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Enumerating points in 0-dimensional ideals over Qbar

I would like to find the points of a 0-dimensional ideal over Qbar. That is I do not want just the rational points,

The problem is that I found multiple problem while doing that.

1) While the code R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)") is legal, the code R.<t1,t2,t3> = PolynomialRing(QQbar,6, order="degrevlex(3)") is not for reasons that esapes me.

2) The code

R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)")

tvars = [t1,t2,t3]

eltsyms = [R((SymmetricFunctions(QQbar).elementary())[i].expand(3,alphabet=tvars)) for i in range(4)]

is not legal, it is if we replace QQbar by QQ. Why?

Enumerating points in 0-dimensional ideals over Qbar

I would like to find the points of a 0-dimensional ideal over Qbar. That is I do not want just the rational points,

The problem is that I found multiple problem while doing that.

1) While the code

R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)") order="degrevlex(3),lex(3)")

is legal, the code

R.<t1,t2,t3> = PolynomialRing(QQbar,6, order="degrevlex(3)") order="degrevlex(3)")

is not for reasons that esapes me.

2) The code

R.<t1,t2,t3,e1,e2,e3> = PolynomialRing(QQbar,6, order="degrevlex(3),lex(3)") order="degrevlex(3),lex(3)") tvars = [t1,t2,t3] [t1,t2,t3] eltsyms = [R((SymmetricFunctions(QQbar).elementary())[i].expand(3,alphabet=tvars)) for i in range(4)]range(4)]

is not legal, it is if we replace QQbar by QQ. Why?