The user interface

This is a screenshot of the Symja online calculator:

Common evaluation buttons

The following buttons are always defined in the user interface:

Sym - symbolic evaluation
Num - numeric evaluation
C - clears the input text area

Persisting formulas

Through the Login link users can sign in with their Google User Account. When logged in, it's possible to persist user defined formulas and constants with the so-called $ user symbols in the Google App Engine datastore.

You can for example create your own rules or formulas for a new defined symbol $cube. Type the following rules in the input area and press the Sym button to define your rules:

 SetAttributes[$cube,Listable];
 $cube[x_]:=x^3

Now you can use this rule by evaluating a symbolic argument

 $cube[a]

and you get the result a^3 in the output area.

Because the $cube symbol has the attribute Listable you can also evaluate a list of numbers like this

 $cube[{1,2,3,4,5}]

and you get the result {1,8,27,64,125}.

In the same way you can define constants:

 $theAnswerToAllQuestions = 42

By evaluating

 $theAnswerToAllQuestions

you get the defined value 42.

If you are logged in again at a later date, you can reuse the $ user symbols without redefining them.

Buttons for logged in users

The following buttons are only defined in the user interface, if you are logged in with your Google Account:

Def - shows the definition of the $ user symbol that the user has typed into the input area (i.e. the $ user symbol $cube used in the example above, will show the defined rules for $cube in the output area).
Vars - shows all defined user variables from the Google App Engine datastore. At the moment a user can define up to 100 $ user symbol formulas.

Advanced configuration

AJAX Evaluation API

The simplified online Eval API lets you dynamically generate calculation forms. To see the Eval API in action, open up a browser window and copy the following URL into it:

http://mobmath.appspot.com/?ci=x1:X:i:10|y1:Y:i:2&ca=x!:x1!|Fibonacci[x]:Fibonacci[x1]|Binomial[x,y]:Binomial[x1,y1]

On testiphone.com you can try the same example online in an iPhone simulator (you should use the Safari browser to get the real experience).

Here is a link for the general iPhone AJAX interface

The corresponding JSP file for the Evaluation API is the index.jsp file

Install additional packages

Symja is extendable through the Package command. If you've installed AJAXSymja on Google Appengine, you can add new packages through the admin.jsp interface. Only users which are administrators for the Google Appengine application are allowed to use the admin.jsp interface.

Example package for generating Laguerre or Legendre polynomials (Note - public symbols have to start with an uppercase character):

Package[ 
  "Polynomials", 
  (* define the public available symbols *)
  {LaguerreP, LegendreP}, 
{ 
  (* Laguerre polynomials 
     http://en.wikipedia.org/wiki/Laguerre_polynomials *) 
  LaguerreP[0,x_]:=1, 
  LaguerreP[1,x_]:=1-x, 
  LaguerreP[n_IntegerQ,x_]:= 
      ExpandAll[(2*n-1-x)*LaguerreP[n-1,x] - (n-1)^2*LaguerreP[n-2,x]] /; NonNegative[n], 
  (* Legendre polynomials 
     http://en.wikipedia.org/wiki/Legendre_polynomials *)
  LegendreP[n_IntegerQ,x_]:=
      1/(2^n)*Sum[ExpandAll[Binomial[n,k]^2*(x-1)^(n-k)*(x+1)^k], {k,0,n}] /; NonNegative[n]
} ]

After installing the package with the Save package button the new command

  LegendreP[7,x]

can be evaluated.

Google Appengine Development

Before starting, please read the Google Appengine for Java Introduction

Install the Google Plugin for Eclipse as described here:

Using the Google Plugin for Eclipse

Checkout the symja.ajax source code from SVN:

svn/trunk/symja.ajax

Change the symja.ajax configuration:

open: symja.ajax/war/WEB-INF/appengine-web.xml
change the your application ID to the ID you configured in your Google Appengine Account
modify the other configuration options as desired

Select menu Run->Run As->Web Application to run the Google Web Application locally.

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