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Res
Syntax
Res(M):TAGGED("$gb.Res")
where M is of type IDEAL or MODULE or TAGGED("Quotient").
Summary
free resolution
Description
This function returns the minimal free resolution of M. If M is a
quotient of the current ring by an ideal I or a quotient of a free
module by a submodule N, then the resolution of M is defined
to be that of I or N, respectively.
Res
only works in the homogeneous context, and the coefficient ring
must be a field.
example
Use R ::= Q[x,y,z];
I := Ideal(x,y,z^2);
Res(R/I);
0 --> R(-4) --> R(-2)(+)R^2(-3) --> R^2(-1)(+)R(-2) --> R
-------------------------------
Describe It;
Mat[
[y, x, z^2]
]
Mat[
[x, z^2, 0],
[-y, 0, z^2],
[0, -y, -x]
]
Mat[
[z^2],
[-x],
[y]
]
-------------------------------
For fine control and monitoring of Groebner basis calculations,
including various types of truncations, see "The Interactive Groebner
Framework" and "Introduction to Panels".
See Also