On 9/28/07, David Stahl <[EMAIL PROTECTED]> wrote: > > I have a system of polynomial equations with rational coefficients and > I have one rational solution. I am trying to find a recurrence > relation that will allow me to generate additional rational > solutions. The equations are: > > A6x0^2+A5x1^2+A4x2^2+A3x0x1+A2x0x2+A1x1x2+A0=0 (a) > B6y0^2+B5y1^2+B4y2^2+B3y0y1+B2y0y2+B1y1y2+B0=0 (b) > C8x0y0+C7x0y1+C6x0y2+C5x1y0+C4x1y1+C3x1y2+C2x2y0+C1x2y1+C0x2y2=0 (c) > > I can find a recurrence relation for the equations separately. If a > solution to (a) is x0=d, x1=e, and x2=f then additional solutions can > be found. First define the x elements as: > > x0=d+t > x1=e+mt > x2=f+nt > > Substitute these values into (a) to get a homogeneous equation in t. > Then solve for t: > > t=(N2m+N1n+N0)/(A5m^2+A1mn+A4n^2+A3m+A2n+A6) > > N2= -2A5e-A3d-A1f > N1= -A1e-A2d-2A4f > N0= -A3e-2A6d-A2f > > Since t is rational in m and n we simply pick rational values for m > and n to generate rational solutions for x0, x1, and x2. Similar > relations can be made for (b) and (c). My problem is that I do not > know how to find a recurrence relation for the simultaneous system. > Any guidance would be appreciated. Thank you.
You might be interested in looking at Martin Rubey's GUESS package in Axiom, a bit of which is described in http://wiki.sagemath.org/Axiom_as_an_OSCAS I think it is included in Bill Page's SAGE package axiom4sage-0.3. > > David > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
