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KustinMiller :: differentials

differentials -- Generate the differentials of the Kustin-Miller resolution



Generate the j-th differential of a Kustin-Miller resolution of length g. So, e.g., for j=1 we obtain the relations of the ring resolved and for j=2 the first syzygies of those.

We use the notation of Section 2.3 of

J. Boehm, S. Papadakis: On the structure of Stanley-Reisner rings associated to cyclic polytopes, [math.AC]

For any j the last entry of L should be the variable T.

For j=1 we assume L = {b1, beta1, a1, T }.

For j=2 we assume L = {b2, beta2, h1, a2, alpha1, T }.

For j=3,...,g-1 we assume L = {bj, betaj, hj-1, aj, alphaj-1, bj-1, T }.

For j=g-1 we assume L = {betag-1, hg-1, ag-1, alphag-2, bg-2, T }.

For j=g we assume L = {alphag-1, ag, bg-1, u, T }.

Finally s equals k1-k2.


This is not really a user level function, however it is exported as occasionally it can be useful. The export may be removed at some point.

See also

Ways to use differentials :

  • differentials(List,ZZ,ZZ,ZZ)