[Maxima-bugs] [maxima:bugs] #4589 guess fails on trivial cases

[Stavros M. <mac...@us...>]

Ah! The documentation is actually at a different place (not devine): /share/contrib/guess/guess.info

That clarifies that "product" here means not multiplication, but an indexed product(...). Which also explains how it handles 2^n = product(2,i,1,n) and n! = product(i,i,1,n).


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**[bugs:#4589] guess fails on trivial cases**

**Status:** open
**Group:** None
**Created:** Wed Jul 30, 2025 04:39 PM UTC by Stavros Macrakis
**Last Updated:** Wed Jul 30, 2025 08:49 PM UTC
**Owner:** nobody


~~~~
load(devine)$
guess([0,0,0]) => expt: undefined: 0 to a negative exponent.
guess([0,1,0,1]) => same error
guess(makelist(1+2^i,i,1,10)) => fails
~~~~

The only documentation for this function is in the source, and it says cryptically 
> it tries to find a closed form for a sequence within the hierarchy of expressions of the form <rational function\>, <product of rational functions>, <product of product of rational functions>, etc. It may give several answers 

Ah, so those sequences (not even 0,0,0?) aren't in its domain.

Also, it appears that the required length of the sequence grows with the exponents -- this should be documented:
~~~~
guess(makelist(i^9,i,1,10)) => []
guess(makelist(i^9,i,1,11)) => [i0^9] <<< OK!
guess(makelist(i^9,i,1,20)) => Extremely slow
guess(makelist(i^5/(i^5+1),i,1,10)) => []    
guess(makelist(i^5/(i^5+1),i,1,14)) => OK
~~~~
At the same time, it looks like time is super-exponential in the length of the sequence.

And surely ''guess'' is an awfully broad name for such a special-purpose function!

5.48.0 SBCL 2.5.7 MacOS


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