def testRoots_7(): # This test sometimes fails due to stability issues...
f1_coeff = np.zeros((3,3,3))
f1_coeff[(0,2,0)] = 1
f1_coeff[(1,1,0)] = -1
f1_coeff[(1,0,1)] = -2
f1 = MultiPower(f1_coeff)
f2_coeff = np.zeros((4,4,4))
f2_coeff[(0,3,0)] = 1
f2_coeff[(0,0,2)] = 1
f2_coeff[(0,0,0)] = 1
f2 = MultiPower(f2_coeff)
f3_coeff = np.zeros((3,3,3))
f3_coeff[(2,1,1)] = 1
f3_coeff[(0,1,1)] = -1
f3 = MultiPower(f3_coeff)
roots = rf.roots([f1, f2, f3])
values_at_roots = [[f1.evaluate_at(root) for root in roots],
[f2.evaluate_at(root) for root in roots],
[f3.evaluate_at(root) for root in roots]]
assert(np.all(np.isclose(values_at_roots, 0)))
def testRoots_4():
f1 = MultiPower(np.array([[5,-1],[1,0]]))
f2 = MultiPower(np.array([[1,-1],[-1,0]]))
root = rf.roots([f1, f2])[0]
assert(all(np.isclose(root, [-2,3])))
def testRoots_5():
f1 = MultiPower(np.array([[0,-1],[0,0],[1,0]]))
f2 = MultiPower(np.array([[1,-1],[1,0]]))
roots = rf.roots([f1, f2])
assert(all(np.isclose(roots[0], [-0.61803399, 0.38196601])))
assert(all(np.isclose(roots[1], [1.61803399, 2.61803399])))
def testRoots_3():
# roots of [x^2-y, x^3-y+1]
f1 = MultiPower(np.array([[0,-1],[0,0],[1,0]]))
f2 = MultiPower(np.array([[1,-1],[0,0],[0,0],[1,0]]))
roots = rf.roots([f1, f2])
values_at_roots = np.array([[f1.evaluate_at(root) for root in roots],
[f2.evaluate_at(root) for root in roots]])
assert(np.all(values_at_roots==0))
def testRoots_2():
f1 = MultiPower(np.array([[[5,0,0],[0,0,0],[0,0,0]],
[[0,-2,0],[0,0,0],[0,0,0]],
[[1,0,0],[0,0,0],[0,0,0]]]))
f2 = MultiPower(np.array([[[1,0,0],[0,1,0],[0,0,0]],
[[0,0,0],[0,0,0],[1,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]]))
f3 = MultiPower(np.array([[[0,0,0],[0,0,0],[3,0,0]],
[[0,-8,0],[0,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]]))
roots = rf.roots([f1, f2, f3])
values_at_roots = np.array([[f1.evaluate_at(root) for root in roots],
[f2.evaluate_at(root) for root in roots],
[f3.evaluate_at(root) for root in roots]])
assert(np.all(abs(values_at_roots)<1.e-5))
def testRoots_6(): # test when ideal is not zero-dimensional
f1 = MultiPower(np.array([[-12,-12],[1,1],[1,1]]))
f2 = MultiPower(np.array([[6,3,-3],[-2,-1,1]]))
roots = rf.roots([f1, f2])
assert(roots == -1)