Difference between revisions of "ApCoCoA-1:IML.Solve"

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<command>
 
<command>
 
   <title>IML.Solve</title>
 
   <title>IML.Solve</title>
   <short_description>Solve a linear equation system.</short_description>
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   <short_description>Solves a system of linear equations.</short_description>
   <syntax>IML.Solve(M:MAT, B:MAT):MAT</syntax>
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<syntax>
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IML.Solve(M:MAT, B:MAT):MAT
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</syntax>
 
   <description>
 
   <description>
 
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
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</example>
 
</example>
 
   </description>
 
   </description>
   <see>LinBox.Solve</see>
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   <see>LinKer</see>
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  <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
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  <see>ApCoCoA-1:LinAlg.Solve|LinAlg.Solve</see>
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   <see>ApCoCoA-1:LinBox.Solve|LinBox.Solve</see>
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   <see>ApCoCoA-1:LinKer|LinKer</see>
 
   <types>
 
   <types>
 
     <type>matrix</type>
 
     <type>matrix</type>
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   <key>solve linear equation system</key>
 
   <key>solve linear equation system</key>
 
   <key>solve linear equation</key>
 
   <key>solve linear equation</key>
   <wiki-category>Package_iml</wiki-category>
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   <wiki-category>ApCoCoA-1:Package_iml</wiki-category>
 
</command>
 
</command>

Latest revision as of 10:09, 7 October 2020

This article is about a function from ApCoCoA-1.

IML.Solve

Solves a system of linear equations.

Syntax

IML.Solve(M:MAT, B:MAT):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.

Let M and B be matrices defined over the ring of integers, a finite field or the field of rationals. This function tries to solve the linear equation system M*X = B by using the ApCoCoAServer supported by the IML library.

The return value will be a solution vector of the linear equation system or an empty matrix if no solution has been found.

  • @param M A matrix with components either of type INT, ZMOD or RAT.

  • @param B A matrix with components either of type INT, ZMOD or RAT.

  • @return A matrix X representing a solution vector of the linear equation system M*X = B if a solution exists or the empty matrix otherwise.

Example

Use ZZ/(19)[x];
M := BringIn(Mat([[1,3,4], [0,2,1]]));
B := BringIn(Mat([[1], [2]]));
IML.Solve(M, B);
-------------------------------
Mat([
  [-2 % 19],
  [1 % 19],
  [0 % 19]
])
-------------------------------

Example

Use QQ[x];
M := Mat([ [1,3,4], [0,2,1], [1,3,4] ]);
B := Mat([ [1], [2], [0] ]);
IML.Solve(M, B);
-------------------------------
Mat([
  [ ]
])
-------------------------------

Introduction to CoCoAServer

LinAlg.Solve

LinBox.Solve

LinKer