_description>Computes a Gröbner Bases over a prime field using the degree reverse lexicographic term ordering in parallel.</short_description> | |
| − | < | + | |
| + | <syntax> | ||
$apcocoa/pgbc.ParallelGBC(Polys:LIST,Threads:INT):LIST; | $apcocoa/pgbc.ParallelGBC(Polys:LIST,Threads:INT):LIST; | ||
| − | </ | + | </syntax> |
| − | + | <description> | |
| − | |||
This command computed the Gröbner Basis of the ideal generated by <tt>Polys</tt> using the degree reverse lexicographic term ordering. | This command computed the Gröbner Basis of the ideal generated by <tt>Polys</tt> using the degree reverse lexicographic term ordering. | ||
The computation can be performed in parallel using <tt>Threads</tt> threads, at which the number of threads should be less or equal the | The computation can be performed in parallel using <tt>Threads</tt> threads, at which the number of threads should be less or equal the | ||
number of processors/cores which are available on the used system. | number of processors/cores which are available on the used system. | ||
| + | To compute the Gröbner Basis of <tt>F</tt> as defined below using two cores you can enter the following sequence of commands: | ||
| − | + | <example> | |
| − | |||
| − | |||
Use R::=ZZ/(32003)[x[1..9],h]; | Use R::=ZZ/(32003)[x[1..9],h]; | ||
F:=[x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + 2*x[6]^2 + 2*x[7]^2 + 2*x[8]^2 + 2*x[9]^2 - x[1]*h, | F:=[x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + 2*x[6]^2 + 2*x[7]^2 + 2*x[8]^2 + 2*x[9]^2 - x[1]*h, | ||
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]; | ]; | ||
G:=$apcocoa/pgbc.ParallelGBC(F,2); | G:=$apcocoa/pgbc.ParallelGBC(F,2); | ||
| − | </ | + | </example> |
| + | </description> | ||
| − | + | <types> | |
| + | <type>groebner</type> | ||
| + | <type>polynomial</type> | ||
| + | <type>apcocoaserver</type> | ||
| + | </types> | ||
| + | <key>pgbc</key> | ||
| + | <key>pgbc.parallelgbc</key> | ||
| + | <key>parallelgbc</key> | ||
| + | <wiki-category>Package_pgbc</wiki-category> | ||
| + | </command> | ||
Revision as of 13:21, 15 June 2012
PGBC.ParallelGBC
Computes a Gröbner Bases over a prime field using the degree reverse lexicographic term ordering in parallel.
Syntax
$apcocoa/pgbc.ParallelGBC(Polys:LIST,Threads:INT):LIST;
Description
This command computed the Gröbner Basis of the ideal generated by Polys using the degree reverse lexicographic term ordering.
The computation can be performed in parallel using Threads threads, at which the number of threads should be less or equal the
number of processors/cores which are available on the used system.
To compute the Gröbner Basis of F as defined below using two cores you can enter the following sequence of commands:
Example
Use R::=ZZ/(32003)[x[1..9],h]; F:=[x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + 2*x[6]^2 + 2*x[7]^2 + 2*x[8]^2 + 2*x[9]^2 - x[1]*h, 2*x[1]*x[2] + 2*x[2]*x[3] + 2*x[3]*x[4] + 2*x[4]*x[5] + 2*x[5]*x[6] + 2*x[6]*x[7] + 2*x[7]*x[8] + 2*x[8]*x[9]- x[2]*h, x[2]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] + 2*x[3]*x[5] + 2*x[4]*x[6] + 2*x[5]*x[7] + 2*x[6]*x[8] + 2*x[7]*x[9] - x[3]*h, 2*x[2]*x[3] + 2*x[1]*x[4] + 2*x[2]*x[5] + 2*x[3]*x[6] + 2*x[4]*x[7] + 2*x[5]*x[8] + 2*x[6]*x[9] - x[4]*h, x[3]^2 + 2*x[2]*x[4] + 2*x[1]*x[5] + 2*x[2]*x[6] + 2*x[3]*x[7] + 2*x[4]*x[8] + 2*x[5]*x[9] - x[5]*h, 2*x[3]*x[4] + 2*x[2]*x[5] + 2*x[1]*x[6] + 2*x[2]*x[7] + 2*x[3]*x[8] + 2*x[4]*x[9] -x[6]*h, x[4]^2 + 2*x[3]*x[5] + 2*x[2]*x[6] + 2*x[1]*x[7] + 2*x[2]*x[8] + 2*x[3]*x[9] - x[7]*h, 2*x[4]*x[5] + 2*x[3]*x[6] + 2*x[2]*x[7] + 2*x[1]*x[8] + 2*x[2]*x[9] - x[8]*h, x[1] + 2*x[2] + 2*x[3] + 2*x[4] + 2*x[5] + 2*x[6] + 2*x[7] + 2*x[8] + 2*x[9] - h ]; G:=$apcocoa/pgbc.ParallelGBC(F,2);
