Merge pull request #1 from kolosovpetro/updates

Updates## [1.0.0] - 2025-02-21

### Changed

- Configure workspace
- Recompile document
- Update CI/CD
- Initial version of manuscript
- Update readme

Author: kolosovpetro

.github/workflows/build-and-deploy-pdf.yml

@@ -15,12 +15,12 @@ jobs:
     uses: kolosovpetro/github-latex-template/.github/workflows/build-and-deploy-pdf-template.yml@main
     secrets: inherit
     with:
-      file_name: 'GithubLatexTemplate'
+      file_name: 'AnEfficientMethodOfSplineApproximation'
       runs_on: 'ubuntu-latest'
       workflow_name: 'Build and Deploy PDF'
       build_assets_path: |
-        src/GithubLatexTemplate.tex
-        src/GithubLatexTemplate.bbl
-        src/GithubLatexTemplate.bib
+        src/AnEfficientMethodOfSplineApproximation.tex
+        src/AnEfficientMethodOfSplineApproximation.bbl
+        src/AnEfficientMethodOfSplineApproximation.bib
         src/sections
       working_directory_for_latex: 'src'

.github/workflows/build-pdf.yml

@@ -20,12 +20,12 @@ jobs:
   build-pdf:
     uses: kolosovpetro/github-latex-template/.github/workflows/build-pdf-template.yml@main
     with:
-      file_name: 'GithubLatexTemplate'
+      file_name: 'AnEfficientMethodOfSplineApproximation'
       runs_on: 'ubuntu-latest'
       workflow_name: 'Build PDF'
       build_assets_path: |
-        src/GithubLatexTemplate.tex
-        src/GithubLatexTemplate.bbl
-        src/GithubLatexTemplate.bib
+        src/AnEfficientMethodOfSplineApproximation.tex
+        src/AnEfficientMethodOfSplineApproximation.bbl
+        src/AnEfficientMethodOfSplineApproximation.bib
         src/sections
       working_directory_for_latex: 'src'

CHANGELOG.md

@@ -5,53 +5,12 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning v2.0.0](https://semver.org/spec/v2.0.0.html).
 
-## [1.3.1] - 2025-01-15
+## [1.0.0] - 2025-02-21
 
 ### Changed
 
-- Update initializer script
-- Move images folder
-- Add figures folder
-- Add default keywords
-- Update README
-- Update bibliography
-
-
-## [1.3.0] - 2024-10-06
-
-### Changed
-
-- Implement powershell build script that can be run from any location
-- Implement powershell build script that searches for latex file in its PSRoot folder
-- Implement powershell script that renames main latex and bibtex files to match repo root directory name
-- Update README with new build instructions
-
-## [1.2.0] - 2024-09-25
-
-### Changed
-
-- Implement latex build template (GitHub Actions)
-- Implement latex deploy template (GitHub Actions)
-
-## [1.1.9] - 2024-07-03
-
-### Changed
-
-- Hotfix update GitHub Actions GitVersion
-
-## [1.1.8] - 2024-07-03
-
-### Changed
-
-- Changelog added
-- README updated
-- Theorem environments update
-- Footnote added
-- Bump GitHub Actions version
-- Hotfix update GitHub Actions GitVersion
-
-## [1.1.7] - 2024-01-31
-
-### Changed
-
-- Initial release before change log introduced.
+- Configure workspace
+- Recompile document
+- Update CI/CD
+- Initial version of manuscript
+- Update readme

README.md

@@ -1,71 +1,15 @@
-# GitHub LaTeX Template
+# An efficient method of spline approximation for power function
 
-[![Build PDF](https://github.com/kolosovpetro/github-latex-template/actions/workflows/build-pdf.yml/badge.svg)](https://github.com/kolosovpetro/github-latex-template/actions/workflows/build.yml/badge.svg)
-[![Build and Deploy PDF](https://github.com/kolosovpetro/github-latex-template/actions/workflows/build-and-deploy-pdf.yml/badge.svg)](https://github.com/kolosovpetro/github-latex-template/actions/workflows/build-and-deploy.yml/badge.svg)
+Let $P(m, X, N)$ be an $m$-degree polynomials in $X\in\mathbb{R}$
+having fixed non-negative integers $m$ and $N$.
+Essentially, the polynomial $P(m, X, N)$ is a result of rearrangement inside Faulhaber's formula
+in context of Knuth's work Johann Faulhaber and sums of powers.
 
