mathS

A library for computer algebra (symbolic computing) and scientific computing.

We start from an imitation of Mathematica. We try to make it more connected to C++, and allow you to enjoy its feature conveniently in C++ programs. For example, parse a text input Sin(1/x)+2*y^2" and instantly get an std::function .

mathS=math+Science|math+Symbol

Features

• Symbolic expression processing. MathS grammar is designed to state an expression clearly and without those ambiguous meanings usually in writing. Vector, matrix, any shape of tensors or general list are supported. Functional operators and some advanced operators like $\nabla,\int,\sum,\prod$ are supported. Equations and inequations are also supported in expression. We have already implemented MathParser. It converts text expressions to varied MathObject.

  Sample input and output:

  (x+y/3)^2-(y/3+x)^2+u*u*v/v
  = u^2
  

  We are still working on the development.

• NMath module offers better performance on numerical tasks. Numerical linear algebra will be strongly supported. It is under developing. We have already implemented Assembler. MathObejct can be converted to NFunction which takes the variables in the expression as parameters. This would support those cases like plotting, numerical integrating when massive computing is needed.

• Convert MathObject to LaTeX format string.

  std::cout << Parse("4*Sin(x^2+Pi/2)+Sum<<i|Cos(Log(i)^2)>>({1,12})")->GetLaTeXString() << std::endl;
  
  /***Output******
  4\,\sin{\left(x^{2}+\frac{{\pi}}{2}\right)}+\sum_{i}^{\left\{1,12\right\}}\cos{\left(\log{i}\right)^{2}}
  ***************/

  Rendered in markdown or LaTeX:

  

• As an C++ library, you can enjoy its features in C++ freely. We use lambda expression to convert MathObject to std::function so that you can use it freely in your program.

  Assembler assembler;
  auto f = assembler.assemble(Parse("Sin(x^2)-y/2"),{"x","y"});
  std::cout << f({1.2, 1.3}) << std::endl;
  
  /******Output*******
  0.3414583
  *******************/

A powerful calculator in 9 line

The simplest application with mathS is a calculator. The follow program is a calculator that supports various operations, vector and matrix.

#include <iostream>
#include <MathParser.h>
#include <LBAssembler.h>

using namespace mathS;

int main() {    
	std::string str;
    Assembler assembler;
    
 	std::cin >> str;
    auto mobj = Parse(str);			// Get MathObject
        
    if (mobj->GetType() == MathObject::ERROR) 	// Check sytanx
        std::cout << mobj->GetString() << std::endl;

    std::vector<std::string> params = {};	// No variables in the expression in a calculator program.

    auto f = assembler.Assemble(mobj, params);	// Get NFunction
    std::cout << " = " << f({})->GetString() << std::endl;
    
    return 0;
}

Sample input and output

E^3+9.1*(3-2.1)
 = 28.275537

Floor(1.34+3)
 = 4.000000

{3,6,9}/3
 = {1.000000,2.000000,3.000000}

{3.1,3.2,{6,2,1}}*{1.1,2.2,{3.1,3.2,4.3}}
 = {3.410000,7.040000,{18.600000,6.400000,4.300000}}

sin({1,PI/6,PI/2})
 = {0.841471,0.500000,1.000000}

Build

TODO.

What's to be done

This is our timeline. We are now at medium term of step 2.

• Step 1: Basic part

  • Parser: Convert text expressions to MathObject
  • Assembler: Convert MathObject to NMathFuncition(numeric math function), also C++ std function.

  When Step 1 is done, mathS is already a quite useful library. It will allow programmers get a function instantly by text expressions.

• Step 2: Essential part

  • Rule: Use a chain of rules to transform MathObject, so that we can perform symbolic integral, differential, simplification to any expression.
  • NAlgorithms: Adopt numeric computing algorithms. Performing interpolation, numeric integral, matrix decomposition, numeric optimization, linear programming, solving linear and non-linear equations, statistics, etc. . Also many other interesting utilities.(This will take a very long time)
  • Interpreter: More controlling functions, and allow user to execute a mathS script. Similar to a Mathematica program.

• Step 3: Advanced part

  Many of the following could be just dreams.

  • Even more diverse objects.

    • SparseList: For large sparse matrix and algorithms.
    • Graph: Build a graph, display and perform graph algorithms.
    • Graphics: Allow users to plot and draw with simple commands. (Very useful, but to make it great is not that easy)
    • Image: Read, process and show images.
    • ...

  • Extensions

    (This is cool but maybe not practical. We are not supposed to repeat useless work, which has been done by others perfectly.)

    • MLlib: Simple implementation of machine learning algorithms

Documentation

TODO.

Development

• See in doc/dev-log-***.md.