ParuhParhat · ParuhParhat · Aug 6, 2026 · Aug 6, 2026
diff --git a/README.md b/README.md
@@ -1,110 +1,97 @@
-# MaxMath（高代计算器 / Higher Algebra Calculator）
+# MaxMath (Higher Algebra Calculator)
 
 [![CI](https://github.com/yueye6811/MaxMath/actions/workflows/ci.yml/badge.svg)](https://github.com/yueye6811/MaxMath/actions/workflows/ci.yml)
 [![Release](https://img.shields.io/github/v/release/yueye6811/MaxMath?label=release)](https://github.com/yueye6811/MaxMath/releases/latest)
 [![License: MIT](https://img.shields.io/badge/license-MIT-blue.svg)](LICENSE)
 
-[下载 MaxMath 1.0.0 APK / Download MaxMath 1.0.0 APK](https://github.com/yueye6811/MaxMath/releases/download/v1.0.0/MaxMath-v1.0.0-arm64-v8a.apk)
-· [发布说明 / Release notes](https://github.com/yueye6811/MaxMath/releases/tag/v1.0.0)
+<p align="center">
+  <strong>English</strong> |
+  <a href="README.zh-CN.md"><strong>简体中文</strong></a>
+</p>
 
-基于 GNU Maxima 的离线 Android 高等代数计算与交互式绘图应用。界面使用
-Kotlin 与 Jetpack Compose，数学输入由纯 Kotlin 解析器处理，复杂符号计算在独立
-引擎进程中执行。
+[Download MaxMath 1.0.0 APK](https://github.com/yueye6811/MaxMath/releases/download/v1.0.0/MaxMath-v1.0.0-arm64-v8a.apk)
+· [Release notes](https://github.com/yueye6811/MaxMath/releases/tag/v1.0.0)
 
 MaxMath is an offline Android app for higher-algebra computation and interactive
 plotting, powered by GNU Maxima. Its interface is built with Kotlin and Jetpack
 Compose, mathematical input is handled by a pure Kotlin parser, and complex
 symbolic computations run in a separate engine process.
 
