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

(Types section update.) |
(Example section update.) |
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</itemize> | </itemize> | ||

<example> | <example> | ||

− | Use | + | Use ZZ/(19)[x]; |

M := BringIn(Mat([[1,3,4], [0,2,1]])); | M := BringIn(Mat([[1,3,4], [0,2,1]])); | ||

B := BringIn(Mat([[1], [2]])); | B := BringIn(Mat([[1], [2]])); | ||

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]) | ]) | ||

------------------------------- | ------------------------------- | ||

− | + | </example> | |

− | Use | + | <example> |

+ | Use QQ[x]; | ||

M := Mat([ [1,3,4], [0,2,1], [1,3,4] ]); | M := Mat([ [1,3,4], [0,2,1], [1,3,4] ]); | ||

B := Mat([ [1], [2], [0] ]); | B := Mat([ [1], [2], [0] ]); |

## Revision as of 13:26, 23 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. Please also note that you need an ApCoCoAServer with enabled IML support.

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