CLI for Mathematica and Symathica

Mathematica

• A library for abstract scientific computations and contains computational methods implementation.

• Uses C++20 concepts to abstract algorithms and data structures on algebraic types such as Field, Real numbers and so on.

• Basic data structures as Matrix, Vector, Polynomial implemented.

• Solve systems of linear equations using Gauss and Simple Iteration methods.

• Solve equations with only variable using Half-Division, Newton, Simple Iteration methods.

• Compute an integral of one-argument continuous function on given interval using Cotes methods.

• Approximate one-argument function with Polynomial using Least Sqares method.

• Find some statistics such as PCC, RSS.

Symatica

• A library for symbolic computations.

• Supports basic operations such as Addition, Substraction, Multiplication, Division, Negation, Exponentiation.

• Leaf of Expression is either a Variable or Literal.

• Has a DSL to build Expression tree easily.

• Use Evaluator visitor to set values (or other expressions) to variables and compute concrete value of a given Expression.

• Use Optimizer visitor to optimize expression by applying transformations such as a + 0 = a, a * 1 = a, 2 + 2 = 4, and many-many others.

• Use Derivativer visitor to find an Expression that is a precise dervivative of a given Expression. Then you can optimize it using Optimizer and compute using Evaluator.

• Goal 1: Add custom functions (sin, cos, ln) and its
  derivatives to expand the application area.

• Goal 2: Integrate it with Mathematica and create an implementation of Field by Expression tree to be able to run abstract algorihms on symbolic expressions.

Build & Run

Requirements:

• cmake
• clang 16
• clang-tidy
• clang-format
• clangd
• vscode

bash ci/project/build.sh
bash ci/project/test.sh
./build/math-tool --help

Reference

• ITMO University Lab reports