The search for polynomials

June 15, 2009 in Research | Comments (3)

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First, some excit­ing news that I’ve added the Pola pro­ject as my first pro­ject. There is a Sub­ver­sion repos­it­ory for it as well. We’ve been talk­ing about get­ting a site set up around Pola, with examples and user’s guides and maybe some inter­act­ive fea­tures, so this is a very small first step towards that.

Code-​​wise, what I’ve been work­ing on lately is finally try­ing to do bounds infer­ence prop­erly in the imple­ment­a­tion. The bounds infer­ence still isn’t entirely done and what’s there still isn’t work­ing entirely per­fectly, but it is excit­ingly close! Type in any well-​​typed func­tion which relies only on induct­ive data types and it will give you poly­no­mial bound on the run­ning time! Coin­duct­ive data types will come soon.

In an effort to mak­ing my “bor­ing” research blog more inter­est­ing, I’ve now even got a screen­shot! Is code any more excit­ing when it’s in screen­shot form?

The biggest prob­lem I’ve had so far is writ­ing my own Poly­no­mial data type in Haskell. I don’t even need any­thing fancy: I need addi­tion, sub­trac­tion and mul­ti­plic­a­tion of poly­no­mi­als over arbit­rary vari­ables. Sadly I haven’t found any­thing suit­able and had to build my own. I’m a little out of my depth here: it would be a pretty big under­state­ment to say that I’m ignor­ant when it comes to com­puter algebra. It’s a vir­tual cer­tainty that I’m doing my data rep­res­ent­a­tions and arith­metic oper­a­tions in the least effi­cient way pos­sible. But I can’t worry too much about; this isn’t really what my research is about.

If I find time today I think I’ll go through some com­puter algebra sys­tems to find one which has a suit­ably free licence and has a reas­on­able For­eign Func­tion Inter­face (so that I can use it pain­lessly from Haskell). Does such a thing exist?


3 Responses to “The search for polynomials”

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  1. Comment by Mark — June 15, 2009 at 4:27 pm   Reply

    Have you con­sidered tak­ing a look at Aldor for your poly­no­mial requirements?

    • Comment by mikeJune 15, 2009 at 4:31 pm   Reply

      I’ve con­sidered it, but I haven’t been able to look at in depth (Stephen forced Aldor on us sur­pris­ingly little in his course). If it’s got a nice cross-​​language inter­face I’m all over it, though.

  2. Comment by Robin’s visit to London « Wizardlike researchJune 17, 2009 at 10:22 pm   Reply

    […] for the prob­lem I men­tioned last time about hav­ing to imple­ment my own poly­no­mial arith­metic: I just rewrote it myself and I’m […]

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