"""Independent dense-minor checks of the split determinantal formula."""
from itertools import combinations
import sympy as sp
import pytest
from noulith.ideals import equal_polynomial_ideals


def minors(matrix, k):
    if k == 0:
        return [sp.Integer(1)]
    return [matrix.extract(rows, cols).det()
            for rows in combinations(range(matrix.rows), k)
            for cols in combinations(range(matrix.cols), k)]


@pytest.mark.parametrize('k', [0, 1, 2, 3])
def test_split_ideal_dense_minors(k):
    a,b,c=sp.symbols('a b c')
    matrix=sp.Matrix([[1,0,0], [0,a,0], [0,b,0], [0,0,c]])
    expected=([1], [1], [a,b,c], [a*c,b*c])[k]
    assert equal_polynomial_ideals(minors(matrix,k), expected, (a,b,c))


@pytest.mark.parametrize('k,order', [(1,0),(2,2),(3,5)])
def test_univariate_determinantal_orders(k,order):
    t=sp.symbols('t')
    matrix=sp.diag(1,t**2,t**3)
    polynomials=[sp.Poly(x,t) for x in minors(matrix,k) if x!=0]
    actual=min(min(monomial[0] for monomial,coefficient in p.terms()) for p in polynomials)
    assert actual==order


def test_four_channel_quadrics_and_carriers():
    x,y,z=sp.symbols('x y z')
    pairs=[x*(z-y), y*(z-x), z*(y-x)]
    quadrics=[x*y-x*z,x*y-y*z]
    assert equal_polynomial_ideals(pairs,quadrics,(x,y,z))
    carriers=[x*x-x*y,y*y-x*y,z*z-x*y,x*y]
    t=sp.symbols('t')
    branches=[(t,0,0),(0,t,0),(0,0,t),(t,t,t)]
    restrictions=sp.Matrix([[sp.expand(f.subs(dict(zip((x,y,z),branch)), simultaneous=True))
        for f in carriers] for branch in branches])
    assert restrictions==t**2*sp.eye(4)