This package is a simple wrapper to integrate most of controlled reduction library code into SageMath.
Given an hypersurface it computes the characteristic polynomial (and matrix) of the Frobenius action on the primitive cohomology group.
sage -pip install --upgrade git+https://github.com/edgarcosta/pycontrolledreduction.git@master#egg=pycontrolledreduction
If you don't have permissions to install it system wide, please add the flag --user to install it just for you.
sage -pip install --user --upgrade git+https://github.com/edgarcosta/pycontrolledreduction.git@master#egg=pycontrolledreduction
sage: from pycontrolledreduction import controlledreduction
sage: R.<x,y,z> = ZZ[]
sage: controlledreduction(x^4 + y^4 + z^4 + 1*x^2*y*z, next_prime(10000), False).factor()
(10007*T^2 - 192*T + 1) * (10007*T^2 - 128*T + 1) * (10007*T^2 + 192*T + 1)
sage: controlledreduction(y^2*z + y*z^2 - (x^3 + y*x^2 -2*x*z^2), 97, false).list() == EllipticCurve([0, 1, 1, -2, 0]).change_ring(GF(97)).frobenius_polynomial().reverse().list()
True
Note: that the polynomial has degree 21, as we are omiting the factor (1-p*T) coming from the polarisation.
sage: from pycontrolledreduction import controlledreduction
sage: R.<x,y,z,w> = ZZ[]
sage: controlledreduction(x^4 + y^4 + z^4 + w^4 + x*y*z*w, 11, False).factor() # long time
(-1) * (11*T + 1)^6 * (11*T - 1)^13 * (121*T^2 + 18*T + 1)
sage: controlledreduction(x^4 + y^4 + z^4 + w^4 + x*y*z*w, 23, False).factor() # long time
(-1) * (23*T - 1)^9 * (23*T + 1)^10 * (529*T^2 - 38*T + 1)