ApCoCoA-1:LinSyz.Resolution

This article is about a function from ApCoCoA-1.

LinSyz.Resolution

Computes syzygy modules of a module generated by linear forms.

Syntax

LinSyz.Resolution(M:MODULE,N:INT):LIST

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

This command computes the resolution of a given module, which is generated by vectors consisting of linear forms. Be aware of the fact that this is not well tested and may contain bugs! Also the linear forms may not have any constant component, so if your system has some, you have to homogenize the system first via introducing a new indeterminate.

• @param M A module.

• @param N A non-negative integer which gives the number of syzygy modules which will be computed .If N=0 all syzygy modules will be computed, otherwise the first N syzygy modules will be computed.

• @return The first set in the resulting lists contains the '0-th' syzygy module and consists of the interreduced generators!

Example

Use P::=QQ[x,y,z];
M:=Module([[x+y+z,x+y+z,x-y+z],[x-y,y-4z,x+2z],[x,y,z]]);
BettiDiagram(M);
        0
----------
 1:     3
----------
Tot:    3
-------------------------------
LinSyz.Resolution(M,0);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[Vector(x + y + z, x + y + z, x - y + z), Vector(x - y, y - 4z, x + 2z), Vector(x, y, z)]
-------------------------------
LinSyz.Resolution(M,1);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[ ]
-------------------------------

See also

LinSyz.BettyNumber

LinSyz.BettyNumbers

Introduction to Modules