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## [Axiom-developer] Clifford Algebra

**From**: |
Martin Baker |

**Subject**: |
[Axiom-developer] Clifford Algebra |

**Date**: |
Thu, 8 Dec 2016 10:55:26 +0000 |

**User-agent**: |
Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.5.1 |

Tim,

`You recently mentioned Clifford Algebra a couple of times so I thought I
``would mention an idea that I had on the subject. The idea is still too
``vague and hand-wavy to turn into code but I would be interested to know
``if anyone thinks its viable?
`

`The idea is to implement a 3-layer architecture in the CAS. The layers
``being:
`
1 - Physics
2 - Geometry
3 - Algebra

`Each of these layers would have the ability to slot in different
``options, for instance:
`
Physics - classical, relativity or quantum.
Geometry - Euclidean, projective, conformal or Minkowski space.
Algebra - Clifford or matrix/tensor.

`The general idea being that, when working at the higher level there is
``some independence from the layers below. For instance, if you are
``working on a physics problem and you have a issue like:
`* It does not scale up.
* It has an awkward singularity.
* Need for different type of transform not supported by algebra.

`Then you can slot on a different algebra or geometry to see if that
``fixes the problem without changing the physics code.
`
Unfortunately I can see some difficulties with this idea:

`1) How to refer to literal values? Even when working at the physics
``level we may still need to refer to concrete values for fixed points,
``planes, transforms and so on. Is there a way to specify these literal
``values in a way that does not use actual Clifford or matrix values? Even
``if the answer is no then I think the model could give some independence
``between the layers.
``2) The model may need 2 or more geometry layers. For instance, we may be
``working in 3 dimensions but we want to combine translate and rotate into
``a single transform, or we want to get rid of singularities, so we add
``extra dimensions but we still want to translate back to original
``coordinates so we need multiple coordinate systems.
`
As I say, this is just a vague idea but I just thought I would mention it.
Martin