⚠️ This text may contain translation errors. You can read the Spanish version here: README-es.md

algex 📐

Flutter application that approximates e^x using the Taylor series method, with configurable convergence settings, error analysis, and four real-time convergence charts.

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🚀 Overview

algex implements the Taylor series expansion of e^x from scratch — no external math libraries — with full control over the convergence criterion, tolerance, and precision. The calculation engine is pure Dart, completely decoupled from Flutter, and covered by unit tests.

Includes:

• Taylor series calculator with two convergence modes
• Per-iteration error analysis (absolute, relative, approximate, percent)
• Significant figures tracking per iteration
• Four convergence charts rendered with fl_chart
• Persistent settings via SharedPreferences
• Responsive layout with breakpoints for compact and wide screens

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🎥 Demo

Mobile view	Desktop view

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✨ Visible features

• Enter any real value of x and compute e^x via Taylor series
• Switch between absolute error convergence (compares against real e^x) and approximate error (compares consecutive iterations)
• Configure tolerance value and maximum iterations
• View per-iteration breakdown: partial sum, term value, all error types, significant figures
• Toggle between iterations table and charts with animated slide indicator
• Show or hide the real e^x value alongside the approximation
• Configure decimal precision (2–12 digits) for all displayed values
• Settings persist across sessions

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🧠 Technical highlights

• Pure Dart calculator

  • ExpCalculator has zero Flutter dependencies — pure logic
  • Covered by unit tests in test/exp_calculator_test.dart
  • Handles NaN/Infinity correctly for all error types in both convergence modes

• State management without external libraries

  • InheritedNotifier<SettingsNotifier> propagates settings through the widget tree
  • No Riverpod, no Bloc, no Provider — only Flutter core APIs
  • SettingsScope.of(context) for clean access at any depth

• Persistence

  • Settings loaded asynchronously on startup via SharedPreferences
  • Writes parallelized with Future.wait — no sequential disk I/O
  • copyWith pattern keeps defaults in a single place in Settings

• Responsive UI

  • LayoutBuilder breakpoints at 400px (input), 600px (cards and metrics)
  • ModeToggle collapses to icon-only below 150px per item
  • All layouts tested at both compact and wide widths

• Charts

  • Four charts sharing a single ChartCard base widget
  • Shared helpers: chartAutoInterval, chartXInterval, chartValidSpots, chartTitles, chartBorder, chartGrid
  • X-axis interval auto-calculated from available width to prevent label overlap
  • ChartUnavailable fallback for modes where data is not computable

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🎯 What this project demonstrates

• State management with InheritedWidget + ChangeNotifier without third-party packages
• Clean separation between pure Dart logic (core/) and Flutter UI (ui/)
• Unit testing of mathematical logic with edge case coverage
• Responsive layout design with LayoutBuilder and breakpoints
• Async persistence with SharedPreferences using parallelized writes
• Custom animated widgets: AnimatedContainer, AnimatedAlign, TweenAnimationBuilder
• Sliver-based scrolling architecture (CustomScrollView, SliverList, SliverAppBar)

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🏗 Architecture

The project separates pure logic from UI into two independent layers (ui + core).

lib/
├── core/                        # Pure Dart — no Flutter dependency
│   ├── model/
│   │   ├── calculation_result.dart   # Output of a calculation run
│   │   ├── iteration_data.dart       # Data for a single iteration
│   │   └── settings.dart             # App settings + ToleranceType enum
│   └── service/
│       └── exp_calculator.dart       # Taylor series engine
│
└── ui/                          # Flutter layer
    ├── pages/
    │   ├── home_page.dart            # Main screen
    │   └── settings_page.dart        # Settings screen
    ├── state/
    │   └── settings_notifier.dart    # InheritedNotifier + ChangeNotifier
    └── widgets/
        ├── adjust/                   # Settings UI components
        │   ├── adjust_convergence.dart
        │   ├── adjust_visualization.dart
        │   ├── adjust_section_header.dart
        │   ├── adjust_textfield.dart
        │   └── chip_option.dart
        ├── charts/                   # Chart components
        │   ├── chart_card.dart       # Base card + shared helpers
        │   ├── convergence_chart.dart
        │   ├── error_chart.dart
        │   ├── significant_figures_chart.dart
        │   └── term_decay_chart.dart
        ├── base_card.dart
        ├── input_sliver.dart
        ├── iterations_view.dart
        ├── mode_toggle.dart
        ├── result_summary_card.dart
        └── algex_sliver_appbar.dart

➡️ See full technical documentation: technical.md

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⚙️ Quick start

Requirements

• Flutter SDK >=3.3.4
• Android or iOS device / emulator

Clone and run

git clone https://github.com/tristecsv/algex.git
cd algex

flutter pub get
dart run flutter_launcher_icons
flutter run

Run tests

flutter test