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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()}
''')
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