i5 : symmetricAlgebra(M, Variables=>{x,y,z})
QQ [x, y, z, a, b, c, d, Degrees => {{1, 0}, {1, 0}, {1, 0}, {0, 1}, {0,
o5 = ------------------------------------------------------------------------
(z*b - y*c, y*a - x*b, z*a - x*c)
------------------------------------------------------------------------
1}, {0, 1}, {0, 1}}]
---------------------
o5 : QuotientRing
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i6 : symmetricAlgebra(M, VariableBaseName=>G, MonomialSize=>16)
QQ [G , G , G , G , G , G , G , Degrees => {{1, 0}, {1, 0}, {1, 0}, {0,
0 1 2 3 4 5 6
o6 = ------------------------------------------------------------------------
(G G - G G , G G - G G , G G
2 4 1 5 1 3 0 4 2 3
------------------------------------------------------------------------
1}, {0, 1}, {0, 1}, {0, 1}}, MonomialSize => 16]
------------------------------------------------
- G G )
0 5
o6 : QuotientRing
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i7 : symmetricAlgebra(M, Degrees=> {7:1})
QQ [x , x , x , a, b, c, d]
0 1 2
o7 = ---------------------------------
(x b - x c, x a - x b, x a - x c)
2 1 1 0 2 0
o7 : QuotientRing
|