JShell usage

Symbolic math scripting with JShell

JShell is a Read-Evaluate-Print-Loop (REPL), a command line tool that allows you to enter Java statements (simple statements, compound statements, or even full methods and classes), evaluate them, and print the result. We'll go through an example that will show you how to use JShell to explore the Symja computer algebra library.

• Installation
• Example shell interactions

Installation

Download the latest Symja release and unzip the files for example in a sub-directory named /symja

In this directory you can run the symja-jshell.bat batch file under Windows. Please adjust the JAVA_HOME path for your environment to a JDK installation greater equal than Java 9.

  SET "JAVA_HOME=C:\Program Files\Java\jdk-11.0.12"
  "%JAVA_HOME%\bin\jshell" --class-path "lib/*" --startup start-symja.jsh

By running the symja-jshell.bat file a start-symja.jsh default scripting file with some additional imports will be executed:

...
import org.matheclipse.core.expression.*;
import org.matheclipse.core.eval.*;
import org.matheclipse.core.interfaces.*;
import static org.matheclipse.core.expression.F.*;
 

• With the static imports of the F.class it's possible to use the formal symbols a,b,c,...x,y,z symbolically and to call functions like Integrate, D or FactorInteger and to omit the F. prefix.
• With the predefined eval method it's possible to evaluate a math string expression like for example eval("D(Sin(x),x)")

Example shell interactions

After starting jshell you should see something like the following:

C:\temp\symja>symja-jshell
|  Welcome to JShell -- Version 11.0.12
|  For an introduction type: /help intro
jshell>

You can now input specific JShell commands or Java Symja API code (referred as snippets). So let's start with a simple expression:

jshell> eval("1+1")
$1 ==> 2

With this snippet you can evaluate a partial derivative:

jshell> D.of(Sin(x),x)  
$2 ==> Cos(x)

Integration of Sin(x)*Cos():

jshell> Integrate.of(Times(Sin(x),Cos(x)),x)
$3 ==> -Cos(x)^2/2

Determine the factors of the integer 324 (use ZZ to define integers; QQ to define rational numbers and CC to define exact complex numbers):

jshell> FactorInteger.of(ZZ(324))
$4 ==> {{2,2},{3,4}}

Print the Horner form of the expression (x+y)^3:

jshell> HornerForm.of(Expand(Power(Plus(x,y),C3)))
$5 ==> x*(x*(x+3*y)+3*y^2)+y^3

Print the TeX form of the expression Sum( f(n), {n, 1, m}):

jshell> TeXForm.of(Sum(unary(f,n),List(n,C1,m)))
$6 ==> \sum_{n = 1}^{m} {f(n)}

Print the internal rules used for the ArcTan function

jshell> Definition.of(ArcTan)
$7 ==> Attributes(ArcTan)={Listable,NumericFunction}
ArcTan(Sqrt(5-2*Sqrt(5)))=Pi/5
...
ArcTan(0)=0
ArcTan(1,1)=Pi/4
ArcTan(Infinity)=Pi/2
...

Evaluate ArcTan(1,1)

jshell> ArcTan.of(C1,C1)
$8 ==> Pi/4

Define a symbolic variable xx and assign x+y

jshell> ISymbol xx=Dummy("xx")
xx ==> xx

jshell> Set.of(xx, Plus(x,y))  // assign x+y  
$10 ==> x+y

jshell> Definition.of(xx)
$11 ==> Attributes(xx)={}
xx=x+y

jshell> eval(xx)
$12 ==> x+y

Print the documentation for the Im function:

jshell> usage(Im)  
$13 ==>
## Im

Im(z)
> returns the imaginary component of the complex number `z`.

### Examples
>> Im(3+4I)
4

>> Im(0.5 + 2.3*I)
2.3

Evaluate expression from Java string input:

jshell> eval("D(Sin(x),x)")
$14 ==> Cos(x)

If you're finished exit jshell with the /exit jshell command:

jshell> /exit
|  Goodbye