Java中的数学表达式“泛型”

Question

Well, I have a math expression in a string

String myExpression = "2-3*(cos(x)+sen(x)-exp(-x))*(sen(2x)+1/(cos(x)))";

and I would like to know how to get the expression (in a string):

2-3*cos(x)*sen(2x)-3*cos(x)/cos(x)-3*sen(x)*sen(2x)-3*sen(x)/cos(x)+3*exp(-x)*sen(2x)+3*exp(-x)/cos(x)

ie, apply the distributive property, but without compute values.

Can anyone help me?

Answer 1

If you looking to convert a mathematically expression to another form, I recommend changing it to a postfix/prefix expressions (< link also tells you how to convert back to 'infix') first, and then try to toy with it (you can treat your functions(eg. sin(x) ) as constants). Hope you can do that yourself, plenty of sources to find references.

Link to a simple Infix/Postfix Calculator so you can try it out if you haven't tried it before.

Next, you convert back to infix, but this time distributing the multiplication and division

eg.

   *
  / \
 A   +
    / \
   B   /
      / \
     C   D

Infix: A*(B+C/D)
Postfix: ABCD/+*

ABCD/+*
C and D division first (distribute)                >>> C/D
B and C/D addition(addition,nothing to distribute) >>> B+C/D
A and B + C/D multiplication (distribute)          >>> A*B+A*C/D

So, generally speaking you do nothing but concatenate the addition and subtractions strings.
But:

1. When you have multiply by A then you add a "A*" string to the very beginning and after every '+' or '-'

2. When you have divide by B then you add a "/B" string to the very end and before every '+' or '-' .

I believe this should cover all simple expressions. You may (or may not) need a few more cases when the expression branched out extensively, haven't completely thought it through. I'll appreciate feedback.