What is it?

This is a Math Engine that not only evaluates simple arithmetic expressions, but can also manipulate Algebraic Expressions. It also has a Mathematical resoning engine.

How to use it?

First you need to include the mathengine package in your project. Alternatively, you can also make a JAR out of this package and include that.

To use this, create an instance of the Engine class:

Engine myEngine = new Engine();

##Algebraic Transformations

The engine can learn Algebraic transformations (aka Dynamic Formulae), such as the formula:

(a+b)^2 = (a^2)+(2*a*b)+(b^2)

They can be added adHoc:

myEngine.learnDynamicFormula("(a+b)^2", "(a^2)+(2*a*b)+(b^2)");

or as part of a file of dynamic formulae:

myEngine.loadDynamicFormulaFile("basicAlgebra.txt");

When adding from a file, each formula needs to be placed on a separate line. Each formula should mention the two states with the => delimieter in between. For example:

(a+b)^2 => (a^2)+(2*a*b)+(b^2)
a*(b+c) => a*b + a*c
a*0 => 0
a*1 => a
a - a => 0
a^1 => a;

Based on the transformations the engine knows, it can be asked to evaluate an algebraic expression:

String result = myEngine.evaluateExpression("(a+b)^2 -a*b");

##Functions

The engine can be taught simple mathematical functions as well. Functions are defined using the general syntax:

functionName:(param1 , param2, param3, ...)

This is what truly lets the engine go into new territories like calculus. For example, we can make a file derivative.txt and fill it with:

	derivate:(u^a,x) => a*u^(a-1)*derivate:(u,x)
	derivate:(u+v,x) => derivate:(u,x)+derivate:(v,x)
	derivate:(u*v,x) => derivate:(u,x)*v+u*derivate:(v,x)
	derivate:(exp:(u),x)=> exp:(u)*derivate:(u,x)
	derivate:(ln:(u),x) => (1/u)*derivate:(u,x)
	derivate:(#,x) => 0
	derivate:(x,x) => 1

Here, we are teaching the engine different possible transformations of the derivate function. Thus now the engine is suddenly able to evaluate expressions like:

    derivate:(5*x^3-2*x^2+exp:(x^2))

##Mathematical Facts (Reasoning)

The engine also supports reasoning, given a set of mathematical "facts" and then a question. Facts can mean:

• A "Static" Formula, eg: Speed = Distance / Time
• A given value of a variable, eg: Distance = 10

For example, we can teach the engine the following Static Formulae:

• DistanceTravelled = FinalPosition - InitialPosition
• TimeTaken = EndTime = StartTime
• Speed = DistanceTravelled / TimeTaken

Then present the following test case:

• InitialPosition = 5
• FinalPosition = 15
• StartTime = 0
• EndTime = 5

Then tell it to find the value of Speed (which it will output as 2).

The above steps can be written in code as:

//Create Engine
Engine myEngine = new Engine();

//Teach Formulae
myEngine.learnFormulaStatic("Speed = DistanceTravelled / TimeTaken");
myEngine.learnFormulaStatic("DistanceTravelled = FinalPosition - InitialPosition");
myEngine.learnFormulaStatic("TimeTaken = EndTime = StartTime");

//Prepare Given Values as key value pairs
HashMap<String, String> GivenValues = new HashMap<String, String>();
GivenValues.put("InitialPosition", "5");
GivenValues.put("FinalPosition", "15");
GivenValues.put("StartTime", "0");
GivenValues.put("EndTime", "5");

//Prepare list of Variables to be found
ArrayList<String> ToFind = new ArrayList<String>();
ToFind.add("Speed");

//Query the Engine with given parameters
ArrayList<String> ans = myEngine.KnowledgeQuery(GivenValues, ToFind);

License

(The MIT License)

Copyright (c) 2014 Syed Musa Ali

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the 'Software'), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Authors

• Assad Ali Memon
• Azka Qaiser
• Syed Musa Ali