Specify IsIdealUnmixed=>true if it is known a priori that an ideal is unmixed. In this case, the program will not check whether the given ideal $I$ is unmixed -- it will assume that it is unmixed -- but it will check whether $C_{y,I}$ and $N_{y,I}$ are unmixed, as well as any ideals defined from further degenerations. The default value is false and in this case, the unmixedness property will be checked for $I$ and all later ideals.
To always skip the unmixedness check (perhaps you know that every ideal you will encounter through repeated geometric vertex decompositions will always be unmixed), use CheckUnmixed.
The object IsIdealUnmixed is a symbol.