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res

free resolution

Syntax
res(M: IDEAL): LIST
res(M: MODULE): LIST

Description
This function returns the minimal free resolution of M . res only works in the homogeneous context, and the coefficient ring must be a field.

NOTE: the current implementation (CoCoA-5.1.0) is very naive so it might be very slow (better slow than nothing?).

Example
/**/  use R ::= QQ[x,y,z];
/**/  I := ideal(x, y, z^2);
/**/  PrintRes(R/I);
0 --> R(-4) --> R(-2)(+)R(-3)^2 --> R(-1)^2(+)R(-2) --> R
/**/  indent(Res(R/I),2);
[
  RingWithID(20, "RingWithID(3)/ideal(x, y, z^2)"),
  ideal(
    y,
    x,
    z^2
  ),
  SubmoduleRows(F, matrix([
    [x, -y, 0],
    [0, z^2, -x],
    [z^2, 0, -y]
  ])),
  SubmoduleRows(F, matrix([
    [z^2, y, -x]
  ]))
]

See Also