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About Java Calculus

JavaCalculus is a Maths String Java Package that has the below:

1. Expression Interface:To obtain the value of a String Equation.
   • Taken initially from StackOverflow. Code written by StackOverflow User:Boann and
   • Code written by StackOverflow User:Mike Scholtes
   • Boann's code was Free Source
   • But modified by me extensively.
   • input: Java string (function)(f(x) )
   • output: Java double (function value)
2. Differentiation Interface:To obtain the Symbolic Differentiation of an String Equation.
   • input : Java string (f(x) )
   • output : differentiation of f(x): f'(x)
3. Integration Interface:To obtain the Symbolic Integration of an String Equation.
   • input : Java string ( f(x) )
   • output : integral of f(x)
4. Algebra Interface :To obtain the expansion of an Algebraic multiplication of 2 equations.
   • input : 2 Java strings: f(x) & g(x)
   • output: Java string : f(x) * g(x)
5. Function Composition Interface :To obtain the Function Composition of 2 equations.
   • input: 2 Java strings : f(x) & g(x)
   • output: Java string : f(g(x)): fog(x)
6. Simple Expression Interface: To obtain the simple mathematical Java equivalent string.
   • input: Java string: f(x)
   • output: Java string: s(x) : such that f(x)=s(x) in all respects mathematically.
   • The purpose of this Interface is to simplify the inputs so that the differentiation & integration Interfaces are not complex. It also has the dual function of simplifying the output of the differentiation and integration interfaces by removing the leftover quirks of the mathematical operations to ensure a neat Java string. Hence it is recommended to use this interface at the input and output.

JavaCalculus is about 12,000 Lines of Lambda Calculus Code which does not use Numeric Analysis Methods (Newton Raphson etc). This is just High School Mathematics Maths Formulae with Java Lambda Calculus Code. This has been been tested for:

1. Constant Coefficients (Integer , Double )
2. X Term (Polynomial) (Can be any primary Variable: z, a1, ao, an, a123 , t etc)

Work In Progress (Future Development):

1. Independent Constants: dy/dx(ax+b) where a & b are independent constants with respect to x.
2. Functions
3. Parenthesis

Development and Test Environment: Windows XP and Java 7 & Netbeans 8.2

Testing has been rigorous with the TestHarness Testing 216 Types(Formats) of Equations This can be checked out by the User by running the Function (method):mainRegresssionDiffTest and mainRegressionIntegrTest.

The Regression Suite has 216 types of equations with their differentiation and integration computed upto order 4. The User can add his/her additional order answers if required. Testing has always been upto 4th order (order=5).

User Intructions:

Run the function mainUser(args) and mainAlgebraUser(args); in File: MathsContxtLAv0_1.java

mainUser(args) does the Differentiation and Integration Interactively. mainAlgebraUser(args) does the multiplication of 2 equations Algebraicly. It also does the Function Composition (FoG) of the 2 equations.

There are 2 other functions:mainDiff and mainIntegral which do a single differentiation and a single integration.

Even though testing has been rigorous,the User is advised to manually compute his/her equation and verify if the software is as per design. If the User is unable to hand compute the equation, at least a tough portion of the equation should be hand computed and verified in a trial run before use.

The User can also check if his/her equation is part of the Regression Suite formats.

While the answers in the Regression Suite have been hand computed and have been checked, some mistakes are still present. The User should bear this in mind.

Release 3.0

Packages JavaCalculus is divided into 1 package of 9 Files: 1) MathsContxtLAv 2) DiffrIntegrSep 3) FuncInvSep 4) SimpleAlgebraSep 5) SubsStrSep 6) CalculusApplication 7) MathematicalTestHarness 8) TestHarnessClass 9) Usage

TestHarness is divided into 1 package of 13 Files: 1) TestHarnessAlgebra 2) TestHarnessCoefficients 3) TestHarnessExpression 4) TestHarnessFInverse 5) TestHarnessFunctions 6) TestHarnessIndConstant 7) TestHarnessInfinityNaN 8) TestHarnessIsolation 9) TestHarnessNames 10) TestHarnessParentheses 11) TestHarnessPredicate 12) TestHarnessSignedX 13) TestHarnessUnitTest

3. RUNNING THE PROGRAMS Using Netbeans 8.2,

   1. Open i.
   2. Right Click
   3. Select Run File

4. ENGINEERING

5. Separation of Interface Code to appropriate files

   1. The Original MathsContxtLAv Code has been decluttered and seperated out to individual files (File Name ending with “Sep”). The Java public & private keywords for variables have been used rationalized.
   2. The parser “state” variables for each interface has been seperated to allow better command and control.

6. Design of Term A term in JavaCalculus follows the below grammar: M*x^Exp * IndConstant * Parenthesis Where

7. M: is a numerical String ( A constant integer or float)

8. X: is the prmary variable (used only by differentiator & Integrator- variable “DiffWithRespTo” in the code- can be alphanumeric as in x123, y256 etc (i.e of any length).)

