M2
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error message in selectVariables
I tried this on M2:
R=QQ[x,y,MonomialOrder=>Lex,Inverses=>true];
selectVariables({0},R)
and obtained as the second output: stdio:12:1:(3): error: Inverses => true not compatible with GRevLex
It seems that selectVariables is not truly keeping the option "MonomialOrder=>Lex" in the subring QQ[x].
Indeed, and in this case, it returns an answer, but the ordering is wrong:
i1 : R=QQ[x,y,z,MonomialOrder=>Lex];
i2 : describe first selectVariables({0,1},R)
o2 = QQ[x..y, Degrees => {2:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1]
{Lex => 0 }
{Position => Up }
{GRevLex => {2:1} }