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

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(Types section update.)
(Example section update.)
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</itemize>
 
</itemize>
 
<example>
 
<example>
Use Z/(19)[x];
+
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]]));
Line 28: Line 28:
 
])
 
])
 
-------------------------------
 
-------------------------------
 
+
</example>
Use Q[x];
+
<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([
  [ ]
])
-------------------------------

LinBox.Solve

LinKer