=ADD= =reftype= 14 =number= 99-49 =url= ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-49.ps.gz =year= 1999 =month= 06 =author= Winkler; Franz =title= Advances and Problems in Algebraic Computation =abstract= In the last years there has been dramatic progress in all areas of algebraic computation. Many working mathematicians have access to and actually use algebraic software systems for their research. No end of this development is in sight. We report on some active topics in algebraic computation, namely the theory of integration and symbolic solution of systems of differential equations, the solution of systems of algebraic equations, the factorization of polynomials, and the design and analysis of algebraic curves and surfaces. =howpublished= Invited talk at 58th Workshop on General Algebra (AAA58), Technical Univ. Vienna, June 1999, to appear in Contributions to General Algebra 12, D. Dorninger et al. (eds.), Verlag Johannes Heyn, Klagenfurt (2000) =sponsor= FWF project P11160-TEC and SFB F013/1304 =keywords= computer algebra, algebraic computation