Third task

1 files changed, 144 insertions, 4 deletions

diff --git a/four.py b/four.py
index 4f7cd54..12074cf 100644
--- a/four.py
+++ b/four.py
@@ -23,8 +23,10 @@ lbdE = Matrix([
     [0, 0, 0, Poly([0, 1])]
 ])
 
-# uncomment to see characteristic poly
-#print((A - lbdE).det())
+print((A - lbdE).det())
+
+
+
 
 
 
@@ -45,11 +47,149 @@ A.make_D(0, -1)
 A.make_U(1, 2)
 A.make_D(1, Fraction(1, 4))
 
-gen_figure('fsr_A_T',
+gen_figure('V_1',
+f'''
+    {before}
+    {FOUR_SIMEQ}
+    {A.to_tex()}
+''')
+
+
+
+
+
+
+
+
+A = Matrix([
+    [-1, 1, 1, -1],
+    [-7, 4, 4, -3],
+    [4, -1, -2, 1],
+    [4, -1, -2, 1]
+])
+A = A@A
+
+before = A.to_tex()
+
+A.triangulate()
+
+
+A.make_D(0, -Fraction(1, 2))
+A.make_D(1, -6)
+
+gen_figure('V_0',
 f'''
     {before}
     {FOUR_SIMEQ}
     {A.to_tex()}
 ''')
 
-print(A)
\ No newline at end of file
+
+
+
+
+
+# solve 16-equation system
+# unknown matrix is (answer_to_system).reshape(4, 4),
+# so we 'flatten' it to solve for each unknown
+
+def make_row(vec, ans):
+    return [
+        [0, 0, 0, 0] * i +
+        vec +
+        [0, 0, 0, 0] * (3 - i) +
+        [ans[i]]
+        for i in range(4)
+    ]
+
+v_11 = [1, 3, 0, 0]
+v_12 = [1, 0, 3, 3]
+v_01 = [-1,-3, 1, 0]
+v_02 = [12, 10, 0, 3]
+e_3 = [0, 0, 1, 0]
+e_4 = [0, 0, 0, 1]
+
+rows = []
+rows += make_row(v_11, [0, 0, 0, 0])
+rows += make_row(v_12, [0, 0, 0, 0])
+rows += make_row(e_3, v_01)
+rows += make_row(e_4, v_02)
+
+sys = Matrix(rows)
+
+before = sys.to_tex()
+
+sys.triangulate(True)
+sys.make_D(1, -Fraction(1, 3))
+sys.make_D(5, -Fraction(1, 3))
+sys.make_D(9, -Fraction(1, 3))
+sys.make_D(13, -Fraction(1, 3))
+
+gen_figure('sys_orig',
+f'''
+    \\begingroup % keep the change local
+    \\setlength\\arraycolsep{{4pt}}
+    {before}
+    {FOUR_SIMEQ}
+    {sys.to_tex()}
+    \\endgroup
+''')
+
+ans = [row[-1] for row in sys.rows]
+reshape = [ans[4 * i:4 * i + 4] for i in range(4)]
+
+psi = Matrix(reshape)
+
+gen_figure('psi', 
+f'''
+\\psi' = {psi.to_tex()}
+''')
+
+
+
+
+
+
+inverse = Matrix([
+    [ 0,  Fraction(1, 3), 0, 0,   1, 0, 0, 0],
+    [ 1, -Fraction(1, 3), 0, 0,   0, 1, 0, 0],
+    [-3, -1, 1, 0,                0, 0, 1, 0],
+    [-3, -1, 0, 1,                0, 0, 0, 1]
+])
+
+before = inverse.to_tex()
+
+inverse.triangulate(True)
+inverse.make_D(1, 3)
+
+gen_figure('inverse',
+f'''
+    {before}
+    {FOUR_SIMEQ}
+    {inverse.to_tex()}
+''')
+
+
+
+
+C = Matrix([
+    [ 0,  Fraction(1, 3), 0, 0],
+    [ 1, -Fraction(1, 3), 0, 0],
+    [-3, -1, 1, 0],
+    [-3, -1, 0, 1]
+])
+
+inv = Matrix([
+    [1, 1, 0, 0],
+    [3, 0, 0, 0],
+    [6, 3, 1, 0],
+    [6, 3, 0, 1]
+])
+
+
+gen_figure('inverse_mul',
+f'''
+    \\psi = C^{{-1}}\\psi'C =
+    {((inv @ psi) @ C).to_tex()}
+'''
+)