Looking at https://en.wikipedia.org/wiki/Degree_of_a_polynomial the degree of a polynomial is determined by the highest power with a non-zero coefficient.
So, there's no difference in degree between 1 2 1 0 0 0 and 1 2 1 -- Raul On Tue, Jan 3, 2023 at 9:00 PM Henry Rich <[email protected]> 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, > >>> > >> > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