-> **中文：** 当前版本 1.0.0；最低系统 Android 8.0（API 26）；原生计算引擎目前仅提供
-> `arm64-v8a` 构建流程。
->
-> **English:** Current release: 1.0.0. Minimum supported version: Android 8.0
-> (API 26). The native computation engine currently provides an `arm64-v8a`
-> build workflow only.
-
-## 功能 / Features
-
-- **矩阵 / Matrices：** 行列式、逆、转置、秩、迹、特征值与特征向量 / determinant, inverse, transpose, rank, trace, eigenvalues, and eigenvectors
-- **方程组 / Systems of equations：** 支持 `x+y=1; 2x-y=3` 一类自然写法，也支持原始 Maxima 输入 / natural syntax such as `x+y=1; 2x-y=3`, plus raw Maxima input
-- **多项式 / Polynomials：** 因式分解、最大公因式、求根、展开与化简 / factorization, greatest common divisor, root finding, expansion, and simplification
-- **向量空间 / Vector spaces：** 内积、范数、Gram-Schmidt 正交化 / inner product, norm, and Gram-Schmidt orthogonalization
-- **二次型 / Quadratic forms：** 展开、特征值与符号差 / expansion, eigenvalues, and signature
-- **微积分 / Calculus：** 极限、任意阶导数、定积分与不定积分 / limits, derivatives of arbitrary order, and definite or indefinite integrals
-- **绘图 / Plotting：** 支持触控交互的 2D 多函数图像、3D 曲面和等高线 / touch-enabled 2D multi-function plots, 3D surfaces, and contour plots
-- **输入 / Input：** 隐式乘法、根号、分数、常用函数、π/e 与自然写法方程组 / implicit multiplication, radicals, fractions, common functions, π/e, and natural equation syntax
-- **输出 / Output：** 离线 LaTeX 渲染、可复制文本，并可保存或分享 PNG / offline LaTeX rendering, copyable text, and PNG saving or sharing
-- **本地化 / Localization：** 中文、English、跟随系统 / Chinese, English, or the system language
-- **隐私 / Privacy：** 不申请网络权限，不包含账号、广告、分析或遥测 / no network permission, accounts, ads, analytics, or telemetry
-
-## 架构 / Architecture
-
-| 路径 / Path | 职责 / Responsibility |
-| --- | --- |
-| `parser/` | 词法分析、AST、表达式求值，以及 Maxima/NumPy 代码生成<br>Lexing, AST construction, expression evaluation, and Maxima/NumPy code generation |
-| `engine/` | 类型化计算任务、Maxima 脚本、JNI 子进程、独立进程服务和 2D 绘图<br>Typed computation tasks, Maxima scripts, JNI subprocesses, the isolated process service, and 2D plotting |
-| `app/` | Compose 页面、状态管理、LaTeX 输出及 OpenGL 3D/等高线交互<br>Compose screens, state management, LaTeX output, and interactive OpenGL 3D/contour rendering |
-| `native/` | ECL 与 Maxima 的 Android 交叉编译和运行时打包脚本<br>Android cross-compilation and runtime packaging scripts for ECL and Maxima |
-| `docs/` | 产品规格与实现约束<br>Product specifications and implementation constraints |
+> Current release: 1.0.0. Minimum supported version: Android 8.0 (API 26).
+> The native computation engine currently provides an `arm64-v8a` build
+> workflow only.
+
+## Features
+
+- Matrices: determinant, inverse, transpose, rank, trace, eigenvalues, and eigenvectors
+- Systems of equations: natural syntax such as `x+y=1; 2x-y=3`, plus raw Maxima input
+- Polynomials: factorization, greatest common divisor, root finding, expansion, and simplification
+- Vector spaces: inner product, norm, and Gram-Schmidt orthogonalization
+- Quadratic forms: expansion, eigenvalues, and signature
+- Calculus: limits, derivatives of arbitrary order, and definite or indefinite integrals
+- Plotting: touch-enabled 2D multi-function plots, 3D surfaces, and contour plots
+- Input: implicit multiplication, radicals, fractions, common functions, π/e, and natural equation syntax
+- Output: offline LaTeX rendering, copyable text, and PNG saving or sharing
+- Localization: Chinese, English, or the system language
+- Privacy: no network permission, accounts, ads, analytics, or telemetry
 
-轻量操作在 UI 进程执行；耗时操作通过 Android Messenger 转发到 `:engine` 独立
-进程。取消或超时会终止对应的 Maxima 子进程。2D 图像由 Maxima 辅助分析并交给
-Matplotlib 渲染；3D 曲面和等高线由同一表达式 AST 在本地采样并交给 OpenGL 绘制。
+## Architecture
+
+| Path | Responsibility |
+| --- | --- |
+| `parser/` | Lexing, AST construction, expression evaluation, and Maxima/NumPy code generation |
+| `engine/` | Typed computation tasks, Maxima scripts, JNI subprocesses, the isolated process service, and 2D plotting |
+| `app/` | Compose screens, state management, LaTeX output, and interactive OpenGL 3D/contour rendering |
+| `native/` | Android cross-compilation and runtime packaging scripts for ECL and Maxima |
+| `docs/` | Product specifications and implementation constraints |
 
 Lightweight operations run in the UI process. Long-running work is forwarded
 through Android Messenger to the isolated `:engine` process. Cancellation or a
 timeout terminates the corresponding Maxima subprocess. Maxima assists with 2D
 plot analysis before Matplotlib renders the image; 3D surfaces and contour plots
 are sampled locally from the same expression AST and rendered with OpenGL.
 
-## 获取源码 / Getting the Source
+## Getting the Source
 
 ~~~bash
 git clone https://github.com/yueye6811/MaxMath.git
 cd MaxMath
 ~~~
 
-### 环境要求 / Requirements
+### Requirements
 
 - JDK 17
-- Android Studio，或 / or Android SDK 36
-- Android NDK 27.2.12479018 与 / and CMake 3.22（编译 JNI 桥时需要 / required to compile the JNI bridge）
-- Python 3.10（Chaquopy 打包 Python 运行时依赖时需要 / required when Chaquopy packages Python runtime dependencies）
-
-SDK 的本机路径应放在未跟踪的 `local.properties` 中。仓库不包含任何签名密钥；
-发布签名配置请写入未跟踪的 `keystore.properties`。
+- Android Studio, or Android SDK 36
+- Android NDK 27.2.12479018 and CMake 3.22 (required to compile the JNI bridge)
+- Python 3.10 (required when Chaquopy packages Python runtime dependencies)
 
 Put the local SDK path in the untracked `local.properties` file. The repository
 does not contain signing keys; place release-signing configuration in the
 untracked `keystore.properties` file.
 
