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- R.<u,v,x,y,z> = PolynomialRing(QQ, order='lex')
- p = (x-u)^2 + (y-v)^2 + z^2 - 1/10
- dpdt = -v*diff(p, u) + u*diff(p, v)
- time = u^2 + v^2 - 1
- I = ideal(p, dpdt, time)
- G = I.groebner_basis()
- eqn = G[-1]
- print(eqn)
- # x^4 + 2*x^2*y^2 + 2*x^2*z^2 - 11/5*x^2 + y^4 + 2*y^2*z^2 - 11/5*y^2 + z^4 + 9/5*z^2 + 81/100
- # plotting
- var('x y')
- eqn = x^4 + 2*x^2*y^2 + 2*x^2*z^2 - 11/5*x^2 + y^4 + 2*y^2*z^2 - 11/5*y^2 + z^4 + 9/5*z^2 + 81/100
- implicit_plot3d(eqn, (-2, 2), (-2, 2), (-2, 2))
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