@Carl Love 

Tanks again. Is there Maple online to can compute this (such Singular online)?

@Carl Love OK, I have Maple 18 too and I see the error again. Is there the package PolyhedralSets in Maple 18?

@Carl Love 

@YasH  Please see the following address:

" https://en.wikipedia.org/wiki/Matrix_equivalence "

@roman_pearce Thank you so much. Could you please introduce me a good reference contains these ideals?

@Carl Love Thank you so much but I need known hard examples.

@Markiyan Hirnyk Thank you so much.

With the best regards,

MDD

@Markiyan Hirnyk why not {a,b,c}?

@Markiyan Hirnyk Rational field $Q$.

@Markiyan Hirnyk Is this true? In my Mapl 15 this is {a, b}. I think according to the definition of maximal independent set it is {a,b,c}. What is your idea?

@vv Thank you so much

@Markiyan Hirnyk How? Reinstall a new version?

@Markiyan Hirnyk But in Maple 15 in my system I have

@Markiyan Hirnyk I reinserted the ideal as a text. Have you any suggestion?

@Markiyan Hirnyk Thank you so much for your replying.

I think that it is easy since this ideal has one generator. Also, Maple 16 compute this very fast! So there is a problem in Maple 15!