-### 运行测试 / Running Tests
+### Running Tests
 
 ~~~bash
 ./gradlew :parser:test
 ./gradlew -Pmaxmath.buildNative=false :engine:testDebugUnitTest :app:testDebugUnitTest
 ~~~
 
-Windows 下请使用 / On Windows, use:
+On Windows, use:
 
 ~~~cmd
 gradlew.bat :parser:test
 gradlew.bat -Pmaxmath.buildNative=false :engine:testDebugUnitTest :app:testDebugUnitTest
 ~~~
 
-### 构建 Android 应用 / Building the Android App
+### Building the Android App
 
 ~~~bash
 ./gradlew :app:assembleDebug
 ~~~
 
-输出位于 / The APK is written to `app/build/outputs/apk/debug/app-debug.apk`.
-
-## 原生 Maxima 引擎 / Native Maxima Engine
+The APK is written to `app/build/outputs/apk/debug/app-debug.apk`.
 
-Maxima/ECL 的下载目录、交叉编译产物和生成后的应用运行时文件体积较大，并受各自
-许可证约束，因此默认不纳入 Git。源码检出后可以先编译和安装 UI，但实际 Maxima
-计算需要先生成并打包原生引擎：
+## Native Maxima Engine
 
 The Maxima/ECL download directories, cross-compilation outputs, and generated
 application runtime are large and governed by their respective licenses, so they
@@ -122,46 +109,37 @@ cd ..
 ./gradlew :app:assembleDebug
 ~~~
 
-当前脚本以 Linux x86_64 主机和 NDK 的 `linux-x86_64` 工具链为目标。完整依赖、
-环境变量与故障说明见 [native/README.md](native/README.md)。
-
 The current scripts target a Linux x86_64 host and the NDK's `linux-x86_64`
 toolchain. See [native/README.md](native/README.md) for complete dependency,
 environment-variable, and troubleshooting information.
 
-生成但不提交的目录 / Generated directories that must not be committed:
+Generated directories that must not be committed include:
 
 - `.build/`
 - `app/src/main/assets/engine/`
 - `app/src/main/jniLibs/`
 
-## 项目文档 / Project Documentation
+## Project Documentation
 
-- [产品与实现规格 / Product and implementation specification](docs/SPEC.md)
-- [原生引擎构建 / Native engine build guide](native/README.md)
-- [发布说明 / Release notes](RELEASE_NOTES.md)
-- [贡献指南 / Contributing guide](CONTRIBUTING.md)
-- [安全策略 / Security policy](SECURITY.md)
-- [隐私说明 / Privacy notice](PRIVACY.md)
-- [第三方许可证说明 / Third-party license notices](THIRD_PARTY_NOTICES.md)
+- [Product and implementation specification](docs/SPEC.md)
+- [Native engine build guide](native/README.md)
+- [Release notes](RELEASE_NOTES.md)
+- [Contributing guide](CONTRIBUTING.md)
+- [Security policy](SECURITY.md)
+- [Privacy notice](PRIVACY.md)
+- [Third-party license notices](THIRD_PARTY_NOTICES.md)
 
-## 已知限制 / Known Limitations
+## Known Limitations
 
-- 原生计算引擎当前只面向 `arm64-v8a`；`x86_64` 构建脚本仍需进一步验证。 / The native computation engine currently targets `arm64-v8a` only; the `x86_64` build scripts still need further verification.
