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Algebraic Foundations 1 Preliminaries
Resultants and elimination
Algebraic dependence Transcendency
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abelian differential adjoints affine coordinates affine transformation algebraic curve algebraic varieties algebraically closed algebraically independent algebroid assume birational model birational transformation canonical series characteristic zero coefficients complete Consider contains coordinate system defined degree denote dimension distinct points divisor double points elements equivalent factor field Kf finite number fixed places formal power series function field G KH[x graph groundfield Hence hyperplane hypersurface ideal aH indeterminate intersection irreducible curve irreducible variety isomorphic Jacobian linear series linearly independent monoidal multiplicity N(rj non-singular non-units normal system obtained one-one ordinary point parameter place 77 place tt plane poles polynomial power series primary ideal prime ideal projection proof prove rational transformation reducible referred regular replace residue ring second kind solution space special polynomial subvariety Suppose surface theorem transc transcendency unique variable xr+1