26-02-2005 01:13									#1
	Script to replace "a^b" in an expression with "pow(a,b)" Support Apolyton, buy GURPS/ Alpha Centauri

I have a few beastly mathematical expressions that I need to use in C++, but I got it from Maple. Maple uses "^" as the exponentiation operator, incompatible with C (which uses pow().

So, I need a script to go from a^b to pow(a,b).

For instance, here's one of them:

1/12/d/k/tan(b)/a*((6*sqrt(3)*r*sqrt(-k^4*a^4-a^4*d^4*tan(b)^4*k^2-2*a^4*d^2*tan(b)^2*k^3+4*k^3*a^3*r*tan(b)^2-4*k^2*a^2*r^2*tan(b)^4-2*a^4*tan(b)^4*d^2*k^2+4*a^3*tan(b)^4*k^2*r-2*a^4*tan(b)^2*k^3-a^4*tan(b)^4*k^2+4*a^3*d^2*tan(b)^4*k^2*r- 16*r*k^4*d*tan(b)^2*a^2+k^3*a^4+a^4*tan(b)^6+3*a^4
*tan(b)^6*d^2+a^4*d^6*tan(b)^6- 8*a*r^3*tan(b)^6+3*a^4*tan(b)^2*k^2+12*a^2*tan(b)^
6*r^2-6*a^3*tan(b)^6*r+3*a^4*tan(b)^6*d^4-12*a^3*d^2*tan(b)^4*k*r+3*a^4*d^2*tan(b)^2*k^2- 12*a^3*tan(b)^6*d^2*r+6*a^4*tan(b)^4*d^2*k+12*a^2*
d^2*tan(b)^6*r^2+27*r^2*tan(b)^4*d^2*k^2+3*a^4*d^4
*tan(b)^4*k-6*a^3*d^4*tan(b)^6*r+12*k*a^2*r^2*tan(b)^4-6*k^2*a^3*r*tan(b)^2- 12*a^3*tan(b)^4*k*r+18*r*d*k^2*tan(b)^4*a^2+18*r*d
^3*k^2*tan(b)^4*a^2+18*r*d*k^3*tan(b)^2*a^2- 36*r^2*d*k^2*tan(b)^4*a+3*a^4*tan(b)^4*k)*d*k*tan(
b)^2+k^3*a^4+a^4*tan(b)^6+3*a^4*tan(b)^6*d^2+a^4*d
^6*tan(b)^6- 8*a*r^3*tan(b)^6+3*a^4*tan(b)^2*k^2+12*a^2*tan(b)^
6*r^2-6*a^3*tan(b)^6*r+3*a^4*tan(b)^6*d^4-12*a^3*d^2*tan(b)^4*k*r+3*a^4*d^2*tan(b)^2*k^2- 12*a^3*tan(b)^6*d^2*r+6*a^4*tan(b)^4*d^2*k+12*a^2*
d^2*tan(b)^6*r^2+54*r^2*tan(b)^4*d^2*k^2+3*a^4*d^4
*tan(b)^4*k-6*a^3*d^4*tan(b)^6*r+12*k*a^2*r^2*tan(b)^4-6*k^2*a^3*r*tan(b)^2- 12*a^3*tan(b)^4*k*r+18*r*d*k^2*tan(b)^4*a^2+18*r*d
^3*k^2*tan(b)^4*a^2+18*r*d*k^3*tan(b)^2*a^2-36*r^2*d*k^2*tan(b)^4*a+3*a^4*tan(b)^4*k)*a^2)^(1/3)-1/ 12*(12*r*k^2*d*tan(b)^2+a^2*tan(b)^4+2*a^2*tan(b)^
4*d^2+2*a^2*tan(b)^2*k- 4*a*tan(b)^4*r+a^2*d^4*tan(b)^4+2*a^2*d^2*tan(b)^2
*k-4*a*d^2*tan(b)^4*r+k^2*a^2-4*k*a*r*tan(b)^2+4*r^2*tan(b)^4)/k/d/tan(b)*a/((6*sqrt(3)*r*sqrt(-k^4*a^4-a^4*d^4*tan(b)^4*k^2-2*a^4*d^2*tan(b)^2*k^3+4*k^3*a^3*r*tan(b)^2-4*k^2*a^2*r^2*tan(b)^4-2*a^4*tan(b)^4*d^2*k^2+4*a^3*tan(b)^4*k^2*r-2*a^4*tan(b)^2*k^3-a^4*tan(b)^4*k^2+4*a^3*d^2*tan(b)^4*k^2*r- 16*r*k^4*d*tan(b)^2*a^2+k^3*a^4+a^4*tan(b)^6+3*a^4
