unexpected behavior of divide



Hi list,

suppose we have the following,
polynomial division, r1 is the remainder,
but why is f1 a rational function?

Regards
Andre

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Maxima 5.19.2 http://maxima.sourceforge.net
Using Lisp SBCL 1.0.40-1.fc14
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1)                      batch(divide-test-1.max)

batching /home/user/divide-test-1.max
(%i2)                          display2d : false
(%o2) false
(%i3) h0:2*b1^2+4*a2*b2-4*a2^2*b2+4*b1*b2+2*b1^2*b2+4*a2*b2^2-4*a2^2*b2^2
                
+4*b1*b2^2+2*b1^2*b2^2-2*b2^3+4*b1*b2^3+2*a2*d-2*a2^2*d+2*b1*d
                -b1^2*d-4*a2^2*b2*d+2*b1^2*b2*d-5*b2^2*d-4*a2*b2^2*d
                +6*b1*b2^2*d-a2*d^2-a2^2*d^2-b1*d^2+b1^2*d^2-4*b2*d^2
                -4*a2*b2*d^2+4*b1*b2*d^2-d^3-a2*d^3+b1*d^3
(%o3) b1*d^3-a2*d^3-d^3+4*b1*b2*d^2-4*a2*b2*d^2-4*b2*d^2+b1^2*d^2-b1*d^2
             -a2^2*d^2-a2*d^2+6*b1*b2^2*d-4*a2*b2^2*d-5*b2^2*d+2*b1^2*b2*d
             -4*a2^2*b2*d-b1^2*d+2*b1*d-2*a2^2*d+2*a2*d+4*b1*b2^3-2*b2^3
             +2*b1^2*b2^2+4*b1*b2^2-4*a2^2*b2^2+4*a2*b2^2+2*b1^2*b2+4*b1*b2
             -4*a2^2*b2+4*a2*b2+2*b1^2
(%i4) [f1,r1]:factor(divide(h0,(2+b2-b1)*(2*b2+d)))
(%o4) [(b1*d^2-a2*d^2-d^2+2*b1*b2*d-2*a2*b2*d-2*b2*d+b1^2*d-b1*d-a2^2*d-a2*d
               
+2*b1*b2^2-b2^2+2*b1*b2-2*a2^2*b2+2*a2*b2-b1^2+2*b1-2*a2^2+2*a2)
         /(b2-b1+2),2*b1^2*(b2+1)^2]
(%o4) "/home/user/divide-test-1.max"
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