cpolinomi'a

valsi

cpolinomi'a

type

fu'ivla

creator

krtisfranks

time entered

Tue Jan 21 19:08:15 2014  

English

Definition #44334 - Preferred

 

definition

x₁ is a formal polynomial with coefficients x2 (ordered list) of degree x₃ (li; nonnegative integer) over structure/ring x₄ (to which coefficients x₂ all belong) and in indeterminant x₅.

notes

x₃ must be greater than or equal to the number of entries in x₂; if these two values are not equal, then the explicitly mentioned entries of x₂ are the values of the coefficients as will be described next, starting with the most important one; all the following coefficients (which are not explicitly mentioned) are xo'ei (taking appropriate values) until and including once the constant term's coefficient (when understood as a function) is reached. If x₂ is presented as an ordered list, the entries represent the 'coefficients' of the particular polynomial and are specified in the order such that the ith entry/term is the (n - i + 1)th 'coefficient', for all positive integers i which are less than or equal to n + 1, where the ordering of 'coefficients' is determined by the exponent of the indeterminate associated therewith (when treated as a function); thus, the last entry is the constant term (when treated as a function), the penultimate term is the coefficient of the argument of x₅ (when treated as a function), and the first term is the coefficient of the argument of x₅ exponentiated by n (which is the degree x₃ of the polynomial x₁); in other words, the ith entry of x₂ (where indexing of the ordered list starts at 1) is the coefficient of MATH

$x^<a class="undefined" href="../dict/(n-i%2b1)?bg=1;langidarg=2">(n-i+1)</a>$

x^(n-i+1), where x₅ = x is the indeterminate. "ze'ai'au" enables for reversal of x₂ so that the first-uttered term is the constant, the next-uttered term is the coefficient of the linear term, ..., and the last ((n+1)st) term is the coefficient of the most-significant term in the polynomial (xⁿ). See also: "tefsujme'o" (brivla: polynomial function), "po'i'oi" (basically, the mekso equivalent to this word), "po'i'ei".

gloss words

• coefficient ; polynomial
• coefficient ring ; of polynomial
• indeterminant ; of formal polynomial
• polynomial ; formal, ring element (not as: a function or a funcion evaluated at a particular input value)

place keywords

3.

         degree ; polynomial

created by

krtisfranks

vote information

2

time

Thu Mar 9 22:04:38 2023

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Examples

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