Talk:Degree of a polynomial
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[edit] Formal definition
I'm new to this Wikipedia thing, so I'll just post my opinion here before editing. Hope that someone with more experience could help.
The point is that there is no formal (mathematically correct) definition given. What you have is just an explanation/illustration.
Generally a polynomial is defind as a sequence of elements (called coefficients) from a ring indexed by natural numbers with the following characteristic: there is a natural number n (called the degree) so that the n-th coefficient is non-zero and all coefficients with index higher than are zero.
i.e. it is something like P={a0,a1,...,an,0,0,...} where a0,...an are ellements of R and 0 is the zero in R.
More formally: a polynomial is a function P from N (natural numbers) to R (where R is a ring) where there is n in N (the degree) so that P(n) is not zero and for all m>n P(m)=0.
The thing is that the definition of the degree is embedded in the definition of the polynomial. What would be the best way to include here the formal/mathematically correct definition of the degree - should we repeat the polynomial definition here? - AdamSmithee 22:25, 17 November 2005 (UTC)
[edit] Degrees 0 and 1
I've had a bit of a debate with someone regarding degrees 0 and 1 of a polynomial. My argument is this: the degree of 10x is 1, as the exponent on the variable is 1. But the degree of any constant term is 0. E.g: 5x0, as 0 is the exponent on x. To my surprise, they were arguing that 5 = 51, therefore the degree is 1. Surely the coefficients can't be used in determining the degree, otherwise the degree of 10x2 would be 3?! I'm not a mathematician so I'm a bit reluctant to change the article, but would it be reasonable to clarify this in the article? Or maybe I was wrong? --146.227.11.232 15:55, 13 January 2006 (UTC)
- The degree = the highest power of X with a non-zero coeff. Indeed, the degree of the polynomial f = 5 = 5X0 is 0. The factorization of the coeff into primes (if available) doesn't change the degree of the polynomial AdamSmithee 09:07, 16 January 2006 (UTC)
[edit] fractional degree
degree of a function being "D", can |D|<1, while squreroots are 1/2 i'm not very sure, on this. but it isn't adressed in the artical
- Thanks for asking. See Degree_of_a_polynomial#The_degree_computed_from_the_function_values. The degree of 3x1/2+5x is 1, while the degree of 3x1/2+17 is 1/2. I moved your question to the bottom of this discussion page where new contributions are expected to appear. You may sign your discussion entries automatically by four tildes '~'. Bo Jacoby 10:50, 9 August 2006 (UTC)
