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I have a simple system that I want to process with the CellDecomposition command of Maple. I don't know why Maple is giving an error here! The code is

f1 := 4*b*(5*b*(13*t^2-tau^2)*(t^2+tau^2)^6-3*a*5*t^6-63*t^4*tau^2+35*t^2*tau^4+7*tau^6)); 
f2 := 56*b*tau*(5*b*(t^2+tau^2)^6+a*(9*t^4-30*t^2*tau^2+9*tau^4)); f3 := 1-z*t;

m := CellDecomposition([f1 = 0, f2 = 0, f3 = 0], [t, tau, z])

and the error is:

Error, (in RootFinding:-Parametric:-CellDecomposition) The number of polynomials is smaller than the number of unknowns

The number of polynomials is obviously the same as the number of variables here!

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I do not have the reputation to make a comment so I'll make my comment an answer. Since I don't know what maple is please realize that with this comment I'm only trying to help. In looking at it from my completely ignorant perspective I do not know what a and b are. To me those are 'unknowns'. Sorry if this was a waste of your time. – CramerTV Jan 5 '13 at 0:30

It looks like the problem is that there's a factor of b that is common between f1 and f2. If I divide both by b then I get a meaningful answer for this modified system.

Looking at the CellPlot of the result, it seems that this decomposition is invariant under multiplying b by a positive value. (There are different cells for b positive or negative, separated at b = 0, but otherwise the only interesting stuff happens in the a direction.) So that suggests that for nonzero b, the picture will be the same for the modified system and the original system... or does it?

Disclaimer: I work for Maplesoft, but I don't really know anything about the RootFinding:-Parametric package.

Edit: I talked to someone who does know about RootFinding:-Parametric, and he confirmed that this is indeed a bug. Am now submitting into our bug tracking system.

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