  Suppose $X$ is a 1-connected simplicial set with finitely many nondegenerate
simplices. We give an effective algorithm to calculate a simplicial set with
the $n$-type of the loop space $\Omega X$. Iterating gives an algorithm to
calculate the $\pi_i(X)$, different from the algorithms already known due to E.
Brown and Kan-Curtis. The method is an effective version of the generalized
Seifert-Van Kampen theorem of alg-geom/9704006. This can be viewed as a Van
Kampen statement concerning the loop space $\Omega X$ with its delooping
structure. We use Segal's delooping machinery but at the end we speculate on
extensions to other delooping machinery.
