Differences of the Arithmetic compared to Java

• The multiplication operator '*' may be omitted
  e.g.:   a b ≡ a * b, 2t ≡ 2 * t, 2(a+3b) ≡ 2 * ( a + 3 * b )
  
  Please note:   a / b c ≡ a / b * c ≡ ( a / b ) * c   ≠   a / ( b c ) ≡ a / ( b * c ) ≅ a / b / c


• Function calls with exactly one parameter can be written without brackets
  e.g.:   sqrt 3 ≡ sqrt(3), sin 2 t ≡ sin( 2 * t ), but  exp 2 * t ≡ exp(2) * t


• The syntactical ambiguity  a b  is resolved as follows:
  a b is interpretered as
      a * b   if variable a is defind
      a(b)    if method a is defined for b
    else error message: identifier a undefined
  



• JXN uses '^' or alternatively "**" as the exponentiation operator
  e.g.:   y^x ≡ y**x ≡ pow( y, x )
  
  The exponentiation operator is of higher priority than '*', '/' and the ommited '*'-operator
  i.e.   a y^x b ≡ a * pow( y, x ) * b
  Caution: avoid the missleading notation e.g.: 2y^3x ≡ 2 y^3 x ≡ 2 * pow( y, 3 ) * x
  
  The exponentiation operator also is of higher priority than the unary '-'-operator (→ Wikipedia)
  i.e.   -y^x ≡ -(y^x) ≡ -pow( y, x )
  



• @ClassName(…) calls the constructor:  @ClassName(…)  in JXN stands for  new ClassName(…)  in Java.



• The predefined variable  $ contains the result of the most recent statement.
  Example:

     sqrt(2)
      = 1.4142135623730951 (double)
     $^2
      = 2.0000000000000004 (double)
    

• Further examples (see also JxnSimplifiedSyntaxTable):

    y = x^2 + p x + q  ≡  y = pow( x, 2 ) + p * x + q
    z = y^sqrt 2x  ≡  z = pow( y, sqrt( 2 * x ) )
  
    x = exp( -0.5 t^2 ) cos( 2 PI f ( t - t0 ) )
      = exp  -0.5 t^2 * cos  2 PI f ( t - t0 )  ≡  x = exp( -0.5 * pow( t, 2 ) ) * cos( 2 * PI * f * ( t - t0 ) )
  

  but

    x = exp  -0.5 t^2   cos  2 PI f ( t - t0 )  ≡  x = exp( -0.5 * pow( t, 2 )   * cos( 2 * PI * f * ( t - t0 ) ) )
  
  

  Avoid the missleading notation using the exponentiation operator (Irrespective of the notation '^' is of higher priority than the omitted '*'-operator):

    exp -2x^2t  ≡  exp -2 x^2 t  ≡     exp( -2   * pow( x, 2 ) * t )
      y^-2x^2t  ≡    y^-2 x^2 t  ≡  pow( y, -2 ) * pow( x, 2 ) * t
  
    exp -2(x+1)                     ≡     exp( -2   * ( x + 1 ) )
      y^-2(x+1)  ≡  y^-2 ( x + 1 )  ≡  pow( y, -2 ) * ( x + 1 )
  
    sqrt(2+3)^-2x  ≡  sqrt(2+3)^-2 x  ≡  pow( sqrt( 2 + 3 ), -2 ) * x
       y(2+3)^-2x  ≡    y (2+3)^-2 x  ≡    y * pow( 2 + 3,   -2 ) * x
  



• Method calls:

  f x.g y ≡ f(x.g(y)) ≠ f(x).g(y)  ( ≡ (f x).g y )
  
  f (x).g() ≡ f(x).g() ≠ f( (x).g() )
  
     sqrt ( 2.5 2.5 ).intValue()  ! avoid
      = 2 (int)
     sqrt( 2.5 2.5 ).intValue()      ! = sqrt( 2.5 * 2.5 ).intValue() => sqrt( 6.25 ) > 2.5 (double) > 2 (int)
      = 2 (int)
     sqrt 2.5 ( 2.5 ).intValue()     ! = sqrt( 2.5 * (2.5).intValue() ) => sqrt( 5.0 )
      = 2.23606797749979 (double)
     sqrt( ( 2.5 2.5 ).intValue() )  ! = sqrt( ( 2.5 * 2.5 ).intValue() ) => sqrt( 6.0 )
      = 2.449489742783178 (double)
     (sqrt 2.5 * 2.5).intValue()     ! = ( sqrt(2.5) * 2.5 ).intValue()
      = 3 (int)
     sqrt 2.5 * (2.5).intValue()     ! = sqrt(2.5) * (2.5).intValue()
      = 3.1622776601683795 (double)
  

  
  
• Constructor calls:

    @class_name object.method_name single_argument
  ≡ @class_name(object.method_name(single_argument))
  ≠ @class_name(single_argument1).method_name(single_argument2)