Other tasksHEADmaster

4 files changed, 128 insertions, 0 deletions

diff --git a/4/libsolve2.py b/4/libsolve2.py
index d723ba3..c4c9106 100644
--- a/4/libsolve2.py
+++ b/4/libsolve2.py
@@ -3,6 +3,7 @@ from typing import Iterable, Union
 from fractions import Fraction
 from itertools import zip_longest
 
+POLY_COLOR = '95'
 
 def is_scalar(obj):
     return isinstance(obj, (Fraction, int))
@@ -295,5 +296,12 @@ class Matrix:
                     break
         return copy
 
+    @property
+    def T(self):
+        return Matrix([
+            [row[i] for row in self.rows]
+            for i in range(self.shape[1])
+        ])
+
 
 x = Poly([0, 1])
diff --git a/4/render.py b/4/render.py
new file mode 100644
index 0000000..9285c72
--- /dev/null
+++ b/4/render.py
@@ -0,0 +1,45 @@
+from libsolve2 import Poly, PolyRenderBase
+
+
+class UnicodeRender(PolyRenderBase):
+    def __init__(self):
+        # may not work. see
+        # https://en.wikipedia.org/wiki/Unicode_subscripts_and_superscripts
+        # to test with your font
+        self.sup = '⁰¹²³⁴⁵⁶⁷⁸⁹'  # must be <sup>0123456789</sup>
+
+    def render(self, poly: Poly) -> str:
+        rev = list(reversed(poly.vec))
+        if all(r == 0 for r in rev):
+            return '0'
+        d = poly.deg()
+        res = []
+        for i in range(len(rev)):
+            if rev[i] == 0:
+                continue
+            if i == 0:
+                if rev[i] < 0:
+                    res.append('-')
+            else:
+                if rev[i] < 0:
+                    res.append(' - ')
+                else:
+                    res.append(' + ')
+
+            if abs(rev[i]) != 1 or i == d:
+                res.append(str(abs(rev[i])))
+            if i != d:
+                res.append(poly.letter)
+            if d - i != 1:
+                res.append(self._int2sup(d - i))
+        return ''.join(res)
+
+    def hint(self, poly: Poly) -> int:
+        return len(self.render(poly))
+
+    def _int2sup(self, n):
+        res = []
+        while n > 0:
+            res.append(self.sup[n % 10])
+            n //= 10
+        return ''.join(reversed(res))
diff --git a/4/two.py b/4/two.py
new file mode 100644
index 0000000..1302f6e
--- /dev/null
+++ b/4/two.py
@@ -0,0 +1,28 @@
+from libsolve2 import *
+from fractions import Fraction
+
+def f_eye(dim):
+    return Matrix([
+        [0 if i != j else 1 for i in range(dim)]
+        for j in range(dim)
+    ])
+
+m = Matrix([
+    [ 4,  -3,  -2,   0,   0,  0],
+    [ 0,   2,  -1,   0,   0,  0],
+    [ 0,   2,   5,   0,   0,  0],
+    [ 1,   1,   1,   2,  -1,  0],
+    [-2,  -3,  -3,   4,   6,  0],
+    [ 1,   8,   7,  -5,  -3,  3]
+])
+
+print('char polynomial is  ', (m - f_eye(6) * x).det())
+print('(x - 3)^2(x - 4)^4 =', (x - 3)*(x - 3)*(x - 4)*(x - 4)*(x - 4)*(x - 4))
+
+root1 = m - f_eye(6) * 3
+print(f'rank of m - 3E = {root1.rank()} => one cell of size 2')
+
+root2 = m - f_eye(6) * 4
+print(f'rank of m - 4E = {root2.rank()} => two cells')
+print(f'rank of (m - 4E)^2 = {(root2@root2).rank()} => two cells of size 2')
+
diff --git a/4/two_basis.py b/4/two_basis.py
new file mode 100644
index 0000000..d1d71a2
--- /dev/null
+++ b/4/two_basis.py
@@ -0,0 +1,47 @@
+from libsolve2 import *
+from fractions import Fraction as F
+
+def f_eye(dim):
+    return Matrix([
+        [0 if i != j else 1 for i in range(dim)]
+        for j in range(dim)
+    ])
+
+eye = f_eye(6)
+
+m = Matrix([
+    [ 4,  -3,  -2,   0,   0,  0],
+    [ 0,   2,  -1,   0,   0,  0],
+    [ 0,   2,   5,   0,   0,  0],
+    [ 1,   1,   1,   2,  -1,  0],
+    [-2,  -3,  -3,   4,   6,  0],
+    [ 1,   8,   7,  -5,  -3,  3]
+])
+
+for_root1 = m - eye * 3
+
+print('(m - 3E)^2 =')
+print((for_root1@for_root1).triangled(swap=True))
+print()
+print()
+
+for_root2 = m - eye * 4
+
+print('(m - 4E)^2 =')
+print((for_root2@for_root2).triangled(swap=True))
+
+def make_vec(iter):
+    return Matrix([[i] for i in iter])
+
+print()
+print('Проверим, лежит ли кто-нибудь из ФСР в ядре:')
+print(((for_root2) @ make_vec([0, -F(1, 3), F(2, 3), 0, 0, 1])).T)
+print(((for_root2) @ make_vec([0, -F(2, 3), F(4, 3), 0, 1, 0])).T)
+print(((for_root2) @ make_vec([0, -1, 2, 1, 0, 0])).T)
+print(((for_root2) @ make_vec([1, 0, 0, 0, 0, 0])).T)
+
+print('кажется, ни один вектор не лежит в ядре.')
+print()
+print('а вот эти уже лежат в ядре')
+print((for_root2 @ make_vec([0, -1, 2, 1, 0, 0])).T)
+print((for_root2 @ make_vec([1, 0, 0, 0, 0, 0])).T)