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Implementation of Jacobi Method to Solve a System of Linear Equations in Python

Dr Pankaj Dumka
Dr Pankaj Dumka
Updated on 27-Mar-2026 3K+ Views

The Jacobi Method is an iterative algorithm for solving systems of linear equations. It starts with initial guesses and repeatedly refines them until convergence is achieved. Mathematical Foundation Consider a system of linear equations: a₁₁x₁ + a₁₂x₂ + ... + a₁ₙxₙ = b₁ a₂₁x₁ + a₂₂x₂ + ... + a₂ₙxₙ = b₂ ... aₙ₁x₁ + aₙ₂x₂ + ... + aₙₙxₙ = bₙ The Jacobi method rearranges each equation to isolate one variable. For the i-th equation: xi = (bi - Σ(aijxj)) / aii The Jacobi Algorithm The algorithm follows these steps: ...

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How to Concatenate Column Values in a Pandas DataFrame?

Mukul Latiyan
Mukul Latiyan
Updated on 27-Mar-2026 8K+ Views

Pandas is a powerful library for data manipulation and analysis in Python. Concatenating column values involves combining the values of two or more columns into a single column, which is useful for creating new variables, merging data from different sources, or formatting data for analysis. There are several methods to concatenate column values in a Pandas DataFrame. In this tutorial, we'll explore two common approaches: using the str.cat() method and using string concatenation with operators. Using the str.cat() Method The str.cat() method is designed specifically for concatenating string values in pandas Series. It provides clean syntax and ...

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How to Collapse Multiple Columns in Python Pandas?

Mukul Latiyan
Mukul Latiyan
Updated on 27-Mar-2026 3K+ Views

Pandas is a popular data manipulation library in Python that is widely used for working with structured data. One common task when working with data is to clean and transform it in order to prepare it for analysis. Sometimes, the data might contain multiple columns that have similar information or are related to each other. In such cases, it might be useful to collapse these columns into a single column for easier analysis or visualization. Pandas provides several methods to collapse multiple columns into a single column. In this tutorial, we will explore the two most common methods: ...

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Circle of Squares using Python Turtle

Mukul Latiyan
Mukul Latiyan
Updated on 27-Mar-2026 3K+ Views

The Circle of Squares is a fascinating geometric pattern that can be created using Python's turtle graphics library. This pattern consists of a circle of squares that are evenly spaced around its circumference, with each square rotated at an angle relative to the previous square. This creates a mesmerizing visual effect that can be customized to suit any color scheme or size. In this tutorial, we will explore how to create the Circle of Squares pattern using Python's turtle library, step by step. We will also discuss different customization options that can be applied to create unique variations of ...

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Python | Measure similarity between two sentences using cosine similarity

Mithilesh Pradhan
Mithilesh Pradhan
Updated on 27-Mar-2026 2K+ Views

Natural Language Processing for finding the semantic similarity between sentences, words, or text is very common in modern use cases. Cosine similarity is a popular method that measures the cosine of the angle between two non-zero vectors using dot product formula notation. Through this article let us briefly explore cosine similarity and see its implementation using Python. What is Cosine Similarity? Cosine similarity is defined as the cosine of the angle between two vectors in space. A sentence or text can be represented as a vector based on word frequencies. The similarity between two sentences depends upon ...

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Draw an Arc Using Arcade in Python

Utkarsha Nathani
Utkarsha Nathani
Updated on 27-Mar-2026 432 Views

Python's Arcade library is a powerful 2D graphics framework for creating games and visual applications. In this article, we'll learn how to draw arcs using two different methods − filled arcs and outlined arcs. What is Arcade Library? Arcade is a modern Python library built on top of Pyglet that provides simple tools for creating 2D games and graphics. It offers cross−platform compatibility and includes features like sprites, shapes, and animation support. Installing Arcade First, install the Arcade library using pip ? pip install arcade Method 1: Using draw_arc_filled() This method ...

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Draw a Tree Using Arcade Library in Python

Utkarsha Nathani
Utkarsha Nathani
Updated on 27-Mar-2026 473 Views

Python's Arcade library is a modern graphics library designed for creating 2D games and graphical applications. In this tutorial, we'll learn how to draw a simple tree using Arcade's drawing functions. What is Arcade Library? Arcade is a Python library built on top of Pyglet that provides a simple interface for creating graphics and games. It offers modern features and cleaner syntax compared to older graphics libraries like Pygame. Key features of Arcade include: Shape drawing functions − draw_circle_filled(), draw_rectangle_filled(), draw_polygon_filled() Sprite support − Sprite and SpriteList classes for animations Physics engines − PhysicsEngine for ...

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Draw a Tic Tac Toe Board Using Python – Turtle

Utkarsha Nathani
Utkarsha Nathani
Updated on 27-Mar-2026 2K+ Views

Python's Turtle library provides an excellent way to create graphics using a virtual turtle that moves around the screen. In this article, we'll learn how to draw a tic-tac-toe board using simple turtle commands. What is Tic Tac Toe Board? Tic-tac-toe is a classic game played on a 3×3 grid board with 9 squares. Players take turns placing X and O marks, trying to get three of their marks in a row horizontally, vertically, or diagonally. ...

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Draw a Sun Using Arcade Library Python

Utkarsha Nathani
Utkarsha Nathani
Updated on 27-Mar-2026 768 Views

Python's Arcade library is a powerful graphics library built on Pyglet that enables creating 2D games and visual applications. In this article, we'll learn how to draw a sun using different methods with the Arcade library. Installing Arcade Library First, install the Arcade library using pip − pip install arcade Method 1: Simple Circle Sun This method creates a basic sun using a filled circle − import arcade # Window dimensions SCREEN_WIDTH = 500 SCREEN_HEIGHT = 500 def draw_sun(): # Draw a filled circle for ...

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Django Shortcuts – get_list_or_404()

Utkarsha Nathani
Utkarsha Nathani
Updated on 27-Mar-2026 660 Views

Django is a popular web framework written in Python that helps web developers create web applications efficiently. One of the most important features of Django is the built-in functions known as shortcuts. These shortcuts provide useful features for completing tasks. In this article, we will learn about one of the commonly used shortcuts in Django: get_list_or_404(). What is Django Shortcut Module? The Django shortcuts module is a collection of useful functions for operations such as rendering templates, handling errors, and more. Some commonly used shortcut functions include render(), get_object_or_404(), get_list_or_404(), and redirect(). By using the shortcut module, you ...

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