9. Exp: is any constant

10. IndConstant: is any other variable(other than the primary variable (x) ). These are treated as constant string during Integration & Differentiation i.e Algebraic Coefficients.

11. Parenthesis: This is a String expression of Constants, x and IndConstants with braces at the beginning & closing braces at the end. The Design Intent has been that JavaCalculus Differentiator & Integrator will appropriately differentiate/integrate it if it contains the primary variable. Infinity /NaN: The String “Infinity” & “NaN” can be used in M. However JavaCalculus uses it appropriately as an IndConstant.

5.c Testing Improvements 1) “Status=Pass Conformal Map TEST” Or Function ConformalMapTestCaseIntegr has been added to check if the mapping holds true for : a. 8 values of x (-3.0 to +4) at the high level followed by a +-DELTA (DELTA = 0.000001) (3 values (-DELTA, 0 , +Delta) ) b. mapping the primary variable to “y” using StrIntegr.replaceAll(DiffWithRespTo, "y"); c. High Level Algebraic Conformal Mapping: The mapping between : 1) Expression supplied by the user is checked with that of Simple Expression. 2) Differentiation / Integration Answer supplied by the user is checked with that of DiffExpr/ IntegrExpr 3) DiffExpr/ IntegrExpr Output is checked with that of Simple Expression (Map2). 4) This is repeated for (b.)

Only if all pass is the status made GREEN.

2) PassFailTestCaseValue

This has been improved from just checking Doublevalue to accomodating rounding off. Thus any numerical random values in the last few digits of Double are accomodated.

5.d Test Results Reporting The Test Report is added at the end of the raw Test Results.(After Test Case 110023 a) Summary: mainDiffTest: TestCase Summary : Total Failed=117 Out of Run TestCases-Dups=311 Passed Count=194 DupCount=17 Section IsolationTestCases Complete # of Failures=6 Out of=22 Test Cases. Dups=0 in Section Section InfinityNaNTestCases Complete # of Failures=0 Out of=20 Test Cases. Dups=0 in Section Section SanityTestCases Complete # of Failures=6 Out of=14 Test Cases. Dups=0 in Section Section UnitTestCases Complete # of Failures=8 Out of=28 Test Cases. Dups=2 in Section Section Names Complete # of Failures=0 Out of=4 Test Cases. Dups=1 in Section Section Coefficients Complete # of Failures=5 Out of=61 Test Cases. Dups=6 in Section Section Exponent Complete # of Failures=2 Out of=11 Test Cases. Dups=0 in Section Section SignedX Complete # of Failures=10 Out of=30 Test Cases. Dups=2 in Section Section IndConstant Complete # of Failures=36 Out of=43 Test Cases. Dups=6 in Section Section Parentheses Complete # of Failures=33 Out of=48 Test Cases. Dups=0 in Section Section Function Test Cases Complete # of Failures=2 Out of=2 Test Cases. Dups=0 in Section Section Function Argument Test Cases Complete # of Failures=5 Out of=5 Test Cases. Dups=0 in Section Section SoftwareEngg Complete # of Failures=4 Out of=23 Test Cases. Dups=0 in Section

mainIntegrTest: j=110023 TestCase=110023 mainIntegrTest: TestCase Summary : Total Failed=135 Out of Run TestCases-Dups=311 Passed Count=176 DupCount=17 Section IsolationTestCases Complete # of Failures=8 Out of=22 Test Cases. Dups=0 in Section Section InfinityNaNTestCases Complete # of Failures=5 Out of=20 Test Cases. Dups=0 in Section Section SanityTestCases Complete # of Failures=7 Out of=14 Test Cases. Dups=0 in Section Section UnitTestCases Complete # of Failures=5 Out of=28 Test Cases. Dups=2 in Section Section Names Complete # of Failures=0 Out of=4 Test Cases. Dups=1 in Section Section Coefficients Complete # of Failures=8 Out of=61 Test Cases. Dups=6 in Section Section Exponent Complete # of Failures=4 Out of=11 Test Cases. Dups=0 in Section Section SignedX Complete # of Failures=8 Out of=30 Test Cases. Dups=2 in Section Section IndConstant Complete # of Failures=34 Out of=43 Test Cases. Dups=6 in Section Section Parentheses Complete # of Failures=47 Out of=48 Test Cases. Dups=0 in Section Section Function Test Cases Complete # of Failures=2 Out of=2 Test Cases. Dups=0 in Section Section Function Argument Test Cases Complete # of Failures=5 Out of=5 Test Cases. Dups=0 in Section Section SoftwareEngg Complete # of Failures=2 Out of=23 Test Cases. Dups=0 in Section

b) Sectionwise Breakup:

