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Question: diophantine equations

Question:diophantine equations

ArcanaNoir 5 Maple 16
November 08 2012
1

I would like to know if there is any way to coax maple into spitting out the solution (1,1,1) for the system of equations {x2+y2+z2=3, x+y+z=3}. So far all I have come up with is

with(RegularChains)[SemiAlgebraicSetTools]:
R:=PolynomialRing([x,y,z]);
Display(SamplePoints([x^2+y^2+z^2=3,x+y+z=3],R),R);

This produces

x=1
y=1
z=1

as desired, but I would like to accomplish this without specifying the polynomial ring. I would be satisfied with any solution involving the real field or real domain, maybe even integers.
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