*tan(b)^6*d^2+a^4*d^6*tan(b)^6- 8*a*r^3*tan(b)^6+3*a^4*tan(b)^2*k^2+12*a^2*tan(b)^
6*r^2-6*a^3*tan(b)^6*r+3*a^4*tan(b)^6*d^4-12*a^3*d^2*tan(b)^4*k*r+3*a^4*d^2*tan(b)^2*k^2- 12*a^3*tan(b)^6*d^2*r+6*a^4*tan(b)^4*d^2*k+12*a^2*
d^2*tan(b)^6*r^2+27*r^2*tan(b)^4*d^2*k^2+3*a^4*d^4
*tan(b)^4*k-6*a^3*d^4*tan(b)^6*r+12*k*a^2*r^2*tan(b)^4-6*k^2*a^3*r*tan(b)^2- 12*a^3*tan(b)^4*k*r+18*r*d*k^2*tan(b)^4*a^2+18*r*d
^3*k^2*tan(b)^4*a^2+18*r*d*k^3*tan(b)^2*a^2- 36*r^2*d*k^2*tan(b)^4*a+3*a^4*tan(b)^4*k)*d*k*tan(
b)^2+k^3*a^4+a^4*tan(b)^6+3*a^4*tan(b)^6*d^2+a^4*d
^6*tan(b)^6- 8*a*r^3*tan(b)^6+3*a^4*tan(b)^2*k^2+12*a^2*tan(b)^
6*r^2-6*a^3*tan(b)^6*r+3*a^4*tan(b)^6*d^4-12*a^3*d^2*tan(b)^4*k*r+3*a^4*d^2*tan(b)^2*k^2- 12*a^3*tan(b)^6*d^2*r+6*a^4*tan(b)^4*d^2*k+12*a^2*
d^2*tan(b)^6*r^2+54*r^2*tan(b)^4*d^2*k^2+3*a^4*d^4
*tan(b)^4*k-6*a^3*d^4*tan(b)^6*r+12*k*a^2*r^2*tan(b)^4-6*k^2*a^3*r*tan(b)^2- 12*a^3*tan(b)^4*k*r+18*r*d*k^2*tan(b)^4*a^2+18*r*d
^3*k^2*tan(b)^4*a^2+18*r*d*k^3*tan(b)^2*a^2-36*r^2*d*k^2*tan(b)^4*a+3*a^4*tan(b)^4*k)*a^2)^(1/3)+1/6*(a*tan(b)^2+a*d^2*tan(b)^2+k*a-2*r*tan(b)^2)/k/d/tan(b)+1/2*I*sqrt(3)*(1/6/d/k/tan(b)/a*((6*sqrt(3)*r*sqrt(-k^4*a^4-a^4*d^4*tan(b)^4*k^2-2*a^4*d^2*tan(b)^2*k^3+4*k^3*a^3*r*tan(b)^2-4*k^2*a^2*r^2*tan(b)^4-2*a^4*tan(b)^4*d^2*k^2+4*a^3*tan(b)^4*k^2*r-2*a^4*tan(b)^2*k^3-a^4*tan(b)^4*k^2+4*a^3*d^2*tan(b)^4*k^2*r- 16*r*k^4*d*tan(b)^2*a^2+k^3*a^4+a^4*tan(b)^6+3*a^4
*tan(b)^6*d^2+a^4*d^6*tan(b)^6- 8*a*r^3*tan(b)^6+3*a^4*tan(b)^2*k^2+12*a^2*tan(b)^
6*r^2-6*a^3*tan(b)^6*r+3*a^4*tan(b)^6*d^4-12*a^3*d^2*tan(b)^4*k*r+3*a^4*d^2*tan(b)^2*k^2- 12*a^3*tan(b)^6*d^2*r+6*a^4*tan(b)^4*d^2*k+12*a^2*
d^2*tan(b)^6*r^2+27*r^2*tan(b)^4*d^2*k^2+3*a^4*d^4
*tan(b)^4*k-6*a^3*d^4*tan(b)^6*r+12*k*a^2*r^2*tan(b)^4-6*k^2*a^3*r*tan(b)^2- 12*a^3*tan(b)^4*k*r+18*r*d*k^2*tan(b)^4*a^2+18*r*d
^3*k^2*tan(b)^4*a^2+18*r*d*k^3*tan(b)^2*a^2- 36*r^2*d*k^2*tan(b)^4*a+3*a^4*tan(b)^4*k)*d*k*tan(
