IntegerDeterminant - Maple Help

LinearAlgebra[Modular]

 IntegerDeterminant
 determinant of an integer matrix using modular methods

 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

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Modular}\right]\right):$
 > $M≔\mathrm{Matrix}\left(\left[\left[2,1,3\right],\left[4,3,1\right],\left[-2,1,-3\right]\right]\right)$
 ${M}{≔}\left[\begin{array}{ccc}{2}& {1}& {3}\\ {4}& {3}& {1}\\ {-2}& {1}& {-3}\end{array}\right]$ (1)
 > $\mathrm{IntegerDeterminant}\left(M\right)$
 ${20}$ (2)

A 100x100 matrix

 > $M≔\mathrm{LinearAlgebra}\left[\mathrm{RandomMatrix}\right]\left(100\right):$
 > $\mathrm{tt}≔\mathrm{time}\left(\right):$
 > $\mathrm{IntegerDeterminant}\left(M\right)$
 ${38562295347802366242417909657285032281105091485000162871067163275296273582728190925949289361981964881806516849833008824879568403928373759144147382030798909099402726531205056808283212790472544339698767179236612577117605985054960334148934541347201762137455}$ (3)
 > $\mathrm{time}\left(\right)-\mathrm{tt}$
 ${0.042}$ (4)