-LaTeX template for GitHub including general CI/CD actions and Mathematica templates.
+In this manuscript we discuss approximation properties of polynomial $P(m,X,N)$.
+In particular, the polynomial $P(m,X,N)$ approximates odd power function $X^{2m+1}$ in certain neighborhood
+of fixed non-negative integer $N$ with percentage error lesser than $1\%$.
 
-- https://dev.azure.com/PetroKolosovProjects/github-latex-template
+By increasing the value of $N$ the length of convergence interval with odd-power $X^{2m+1}$ increasing as well.
 
-## GitHub Actions used
-
-- https://github.com/actions/checkout
-- https://github.com/GitTools/actions/blob/main/docs/examples/github/gitversion/index.md
-- https://github.com/xu-cheng/latex-action
-- https://github.com/actions/upload-artifact
-
-## Build and run using PowerShell (Windows)
-
-- Install `MikTeX`: https://miktex.org/download
-- Update `MikTeX`
-- Install `SumatraPDF` viewer: https://www.sumatrapdfreader.org/download-free-pdf-viewer
-- `Rename-Tex-Files.ps1` renames main LaTeX and BibTeX files to match the repository root directory name
-- `Build-Latex.ps1`
-
-## Build and run in Intellij IDEA (Windows)
-
-- Install `MikTeX`: https://miktex.org/download
-- Update `MikTeX`
-- Install `SumatraPDF` viewer: https://www.sumatrapdfreader.org/download-free-pdf-viewer
-- Path to SumatraPDF: `C:\Program Files\SumatraPDF`
-- Install `Intellij IDEA Ultimate`: https://www.jetbrains.com/idea/download/#section=windows
-- Activate `Intellij IDEA Ultimate`
-- Install `TeXiFy IDEA` plugin: https://plugins.jetbrains.com/plugin/9473-texify-idea
-- Clone this repository locally: `https://github.com/kolosovpetro/github-latex-template.git`
-- Open `github-latex-template` folder in `Intellij IDEA Ultimate` and configure as follows
-    - LaTeX Configuration
-      ![LaTeX Configuration](./src/sections/images/latex_configuration.png "LaTeX Configuration")
-    - BibTeX Configuration
-      ![BibTeX Configuration](./src/sections/images/bibtex_configuration.png "BibTeX Configuration")
-- Configure Inverse Search in `Intellij IDEA` for SumatraPDF: `Tools -> LaTeX -> Configure Inverse Search`
-- Compile document using `Shift + F10`
-
-## How to use Mathematica package
-
-- Open the package file `GithubLatexTemplateMathematicaPackage.m` in Wolfram Mathematica, I use version 13.0
-- Execute the package using `Shift+Enter`
-- Open the notebook file `GithubLatexTemplateMathematicaNotebook.nb`
-- Execute the line: `Needs["GithubLatexTemplateMathematicaPackage"]`
-- Continue your work as desired
-
-## Configure CI / CD
-
-- Update root file name in `build-pdf.yml` and `build-and-deploy-pdf.yml`
-- Set repository secrets
-    - `GH_ACCESS_TOKEN`: Generate GitHub Personal access token at
-      `Settings -> Developer Settings -> Personal access tokens -> Generate mew token`
-
-## Actions and their trigger policy
-
-- `build-pdf.yml` builds project using `TeXLive`. Triggered on `pull_request`, `push` to `develop` branch
-- `build-and-deploy-pdf.yml` builds project using `TeXLive` and deploys to `GitHub Pages`. Triggered on `push` to `main`
-  branch
-
-## Template example
-
-Compiled document looks like as follows
-
-<p align="center">
-  <img src="src/sections/images/template_example.png" alt="template_example"/>
-  <img src="src/sections/images/template_example2.png" alt="template_example"/>
-</p>
+Furthermore, this approximation technique is generalized for arbitrary non-negative exponent power function $X^j$
+by using splines.