🔒 Using the "solve" function in a field extension in SageMath

[crisp blade]

Hello, this is my code :

K0.<j> = NumberField(x^2+x+1)
K1.<k> = K0.extension(2*x^2 + 3*x + 3)
var("a,b,c")
u = Matrix(1,3,[a,b,c]).transpose()

A2 = Matrix(3,3,[[1,0,0],[0,j,0],[0,0,j^2]])
A3 = Matrix(3,3,[[1,k*j,k*j^2],[k*j,j^2,k],[k*j^2,k,j]])```
And I would like this line of code :
```python
solve([(u.transpose()*A2*u)[0][0] == 0, (u.transpose()*A3*u)[0][0] == 0, a==1],[a,b,c])``` to work and give me the 4 solutions (I need to do that for a lot of pair of matrices). What should I do ? Thank you ^^

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@crisp blade

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[native ore]

ure likely to struggling maybe because solve is optimized for simpler fields or symbolic ring, not general number field extensions. what u should do here instead is consider using a PolynomialRing and reduce the problem to solving a zero-dimensional ideal, which you can do with grobner bases plus if u wish to yield solutions which are under C try using .roots() or numerical methods are good too.

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