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from libsolve import *
from fractions import Fraction
import numpy as np
ONE_SIMEQ = '\\overset{{\\texttt{{one.py}}}}\\simeq'
# generate figure as plain file, so we can \input it
def gen_figure(figname, text):
with open(f'figures/fig_one_{figname}.tex', 'w') as fd:
fd.write('$$' + text + '$$')
m = Matrix([
[-1, 4, 1, -2, 1, 3],
[-1, 4, 1, -2, 1, 3],
[1, -4, 3, -2, 7, 5]
])
vectors = [
[3, 1, -7, -3, 3, -1],
[2, 2, 5, 3, 1, -2],
]
for i, v in enumerate(vectors):
v_t = Matrix([[i] for i in [3, 1, -7, -3, 3, -1]])
gen_figure(f'proof_v{i}',
f'''
{m.to_tex()}
\\times
{v_t.to_tex()}
=
{(m @ v_t).to_tex()}
''')
init = m.to_tex()
m.make_S(0, 1, -1)
m.make_S(1, 2, 1)
m.make_D(1, Fraction(1, 4))
m.make_S(2, 1, -3)
init_triang = m.to_tex()
gen_figure('init_to_triang',
f'''
{init}
{ONE_SIMEQ}
{init_triang}
''')
# steps are the same every time, cause we change only last col
def convert_steps(mat, mat_no):
before = mat.to_tex()
mat.make_S(0, 1, -4)
mat.make_S(2, 0, 1)
mat.make_S(3, 0, 1)
mat.make_D(0, -1)
mat.make_S(0, 4, -1)
mat.make_S(2, 4, 3)
mat.make_S(3, 4, 1)
mat.make_S(0, 5, 1)
mat.make_S(2, 5, 1)
mat.make_S(3, 5, -1)
after = mat.to_tex()
gen_figure(f'convert_v{mat_no}',
f'''
{before}
{ONE_SIMEQ}
{after}
''')
convert_steps(Matrix([
[4,-1,-1,1,3],
[1,0,0,0,1],
[0,1,-2,-2,-7],
[0,1,0,0,-3],
[0,0,1,0,3],
[0,0,0,1,-1]
]), 1)
convert_steps(Matrix([
[4,-1,-1,1,2],
[1,0,0,0,2],
[0,1,-2,-2,5],
[0,1,0,0,3],
[0,0,1,0,1],
[0,0,0,1,-2]
]), 2)
m = Matrix([
[1, -3, 3, 1],
[2, 3, 1, -2]
])
before = m.to_tex()
m.make_S(1, 0, -2)
after = m.to_tex()
gen_figure('solve_last',
f'''
{before}
{ONE_SIMEQ}
{after}
''')
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