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 4.13.6 Example: Interactive Resolution Computation
In this example we compute the minimal free resolution of the ideal I generated by the 2 by 2 minors of a catalecticant matrix, A, using the interactive environment of the system. We define the ideal I, and start the computation of its minimal free resolution using the Hilbert-driven algorithm described in

A. Capani, G. De Dominicis, G. Niesi, L. Robbiano, Computing Minimal Finite Free Resolutions, J. Pure Appl. Algebra, Vol. 117--118, Pages 105--117, 1997.

 Example
 ``` Use R ::= ZZ/(32003)[z[0..3,0..3,0..3]]; -- set up the ring A := Mat([ -- define the ideal [z[3,0,0], z[2,1,0], z[2,0,1]], [z[2,1,0], z[1,2,0], z[1,1,1]], [z[2,0,1], z[1,1,1], z[1,0,2]], [z[1,2,0], z[0,3,0], z[0,2,1]], [z[1,1,1], z[0,2,1], z[0,1,2]], [z[1,0,2], z[0,1,2], z[0,0,3]] ]); I := Ideal(Minors(2, A)); \$gb.Start_Res(I); -- start interactive framework \$gb.Steps(I,1000); -- first 1000 steps \$gb.GetRes(I); 0 --> R^176(-5) --> R^189(-4) --> R^105(-3) --> R^27(-2) ------------------------------- \$gb.ResReport(I); -------------------------------------------------------------- Minimal Pairs, : 650 Groebner Pairs : 14 Minimal (Type S) : 636 H-Killed (Type S0) : 9 -------------------------------------------------------------- ------------------------------- \$gb.Complete(I); -- complete the calculation \$gb.GetRes(I); 0 --> R(-9) --> R^27(-7) --> R^105(-6) --> R^189(-5) --> R^189(-4) --> R^105(-3) --> R^27(-2) ------------------------------- \$gb.ResReport(I); -------------------------------------------------------------- Minimal Pairs, : 730 Groebner Pairs : 25 Minimal (Type S) : 705 Minimal (Type Smin) : 616 Minimal (Type S0) : 89 H-Killed (Type S0) : 78 Hard (Type S0) : 11 -------------------------------------------------------------- ------------------------------- ```