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Hello I computed buchberger algorithm as R.<x,y,z>=PolynomialRing(QQ,3) I=ideal(x^6-y^2+z, z^3+y^2) set_verbose(3) I.groebner_basis('toy:buchberger') (x^6 - y^2 + z, z^3 + y^2) => 0 G: set([x^6 - y^2 + z, z^3 + y^2])

(z^3 + y^2, x^6 - y^2 + z) => 0 G: set([x^6 - y^2 + z, z^3 + y^2])

2 reductions to zero. [x^6 - y^2 + z, z^3 + y^2] I just want to know what is "set_verbose(3)" command for in this? also "toy:" ... thank you

Hello I computed buchberger algorithm as

R.<x,y,z>=PolynomialRing(QQ,3)
I=ideal(x^6-y^2+z, z^3+y^2)
set_verbose(3)
I.groebner_basis('toy:buchberger')
(x^6 - y^2 + z, z^3 + y^2) => 0
G: set([x^6 - y^2 + z, z^3 + y^2])
y^2])
  
(z^3 + y^2, x^6 - y^2 + z) => 0
G: set([x^6 - y^2 + z, z^3 + y^2])y^2])

2 reductions to zero. zero.

[x^6 - y^2 + z, z^3 + y^2]

I just want to know what is "set_verbose(3)" set_verbose(3) command for in this? also "toy:" toy: ... thank you

Hello I computed buchberger algorithm as

R.<x,y,z>=PolynomialRing(QQ,3)
I=ideal(x^6-y^2+z, z^3+y^2)
set_verbose(3)
I.groebner_basis('toy:buchberger')
(x^6 - y^2 + z, z^3 + y^2) => 0
G: set([x^6 - y^2 + z, z^3 + y^2])

(z^3 + y^2, x^6 - y^2 + z) => 0
G: set([x^6 - y^2 + z, z^3 + y^2])

[x^6 - y^2 + z, z^3 + y^2]