b)^2+k^3*a^4+a^4*tan(b)^6+3*a^4*tan(b)^6*d^2+a^4*d
^6*tan(b)^6- 8*a*r^3*tan(b)^6+3*a^4*tan(b)^2*k^2+12*a^2*tan(b)^
6*r^2-6*a^3*tan(b)^6*r+3*a^4*tan(b)^6*d^4-12*a^3*d^2*tan(b)^4*k*r+3*a^4*d^2*tan(b)^2*k^2- 12*a^3*tan(b)^6*d^2*r+6*a^4*tan(b)^4*d^2*k+12*a^2*
d^2*tan(b)^6*r^2+54*r^2*tan(b)^4*d^2*k^2+3*a^4*d^4
*tan(b)^4*k-6*a^3*d^4*tan(b)^6*r+12*k*a^2*r^2*tan(b)^4-6*k^2*a^3*r*tan(b)^2- 12*a^3*tan(b)^4*k*r+18*r*d*k^2*tan(b)^4*a^2+18*r*d
^3*k^2*tan(b)^4*a^2+18*r*d*k^3*tan(b)^2*a^2-36*r^2*d*k^2*tan(b)^4*a+3*a^4*tan(b)^4*k)*a^2)^(1/3)-1/ 6*(12*r*k^2*d*tan(b)^2+a^2*tan(b)^4+2*a^2*tan(b)^4
*d^2+2*a^2*tan(b)^2*k- 4*a*tan(b)^4*r+a^2*d^4*tan(b)^4+2*a^2*d^2*tan(b)^2
*k-4*a*d^2*tan(b)^4*r+k^2*a^2-4*k*a*r*tan(b)^2+4*r^2*tan(b)^4)/k/d/tan(b)*a/((6*sqrt(3)*r*sqrt(-k^4*a^4-a^4*d^4*tan(b)^4*k^2-2*a^4*d^2*tan(b)^2*k^3+4*k^3*a^3*r*tan(b)^2-4*k^2*a^2*r^2*tan(b)^4-2*a^4*tan(b)^4*d^2*k^2+4*a^3*tan(b)^4*k^2*r-2*a^4*tan(b)^2*k^3-a^4*tan(b)^4*k^2+4*a^3*d^2*tan(b)^4*k^2*r- 16*r*k^4*d*tan(b)^2*a^2+k^3*a^4+a^4*tan(b)^6+3*a^4
*tan(b)^6*d^2+a^4*d^6*tan(b)^6- 8*a*r^3*tan(b)^6+3*a^4*tan(b)^2*k^2+12*a^2*tan(b)^
6*r^2-6*a^3*tan(b)^6*r+3*a^4*tan(b)^6*d^4-12*a^3*d^2*tan(b)^4*k*r+3*a^4*d^2*tan(b)^2*k^2- 12*a^3*tan(b)^6*d^2*r+6*a^4*tan(b)^4*d^2*k+12*a^2*
d^2*tan(b)^6*r^2+27*r^2*tan(b)^4*d^2*k^2+3*a^4*d^4
*tan(b)^4*k-6*a^3*d^4*tan(b)^6*r+12*k*a^2*r^2*tan(b)^4-6*k^2*a^3*r*tan(b)^2- 12*a^3*tan(b)^4*k*r+18*r*d*k^2*tan(b)^4*a^2+18*r*d
^3*k^2*tan(b)^4*a^2+18*r*d*k^3*tan(b)^2*a^2- 36*r^2*d*k^2*tan(b)^4*a+3*a^4*tan(b)^4*k)*d*k*tan(
b)^2+k^3*a^4+a^4*tan(b)^6+3*a^4*tan(b)^6*d^2+a^4*d
^6*tan(b)^6- 8*a*r^3*tan(b)^6+3*a^4*tan(b)^2*k^2+12*a^2*tan(b)^
6*r^2-6*a^3*tan(b)^6*r+3*a^4*tan(b)^6*d^4-12*a^3*d^2*tan(b)^4*k*r+3*a^4*d^2*tan(b)^2*k^2- 12*a^3*tan(b)^6*d^2*r+6*a^4*tan(b)^4*d^2*k+12*a^2*
d^2*tan(b)^6*r^2+54*r^2*tan(b)^4*d^2*k^2+3*a^4*d^4
*tan(b)^4*k-6*a^3*d^4*tan(b)^6*r+12*k*a^2*r^2*tan(b)^4-6*k^2*a^3*r*tan(b)^2- 12*a^3*tan(b)^4*k*r+18*r*d*k^2*tan(b)^4*a^2+18*r*d
^3*k^2*tan(b)^4*a^2+18*r*d*k^3*tan(b)^2*a^2-36*r^2*d*k^2*tan(b)^4*a+3*a^4*tan(b)^4*k)*a^2)^(1/3));

