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Richard Fateman | 15 May 22:58

Re: Maxima divide question

This is not a maxima issue, it is a mathematical issue of division with remainder in a polynomial ring, whose coefficients are in a field.
 
 
main variable x:
 
  x+y divided by x  quotient 1 remainder y.  Easy.
 
main variable y
 
 x+y divided by x  quotient (x+y)/x, remainder 0.
 
in this latter case, the polynomial x+y   looks like this :    y^1 + (1*x^1+0*x^0)*y^0.  
 
The first trial subtraction asks what value v can you come up with such that v*x= y?  v=y/x is the answer.
Now subtract.
The next step is, what value of v can you come up with such that v*x=x?   v=1 is the answer.
 
The quotient is y/x+1   or  (y+x)/x
The remainder is 0.
 
 

From: maxima-bounces <at> math.utexas.edu [mailto:maxima-bounces <at> math.utexas.edu] On Behalf Of Ronald Modesitt
Sent: Thursday, May 15, 2008 12:26 PM
To: maxima <at> math.utexas.edu
Subject: [Maxima] Maxima divide question

All,

Could someone explain the concept of the ‘main polynomial variable’ for the Maxima function divide. I do not understand it’s purpose.

 

Function: divide (p_1, p_2, x_1, ..., x_n)

computes the quotient and remainder of the polynomial p_1 divided by the polynomial p_2, in a main polynomial variable, x_n…

 

Ron

 

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