Ah, I see--per wikipedia, it's so that the degree of the product of two
polynomials is the sum of their degrees. Eh.
On Tue, 3 Jan 2023, Henry Rich wrote:
That's the most common definition of polynomial degree.
Henry Rich
On 1/3/2023 7:55 PM, Elijah Stone wrote:
A polynomial is a sum. An empty polynomial has no summands; and no
summands sum to 0.
An empty polynomial should have degree 0. Why do you say a polynomial
with a singular term of 0 has degree __?
I agree with raul.
On Tue, 3 Jan 2023, Henry Rich wrote:
I disagree. A polynomial must have at least one term, in
mathematical usage. A polynomial with only one term is already a
weird case: all except the zero polynomial have no roots; and if the
term is nonzero, the degree of the polynomial is considered 0, but if
the term is 0, the degree is __ . What would the degree of the empty
polynomial be?
The derivative of a polynomial with 1 constant term should be the
zero polynomial, not empty.
What would the integral of the empty polynomial be?
I think the original implementation of p. was wrong.
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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