Warning: This is an experimental project.

SCAS (Smile Computer Algebra System)

SCAS is a lightweight, purely functional symbolic algebra library in Scala, originally forked from the open-source Smile CAS module. It has been restructured to work simply with scala-cli, allowing you to experiment with symbolic expressions, differentiation, expansion, and factoring using a simple REPL.

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Table of Contents

• Features
• Getting Started
• Usage
• Example: Differentiation
• Project Structure
• Contributing
• License

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Features

• Symbolic Variables & Constants
  Create symbolic variables (Var) and constants (Val, Const), including integer analogues (IntVar, IntVal, IntConst).

• Basic Operations
  Support for +, -, *, /, ** (power), unary -, and a variety of built-in functions (sin, cos, exp, log, etc.).

• Algebraic Simplification
  Automatic simplification rules (e.g., 0 + x = x, x * 1 = x, x - x = 0, constant folding, and some trigonometric/log identities).

• Expansion & Factoring

  • expand will distribute products and binomial powers (e.g., (x + 2)^3 → x^3 + 6*x^2 + 12*x + 8).
  • factor will attempt to identify perfect squares of the form x^2 + 2·b·x + b^2 → (x + b)^2.

• Differentiation

  • d(dx: Var): Scalar computes the derivative with respect to a single symbolic variable.
  • d(dx: VectorVar): Vector computes a gradient vector (for multivariate cases).
  • Chain rule is implemented via the SymFunc case class for arbitrary symbolic functions.

• Purely Functional Design
  No mutable state—every transformation returns a new Scalar or Vector instance.

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Getting Started

1. Clone this repository

   git clone https://your-git-server.com/your-username/scas.git
   cd scas

2. Launch a Scala REPL
   From the scas/ directory, run:

   scala-cli repl .

   This will start a REPL session with all source files under src/ on the classpath. You can then import and work with the CAS API interactively.

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Usage

Once inside the REPL, you can import the top-level package and begin defining symbolic expressions:

scala> import smile.cas._

• Create Variables

  scala> val x = Var("x")
  scala> val y = Var("y")

• Build Expressions

  scala> val expr1: Scalar = (x + Val(2)) ** Val(3)           // (x + 2)**3
  scala> val expr2: Scalar = Sin(x) * Exp(x) + x ** Val(2)    // sin(x)*e(x) + x**2

• Evaluate / Apply

  scala> expr1(Map("x" -> Val(5)))   // substitutes x = 5
  val res0: Scalar = 343.0

• Simplify / Expand / Factor

  scala> expr1.expand
  val res1: Scalar = x**3.0 + 6.0*(x**2.0) + 12.0*x + 8.0
  
  scala> (x**Val(2) + Val(2)*x + Val(1)).factor
  val res2: Scalar = (x + 1.0)**2.0

• Differentiate

  scala> expr2.d(x).simplify
  val res3: Scalar = (sin(x) + cos(x) * x)*e(x) + 2.0*x

  (Here e(x) denotes exp(x) under the hood.)

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Project Structure

scas/
├── README.md
├── project.scala
├── LICENSE               # GPLv3 as inherited from Smile (see below)
└── src
    └── smile
        └── cas
            ├── Scalar.scala
            ├── Vector.scala
            ├── Matrix.scala
            ├── Tensor.scala
            ├── … (all other case classes and traits)
            └── combinations (private helper)

Note: All code lives under src/smile/cas. When you run scala-cli repl . from the scas/ folder, scala-cli automatically picks up the entire src/ directory so you can import smile.cas._ directly.

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Contributing

1. Fork this repository.
2. Create a feature branch:

   git checkout -b feature/your-feature-name

3. Commit your changes.
4. Push to your branch:

   git push origin feature/your-feature-name

5. Open a Pull Request with a clear description of your changes.

Please follow the existing style:

• Purely functional implementations.
• No mutable state.
• Consistent naming conventions (CamelCase for types, lowerCamelCase for methods).
• Adequate unit tests (e.g., using uTest or ScalaTest).

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License

This project is derived from the Smile CAS module, which is licensed under the GNU General Public License v3.0 (GPL-3.0). All modifications made by Daniel Meyer in 2025 retain that license.

See the LICENSE file for full details.

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Happy Symbolic Algebra!