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duction ideals of differential polynomials bases strong and weak bases decomposition
generic zeros of a prime ideal the theorem of zeros general solutions singular zeros and solu
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algebraic differential equations algebraically irreducible analytic analytic functions called chain Chapter characteristic set coefficients in SF component of F consider degree less determine differential algebra differential equations differential field differential polynomials dimension zero distinct from zero divisible element of SF elimination theory essential prime divisors exceed exist exponent expression extension of SF finite number finite system functions given higher holds indeterminates initial intersection involves irreducible manifold Let F Let G linear combination low power theorem lower degree monomials nonzero d.p. nonzero polynomial obtained parametric derivatives parametric set partial derivatives perfect ideal positive degree positive integer power product prime p.i. proof rank reduced with respect relatively prime remainder classes replace restricted manifold second member singular solutions solution of F Suppose system of d.p. system of polynomials theorem of zeros unity vanishes zero of F