Determinant and Other Properties

Determinant(A: parameters) : MtrxSprs -> RngElt
    MonteCarloSteps: RngIntElt          Default: 
Given a square sparse matrix A over the ring R, return the determinant of A as an element of R. R may be any commutative ring.

The algorithm first performs sparse elimination using Markowitz pivoting ([DEJ84, Sec. 9.2]) to obtain a smaller dense matrix, then the determinant algorithm for dense-representation matrices is applied to this matrix. If the parameter MonteCarloSteps is given, then this is passed to the dense algorithm for the dense matrix.

V2.29, 28 November 2025