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 | 1 | initial version |
Here are the roots with multiplicities, using a different solution method:
sage: R.<a,b,c,d,e,f,g,x> = QQ[]
sage: I = R.ideal([(a - g) + 2, - (a*g - b) - 1, - (b*g - c), - (c*g - d) + 10, - (d*g - e) - 22, - f*g - 2, - (e*g - f) + 14])
sage: f_g = I.elimination_ideal([a,b,c,d,e,f,x]).gen(0).polynomial(g); f_g
g^7 - 2*g^6 + g^5 - 10*g^3 + 22*g^2 - 14*g + 2
sage: f_g.roots(QQbar)
[(-1.825113480833768?, 1),
(0.2000320256287094?, 1),
(1, 2),
(1.724306474243468?, 1),
(-0.04961250951920454? - 1.781741795058673?*I, 1),
(-0.04961250951920454? + 1.781741795058673?*I, 1)]
Indeed, the root 1 has multiplicity two.
| | 2 | No.2 Revision |
Here are the roots with multiplicities, using a different solution method:
sage: R.<a,b,c,d,e,f,g,x> = QQ[]
sage: I = R.ideal([(a - g) + 2, - (a*g - b) - 1, - (b*g - c), - (c*g - d) + 10, - (d*g - e) - 22, - f*g - 2, - (e*g - f) + 14])
sage: f_g F_g = I.elimination_ideal([a,b,c,d,e,f,x]).gen(0).polynomial(g); f_g
F_g
g^7 - 2*g^6 + g^5 - 10*g^3 + 22*g^2 - 14*g + 2
sage: f_g.roots(QQbar)
F_g.roots(QQbar)
[(-1.825113480833768?, 1),
(0.2000320256287094?, 1),
(1, 2),
(1.724306474243468?, 1),
(-0.04961250951920454? - 1.781741795058673?*I, 1),
(-0.04961250951920454? + 1.781741795058673?*I, 1)]
Indeed, the root 1 has multiplicity two.
