Talk:Polynomial synthetic division

Dup?

I think this task is a duplicate of Polynomial long division

That said, when I use an implementation from that page to divide 1, -12, 0, -42 by 1, -3 I get a result of 2.44444, -4.66667, -14 and a remainder of -1.44444 (or quite similar numbers expressed as fractions with 9 in the denominator if I ask for exact results). This is because that implementation places the constant on the left hand side and powers increase to the right. If I reverse the representation of the polynomials I get an answer similar to that of the current python example here.

But that just illustrates that the task is also underspecified (since the task description says nothing about this issue - though it's true that if I follow the seventh link in the current version of the proposed task page I do find a representation where the constant coefficient is rightmost and powers increase to the left).

Anyways, I think maybe the best approach here would be to merge useful content onto the other page and create a #redirect link so that either page title will get to the content. Does that seem reasonable? --Rdm (talk) 23:16, 5 June 2015 (UTC)

Task itself shouldn't need to specify how a polynomial is represented, since growing power in either direction could make sense, so we could just let the code providing the interface choose. I personally would prefer zero-th term in the front because it would make infinite power series possible, but that clearly is not the intended goal here. The real issue is, long division and synthetic division may look different with pen and paper, there doesn't seem to be a meaningful difference in terms of math or computer implementation: one subtracts, the other inverts and adds, that's about it. I agree that this looks like a dup. --Ledrug (talk) 03:12, 6 June 2015 (UTC)

Ok, so, since it seems to be a dup, what's the path forward? Also, if we are going to be order agnostic, shouldn't that mean that the implementation must specify what it has chosen? (Ok, that will not matter here, if the page is going to be replaced with a #redirect, but should that point be made on the other task?) --Rdm (talk) 11:36, 6 June 2015 (UTC)

I am the author of the first draft with Python code. I do not agree this is a dup: the computational complexity is totally different between the two, and the approach is quite different (we only work on the coefficients instead of accounting for the degrees in a recursive fashion). This can be seen as an extension of the Horner's scheme (which is commonly used to evaluate polynomials). What may confuse you is that on the page for Polynomial long division, some snippets are actually implementing synthetic division instead of polynomial long division, so I guess it would be more logical to move these snippets here instead of the other way around. --Lrq3000 (talk) 06:38, 14 June 2015 (UTC)