By Ziming Li.

Those notes list seven lectures given within the machine algebra path within the fall of 2004. the speculation of suhrcsultants isn't required for the ultimate схаш because of its complex buildings.

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It is straightforward to show that S ⊂ V(J). Let H be an ideal of R such that S ⊂ V(H). We √ to prove that V(J) ⊂ V(H). By Theorem 8 √ have we need only to show H ⊂ J. Assume that h ∈ (H), then h vanishes on S. Hence gh vanishes on V(I). Theorem 8 √ then implies that (gh)k ∈ I k for some k ∈ N. Hence, h is in J, that is, h ∈ J. References [1] B. Buchberger, G. Collins, and R. Loos. (eds) Computer Algebra, symbolic and algebraic computation. Springer, 1982. E. J. Encarnacion. Efficient rational number reconstruction.

Loos. (eds) Computer Algebra, symbolic and algebraic computation. Springer, 1982. E. J. Encarnacion. Efficient rational number reconstruction. J. of Symbolic Computation 20, pp. 299–297, 1995. [3] G. Collins, R. Loos, and F. Winkler. Arithmetic in basic algebraic domains. In [1], pages 189–220. [4] R. Feng, X. Gao. Rational general solutions of algebraic ordinary differential equations. In the Proceedings of ISSAC 2004, pp. 155-161. [5] J. von zur Gathen, J. Gerhard. Modern Computer Algebra, Cambridge Press, First Edition, 1999.

155-161. [5] J. von zur Gathen, J. Gerhard. Modern Computer Algebra, Cambridge Press, First Edition, 1999. 30 [6] K. Geddes, S. Czapor, and G. Labahn. Algorithms for Computer Algebra. Kluwer Academic Publisher, 1992. [7] D. Kunth. The Art of Computer Programming. Vol. II, Addison-Wesley, 1981. [8] F. Winkler. Polynomial Algorithms in Computer Algebra. Springer, 1996. [9] M. Monagan. Maximal quotient rational reconstruction: an almost optimal algorithm for rational reconstruction. In the Proceedings of ISSAC 2004, pp.