On Friday, October 23, 2015 at 7:27:45 PM UTC-4, Nathan Goldbaum wrote:
>
>
>
> On Fri, Oct 23, 2015 at 6:25 PM, Justin <jbly...@gmail.com <javascript:>> 
> wrote:
>
>> I have a terrible way of wording things.. more of a discussion between 
>> myself and the author where he mentioned that I should ask the community 
>> what they think.
>>
>> On Friday, October 23, 2015 at 6:43:51 PM UTC-4, Jason Moore wrote:
>>>
>>> Justin,
>>>
>>> I don't think there is a debate. We have a very nice vector 
>>> representation in the physics package, but it is based on mutable types and 
>>> isn't very general. We created the sympy.vector package to make a more 
>>> general vector object that was based on immutable types with the idea that 
>>> the physics vector could eventually be deprecated. Our new implementation 
>>> may not be general enough for the mathematicians' taste and we are willing 
>>> to improve it so that it is, but we would still want it to eventually allow 
>>> us to deprecate sympy.physics.vector. The addition of vectors from 
>>> different coordinate systems is essential to this plan. So whatever you 
>>> want to do to improve the package will have my support but I hope that you 
>>> will keep this intended use case in mind when you think about bigger design 
>>> changes.
>>>
>>
>> I come from a physics background and can't see when or why this would be 
>> useful so my opinion is certainly biased.  As to the generality of the 
>> package there are no constrains on doing this and, bias and all, this tells 
>> me there ought to be some.  I am new to contributing so I will keep my head 
>> down and add functionality as you mentioned.  I am not trying to step on 
>> toes here...
>>
>
> A vector (e.g. the mathematical object, not necessarily its 
> representation) should be independent of the coordinate system, no?  So 
> long as there are well-defined translations between the coordinate systems, 
> it should certainly be possible to do arithmetic operations on two vectors 
> whose representations are written down in different coordinate systems.
>

The way I see it is that well are defining two different (or the same) 
coordinate systems with different (or the same) basis and allowing 
arithmetic operations between these two different (or the same) coordinate 
system.  The thing is we don't know until we make some definitions of the 
coordinate system whether the vector is well defined. For example:

Say C1 is defined and the origin is set at (0,0,0).  C2 is defined where 
it's y-axis aligns along C1's x-axis and origin is set at (0,0,0).  Any 
scaling could be set on C2 wrt C1. Is the operation 
C1.x * C1.i + C2.y * C2.j a well-defined vector?

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