Polynomials of 2 Variables: General Form & Matrix Representation

  • Context: Undergrad 
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Discussion Overview

The discussion focuses on the general form of polynomials in two variables and their matrix representation. Participants explore the structure of such polynomials and seek clarification on how to express them mathematically.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks for the general form of a polynomial in two variables, comparing it to the known form for a single variable polynomial.
  • Another participant proposes a specific form for a two-variable polynomial, including terms with coefficients and powers of both variables, and suggests the inclusion of additional polynomials P(x) and Q(y).
  • A subsequent participant seeks clarification on the term "respective arguments" used in the proposed polynomial form.
  • Another participant explains that "respective arguments" refers to P(x) being a polynomial in x and Q(y) being a polynomial in y.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus on the general form of polynomials in two variables, as participants are exploring different representations and clarifying terms used.

Contextual Notes

There are unresolved aspects regarding the completeness of the proposed polynomial forms and the matrix representation, as well as potential dependencies on definitions of terms used.

complexhuman
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how does one look like?I mean what's the general form? e.g. for a 1 var poly...general form = a0+a1x+a2^2+...+anx^n

and how could I represent that by a matrix?


Thanks
 
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How about

[tex]a_0 x^n + a_1 x^{n-1} y + a_3 x^{n-2} y^2 + \cdot \cdot \cdot + a_n y^n + P(x) + Q(y)[/tex]

where P and Q are polynomials in their respective arguments?
 
Last edited:
respective arguments?
 
Arguments - meaning P(x) is a polynomial in x and Q(y) is a polynomial in y.
 

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