M. Bronstein
ABSTRACT
We describe an algorithm, based on Risch's real structure theorem, that determines explicitly all the algebraic relations among a given set of real elementary functions. We also provide examples from its implementation that illustrate the advantages over the use of complex logarithms and exponentials.
- Flory, G. (1978), "Pornlnlnlre de Mnth~.matiques sp6. ciales," 5''n' Ed., V, ibcrt., Paris.Google Scholar
- l~iouvillc, J. (1837), Me.'moirc s?l.r la clnssificalioa des transcendantes et sftr I'ivapossibilitd d'er. primer les racines de certaines dqnations en /onction finie erplicile des coeff/icients, JournM de mnLh6Tnatiq,cs putts et appliqu~es II, 56-10,1.Google Scholar
- R.isch, R. (1979), Algebraic Properties o.1 tae E&,,,~,. tary Fllnclions o! Anal.ltsis, American Jour, al of Mathcmatics 101, 7,1,3 759.Google Scholar
Index Terms
Simplification of real elementary functions
Recommendations
Integration of elementary functions
We extend a recent algorithm of Trager to a decision procedure for the indefinite integration of elementary functions. We can express the integral as an elementary function or prove that it is not elementary. We show that if the problem of integration ...
On multivariate orthogonal polynomials and elementary symmetric functions
AbstractWe study families of multivariate orthogonal polynomials with respect to the symmetric weight function in d variables
for , where is an univariate weight function in and with ...Orthogonal rational functions and quadrature on the real half line
In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and ...
Comments