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LinearAlgebra[Modular]

  

IntegerDeterminant

  

determinant of an integer matrix using modular methods

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IntegerDeterminant(M)

Parameters

M

-

Square Matrix with integer entries

Description

• 

The IntegerDeterminant function computes the determinant of the integer matrix M. This is a programmer level function, it does not perform argument checking. Thus, argument checking must be handled external to this function.

• 

Note: The IntegerDeterminant command uses a probabilistic approach that achieves great gains for structured systems. Information on controlling the probabilistic behavior can be found in EnvProbabilistic.

• 

This function is used by the Determinant function in the LinearAlgebra package when a Matrix is determined to contain only integer entries.

• 

This command is part of the LinearAlgebra[Modular] package, so it can be used in the form IntegerDeterminant(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][IntegerDeterminant](..).

Examples

A 3x3 matrix

withLinearAlgebra[Modular]:

MMatrix2,1,3,4,3,1,2,1,3

M:=213431213

(1)

IntegerDeterminantM

20

(2)

A 100x100 matrix

MLinearAlgebra[RandomMatrix]100:

tttime:

IntegerDeterminantM

38562295347802366242417909657285032281105091485000162871067163275296273582728190925949289361981964881806516849833008824879568403928373759144147382030798909099402726531205056808283212790472544339698767179236612577117605985054960334148934541347201762137455

(3)

timett

0.030

(4)

See Also

LinearAlgebra/Details

LinearAlgebra[Determinant]

LinearAlgebra[Modular]

LinearAlgebra[RandomMatrix]

 


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