how to simplify an arithmetic expression includes unknown symbol

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I want to use c/c++ to simplify an arithmetic expression but it includes unknown symbol;
etc:

(3*x+2*y)*2+x+3 the result will be：7*x+4*y+3

looking for help

thank you

Posted 26-Mar-13 16:56pm

WaveCQU

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H.Brydon 26-Mar-13 23:03pm

Your question is not clear. What is the unknown symbol?

WaveCQU 26-Mar-13 23:04pm

thank you for your reply,just like the expression (3*x+2*y)*2+x+3，the 'x'and 'y' is the unknown symbol,

2 solutions

Solution 1

If you are saying that 'x' and 'y' are unknowns, then what you have is an expression that describes a linear plot. Traditionally you would solve for y, then plot y vs x for some range. Solving for y, you would get

y = -(7*x + 3)/4

-[30]-

Posted 26-Mar-13 17:12pm

H.Brydon

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WaveCQU 26-Mar-13 23:20pm

maybe you misunderstood my queston, my question is that: in the c++ program, I hava a string like: (3*x+2*y)*2+x+3 ， then I want to change this string into a style like: a*x+b*y+c , the a,b,c are constant , I do not have useful way to solve this problem. thank you for your reply

Sergey Alexandrovich Kryukov 26-Mar-13 23:52pm

I did understand your question correctly in first place. Please see my answer.
—SA

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Sergey Alexandrovich Kryukov · Accepted Answer · 2013-03-26T17:52:00

I don't think you really understand it: what you want is called Computer Algebra System (CAS). Please see:
http://en.wikipedia.org/wiki/Computer_algebra_system[^].

At this time, I don't know a CAS library which can be embedded into C++. Besides, I don't think your formulation of the problem is any good. Imaging you got the possibility to perform the symbolic string calculations, but what are you going to do with it? To use it in some sensible way, you would ultimately need to compile it as a C++ expression, but how? C++ is not really a self-compiling system (but I knew some naive people who thought it is, and I would not blame them).

This is not how real CAS systems work. Basically, they are generally based on Expression Trees:
http://en.wikipedia.org/wiki/Expression_tree[^].

Now, if you read this, you can get some ideas. If you are going to implement your own CAS library in C++ and offer the reasonable ways to use it, it would be great. This is quite a feasible problem, but it would require a lot of work.

Good luck,

—SA