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 v2.0.0-apps release and unzip the files for example in a sub-directory named /symja. Install the files start-symja.jsh and symja-jshell.bat also 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 11.

  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 the start-symja.jsh default JShell 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:\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 to 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 $\sin(x)*\cos(x)$:

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> InputForm.of(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

When you enter snippets, use the <Tab> key to automatically complete the F. function name. If the function name can’t be determined from what was entered, then possible symbol and function names are provided.

jshell> F.Arc<TAB>
ArcCos      ArcCos(     ArcCosh     ArcCosh(    ArcCot      ArcCot(     ArcCoth     ArcCoth(    ArcCsc      ArcCsc(
ArcCsch     ArcCsch(    ArcLength   ArcSec      ArcSec(     ArcSech     ArcSech(    ArcSin      ArcSin(     ArcSinh
ArcSinh(    ArcTan      ArcTan(     ArcTanh     ArcTanh(

If you only want to see the predefined symbol names, use the <Tab> key to automatically complete the S. symbol name. If the symbol name can’t be determined from what was entered, then possible symbol names are provided.

jshell> S.Int
Integer                   IntegerDigits             IntegerExponent           IntegerLength
IntegerName               IntegerPart               IntegerPartitions         IntegerQ
Integers                  Integrate                 InterpolatingFunction     InterpolatingPolynomial
Interpolation             InterquartileRange        Interrupt                 IntersectingQ
Intersection              Interval                  IntervalIntersection      IntervalMemberQ
IntervalUnion

Evaluate expression from Java string input:

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

Convert string expressions into a Symja Java form:

jshell> eval("JavaForm(Sin(x)^2,Prefix->True)")
$15 ==> F.Sqr(F.Sin(F.x))

Plot a 3D function. This command will open a browser window which should display the plot and a button to refine the JavaScript output on JSFiddle

jshell> F.show(eval("Plot3D(Sin(x*y), {x,0, 5}, {y, 0, 5}, ColorFunction->\"Rainbow\")"))

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

jshell> /exit
|  Goodbye