Hi, Some help is appreciated concerning the following.
Suppose P1,P2,P3 are two-variate polynomials. I search for all sets of (P1,P2,P3) such that: i) P1(A,B)+P2(A,B)=P3(A,B) ii) Greatest common denominator P1 and P2 equals 1 [Thus gcd( P1, P2 )=1] iii) P1*P2*P3 can be divided by A*B*(A+B) [Thus gcd( P1*P2*P3, A*B*(A+B) )=A*B*(A+B)] The most elementary forms are A + B = A+B, A^2 + B*(A+B) = (A+B)^2 and (B-A)^2 + 4*A*B = (A+B)^2. Somewhat more appealing is the following identity: (A+2*B)*A^3 + B*(2*A +3*B)^3 = (A+B)*(A+3*B)^3 In general, there should be many more of these 'nice' examples. I'm curious if via Sage one could develop a generating algorithm. Thanks in advance! Roland -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
