Difference between revisions of "ApCoCoA-1:LinAlg.EF"
From ApCoCoAWiki
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<command> | <command> | ||
<title>LinAlg.EF</title> | <title>LinAlg.EF</title> | ||
| − | <short_description>Computes a row echelon form of a matrix with | + | <short_description>Computes a row echelon form of a matrix with record keeping.</short_description> |
<syntax> | <syntax> | ||
| − | LinAlg.EF(M: | + | LinAlg.EF(M:LIST, L1:LIST, L2:LIST):MAT |
</syntax> | </syntax> | ||
<description> | <description> | ||
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This function allows you to compute a row echelon form of a matrix <tt>M</tt> defined over the field <tt>F_2</tt>. | This function allows you to compute a row echelon form of a matrix <tt>M</tt> defined over the field <tt>F_2</tt>. | ||
<par/> | <par/> | ||
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Revision as of 12:24, 7 December 2010
LinAlg.EF
Computes a row echelon form of a matrix with record keeping.
Syntax
LinAlg.EF(M:LIST, L1:LIST, L2:LIST):MAT
Description
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.
This function allows you to compute a row echelon form of a matrix M defined over the field F_2.
@param M: A List of Lists whose row echelon form to compute.
@param L1: List of integers. For example, the integers could represent the order of lists in the list M.
@param L2: List of integers. For example, the integers could be 0-1 to represent the lists already reduced(0) and to be reduced(1).
@return A row echelon form of M together with lists L1 and L2.
Example
Use ZZ/(2)[x,y];
M := [
[1, 1, 0, 1, 0],
[0, 1, 1, 0, 1],
[1, 0, 1, 0, 0],
[1, 1, 1, 0, 1]
];
-- order of lists in M
L1:=[1, 2, 3, 4];
-- 0 for lists which are already in echelon form and 1 for those to be reduced.
L2:=[0, 0, 1, 1];
LinAlg.EF(M, L1, L2);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[ [[1, 1, 0, 1, 0], [0, 1, 1, 0, 1], [0, 0, 1, 1, 1], [0, 0, 0, 1, 1]], [1, 2, 4, 3], [0, 0, 1, 1]]
-- The last two lists represent the new order of lists in M.
Example
Use ZZ/(2)[x,y];
M := [
[0, 1, 0, 1, 0],
[0, 1, 0, 0, 1],
[1, 0, 1, 1, 0],
[1, 1, 0, 0, 1]
];
-- order of lists in M
L1:=[1, 2, 3, 4];
-- 0 for lists which are already in echelon form and 1 for those to be reduced.
L2:=[0, 0, 1, 1];
LinAlg.EF(M, L1, L2);
-- CoCoAServer: computing Cpu Time = 0.015
-------------------------------
[[[1, 0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]], [3, 1, 4, 2], [1, 0, 1, 0]]
-------------------------------
-- The last two lists represent the new order of lists in M.
