On Sep 3, 6:56 pm, Jason Bandlow <[email protected]> wrote: > For polynomial equations, the following should work in general. > > sage: R.<x,y> = CC['x','y'] > sage: f = x-y > sage: g = x^2 - y^2 > sage: I = R.ideal([f]).radical() > sage: g in I > True > > In general, to see if the equation g == 0 is implied by the equations > f1==0, f2==0, ..., fn==0 you can do > > I = R.ideal([f1, f2, ..., fn]).radical() > g in I Assuming that you are working over the complexes (or more generally any algebraically closed field, subject to changing CC appropriately), yes. Ove rthe reals it is solved, but more difficult and I don't know if SAGE has the tools. > and sage should appropriately return True or False. I should mention > that I don't actually use this very much, so there may be some caveats > that I'm not aware of.
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