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implicit

implicitization

Syntax
implicit(SubalgebraGens: LIST): IDEAL
implicit(R: RING, SubalgebraGens: LIST): IDEAL

Description
This function returns the implicitization of the subalgebra generated by the list SubalgebraGens .

If provided with a ring R , the result is in R , otherwise it is in a newly created ring.

NOTE: Some cases have been optimized: if the input is a list of power-products then use toric . if you know the answer is a hypersurface then use ImplicitHypersurface .

Example
/**/  use S ::= QQ[s,t];
/**/  implicit([s^3, s^2*t, s*t^2, t^3]);
ideal(x[3]^2 -x[2]*x[4], x[2]*x[3] -x[1]*x[4], x[2]^2 -x[1]*x[3])

/**/  P ::= QQ[x,y,z,w];
/**/  implicit(P, [s^3, s^2*t, s*t^2, t^3]);
ideal(z^2 -y*w, y*z -x*w, y^2 -x*z)

See Also