12. Calculus of Simplex-Valued Functions

  1. Vera Pawlowsky-Glahn2 and
  2. Antonella Buccianti3
  1. Juan José Egozcue,
  2. Eusebi Jarauta-Bragulat and
  3. José Luis Díaz-Barrero

Published Online: 28 JUL 2011

DOI: 10.1002/9781119976462.ch12

Compositional Data Analysis: Theory and Applications

Compositional Data Analysis: Theory and Applications

How to Cite

Egozcue, J. J., Jarauta-Bragulat, E. and Díaz-Barrero, J. L. (2011) Calculus of Simplex-Valued Functions, in Compositional Data Analysis: Theory and Applications (eds V. Pawlowsky-Glahn and A. Buccianti), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119976462.ch12

Editor Information

  1. 2

    Department of Computer Science and Applied Mathematics, University of Girona, Spain

  2. 3

    Department of Earth Sciences, University of Florence, Italy

Author Information

  1. Department of Applied Mathematics III, Technical University of Catalonia, Spain

Publication History

  1. Published Online: 28 JUL 2011
  2. Published Print: 23 SEP 2011

ISBN Information

Print ISBN: 9780470711354

Online ISBN: 9781119976462



  • calculus of simplex-valued (sv) functions;
  • changes of a chemical composition - changes of vote intention and evolution of employment in time;
  • compositions, represented in the simplex - and its Aitchison geometry;
  • Aitchison geometry of the simplex - a Euclidean geometry, concepts of real geometry and calculus of real spaces, translated into the simplex;
  • limits, continuity and differentiability - of sv functions, analogous to standard definitions in calculus;
  • differentiable function, approximated in neighbourhood of a point - by tangent function;
  • higher order derivatives;
  • integration and antiderivatives;
  • calculus of sv functions of real variable - analogous to standard calculus of vector valued real functions;
  • expression of simplicial derivatives - and integrals, in simplicial notation


This chapter contains sections titled:

  • Introduction

  • Limits, Continuity and Differentiability

  • Integration

  • Conclusions

  • Acknowledgements

  • References