Considering some of the applications you are developing GiNaC for I wonder if you familiar with the book "Geometric Algebra for Physicists," by Chis Doran and Anthony Lasenby, especially with regard to the geometric algebra formulation of tensor analysis for gravitation and quantum mechanics? The geometric algebra/calculus formulation leads to simplifications and unification of several areas of mathematical physics. Question, in your representation of Clifford algebra do you use a multiplication table or a matrix representation?
"AB" == Alan Bromborsky <brombo@comcast.net> writes:
AB> Considering some of the applications you are developing GiNaC AB> for I wonder if you familiar with the book "Geometric Algebra AB> for Physicists," by Chis Doran and Anthony Lasenby, especially AB> with regard to the geometric algebra formulation of tensor AB> analysis for gravitation and quantum mechanics? I am personally saw that book but did not have a chance yet to read it carefully (btw, my main area of specialisation is analysis). AB> The geometric algebra/calculus formulation leads to simplifications and AB> unification of several areas of mathematical physics. I completely agree with this statement and this is the reason why I am using Clifford algebras in my research. AB> Question, in your representation of Clifford algebra do you use a AB> multiplication table or a matrix representation? GiNaC currently is using multiplication tables for calculations with Clifford algebras. There are two questions in this connection: 1. Is there a Clifford algebras tasks which cannot be handled with multiplication tables but are accessible for matrix multiplication. On computer language: can we write a program using Clifford algebras which will behave differently depending from the internal representation of Clifford algebras. 2. Are there computational advantages in term of speed/memory/etc of matrix representation over the multiplication table? Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv@maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/
participants (2)
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Alan Bromborsky
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Vladimir Kisil