1 | initial version |
The polynomial Phi
can only be evaluated at two inputs (using the function call syntax). The method roots
is only available for single variable polynomials. Your Phi(33,Y)
is (in SageMath) still a multivariable polynomial (in which X
does not appear). To convert it to a single variable polynomial in Y
, use the univariate_polynomial
method:
sage: f = Phi.subs(X=33).univariate_polynomial(); f
Y^3 + 6150*Y^2 + 5541*Y + 1175
sage: f.parent()
Univariate Polynomial Ring in Y over Finite Field of size 8009
sage: f.roots()
[(898, 1)]
sage: f.roots(multiplicities=False)
[898]
Alternatively:
sage: R.ideal([Phi, X-33]).variety()
[{Y: 898, X: 33}]