-- 新检出的源码仓库不含预编译 Maxima/ECL 运行时，必须按上文生成后才能执行完整计算。 / A fresh source checkout does not include a prebuilt Maxima/ECL runtime. Generate it as described above before running full computations.
-- 计算结果来自计算机代数与数值算法，不应被视为形式化证明。 / Results come from computer algebra and numerical algorithms and should not be treated as formal proofs.
+- The native computation engine currently targets `arm64-v8a` only; the `x86_64` build scripts still need further verification.
+- A fresh source checkout does not include a prebuilt Maxima/ECL runtime. Generate it as described above before running full computations.
+- Results come from computer algebra and numerical algorithms and should not be treated as formal proofs.
 
-## 许可证 / License
-
-MaxMath 贡献者原创、且没有独立许可证声明的源代码采用 [MIT License](LICENSE)。
+## License
 
 Source code contributed to MaxMath that is original to the project and does not
 carry a separate license notice is licensed under the [MIT License](LICENSE).
 
-构建会解析 GPL-2.0 的 `jlatexmath-android`，并可包含 GPL 的 GNU Maxima；ECL、
-Chaquopy、Matplotlib、NumPy 等组件也保留各自许可证。分发完整 APK 时必须履行
-这些第三方许可证的义务。详情见 [THIRD_PARTY_NOTICES.md](THIRD_PARTY_NOTICES.md)。
-
 The build resolves the GPL-2.0-licensed `jlatexmath-android` and may include the
 GPL-licensed GNU Maxima. ECL, Chaquopy, Matplotlib, NumPy, and other components
 also retain their respective licenses. Distribution of a complete APK must

diff --git a/README.zh-CN.md b/README.zh-CN.md
@@ -0,0 +1,137 @@
+# MaxMath（高代计算器）
+
+[![CI](https://github.com/yueye6811/MaxMath/actions/workflows/ci.yml/badge.svg)](https://github.com/yueye6811/MaxMath/actions/workflows/ci.yml)
+[![Release](https://img.shields.io/github/v/release/yueye6811/MaxMath?label=release)](https://github.com/yueye6811/MaxMath/releases/latest)
+[![License: MIT](https://img.shields.io/badge/license-MIT-blue.svg)](LICENSE)
+
+<p align="center">
+  <a href="README.md"><strong>English</strong></a> |
+  <strong>简体中文</strong>
+</p>
+
+[下载 MaxMath 1.0.0 APK](https://github.com/yueye6811/MaxMath/releases/download/v1.0.0/MaxMath-v1.0.0-arm64-v8a.apk)
+· [发布说明](https://github.com/yueye6811/MaxMath/releases/tag/v1.0.0)
+
+基于 GNU Maxima 的离线 Android 高等代数计算与交互式绘图应用。界面使用
+Kotlin 与 Jetpack Compose，数学输入由纯 Kotlin 解析器处理，复杂符号计算在独立
+引擎进程中执行。
+
+> 当前版本 1.0.0；最低系统 Android 8.0（API 26）；原生计算引擎目前仅提供
+> `arm64-v8a` 构建流程。
+
+## 功能
+
+- 矩阵：行列式、逆、转置、秩、迹、特征值与特征向量
+- 方程组：支持 `x+y=1; 2x-y=3` 一类自然写法，也支持原始 Maxima 输入
+- 多项式：因式分解、最大公因式、求根、展开与化简
+- 向量空间：内积、范数、Gram-Schmidt 正交化
+- 二次型：展开、特征值与符号差
+- 微积分：极限、任意阶导数、定积分与不定积分
