correction:
In last line
-unlimited should read negative infinity.
-M
At 2023-01-04 10:27, you wrote:
Not trying to make a point here, simply citing
E.J. Barbeau, "Polynomials", pp 1,2:
[my transcription- beware of typos]
\"
In the title of this section, we promised you some anatomy. Here it is.
For the polynomial, a[n] * t^n+ a[n-1] *
t^(n-1)+ ... a[1] * t+ a[0], with a[n] /= 0, the
numbers a[i] (0 <= i <= n) are called oefficients.
a[n] is the leading coefficient, and a[n] * t^n
the leading term, a[0] is the constant term or the constant coefficient.
a[1] is the linear coefficient and a[1] * t the linear term.
When the leading coefficient an is 1, the polynomial is said to be monic.
The nonnegative integer n is the degree of the polynomial;
we write degp = n.
A constant polynomial has but a single term, a[0].
A nonzero constant polynomial has degree 0, but,
by convention, the zero polynomial (all
coefficients vanishing) has degree -unlimited (__). <<<<<<
"\
Thanks.
-M
At 2023-01-04 03:40, you wrote:
You are essentially saying that ((i. 0) p. y)
should be defined the same as (0 p. y). I see
no justification for this. We don't treat (i.
0) as identical to (0). (i. 0) is not a
polynomial and trying to make it one is a
kludge that will come to grief. I think it already has:
What is the integral of (i. 0)?
If (i. 0) as a polynomial is the same as 0, the
answer has to be 0 1, which is inconsistent with simple definitions.
It is not always a good thing to expand the
domain of a verb.Ã If you expanded the domain
of + to include characters, there would be
fewer errors but much more gnashing of teeth by
users. I say that if a user thinks that x is a
polynomial and x is empty, they have a bug and
the sooner they learn that, the better.
Henry Rich
On 1/3/2023 5:06 PM, Raul Miller wrote:
In J807:
(i.0) p. 2
0
In the current j904 beta:
(i.0) p. 2
|domain error, executing dyad p.
|polynomial may not be empty
| (i.0) p.2
I think this change should be reverted.
I have not researched the full history of this change, but J
polynomials may be padded with an arbitrary number of trailing zeros
without changing their significance. So, mathematically speaking,
empty polynomials should be within the domain of the p. verb.
But, also, this breaks typical general case implementation of a
derivative operation on polynomials. In other words, this worked fine
under j807:
pderiv=: 1 }. (* i.@#)
(pderiv 5) p. 2
0
Thanks,
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