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RationalSolve    --    Rational solutions for 0-dim polynomial system


Syntax 
RationalSolve(L: LIST of RINGELEM): RECORD

Description
This function computes all rational solutions (aka. points) of a 0-dimensional polynomial system L; approximate real solutions can be computed using ApproxSolve . Projective solutions of a homogenous system can be obtained using RationalSolveHomog .

Result is a record saying which indeterminates are "active", and list of the solution points.

Example 
/**/  use QQ[x,y,z];
/**/  L := [x^3-y^2+z-1, x-2, (y-3)*(y+2)];
/**/  RationalSolve(L);
record[AffinePts := [[2, -2, -3],  [2, 3, 2]],  indets := [x, y, z]]

/**/  L := [x^2+y^2-1,  x*y-1];  -- indet z not used
/**/  RationalSolve(L);
record[AffinePts := [],  indets := [x, y]]

See Also