SchantAlgebra - Java

SchantAlgebra is a Java library for manipulating and solving equations in SchantAlgebra, a non-commutative algebraic structure that generalizes Boolean algebra. SchantAlgebra is used in areas such as control theory, signal processing, and cryptography.

Features

• SchantAlgebra equation parsing and evaluation
• Support for variables and constants
• Solving equations
• Simplification of expressions
• Factoring of expressions
• Substitution of variables with expressions

Installation

You can download the SchantAlgebra library from the GitHub repository. Then, you can add the SchantAlgebra library to your Java project by adding the JAR file to your project's build path.

Usage

Equation Parsing and Evaluation

To parse and evaluate a SchantAlgebra equation, you can use the EquationParser class:

String equationString = "(a+b)c = ac + bc";
EquationParser parser = new EquationParser();
Equation equation = parser.parse(equationString);
boolean result = equation.evaluate();

The parse method of the EquationParser class takes a string representation of a SchantAlgebra equation and returns an Equation object. You can then use the evaluate method to evaluate the equation.

Variable and Constant Support

SchantAlgebra allows for variables and constants to be used in equations. You can define variables and constants using the Variable and Constant classes:

Variable a = new Variable("a");
Variable b = new Variable("b");
Constant c = new Constant(2);

Solving Equations

To solve a SchantAlgebra equation, you can use the EquationSolver class:

Equation equation = new Equation("(a+b)c = ac + bc");

EquationSolver solver = new EquationSolver();
List<Equation> solutions = solver.solve(equation);

for(Equation solution : solutions) {
    System.out.println("Solution: " + solution);
}

Simplification of Expressions

SchantAlgebra offers methods to simplify expressions. To simplify an expression, you can use the Simplifier class:

Expression expression = SchantAlgebra.parse("a(a+b)");

Simplifier simp = new Simplifier();
Expression simplified = simp.simplify(expression);

System.out.println("Original expression: " + expression);
System.out.println("Simplified expression: " + simplified);

Factoring of Expressions

You can factorize expressions in SchantAlgebra using the Factorizer class:

Expression expression = SchantAlgebra.parse("(a+b)c + bc");

Factorizer factorizer = new Factorizer();
List<Expression> factors = factorizer.factorize(expression);

for(Expression factor : factors) {
    System.out.println("Factor: " + factor);
}

Substitution of Variables with Expressions

To substitute a variable with an expression, you can use the Substitutor class:

Expression expression = SchantAlgebra.parse("ac + bc + (a+b)c");

Substitution substitution = new Substitution();
substitution.addSubstitution("a", SchantAlgebra.parse("x"));
substitution.addSubstitution("b", SchantAlgebra.parse("y"));

Expression substituted = substitution.substitute(expression);

System.out.println("Original expression: " + expression);
System.out.println("Substituted expression: " + substituted);

Conclusion

SchantAlgebra is a powerful and flexible tool for solving equations in non-commutative algebraic systems. The SchantAlgebra library provides a comprehensive set of features for manipulating and solving SchantAlgebra equations in Java.