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Re: (Golf) Multiply polynomials

by jeroenes (Priest)
on May 11, 2001 at 13:30 UTC ( #79662=note: print w/replies, xml ) Need Help??

in reply to (Golf) Multiply polynomials

I know it's a tad late, but here is my $0.01. To my opinion PDL is neglected around here, and I know I use it too little myself.

With the help of PDL I only use 43 chars for the sub, and if I looked right, it's a record in this thread. You may add 8 chars if you want to account for the extra 'use PDL;' statement:

use PDL: sub p{$t=pdl+pop;$t=$t*(pdl$_)for@_;[list$t]}
This doesn't work with arrays of unequal length, but that wasn't in the spec. The output:
print join " ", @{p([1..5],[1..5])}; 1 4 9 16 25
BTW, tilly, why did you name it 'polynomials'? Isn't it just a breed of recursive vector multiplication? Do I miss something?

And, 'strictness' requires only 3 extra chars with a total of 46/54 chars (54 still is the record):

sub p{my $t=pdl+pop;$t=$t*(pdl$_)for@_;[list$t]}
"We are not alone"(FZ) Update Thx to tye I now know why tilly talked about polynomials. Sorry. If we still want a matrix-kind solution, it would be like:
A = p1'*p2; product = crossdiags(A);
But that's difficult to code in PDL, unfortunately. Here is my 2nd attempt, works only if poly's are equal length (pathetic 164 chars):
sub p{$t=pdl+pop;for(@_){ my $a=outer$t,pdl+pop; transpose($a); my $n=-1+nelem$t; $t=zeroes($n*2+1); $t->slice("$_:".($_+$n))+=$a->slice("$_,:")for 0..$n; } [list$t]}
Will ponder it a bit more and get back....

Replies are listed 'Best First'.
Re: Re: (Golf) Multiply polynomials
by tye (Sage) on May 11, 2001 at 13:43 UTC

    Sorry, wrong problem.

    p([1..5],[1..5]) should produce [qw(1 4 10 20 35 44 46 40 25)] because ( 1 + 2x + 3x^2 + 4x^3 + 5x^4 ) * ( 1 + 2x + 3x^2 + 4x^3 + 5x^4 )
    is equal to 1 + 4x + 10x^2 + 20x^3 + 35x^4 + 44x^5 + 46x^6 + 40x^7 + 25x^8
    where ^ is exponentiation (** in Perl), not bit-wise XOR.

            - tye (but my friends call me "Tye")

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