from libsolve import *
from fractions import Fraction
import numpy as np

FOUR_SIMEQ = '\\overset{{\\texttt{{two.py}}}}\\simeq'

# generate figure as plain file, so we can \input it
def gen_figure(figname, text):
    with open(f'figures/fig_four_{figname}.tex', 'w') as fd:
        fd.write('$$' + text + '$$')

A = Matrix([
    [-1, 1, 1, -1],
    [-7, 4, 4, -3],
    [4, -1, -2, 1],
    [4, -1, -2, 1]
])

lbdE = Matrix([
    [Poly([0, 1]), 0, 0, 0],
    [0, Poly([0, 1]), 0, 0],
    [0, 0, Poly([0, 1]), 0],
    [0, 0, 0, Poly([0, 1])]
])

# uncomment to see characteristic poly
#print((A - lbdE).det())



A = A - Matrix([
    [1, 0, 0, 0],
    [0, 1, 0, 0],
    [0, 0, 1, 0],
    [0, 0, 0, 1]
])

A = A@A

before = A.to_tex()

A.triangulate()

A.make_D(0, -1)
A.make_U(1, 2)
A.make_D(1, Fraction(1, 4))

gen_figure('fsr_A_T',
f'''
    {before}
    {FOUR_SIMEQ}
    {A.to_tex()}
''')

print(A)