def test_piecewise_simplification():
d2d3_11 = (c * d * TP(x, sp.Piecewise(
(x, sp.Eq(k, 0)),
(0, True))) + c * d * TP(sp.Piecewise(
(x, sp.Eq(k, 0)),
(0, True)), x) + d * TP(1, sp.Piecewise(
(x, sp.Eq(k, 0)),
(0, True))) + d * TP(sp.Piecewise((x, sp.Eq(k, 0)),
(0, True)), 1))
assert texpand(d2d3_11) == 0
expr = sp.Sum(
sp.Piecewise(
(c * TP(xy**k,
y * xy**(k - q - 1) * y) + TP(y * xy**(k - 1),
y * xy**(k - q - 1) * y),
sp.Eq(q, 0)), (0, True)), (q, 0, k - 1))
assert texpand(expr) == 0
def composition(d2, d1):
""" Computes composition of d1 and d2, i.e. λx -> d2(d1(x)). """
product_rows = len(d2)
product_cols = len(d1[0])
product = [[None] * product_cols for _ in range(product_rows)]
for i in range(product_rows):
for j in range(product_cols):
row = d2[i]
col = [d1[k][j] for k in range(len(d1))]
product[i][j] = texpand(dot(row, col))
return product
def test_x_cubed_reduces_to_xy_k():
left = TP(x, y) * X
right = X + TP(xy**k, xy**k)
assert texpand(left * right) == texpand(texpand(left) * texpand(right))
def test_misc():
assert texpand(2 * x) == 0
assert texpand(y * x * y * x) == yx**2
assert texpand(d * xy**(k + 1)) == 0
assert texpand(x * y * xy**(k - 1)) == xy**k
assert texpand(y * xy**(k - 1) * yx**(k - 1)) == 0
def test_sign_removal():
X = TP(x, 1) - TP(1, x)
assert texpand(X) == TP(x, 1) + TP(1, x)
def test_zero_propagation():
assert texpand(TP(x, 0)) == 0
assert texpand(TP(0, y)) == 0
assert texpand(TP(xy**k, y) * TP(x, 1)) == 0
assert texpand(TP(x * c**2 * d * xy**k, y)) == 0
def ast_matrix(expr):
expr_expanded = texpand(expr)
col1 = basis
col2 = [texpand(ast(expr_expanded, r)) for r in basis]
return sp.Matrix([col1, col2]).T
def ast_table(expr):
expr_expanded = texpand(expr)
for r in basis:
product = ast(expr_expanded, r)
product = texpand(product)
print('({}) ∗ {}\n = {}'.format(expr, r, product))