Geometric Algebra with wxMaxima Icon

Geometric Algebra with wxMaxima

Definition and validation of the GAwxM operator syntax

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In this project it was shown how wxMaxima (a front end for the Maxima computer algebra system) was used to develop and test Maxima code functions for Geometric Algebra.

The algebraic blade and multivector operators were briefly described under the 'Wiki' page.

User defined infix operators were defined within the Maxima computer algebra system and this allowed geometric algebraic expressions resembling vector equations to be coded. The functions called by the operators allowed rational parametric coefficients for the bases in a multivector (or in any vector).

Worked examples were taken from a reference book...Linear and Geometric Algebra (LAGA) and also from ...Vector and Geometric Calculus (VAGC). Each valid example helped to validate the GAwxM syntax.

Work has now ceased on a Windows version and the obsolete code has been removed. Only the year numbered papers remain.

Geometric Algebra with wxMaxima Web Site


  • Pseudoscalar definition (specifies the space dimension)
  • Calculation of the inverse pseudoscalar used to generate the dual of a multivector
  • Enumeration of the standard basis for the specified dimension
  • Full dimension multivector generation
  • Associativity test for the triple geometric product
  • Associativity test for the triple outer product
  • Test for the Jakobi expansion of the triple commutator product
  • Consistency checks with the left inner product...; using two particular pure grade multivectors (generation of multivectors containing particular grades only) ; using the dual of the dual of a pure grade multivector ; testing the left inner product in the fundamental identity ; checking the first duality identity for multivectors, (A.B)* = A^B* ; testing the other duality identity for multivectors; (A^B)* = A.B*
  • Check that the reverse of the geometric product equals the juxtaposed product of the reverses
  • Check the scalar product function is symmetric and positive definite
  • Test the norm (modulus) function


Additional Project Details



Intended Audience

Science/Research, Education

Programming Language



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