Toy computer algebra system in pure python.
Note: This code is entirely experimental and is not written to be performant. I'm implementing this for fun and practice.
The only interesting thing implemented so far is multivariate polynomial rings.
The implementation would probably work over arbitrary fields, but currently the only implemented field is the rationals.
from pyalgebra import *
R = PolynomialRing(QQ(), 4, ['x0', 'x1', 'x2', 'z'])
x0, x1, x2, z = R.gens()
I = R.ideal(x0*z + 1 - x1, x0*z - 1 - x2, x2*z - x1, x1*z - x0)
print(I.groebner_basis())would output
[z**2 + z + 1/2, x2 + 4/5*z + 8/5, x1 + 4/5*z - 2/5, x0 - 6/5*z - 2/5]