import numpy as np

from .carry import Carry

xy_2 = Carry([[-2,1],[1,0]])
xy_3 = Carry([[-3,1],[1,0]])
x2y_3 = Carry([[-3,2],[1,0]])
x3y_4 = Carry([[-4,3],[1,0]])

laplace = Carry([[0,1,0],[1,-4,1],[0,1,0]])
laplace3 = Carry([[0,0,0],[1,-3,1],[0,1,0]])

almost_folium = Carry([[0,0,1], [0,-2,0], [1,0,0]])
folium = Carry([
    [ 0, 0,0, 1],
    [ 0,-2,0, 0],
    [ 0, 0,0, 0],
    [ 1, 0,0, 0]
])
folium3 = Carry([
    [ 0, 0,0, 1],
    [ 0,-3,0, 0],
    [ 0, 0,0, 0],
    [ 1, 0,0, 0]
])
folium4 = Carry([
    [ 0, 0, 0, 1, 0],
    [ 0, 0, 0, 0, 1],
    [ 0, 0,-4, 0, 0],
    [ 1, 0, 0, 0, 0],
    [ 0, 1, 0, 0, 0]
])

def triangle_spread(n):
    ret = np.zeros((n + 1, n + 1), dtype=np.int32)
    ret[0, 0] = 1
    ret[1, 1] = -3
    ret[n, 0] = 1
    ret[0, n] = 1
    return ret

triangle1 = Carry(triangle_spread(1))
triangle2 = Carry(triangle_spread(2))
triangle3 = Carry(triangle_spread(3)) #factorable!
triangle4 = Carry(triangle_spread(4))

tri3_rot = Carry([
    [ 0, 0, 1, 0, 0],
    [ 0, 0,-3, 0, 0],
    [ 1, 0, 0, 0, 1]
])

tri3_rot_real = Carry([
    [ 0, 0, 0, 1, 0, 0, 0],
    [ 0, 0, 0, 0, 0, 0, 0],
    [ 0, 0, 0,-3, 0, 0, 0],
    [ 1, 0, 0, 0, 0, 0, 1]
])

tri3_rot2 = Carry([
    [ 0, 1, 0],
    [ 0,-3, 0],
    [ 1, 0, 1]
])

tri3_tall = Carry([
    [ 0, 1, 0],
    [ 0, 0, 0],
    [ 0,-3, 0],
    [ 1, 0, 1]
])

tri3_tall2 = Carry([
    [ 0, 1, 0],
    [ 0,-3, 0],
    [ 0, 0, 0],
    [ 1, 0, 1]
])