Multivalued Elementary Functions in Computer-Algebra Systems
نویسنده
چکیده
An implementation (in Maple) of the multivalued elementary inverse functions is described. The new approach addresses the difference between the single-valued inverse function defined by computer systems and the multivalued function which represents the multiple solutions of the defining equation. The implementation takes an idea from complex analysis, namely the branch of an inverse function, and defines an index for each branch. The branch index then becomes an additional argument to the (new) function. A benefit of the new approach is that it helps with the general problem of correctly simplifying expressions containing multivalued functions.
منابع مشابه
Characterizing sub-topical functions
In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...
متن کاملPartition Analysis, Modular Functions, and Computer Algebra
This article describes recent developments connecting problems of enumerative combinatorics, constrained by linear systems of Diophantine inequalities, with number theory topics like partitions, partition congruences, and q-series identities. Special emphasis is put on the role of computer algebra algorithms. The presentation is intended for a broader audience; to this end, elementary introduct...
متن کاملAn Approach for the Effective Integration of Computer Algebra in an Undergraduate Calculus and Linear Algebra Course
In this paper we describe an approach for an effective integration of computer algebra systems in an elementary calculus and linear algebra course. In our mathematics courses at Wageningen University, an education and research centre for the biological, environmental, agrotechnical and social sciences, we have noted that students often show a lack of conceptual understanding while using compute...
متن کاملKeynote Lecture: Integration in the Era of Computer Algebra
The use of computer algebra systems in Mathematics education could and should in uence the future curriculum how to teach integration. The traditional way only brie y touches the area problem, to switch very quickly to antidi erentiation. Graphical representations as well as symbolic and numeric capabilities of modern computer algebra systems like DERIVE enable enhanced teaching techniques: stu...
متن کاملGeneralized multivalued $F$-contractions on non-complete metric spaces
In this paper, we explain a new generalized contractive condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresp...
متن کامل