+- 绘图：2D 多函数图像、3D 曲面和等高线，支持触控交互
+- 输入：隐式乘法、根号、分数、常用函数、π/e 与自然写法方程组
+- 输出：离线 LaTeX 渲染，可复制文本，并可保存或分享 PNG
+- 本地化：中文、English、跟随系统
+- 隐私：不申请网络权限，不包含账号、广告、分析或遥测
+
+## 架构
+
+| 路径 | 职责 |
+| --- | --- |
+| `parser/` | 词法分析、AST、表达式求值，以及 Maxima/NumPy 代码生成 |
+| `engine/` | 类型化计算任务、Maxima 脚本、JNI 子进程、独立进程服务和 2D 绘图 |
+| `app/` | Compose 页面、状态管理、LaTeX 输出及 OpenGL 3D/等高线交互 |
+| `native/` | ECL 与 Maxima 的 Android 交叉编译和运行时打包脚本 |
+| `docs/` | 产品规格与实现约束 |
+
+轻量操作在 UI 进程执行；耗时操作通过 Android Messenger 转发到 `:engine` 独立
+进程。取消或超时会终止对应的 Maxima 子进程。2D 图像由 Maxima 辅助分析并交给
+Matplotlib 渲染；3D 曲面和等高线由同一表达式 AST 在本地采样并交给 OpenGL 绘制。
+
+## 获取源码
+
+~~~bash
+git clone https://github.com/yueye6811/MaxMath.git
+cd MaxMath
+~~~
+
+### 环境要求
+
+- JDK 17
+- Android Studio，或 Android SDK 36
+- Android NDK 27.2.12479018 与 CMake 3.22（编译 JNI 桥时需要）
+- Python 3.10（Chaquopy 打包 Python 运行时依赖时需要）
+
+SDK 的本机路径应放在未跟踪的 `local.properties` 中。仓库不包含任何签名密钥；
+发布签名配置请写入未跟踪的 `keystore.properties`。
+
+### 运行测试
+
+~~~bash
+./gradlew :parser:test
+./gradlew -Pmaxmath.buildNative=false :engine:testDebugUnitTest :app:testDebugUnitTest
+~~~
+
+Windows 下请使用：
+
+~~~cmd
+gradlew.bat :parser:test
+gradlew.bat -Pmaxmath.buildNative=false :engine:testDebugUnitTest :app:testDebugUnitTest
+~~~
+
+### 构建 Android 应用
+
+~~~bash
+./gradlew :app:assembleDebug
+~~~
+
+输出位于 `app/build/outputs/apk/debug/app-debug.apk`。
+
+## 原生 Maxima 引擎
+
+Maxima/ECL 的下载目录、交叉编译产物和生成后的应用运行时文件体积较大，并受各自
+许可证约束，因此默认不纳入 Git。源码检出后可以先编译和安装 UI，但实际 Maxima
+计算需要先生成并打包原生引擎：
+
+~~~bash
+cd native
+./download-sources.sh
+./build-host-ecl.sh
+./build-ecl-android.sh arm64-v8a
+./build-maxima-android.sh arm64-v8a
+./package-engine.sh arm64-v8a
+cd ..
+./gradlew :app:assembleDebug
+~~~
+
+当前脚本以 Linux x86_64 主机和 NDK 的 `linux-x86_64` 工具链为目标。完整依赖、
+环境变量与故障说明见 [native/README.md](native/README.md)。
+
+生成但不提交的目录包括：
+
+- `.build/`
+- `app/src/main/assets/engine/`
+- `app/src/main/jniLibs/`
+
+## 项目文档
+
+- [产品与实现规格](docs/SPEC.md)
+- [原生引擎构建](native/README.md)
+- [发布说明](RELEASE_NOTES.md)
+- [贡献指南](CONTRIBUTING.md)
+- [安全策略](SECURITY.md)
+- [隐私说明](PRIVACY.md)
+- [第三方许可证说明](THIRD_PARTY_NOTICES.md)
+
+## 已知限制
+
+- 原生计算引擎当前只面向 `arm64-v8a`；`x86_64` 构建脚本仍需进一步验证。
+- 新检出的源码仓库不含预编译 Maxima/ECL 运行时，必须按上文生成后才能执行完整计算。
+- 计算结果来自计算机代数与数值算法，不应被视为形式化证明。
+
+## 许可证
+
+MaxMath 贡献者原创、且没有独立许可证声明的源代码采用 [MIT License](LICENSE)。
+
+构建会解析 GPL-2.0 的 `jlatexmath-android`，并可包含 GPL 的 GNU Maxima；ECL、
+Chaquopy、Matplotlib、NumPy 等组件也保留各自许可证。分发完整 APK 时必须履行
+这些第三方许可证的义务。详情见 [THIRD_PARTY_NOTICES.md](THIRD_PARTY_NOTICES.md)。