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Finding roots polynomial 2D

asked 2022-09-18 10:43:54 +0200

Andr gravatar image

I have polynomial 2D degree 2 $(1,x,y,xy,x^2,y^2) $ defined on triangle. How to find all roots?

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answered 2022-09-18 16:57:53 +0200

Max Alekseyev gravatar image

updated 2022-09-18 16:59:31 +0200

You can solve exactly in algebraic numbers (AA) and then get results in reals with any precision by using .n() method:

R.<x,y> = AA[]
eq1 = 2*x^2 + x*y +x - 6
eq2 = 3*x^2 + 2*y^2- y  - 6
sols = R.ideal([eq1,eq2]).variety()
[tuple(map(lambda t: s[t].n(digits=20), R.gens())) for s in sols]
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answered 2022-09-18 11:31:52 +0200

Andr gravatar image

I found sequence:

var('x y')
eq1 = 2*x^2 + x*y +x == 6
eq2 = 3*x^2 + 2*y^2- y  == 6
solutions = solve([eq1, eq2], x, y)
print(solutions)

now I want increase precision: R = RealField(100) how use with solve?

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Asked: 2022-09-18 10:43:54 +0200

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Last updated: Sep 18