Corpus ID: 119598991

Sobczyk's simplicial calculus does not have a proper foundation

@article{Macdonald2017SobczyksSC,
  title={Sobczyk's simplicial calculus does not have a proper foundation},
  author={A. Macdonald},
  journal={arXiv: General Mathematics},
  year={2017}
}
  • A. Macdonald
  • Published 2017
  • Mathematics
  • arXiv: General Mathematics
The pseudoscalars in Garret Sobczyk's paper \emph{Simplicial Calculus with Geometric Algebra} are not well defined. Therefore his calculus does not have a proper foundation. 

Figures from this paper

Logic and the 2-Simplicial Transformer
We introduce the $2$-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention toExpand
L OGIC AND THE 2S IMPLICIAL T RANSFORMER
We introduce the 2-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention toExpand

References

SHOWING 1-5 OF 5 REFERENCES
Simplicial calculus with Geometric Algebra
We construct geometric calculus on an oriented k-surface embedded in Euclidean space by utilizing the notion of an oriented k-surface as the limit set of a sequence of k-chains. This method providesExpand
Advanced Calculus
TLDR
It is quite impossible to include in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages, so it becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. Expand
A Treatice on Advanced Calculus
  • Dover
  • 2016
Surface Area and the Cylinder Area Paradox
Cours de calcul differentiel