Computing the twisted $L^2$-Euler characteristic

We present an algorithm that computes Friedl and L\"uck's twisted $L^2$-Eulercharacteristic for a suitable regular CW complex, employing Oki's matrixexpansion algorithm to indirectly evaluate the Dieudonn\'e determinant. Thealgorithm needs to run for an extremely long time to certify its outputs, but atruncated, human-assisted version produces very good results in many cases,such as hyperbolic link complements, closed census 3-manifolds, free-by-cyclicgroups, and higher-dimensional examples, such as the fiber of theRatcliffe-Tschantz manifold.