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Span of an equation

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0

$begingroup$

I use this term to denote a set of numbers of the form $sum z_n x^n$, where $x$ is the solution of some polynomial $x^a=sum z_ix^i$ for $i=0$ to $a-1$.

$a$, $i$, and the $z_j$ are all in $mathbbZ$.

For example, “the span” of $a^3=7$ would be all numbers of the form $xa^2+ya+z$, $x,y,zinmathbbZ$, where $a^3=7$.

Is there a standard term for it?

elementary-number-theory polynomials notation terminology roots

share|cite|improve this question

edited Mar 11 at 20:36

Servaes

28.3k34099

asked Mar 6 at 2:43

wendy.kriegerwendy.krieger

5,85511427

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I've edited the question. They're all in Z.
  $endgroup$
  – wendy.krieger
  Mar 6 at 3:05
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It’s the subring of $mathbbQ(a)$ generated by $a$.
  $endgroup$
  – Arturo Magidin
  Mar 6 at 3:12
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I really was looking for something like the title i was using for it. It's something i use a great deal.
  $endgroup$
  – wendy.krieger
  Mar 6 at 11:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, but that's just not what it's called. I told you what the standard name for it is. If you go around talking about the "span of an equation", nobody is going to have any idea what you are talking about.
  $endgroup$
  – Arturo Magidin
  Mar 6 at 19:34
  

  
  
  
  

add a comment | 

0

$begingroup$

I use this term to denote a set of numbers of the form $sum z_n x^n$, where $x$ is the solution of some polynomial $x^a=sum z_ix^i$ for $i=0$ to $a-1$.

$a$, $i$, and the $z_j$ are all in $mathbbZ$.

For example, “the span” of $a^3=7$ would be all numbers of the form $xa^2+ya+z$, $x,y,zinmathbbZ$, where $a^3=7$.

Is there a standard term for it?

elementary-number-theory polynomials notation terminology roots

share|cite|improve this question

edited Mar 11 at 20:36

Servaes

28.3k34099

asked Mar 6 at 2:43

wendy.kriegerwendy.krieger

5,85511427

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I've edited the question. They're all in Z.
  $endgroup$
  – wendy.krieger
  Mar 6 at 3:05
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It’s the subring of $mathbbQ(a)$ generated by $a$.
  $endgroup$
  – Arturo Magidin
  Mar 6 at 3:12
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I really was looking for something like the title i was using for it. It's something i use a great deal.
  $endgroup$
  – wendy.krieger
  Mar 6 at 11:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, but that's just not what it's called. I told you what the standard name for it is. If you go around talking about the "span of an equation", nobody is going to have any idea what you are talking about.
  $endgroup$
  – Arturo Magidin
  Mar 6 at 19:34
  

  
  
  
  

add a comment | 

$begingroup$

I use this term to denote a set of numbers of the form $sum z_n x^n$, where $x$ is the solution of some polynomial $x^a=sum z_ix^i$ for $i=0$ to $a-1$.

$a$, $i$, and the $z_j$ are all in $mathbbZ$.

For example, “the span” of $a^3=7$ would be all numbers of the form $xa^2+ya+z$, $x,y,zinmathbbZ$, where $a^3=7$.

Is there a standard term for it?

elementary-number-theory polynomials notation terminology roots

share|cite|improve this question

edited Mar 11 at 20:36

Servaes

28.3k34099

asked Mar 6 at 2:43

wendy.kriegerwendy.krieger

5,85511427

$endgroup$

share|cite|improve this question

edited Mar 11 at 20:36

Servaes

28.3k34099

asked Mar 6 at 2:43

wendy.kriegerwendy.krieger

5,85511427

share|cite|improve this question

edited Mar 11 at 20:36

Servaes

28.3k34099

asked Mar 6 at 2:43

wendy.kriegerwendy.krieger

5,85511427

edited Mar 11 at 20:36

Servaes

28.3k34099

edited Mar 11 at 20:36

Servaes

28.3k34099

asked Mar 6 at 2:43

wendy.kriegerwendy.krieger

5,85511427

asked Mar 6 at 2:43

wendy.kriegerwendy.krieger

5,85511427