Difference between revisions of "ApCoCoA-1:Slinalg.SEF"

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<short_description>Solves zero dimensional non-homogeneous polynomial system using multi-homogenization with User Configurations.</short_description>
<short_description>Calculates the Echelon form of a sparse matrix over F2.</short_description>
Bertini.BCMSolve(M:LIST, ConfigSet:LIST)
Slinalg.SEF(NRow,NCol, Mat:LIST)
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<item>@param <em>M</em>: List of polynomials in the system.</item>
<item>@param <em>NRow</em>: Number of rows of matrix.</item>
<item>@param <em>ConfigSet</em>: List of strings representing Configurations to be used by Bertini. For details about configuration settings see Bertini mannual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</item>
<item>@param <em>NCol</em>: Number of Columns of matrix.</item>
<item>@return A list of lists containing the finite solutions of the polynomial system.</item>
<item>@return A list of lists containing the Echelon form of matrix.</item>

Revision as of 16:17, 8 July 2009


Calculates the Echelon form of a sparse matrix over F2.


Slinalg.SEF(NRow,NCol, Mat:LIST)


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.

  • @param NRow: Number of rows of matrix.

  • @param NCol: Number of Columns of matrix.

  • @return A list of lists containing the Echelon form of matrix.


-- We want to solve the system x^2+y^2-5=0,xy-2=0, using multi-homogenization, for adaptive precision. 

Use S ::= QQ[x,y];             --  Define appropriate ring 
M := [x^2+y^2-5,xy-2];
ConfigSet := [<quotes>MPTYPE: 2</quotes>];

-- Then we compute the solution with

-- And we achieve a list of lists containing finite solutions:
[[Vector(1000000000000017/1000000000000000, 145132717332349/15625000000000000000000000000),
 Vector(49999999999999/25000000000000, -3537662353156057/100000000000000000000000000000)],
 [Vector(-62500000000003/62500000000000, 4415730565392687/100000000000000000000000000000),
 Vector(-499999999999983/250000000000000, -66866973306543/400000000000000000000000000)],
 [Vector(999999999999983/500000000000000, -1787591178181031/50000000000000000000000000000),
 Vector(1000000000000013/1000000000000000, 281412486737749/25000000000000000000000000000)],
 [Vector(-499999999999999/250000000000000, -3956938527452181/1000000000000000000000000000000),
 Vector(-9999999999999989/10000000000000000, -596634837824491/1250000000000000000000000000000)]]

--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).

See also

Introduction to CoCoAServer