Use A4::=QQ[x[1..4],d[1..4]];
I4:=Ideal(d[2]d[3]-d[1]d[4],x[1]d[1]-x[4]d[4]-1,x[2]d[2]+x[4]d[4]+1,x[3]d[3]+x[4]d[4]+2);
Weyl.InIw(I4,[0,0,0,0,1,1,1,1]); --This function is implemented only for positive weights!
ERROR: All weights shoud be strictly positive
CONTEXT: Error("All weights shoud be strictly positive")
-------------------------------
Weyl.InIw(I4,[1,1,1,1,2,2,1,1]);
-- CoCoAServer: computing Cpu Time = 0.016
-------------------------------
Ideal(x[2]x[3]x[4]d[4]^2 - x[1]x[4]^2d[4]^2, x[1]x[4]d[3]d[4] + x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4], x[2]d[1]d[4],
x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1], x[2]d[2], x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4])
-------------------------------
Weyl.InIw(I4,[1,2,1,1,2,2,1,1]);
-- CoCoAServer: computing Cpu Time = 0.032
-------------------------------
Ideal(x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4], x[2]d[1]d[4], x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1], x[2]d[2],
x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4])
-------------------------------
Weyl.InIw(I4,[2,2,2,2,1,1,1,1]);
-- CoCoAServer: computing Cpu Time = 0.031
-------------------------------
Ideal(x[2]x[3]x[4]d[4]^2 - x[1]x[4]^2d[4]^2, x[1]x[4]d[3]d[4] + x[2]x[4]d[4]^2, x[1]x[4]d[2]d[4] + x[3]x[4]d[4]^2,
x[2]d[1]d[4] + x[4]d[3]d[4], x[3]d[1]d[4] + x[4]d[2]d[4], x[1]d[1] - x[4]d[4], x[2]d[2] + x[4]d[4],
x[3]d[3] + x[4]d[4], d[2]d[3] - d[1]d[4])
-------------------------------
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