ISSN:
1573-7640
Schlagwort(e):
Symbolic mathematical computation
;
algebraic simplification
;
canonical form
;
regular form
;
structure theorem
;
elementary transcendental functions
;
exponential function
;
logarithm function
;
trigonometric functions
;
hyperbolic functions
;
algebraic independence
;
differential algebra
;
Liouville fields
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Informatik
Notizen:
Abstract This paper uses elementary algebraic methods to obtain new proofs for theorems on algebraic relationships between the logarithmic and exponential functions. The main result is a multivariate version of a special case of the structure theorem due to Risch that gives, in a very explicit fashion, the possible algebraic relationships between the exponential and logarithm functions. The structure theorem has important applications to symbolic mathematical computation in that it in essence provides a canonical form for the elementary transcendental functions, and hence solves the identity problem for this class of functions. Such applications are discussed in the last section.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00995426
Permalink
