For those of you who have learned about geometric algebra, you know of specialized functions such as wedge product, regressive product, geometric product, join operations, etc. I have been doing geometric algebra manually in smath with only rudimentary automation from smath as it has no facility.

e.g.,

a, b vectors

a^b is the wedge product, but in smath it is the logical AND which is undefined for vectors.

Also, smath doesn't handle vector, bivectors, trivectors, etc., multivectors, etc., or quaternions. In vector math (as opposed to matrix operations), vectors are expanded in terms of abstract basis vectors i, j, k as a = x*i + y*j + z*k and I can do wedge products, inner products, dot products, direct vector multiplication and division (via the geometric product), etc. These are missing from smath. In two dimensions, I often substitute i := 1 and j := i (the square root of -1) so that the complex facility built into smath can maintain separation of the vector directions in calculations. In 3 or more dimensions, I have no way to keep the basis vectors abstract and do calculations (which are a mix of symbolic and numeric). I must turn to matrix facilities, but they are inadequate to the task.

e.g., I cannot assign three coefficients simultaneously as in

|a|........|l m n||x|
|b|..:=..|o p q||y|
|c|........|r s t||z|

And I cannot do symbolic math with matrices very well with the current smath facilities. Instead, I have to define a vector symbol as a column matrix, do the assignment, and then interrogate the components of the matrix. In other instances, vector operations cannot be done directly as vector symbols and the whole fluency of the mathematical derivation is cluttered.

Any chance these facilities can be added to smath?

Edited by user 15 December 2012 02:40:55(UTC)  | Reason: Not specified