I tried doing a find and replace shtick over and over again, but I definitely missed some things.

Any ideas?

	26-02-2005 01:15									#2
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What editor are you using? Emacs?

	26-02-2005 01:16									#3
	Avatar Enlargement: We've got the solution

MS Visual Studio.

But I can use another editor if needed of course...

I should probably just go back and rewrite the program in Fortran which doesn't have this stupid restriction...

	26-02-2005 02:10									#4
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Probably be easier to turn ^ into an operator in C++. Forget how that's done, though.

Or maybe you can only overload operators, not create new ones. I forget offhand, and my C++ blackbook is at work.

Edit: Nevermind, you can't define new operators, you can only overload existing ones. Piece of crap language...

	26-02-2005 02:12									#5
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Problem is, the ^ operator is already defined on numbers and such in C++ - it's the bitwise xor.

	26-02-2005 02:23									#6
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The problem with overloading ^ is the order in which C evaluates * and / in relation to it.

So 2*k^2 will end up being evaluated as (2*k)^2.

	26-02-2005 02:30									#7
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s/+\w\^+\w/pow($1,$2)/g;

in a perl script should do the trick
(if this is not the exact line, it comes real close)

edit: added + since your expressions may be more than 1 character long.

	26-02-2005 02:35									#8
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Thanks, I'll try that out.

	26-02-2005 03:05									#9
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That doesn't even remotely cover it, pchang, I'm afraid... See the last use of the ^ in the one Ramo provided, for instance. It's got complex nested expressions. The one you suggested wouldn't even work with "tan(b)^4".

And, um, the one you suggested doesn't work. It should be:
s/(\w+)\^(\w+)/pow($1,$2)/g;

This one works a bit better, it'll also take functions (e.g. "tan(b)") or parenthesized expressions, but it won't work with nested parentheses:
s/(\w+(?:\([^()]*\))?)\^(\w*(?:\(.*?\))?)/pow($1,$2)/g;

That reduces the number of ^ from 794 to 4 in the one in your first post though, so you can reasonably finish it off manually.

	26-02-2005 03:10									#10
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I bow to the superior intellect

	26-02-2005 03:11									#11
	Got spare money?

WTF is that thing anyway?

	26-02-2005 03:21									#12
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quote: Originally posted by pchang I bow to the superior intellect

You beat me to mentioning regular expressions though. I didn't mean to be too harsh.

quote: Originally posted by Kuciwalker WTF is that thing anyway?

I hope you're not talking about that regular expression. I'm wondering what the hell Ramo's monster expressions are.

	26-02-2005 03:27									#13
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I'm talking about Ramo's monster.

	26-02-2005 03:27									#14
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quote: s/(\w+(?:\([^()]*\))?)\^(\w*(?:\(.*?\))?)/pow($1,$2)/g;

And to think, that was going be the name of my next DL...

