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Topic: Understanding the quotient ring nomenclature
Replies: 423   Last Post: Aug 3, 2012 7:42 AM

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 galathaea Posts: 1,646 Registered: 7/2/05
Re: understanding formal objects in computer languages
Posted: Jun 20, 2009 2:06 AM

On Jun 19, 5:48 am, "Tim BandTech.com" <tttppp...@yahoo.com> wrote:

> A slim disproof exists, for upon coming down to a single term in that
> polynomial
>    a x
> we should freely replace this value ax with two polynomials
>    (a) (x)
> and within the the ring context with a third polynomial c
>    a x = c
> by the closure axiom of the product operator which had been declared
> on a higher form than A so named 'the polynomial ring A[X]'. If this
> is not true then the value under scrutiny is not a ring and so the
> usage of the term ring was not only polluted by the formal
> interpretation on x, but it was destroyed. The polynomial ring is a
> misnomer when interpreted the 'formal' way.

in the class
the identity would simply be

(think about how the polynomials are stored as vectors here)

(a) . (0, 1) = (0, a)

do you see a x = c here?

i think if you focus consistently on a form you understand
it can make advanced things appear more graspable

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar

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