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1.6. Expression Conversions

• It's really simple to convert an expression. The ExpressionConfiguration class provides an appropriate method for any kind of conversion. Such a method returns a new Expression object presenting the converted expression. There are two possibilities of converting as yet:

  • simplify an expression
  • differentiate an expression

• ---

  Simplify an expression

  To simplify an expression you have to call the method

  • simplify()

  on an ExpressionConfiguration object. For Example:

    ExpressionConfiguration config=new ExpressionConfiguration(RealType.TYPE);
    config.setExpression("0+9");
    config.setExpression(config.simplify());

  After this, the Expression of config will be "9".

  The following table shows source operations and it's simplifications. a and b are arbitrary expressions. Note that often there is no simplification (e.g. 1 + a).

  source operation #	+	-	*	/	^
  #a	a	-a
  #(#a)	a	a
  0 # a	a	-a	0	0	0
  a # 0	a	a	0	a / 0	1
  1 # a	1 + a	1 - a	a	1 / a	1
  a # 1	a + 1	a - 1	a	a	a
  a # a	a + a	0	a * a	1	a ^ a
  a # b	a + b	a - b	a * b	a / b	a ^ b
  -a # b	b - a	-(a + b)	-(a * b)	-(a / b)	-a ^ b
  a # -b	a - b	a + b	-(a * b)	-(a / b)	a ^ -b
  -a # -b	-(a + b)	b - a	a * b	a / b	-(a ^ -b)

  Note: An Expressions wont be simplified in the following cases:

  • constant expressions, e.g.: "9+1" wont be simplified to "10"
  • cancel down divisions, e.g.: "a^2/a" wont be simplified to "a"
  • commutative law wont be detected, e.g.: "(a+b)/(b+a)" wont be simplified to "1"

• ---

  Differentiate an expression

  To get the derivative of an Expression with respect to any Symbol you have to call one of the following methods on an ExpressionConfiguration object:

  • differentiate(String s)
  • differentiate(Symbol s)

  The easiest way is to give the respection by a String. Example:

    ExpressionConfiguration config=new ExpressionConfiguration(RealType.TYPE);
    config.setExpression("a^2");
    config.setExpression(config.differentiate("a"));

  After this, the Expression of config will be "a^2 * (2/a)". It's not simplified to "2*a" because cancel down simplification is not implemented yet.

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