From 1577ed77ed1b50420c8e417a1e3df832aca77946 Mon Sep 17 00:00:00 2001
From: helldh <danya3utckin@yandex.ru>
Date: Sat, 17 Jan 2026 00:16:14 +0300
Subject: [PATCH] Gauss implementation

---
 .gitignore                                    |   1 +
 .idea/.gitignore                              |   3 +
 .../inspectionProfiles/profiles_settings.xml  |   6 ++
 .idea/mathing.iml                             |  10 ++++
 .idea/misc.xml                                |   7 +++
 .idea/modules.xml                             |   8 +++
 __pycache__/algo.cpython-313.pyc              | Bin 0 -> 3150 bytes
 __pycache__/tests.cpython-313.pyc             | Bin 0 -> 2564 bytes
 algo.py                                       |  56 ++++++++++++++++++
 tests.py                                      |  45 ++++++++++++++
 10 files changed, 136 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 .idea/.gitignore
 create mode 100644 .idea/inspectionProfiles/profiles_settings.xml
 create mode 100644 .idea/mathing.iml
 create mode 100644 .idea/misc.xml
 create mode 100644 .idea/modules.xml
 create mode 100644 __pycache__/algo.cpython-313.pyc
 create mode 100644 __pycache__/tests.cpython-313.pyc
 create mode 100644 algo.py
 create mode 100644 tests.py

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..1d17dae
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+.venv
diff --git a/.idea/.gitignore b/.idea/.gitignore
new file mode 100644
index 0000000..26d3352
--- /dev/null
+++ b/.idea/.gitignore
@@ -0,0 +1,3 @@
+# Default ignored files
+/shelf/
+/workspace.xml
diff --git a/.idea/inspectionProfiles/profiles_settings.xml b/.idea/inspectionProfiles/profiles_settings.xml
new file mode 100644
index 0000000..105ce2d
--- /dev/null
+++ b/.idea/inspectionProfiles/profiles_settings.xml
@@ -0,0 +1,6 @@
+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>
\ No newline at end of file
diff --git a/.idea/mathing.iml b/.idea/mathing.iml
new file mode 100644
index 0000000..b918ff6
--- /dev/null
+++ b/.idea/mathing.iml
@@ -0,0 +1,10 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$">
+      <excludeFolder url="file://$MODULE_DIR$/.venv" />
+    </content>
+    <orderEntry type="jdk" jdkName="Python 3.13 (mathing)" jdkType="Python SDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>
\ No newline at end of file
diff --git a/.idea/misc.xml b/.idea/misc.xml
new file mode 100644
index 0000000..dcca035
--- /dev/null
+++ b/.idea/misc.xml
@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Black">
+    <option name="sdkName" value="Python 3.13 (mathing)" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.13 (mathing)" project-jdk-type="Python SDK" />
+</project>
\ No newline at end of file
diff --git a/.idea/modules.xml b/.idea/modules.xml
new file mode 100644
index 0000000..e1b379b
--- /dev/null
+++ b/.idea/modules.xml
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/mathing.iml" filepath="$PROJECT_DIR$/.idea/mathing.iml" />
+    </modules>
+  </component>
+</project>
\ No newline at end of file
diff --git a/__pycache__/algo.cpython-313.pyc b/__pycache__/algo.cpython-313.pyc
new file mode 100644
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diff --git a/algo.py b/algo.py
new file mode 100644
index 0000000..fffd685
--- /dev/null
+++ b/algo.py
@@ -0,0 +1,56 @@
+from typing import List
+
+def gauss_method(coefficients: List[List[float]],
+                 free_members: List[float]) -> List[float]:
+    """
+    Реализация метода Гаусса для квадратной системы уравнений Ax = b.
+
+    Алгоритм:
+    1. Формируем расширенную матрицу [A|b].
+    2. Для каждого столбца:
+       - Ищем pivot: первый ненулевой элемент в текущем столбце от текущей строки вниз.
+       - Если pivot ≠ текущая строка, меняем строки местами.
+    3. Обнуляем все элементы под pivot:
+       - Для каждой строки ниже: factor = current / pivot
+       - Текущая строка -= factor * строка с pivot
+    4. После приведения к ступенчатой форме выполняем обратную подстановку:
+       - Проходим снизу вверх
+       - Для каждой переменной: x[i] = (свободный член - сумма(коэффициентов[i][j] * x[j] для j>i)) / pivot
+    5. Возвращаем список решений x.
+
+    Входные данные:
+    - coefficients: квадратная матрица коэффициентов A
+    - free_members: вектор свободных членов b
+
+    Выход:
+    - Список решений x
+    """
+    n = len(coefficients)
+    for i in range(n):
+        coefficients[i].append(free_members[i])
+
+    for i in range(n):
+        pivot_row = None
+        for r in range(i, n):
+            if coefficients[r][i] != 0:
+                pivot_row = r
+                break
+        if pivot_row is None:
+            raise ValueError("Система несовместна или вырождена")
+
+        if pivot_row != i:
+            coefficients[i], coefficients[pivot_row] = coefficients[pivot_row], coefficients[i]
+
+        pivot = coefficients[i][i]
+
+        for r in range(i + 1, n):
+            factor = coefficients[r][i] / pivot
+            for c in range(i, n + 1):
+                coefficients[r][c] -= factor * coefficients[i][c]
+
+    x = [0] * n
+    for i in range(n - 1, -1, -1):
+        sum_ax = sum(coefficients[i][j] * x[j] for j in range(i + 1, n))
+        x[i] = (coefficients[i][n] - sum_ax) / coefficients[i][i]
+
+    return x
diff --git a/tests.py b/tests.py
new file mode 100644
index 0000000..bd1a125
--- /dev/null
+++ b/tests.py
@@ -0,0 +1,45 @@
+import unittest
+from algo import gauss_method
+
+class TestGaussMethod(unittest.TestCase):
+    def test_2x2_unique_solution(self):
+        """Простейшая 2x2 система с уникальным решением"""
+        coef = [[1, 1],
+                [2, 3]]
+        free_mem = [5, 11]
+        result = gauss_method(coef, free_mem)
+        expected = [4.0, 1.0]
+        for r, e in zip(result, expected):
+            self.assertAlmostEqual(r, e, places=7)
+
+    def test_2x2_another(self):
+        """Ещё одна 2x2 система"""
+        coef = [[2, 1],
+                [4, 3]]
+        free_mem = [5, 11]
+        result = gauss_method(coef, free_mem)
+        expected = [2.0, 1.0]
+        for r, e in zip(result, expected):
+            self.assertAlmostEqual(r, e, places=7)
+
+    def test_3x3_unique_solution(self):
+        """3x3 система с уникальным решением"""
+        coef = [[1, 1, 1],
+                [2, 3, 1],
+                [1, 2, 3]]
+        free_mem = [6, 11, 14]
+        result = gauss_method(coef, free_mem)
+        expected = [1.0, 2.0, 3.0]
+        for r, e in zip(result, expected):
+            self.assertAlmostEqual(r, e, places=7)
+
+    def test_degenerate_system(self):
+        """Вырожденная система должна выбросить исключение"""
+        coef = [[1, 1],
+                [2, 2]]
+        free_mem = [2, 4]
+        with self.assertRaises(ValueError):
+            gauss_method(coef, free_mem)
+
+if __name__ == "__main__":
+    unittest.main()
\ No newline at end of file