Use the function resolution, often abbreviated as `res`, to compute a free resolution of a module.

See chain complexes for further details about how to handle and examine the result.

If the user has a chain complex in hand that is known to be a projective resolution of `M`, then it can be installed with `M.cache.resolution = C`.

i1 : R = QQ[x..z]; |

i2 : M = cokernel vars R o2 = cokernel | x y z | 1 o2 : R-module, quotient of R |

i3 : C = res M 1 3 3 1 o3 = R <-- R <-- R <-- R <-- 0 0 1 2 3 4 o3 : ChainComplex |

A reference to the result is stored within the module `M`, so that requesting a computation of `res M` a second time yields the formerly computed result immediately.

If the computation is interrupted or discontinued after the skeleton has been successfully computed, then the partially completed resolution is available as `M.cache.resolution`, and can be examined with status. The computation can be continued with `res M`. Here is an example, with an alarm interrupting the computation several times before it's complete. (On my machine, the computation takes a total of 14 seconds.)

i4 : R = ZZ/2[a..d]; |

i5 : M = coker random(R^4, R^{5:-3,6:-4}); |

i6 : (<< "-- computation started: " << endl; while true do try ( alarm 1; time res M; alarm 0; << "-- computation complete" << endl; status M.cache.resolution; << res M << endl << endl; break; ) else ( << "-- computation interrupted" << endl; status M.cache.resolution; << "-- continuing the computation" << endl; )) -- computation started: -- used 1.00768 seconds -- computation interrupted -- continuing the computation -- used 0.381858 seconds -- computation complete 4 11 89 122 40 R <-- R <-- R <-- R <-- R <-- 0 0 1 2 3 4 5 |

There are various optional arguments associated with resolution which allow detailed control over the progress of the computation.