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Symbolic Integration

Started by Sagar_Indurkhya Jun 26, 2007 at 4:33 PM 7 replies 1.4k views
Original Post
Sagar_Indurkhya
Sagar_Indurkhya
I was wondering if anyone could point me towards any literature or such on symbolic integration and computer algebra systems, but googling mostly turns up definitions and histories of the subject. I've also been trying to get ahold of Slagle's thesis since he apparently wrote the first symbolic integrator program, but have not had any luck.
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superpig
superpig
I thought symbolic integrators were mostly just pattern-matchers: x^y -> 1/(y+1) x^(y+1), etc.
Richard "Superpig" Fine - saving pigs from untimely fates - Microsoft DirectX MVP 2006/2007/2008/2009
"Shaders are not meant to do everything. Of course you can try to use it for everything, but it's like playing football using cabbage." - MickeyMouse
furby100
furby100
Quote:
Original post by superpig
I thought symbolic integrators were mostly just pattern-matchers: x^y -> 1/(y+1) x^(y+1), etc.


That rule only works for polynomials. What a proper symbolic integrator needs is a full method for doing any kind of expression involving the elementary operators, and spotting if it's an impossible integral like an elliptic integral or e^(x^2). So there are a lot more cases.
twix
twix
Quote:
Original post by furby100
Quote:
Original post by superpig
I thought symbolic integrators were mostly just pattern-matchers: x^y -> 1/(y+1) x^(y+1), etc.


That rule only works for polynomials. What a proper symbolic integrator needs is a full method for doing any kind of expression involving the elementary operators, and spotting if it's an impossible integral like an elliptic integral or e^(x^2).

Why would pattern matching not be able to do this?

I know that Mathematica has a very competent symbolic integrator, and the entire core of that system is nothing more than a huge pattern matching engine.
superpig
superpig
My thoughts exactly. Certainly the way I was taught to integrate things by hand involved learning a load of different forms and then simply applying the right ones in turn.
Richard "Superpig" Fine - saving pigs from untimely fates - Microsoft DirectX MVP 2006/2007/2008/2009
"Shaders are not meant to do everything. Of course you can try to use it for everything, but it's like playing football using cabbage." - MickeyMouse
furby100
furby100
Quote:
Original post by twix
Quote:
Original post by furby100
Quote:
Original post by superpig
I thought symbolic integrators were mostly just pattern-matchers: x^y -> 1/(y+1) x^(y+1), etc.


That rule only works for polynomials. What a proper symbolic integrator needs is a full method for doing any kind of expression involving the elementary operators, and spotting if it's an impossible integral like an elliptic integral or e^(x^2).

Why would pattern matching not be able to do this?

I know that Mathematica has a very competent symbolic integrator, and the entire core of that system is nothing more than a huge pattern matching engine.


Who said it couldn't? The point is that forming the correct set of rules and doing the right transformations is far from simple. Did either of you look at the link I gave? If this is the sort of treatment I can expect when I try to help people I shall fall back to my old habits and refrain from doing so in future.
twix
twix
Quote:
Original post by furby100
Quote:
Original post by twix
Quote:
Original post by furby100
Quote:
Original post by superpig
I thought symbolic integrators were mostly just pattern-matchers: x^y -> 1/(y+1) x^(y+1), etc.


That rule only works for polynomials. What a proper symbolic integrator needs is a full method for doing any kind of expression involving the elementary operators, and spotting if it's an impossible integral like an elliptic integral or e^(x^2).

Why would pattern matching not be able to do this?

I know that Mathematica has a very competent symbolic integrator, and the entire core of that system is nothing more than a huge pattern matching engine.


Who said it couldn't? The point is that forming the correct set of rules and doing the right transformations is far from simple. Did either of you look at the link I gave? If this is the sort of treatment I can expect when I try to help people I shall fall back to my old habits and refrain from doing so in future.

That... wasn't exactly supposed to be a personal attack. Sorry?
furby100
furby100
Quote:
Original post by twix
Quote:
Original post by furby100
Quote:
Original post by twix
Quote:
Original post by furby100
Quote:
Original post by superpig
I thought symbolic integrators were mostly just pattern-matchers: x^y -> 1/(y+1) x^(y+1), etc.


That rule only works for polynomials. What a proper symbolic integrator needs is a full method for doing any kind of expression involving the elementary operators, and spotting if it's an impossible integral like an elliptic integral or e^(x^2).

Why would pattern matching not be able to do this?

I know that Mathematica has a very competent symbolic integrator, and the entire core of that system is nothing more than a huge pattern matching engine.


Who said it couldn't? The point is that forming the correct set of rules and doing the right transformations is far from simple. Did either of you look at the link I gave? If this is the sort of treatment I can expect when I try to help people I shall fall back to my old habits and refrain from doing so in future.

That... wasn't exactly supposed to be a personal attack. Sorry?


Ah, I see. OK then.

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