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

TWO_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_two_{figname}.tex', 'w') as fd:
        fd.write('$$' + text + '$$')

AT = Matrix([
    [-2, 14, 18, 14],
    [-3, -9, -3, -3],
    [-12, -6, 18, 12],
    [6, 18, 6, 6]
])


before = AT.to_tex()

AT.make_D(0, -Fraction(1, 2))
AT.make_D(1, -Fraction(1, 3))
AT.make_D(2, -Fraction(1, 6))
AT.make_D(3, Fraction(1, 6))

AT.make_S(1, 0, -1)
AT.make_S(2, 0, -2)
AT.make_S(3, 0, -1)

AT.make_S(2, 1, -Fraction(3, 2))
AT.make_S(3, 1, -1)

AT.make_D(1, Fraction(1, 2))

gen_figure('fsr_A_T',
f'''
    {before}
    {TWO_SIMEQ}
    {AT.to_tex()}
''')


AB = Matrix([
    [-2, -3, -12, 6],
    [14, -9, -6, 18],
    [18, -3, 18, 6],
    [14, -3, 12, 6],
    [2, -1, 1, 0],
    [7, -4, 0, 5]
])

before = AB.to_tex()

AB.triangulate()

AB.make_D(0, Fraction(1, 2))
AB.make_D(1, -Fraction(1, 30))
AB.make_U(2, 4)


gen_figure('AB_sol',
f'''
{before}
{TWO_SIMEQ}
{AB.to_tex()}
''')


A = Matrix([
    [-2, -3, -12, 6],
    [14, -9, -6, 18],
    [18, -3, 18, 6],
    [14, -3, 12, 6]
])

before = A.to_tex()
A.triangulate()

A.make_D(0, -1)
A.make_D(1, -Fraction(1, 30))

gen_figure('ker_A',
f'''
    {before}
    {TWO_SIMEQ}
    {A.to_tex()}
''')

imker = Matrix([
    [-2, 14, 18, 14],
    [-3, -9, -3, -3],
    [-12, -6, 18, 12],
    [6, 18, 6, 6],
    [-3, -6, 2, 0],
    [0, 2, 0, 1]
])

before = imker.to_tex()
imker.triangulate()

gen_figure('imker',
f'''
    {before}
    {TWO_SIMEQ}
    {imker.to_tex()}
''')