Apologies for a mistake in my previous post, below.
This was where I said
"This trick for my [function] div is analogous to allowing for
leading decimal zeros
in 1234 % 0.0001 in "ordinary" long division."
I'd forgotten that J's representation of polynomials is not the same as its
representation of numbers to some base; the former has the zero power
leading (leftmost), whereas number representation has the highest power
leading. My remark applies ok for the number representation but not
for polynomial coefficients. In the latter case, extra leading zeros
add to
the power of the polynomial, so their effect on a divisor is to DECREASE
the power of the result, the quotient. I haven't yet had time to correct
"div" to allow for this.
Also, I realise I'd misused "quotient" when I meant "divisor" in earlier
postings!
Not so cheerily,
Mike
On 20/02/2022 18:05, 'Michael Day' via Programming wrote:
I suppose dyad |. !0 is better than dyad }. by keeping the result in
place.
Anyway, although I agree that it seems attractive to ignore those
zeros,
your get-around doesn't seem to apply!!! - unless I'm missing something.
I embedded an echo:
...
if. 0={.y do. j=. j-i=. 0 i.~ 0=y
echo '0={.y';x;y
...
I encountered an error in this mickey mouse test:
1 0 0 0 0 0 0 0 0 1 pDiv 0 0 0 1 0 1
┌─────┬───────────────────┬───────────────────┐
│0={.y│1 0 0 0 0 0 0 0 0 1│0 0 0 1 0 1 0 0 0 0│
└─────┴───────────────────┴───────────────────┘
┌─────┬───────────────────┬───────────────────┐
│0={.y│0 0 0 0 0 0 0 1 0 0│0 0 0 1 0 1 0 0 0 0│
└─────┴───────────────────┴───────────────────┘
|domain error: pDiv
| q=.q,j #0
but maybe these arguments aren't like those for pDiv in the Rosetta
Code task.
This trick for my div is analogous to allowing for leading decimal zeros
in 1234 % 0.0001 in "ordinary" long division. I wonder if it's what you
intended.
NB. x % y
div =: 3 : 0 NB. similar result to Ken's dbho
:
q =. ''
NB. allow for leading zeros in quotient
if. 0 = {. y do.
j =. 0 i.~ 0 = y
y =. j }. y
x =. x, 0#~ >: j
end.
yx=. y,:x
assert. 2 <: n =. 2 + x -&# y
while. n =. <: n do.
q =. q, r =. %~/ {."1 yx
yx =. y,: }. -~/ yx * r,1
end.
q
)
1 2 3 4 div 0 0 0 1
1 2 3 4 0 0 0 0
1234 % 0.0001
12340000
Anyway, my extra echo reports nothing when running this:
cyclotomic >: i.1000
so I suspect that the check is not necessary here.
Mike
On 20/02/2022 16:35, Raul Miller wrote:
For what it's worth, here's what I was focusing on:
http://rosettacode.org/wiki/Cyclotomic_polynomial#J
As you can see, I altered your polynomial division algorithm --
there's enough zeros in the polynomials I was working with, there,
that iterating through them seemed unwise.
If there's any other significant improvements that you notice -- or
any errors which I overlooked, of course, please let me know!
Thanks,
--
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