mainIntegrTest: TestCase Summary : Failed Test Cases are: TestCase=1003:Order=1:Str=false:Val=false:ConfValFlag=false,:Order=2:Str=false:Val=false:ConfValFlag=false,:Order=3:Str=false:Val=false:ConfValFlag=false,:Order=4:Str=false:Val=false:ConfValFlag=false, TestCase=1004:Order=4:Str=false:Val=false:ConfValFlag=false, TestCase=1005:Order=1:Str=false:Val=true:ConfValFlag=false, TestCase=1015:Order=1:Str=false:Val=false:ConfValFlag=false, TestCase=1016:Order=1:Str=false:Val=false:ConfValFlag=false, TestCase=1019:Order=1:Str=false:Val=false:ConfValFlag=false, TestCase=1020:Order=1:Str=false:Val=false:ConfValFlag=false, TestCase=1021:Order=1:Str=false:Val=false:ConfValFlag=false, null , Section IsolationTestCases Complete # of Failures=8 Out of=22 Test Cases. Dups=0 in Section , TestCase=2003:Order=1:Str=false:Val=true:ConfValFlag=true, TestCase=2004:Order=1:Str=false:Val=true:ConfValFlag=true, TestCase=2006:Order=1:Str=false:Val=true:ConfValFlag=true, TestCase=2008:Order=1:Str=false:Val=true:ConfValFlag=true, TestCase=2017:Order=1:Str=false:Val=true:ConfValFlag=true, null , Section InfinityNaNTestCases Complete # of Failures=5 Out of=20 Test Cases. Dups=0 in Section c) Exception Breakup mainIntegrTest: Exception TestCase Summary : Total Exceptions=5 Exception Test Cases are: TestCase=40046:Order=1:Str=false:Val=false, TestCase=40047:Order=1:Str=false:Val=false, TestCase=40048:Order=1:Str=false:Val=false, TestCase=40049:Order=1:Str=false:Val=false, TestCase=80035:Order=1:Str=false:Val=false, mainIntegrTest: TestCase Duplicate Summary : EqnDBIndex=328 d) Dups TestCase@5038@:Dup with :5036: TestCase@5042@:Dup with :5037: TestCase@10001@:Dup with :1000: TestCase@20001@:Dup with :4026: TestCase@20020@:Dup with :4030: TestCase@20022@:Dup with :4031: TestCase@20023@:Dup with :4032: TestCase@20031@:Dup with :4027: TestCase@20093@:Dup with :4026: TestCase@40005@:Dup with :4026: TestCase@40006@:Dup with :20002: TestCase@50003@:Dup with :4019: TestCase@50004@:Dup with :4020: TestCase@50012@:Dup with :40020: TestCase@50013@:Dup with :40021: TestCase@50048@:Dup with :50047: TestCase@50050@:Dup with :50049: e) Exception Cause Breakup 40046:For input string: "0.0E+0.010", 40047:For input string: "0.0E-0.010", 40048:For input string: "0.0E-0.010", 40049:For input string: "0.0E-1.010", 80035:String index out of range: -1,

5.e Algebraic Conformal Mapping JavaCalculus 3.0 has been improved to output algebraic conformal strings. SimpleExpression has been improved to output algebraic conformal. DiffExpr has been improved to output algebraic conformal. IntegrExpr has been improved to output algebraic conformal.

Thus (TestCase = 2000) "1.0/-0/x^8 + 1.0/-0/x^5 + 1.0/-0/x^4 - 1.0/-0/x - 25/-0"; Simple Expression Map1: "-Infinity/x^8.0-Infinity/x^5.0-Infinity/x^4.0+Infinity/x+Infinity"; DiffExpr : "-Infinity*-8.0/x^9.0-Infinity*-5.0/x^6.0-Infinity*-4.0/x^5.0-Infinity/x^2.0+Infinity"; IntegrExpr: "-Infinity/-7.0/x^7.0-Infinity/-4.0/x^4.0-Infinity/-3.0/x^3.0+Infinityln(x)+Infinityx"; Simple Expression Map2(IntegrExpr): "Infinity/7.0/x^7.0+Infinity/4.0/x^4.0+Infinity/3.0/x^3.0+Infinityln(x)+Infinityx";

The Design intent has been to allow extremely small values(Delta x) to be properly algebraicly mapped and Differentiated.It also helps in the debugging of very large Strings Equations to check which term is causing the error.

Release 5.0

#a) To run Program :

1) Open ExprSimpleStrSep.java

2) Right Click

3) Select Run File

#b) 2 new Interfaces have been created in ExprSimpleStrSep.java: #a) SimpleStr : Does a 1 to 1 mapping of input Equation #b) AlgebraicConfrmStr: Maps input Equation to its Algebraic Conformal Equation. That is if Input Equation is :32x Algebraic Conformal Map is :6*x #c) PassFailTestCaseValueEasy Created and PassFailTestCaseValue renamed as PassFailTestCaseValueStrict: This allows 4th Order and 4th Degree Euqation Error due to numerical Noise to be filtered out of the Test Results. #d) Test Results Output Tags the main program : MathsContxtLAv System.out.println("MathematicalTestHarness:Started:MathsContxtLAv:Run Started Time:" + current + " "); OR ExprSimpleStrSep.java System.out.println("MathematicalTestHarness:Started:ExprSimpleStrSep:Run Started Time:" + current + " "); #e) CalculusApplication.java: Schrodinger Equation is also working.

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