I apologize for the tone of that post. I was getting frustrated that I couldn't accurately explain what I was looking for and that I felt like we weren't making progress.

However, thanks to your output from Mathematica, I see that Equal[ ] will do what I need it to, and that I also do need to use Simplify[ ]. So, thank you very much for providing that output and also for adding Simplify[ ] to the tests! And luckily, it looks like I can programmatically generate strings and use the ToExpression[ ] function to compare them. In my program, I'll check for True to know if two expressions are equal, and if the comparison does not return True (because it looks like Mathematica returns an expression in this case) I'll know they were different.

Thanks again for your help!

I need symbolic comparisons of mathematical expressions. Symbolically, b is not the same as c. And to be verbose, since this seems like a difficult concept:

• Symbolically a is the same as a
• Symbolically b is the same as b
• Symbolically c is the same as c
• Symbolically a is different from b
• Symbolically a is different from c
• Symbolically b is different from c
• etc for all other letters I use in an expression

So I need some function in Mathematica to return False when comparing

Function[(a - b) + c, (a - c) + b]

The following comparison already works fine in Wolfram Alpha, it doesn't need Simplify[ ]

Equal[(a - b)/(c - d), (b - a)/(d - c)]

This may be because they are the same symbolic mathematical expression. When I give two different symbolic mathematical expressions, Wolfram Alpha tries to "solve" it, which you can see with this example:

Equal[(a - b)/(c - d), (a - b)/(d - c)]

I don't know what the function ToExpression actually does, but when I give Wolfram Alpha the following code:

Equal[ToExpression["(a-b)+c"],ToExpression["(c-b)+a"]]

It gets confused and tells me the meaning of the word equal. And actually, giving it the same input for both sides of the comparison again just gives me the definition of the word equal, which you can see with this:

Equal[ToExpression["(a-b)+c"],ToExpression["(a-b)+c"]]

By the way do you, or anyone else reading this, have Mathematica? I'm curious what Mathematica returns with my set of test cases, ie:

• Equal[(a-b)+c,(c-b)+a] : Expecting True, Wolfram Alpha returns True
• Equal[(a-b)+c,(a-c)+b] : Expecting False, Wolfram Alpha returns forms and solutions
• Equal[(a-b)/(c-d),(b-a)/(d-c)] : Expecting True, Wolfram Alpha returns True
• Equal[(a-b)/(c-d),(b-a)/(c-d)] : Expecting False, Wolfram Alpha returns forms and solutions
• Equal[(a-b)/((c-d)^(d-e)), (a-b)*((c-d)^(e-d))] : Expecting True, Wolfram Alpha returns True
• Equal[(a-b)/((c-d)^(d-e)), (a-b)*((d-c)^(e-d))] : Expecting False, Wolfram Alpha returns forms and solutions
• Equal[ToExpression["(a-b)+c"],ToExpression["(c-b)+a"]] : Expecting True, Wolfram Alpha defines the word "equal"
• Equal[ToExpression["(a-b)+c"],ToExpression["(a-c)+b"]] : Expecting False, Wolfram Alpha defines the word "equal"

I want to write a program to generate some expressions, and then compare those expressions to see if they are symbolically the same. I won't be assigning values to the "variables" in these expressions. I just need true/false on whether two symbolic expressions are equal.

I've had problems with both Equal and SameQ. I just checked a few more examples and SameQ fails to correctly compare the following symbolic equations: SameQ[(a-b)/(c-d), (b-a)/(d-c)]. Equal[] correctly identifies that those two symbolic equations are equal.

However, Equal[] doesn't always return a True/False answer like I am looking for. When I run Equal[(a-b)+c,(a-c)+b], it returns a plot and different forms/solutions of the input. If there was an EqualQ, that would probably be what I need. Is there some way to get Equal[] to just return True/False instead of trying to "solve" the input?

Also, does Mathematica do anything different when running the above statements? Does Equal[] in Mathematica just return True/False, or does it try to "solve" the input?

Here are some sample inputs and associated outputs I would like to get:

• Equal[(a-b)+c,(c-b)+a] -> True
• Equal[(a-b)+c,(a-c)+b] -> False
• Equal[(a-b)/(c-d),(b-a)/(d-c)] -> True
• Equal[(a-b)/(c-d),(b-a)/(c-d)] -> False
• Equal[(a-b)/((c-d)^(d-e)), (a-b)*((c-d)^(e-d))] -> True
• Equal[(a-b)/((c-d)^(d-e)), (a-b)*((d-c)^(e-d))] -> False

And, this is just finding the correct function to get the results I would like. Then there is the question of how to programmatically generate "something" that can be fed into that function to symbolically compare for equality. It would be easy to generate strings, but Equal[] (at least on Wolfram Alpha) doesn't seem to understand strings. ie, it fails to correctly interpret Equal["(a-b)+c","(c-b)+a"].