-- Advanced linear algebra: solve, inv, det via LU decomposition with
-- partial pivoting. Matrices are row-major nested lists (L (L n));
-- vectors are flat lists (L n). Singular and non-square inputs raise.
-- Determinant of a square matrix.
de a:L (L n)>n;det a
-- Solve Ax = b for x.
sv a:L (L n) b:L n>L n;solve a b
-- Matrix inverse.
iv a:L (L n)>L (L n);inv a
-- run: de [[1,0],[0,1]]
-- out: 1
-- run: de [[2,1],[1,3]]
-- out: 5
-- run: sv [[1,1],[1,-1]] [3,1]
-- out: [2, 1]
-- run: iv [[2,0],[0,2]]
-- out: [[0.5, 0], [0, 0.5]]