Let S be a polynomial ring and consider a quotient Q=S^p/N where N is a submodule generated in degrees at most d. If the graded component Q_d is free of rank n, then N_d is free as well, and N_d\otimes S_1 \to S^p_{d+1} \to Q_{d+1}\to 0 gives a free resolution of Q_{d+1}. Let K be the matrix corresponding to the map N_d\otimes S_1\to S^p_{d+1}. The function co1Fitting calculates the (n-1)'th Fitting ideal of Q_{d+1} assuming that the basis of Q_d was given by a Gotzmann set.
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The object co1Fitting is a method function.