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

Line 2: | Line 2: | ||

<title>IML.Solve</title> | <title>IML.Solve</title> | ||

<short_description>Solve a linear equation system.</short_description> | <short_description>Solve a linear equation system.</short_description> | ||

− | <syntax>IML.Solve(M:MAT, B:MAT):MAT</syntax> | + | |

+ | <syntax> | ||

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

+ | </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. |

## Revision as of 15:02, 24 April 2009

## IML.Solve

Solve a linear equation system.

### 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([ [ ] ]) -------------------------------