	26-02-2005 03:30									#15
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Why don't you just write a C program to do what you need, to replace a^b with pow(a,b) should be too hard of a program to make.

	26-02-2005 03:58									#16
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Because I'm lazy, I hate programming, and it's not quite trivial given that "a" can be tan(b), parenthetical expressions, etc.

quote: WTF is that thing anyway?

Shining light down on a plasma, and seeing where the ray intersects its surface. I can't solve it analytically since the plasma's surface has a funky transcendental shape, so I'm using Newton's method to find the solutions. For my initial guesses I quadratically expanded around a certain parameter of the plasma (something that I had absolutely no right to assume as being << 1), to get a cubic equation in the sine of the parametric variable for the plasma's surface. And that expression above is one of the solutions to that equation.

Thanks Mercator.

	26-02-2005 04:04									#17
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I applied for a job in Austin...

	26-02-2005 04:09									#18
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Where at?

	26-02-2005 04:13									#19
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quote: Originally posted by Ramo Because I'm lazy, I hate programming, and it's not quite trivial given that "a" can be tan(b), parenthetical expressions, etc. quote: WTF is that thing anyway? Shining light down on a plasma, and seeing where the ray intersects its surface. I can't solve it analytically since the plasma's surface has a funky transcendental shape, so I'm using Newton's method to find the solutions. For my initial guesses I quadratically expanded around a certain parameter of the plasma (something that I had absolutely no right to assume as being << 1), to get a cubic equation in the sine of the parametric variable for the plasma's surface. And that expression above is one of the solutions to that equation. Thanks Mercator.

...

couldn't you just check random values until it fit? That'd be simpler...

	26-02-2005 04:14									#20
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quote: Where at?

Abbott Labs

	26-02-2005 04:17									#21
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quote: Originally posted by Ramo Shining light down on a plasma, and seeing where the ray intersects its surface. (...)

quote: Thanks Mercator.

No problem

	26-02-2005 04:18									#22
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quote: Shining light down on a plasma, and seeing where the ray intersects its surface. I can't solve it analytically since the plasma's surface has a funky transcendental shape, so I'm using Newton's method to find the solutions. For my initial guesses I quadratically expanded around a certain parameter of the plasma (something that I had absolutely no right to assume as being << 1), to get a cubic equation in the sine of the parametric variable for the plasma's surface. And that expression above is one of the solutions to that equation.

That's the nerdiest thing I have heard... since the OP

	26-02-2005 04:24									#23
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Hopefully I'll finish this soon so I can get well drunk and stoned and forget that I wasted a week on this.

quote: couldn't you just check random values until it fit? That'd be simpler...

Yeah, but it'd take forever to compute.

	26-02-2005 04:25									#24
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quote: Originally posted by Kuciwalker ... couldn't you just check random values until it fit? That'd be simpler...

That's essentially what Newton's method is.

	26-02-2005 04:30									#25
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Forget about doing that automaticlly - it's a waste of time. Also drop using MS tools - they sucks - use vi (no, this is not std MS bashing - I work on both unix and MS platforms, and vi is the winner).

Repeat search for ^ and make global subsititute for what you find one by one. It may sound tedious, but is much more effective than trying to figure out a way to solve it in one step. It isn't as bad as it may sound - there are of repeated statements that will be fixed by one statement.

	26-02-2005 04:32									#26
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Watch Numb3rs tonight, I hear they go over this!

	26-02-2005 04:39									#27
	Increase Your PM Length

If you have multiple files, then try using cscope to make changes in those files involved. It's quite effective - I once turned a pascal program into c with this tool.

	26-02-2005 04:46									#28
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I don't know BC, Mercator's solution seems pretty good. Like I said, I tried finding and replacing, and screwed up somehow.

Mercator, I just installed Active Perl. Now, how would I run your script?

	26-02-2005 04:55									#29
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That is insane...

	26-02-2005 04:56									#30
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Problem is that you easily spend much more time trying to invent the smart solution than just do the boring stuff.

If it is something that you expect to do a lot in the future, then I'm in for the smart thing - otherwise it's my experience it's just a waste of time (admitted, it can be fun to make such a regexp )