/**/ use P ::= QQ[x,y,z];
/**/ depth(P); -- the (x,y,z)-depth of the entire ring is 3
3
/**/ I := ideal(x^5,y^3,z^2);
/**/ depth(P/I);
0
//----- ***** NOT YET IMPLEMENTED ***** ----->>
N := Module([x^2,y], [x+z,0]);
depth(I, P^2/N); --- a max reg sequence would be (z^2,y^3)
2
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use P ::= QQ[x,y,z,t,u,v];
-- Cauchy-Riemann system in three complex vars!
N := Module([x,y], [-y,x], [z,t], [-t,z], [u,v], [-v,u]);
--- is it CM?
depth(P^2/N);
3
-------------------------------
dim(P^2/N);
3
-------------------------------
--- yes!
M := Module([x,y,z],[t,v,u]);
res(P^3/M);
0 --> P^2(-1) --> P^3
-------------------------------
depth(P^3/M); -- using Auslander Buchsbaum 6-1=5
5
-------------------------------
dim(P^3/M); -- not CM
6
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depth(ideal(x,y,z,t), P^2/N);
2
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