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 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