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RationalSolve

Rational solutions for polynomial system

Syntax
RationalSolve(L: LIST of RINGELEM): LIST of LIST of RINGELEM

Description
This function returns the list of rational solutions (points) of a 0-dimensional polynomial system L (see also ApproxSolve ). Tries to be clever: if some indeterminates do not appear in L they are ignored, if the polynomials in L are homogeneous it returns the projective points.

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

/**/  L := [x^3-y^2+z-1, x^2-2, (y-3)*(y+2)];
/**/  RationalSolve(L);
[]
/**/  len(ApproxSolve(L));
4

/**/  L := [x^3-y^2+1, (y-3)*(y+2)];  -- ignores the indeterminate z
/**/  RationalSolve(L);
[[2, 3]]

See Also