Macaulay2 » Documentation
Packages » CellularResolutions :: isFree
next | previous | forward | backward | up | index | toc

isFree -- checks if the labels of a cell complex are free modules



This command checks if the modules associated to the labels in the cell complex are all free, which is necessary for the complex to give a free resolution.

A monomial label always gives a free module, since the module for a monomial label is the free module generated by that monomial.

Additionally, this function does not simply apply isFreeModule(Module) to every label, as in general, the labels are given as submodules, and so isFreeModule(Module) would return false in nearly all cases. Instead the labels are first pruned prior to calling isFreeModule(Module).

i1 : R = QQ[x,y,z];
i2 : v1 = newCell({},ideal(x,y));
i3 : C1 = cellComplex(R,{v1});
i4 : isFree C1

o4 = false
i5 : v2 = newCell({},x*y);
i6 : C2 = cellComplex(R,{v2});
i7 : isFree C2

o7 = true

Ways to use isFree :

For the programmer

The object isFree is a method function.