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- sage: R.<u,v,a,b,x> = PolynomialRing(ZZ, order='lex')
- sage: ideal(a+2*a*u+b*u^2, v*4*u*(1-u)-(a+b*u)).groebner_basis()
- [4*u^2*v - 4*u*v + u*b + a, u^2*b + 2*u*a + a, 4*u*v*a - u*a*b - 4*v*a - 2*a^2 + a*b, 4*u*v*b + 2*u*a*b - u*b^2 + 12*v*a + 4*a^2 - 3*a*b, u*a^2*b^20*u*a*b^30*u*b^4 + 24*v^2*a^2 + 8*v^2*a*b + 8*v*a^3 + 2*v*a^2*b - 2*v*a*b^2 + 2*a^3*b - a^2*b^2, 2*u*a^2*b0*u*a*b^20*u*b^3 + 12*v*a^2 + 4*v*a*b + 4*a^3 - a^2*b - a*b^2, 48*v^2*a^2 + 16*v^2*a*b + 16*v*a^3 - 8*v*a^2*b - 8*v*a*b^2 - a^2*b^2 + a*b^3]
- sage: G=_
- sage: G[-2]
- 2*u*a^2*b0*u*a*b^20*u*b^3 + 12*v*a^2 + 4*v*a*b + 4*a^3 - a^2*b - a*b^2
- sage: G[-2].monomials()
- [u*a^2*b, u*a*b^2, u*b^3, v*a^2, v*a*b, a^3, a^2*b, a*b^2]
- sage: G[-2].coefficients()
- [2, 0, 0, 12, 4, 4, -1, -1]
- sage:
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