The function that does the simplification you want is factor():
In [22]: var('a b c d')
Out[22]: (a, b, c, d)
In [23]: factor(a*c + b*d - a*d - b*c)
Out[23]: (a - b)⋅(c - d)
However, I'm not sure how to apply it here. You can't just convert
your dot products to multiplications because it isn't true that <a,
b>*<c, d> = <a, c>*<b, d>.
You might need to write a naive factor that recursively collects terms
with the same coefficient. For instance
<a, c> + <b,d> - <b,c> - <a, d>
-> <a, c - d> + <b, d - c>
-> <a - b, c - d>
This also needs to recognize that c - d = -(d - c).
could_extract_minus_sign is useful for this.
I don't recall if something like this is already written in SymPy.
Aaron Meurer
On Mon, Feb 27, 2017 at 12:44 PM, Nico Schlömer
<[email protected]> wrote:
> Thanks for the reply.
>
>> I assume e0, e1, and e2 are arbitrary vectors.
>
> Indeed, they can be anything. (I'm looking at 3 dimensions here but given
> the fact that everything is a dot product I assume that doesn't play much of
> a role.)
>
> Cheers,
> Nico
>
>
>
> On Monday, February 27, 2017 at 6:37:59 PM UTC+1, brombo wrote:
>>
>> How the expression zeta obtained. Do input the expression you show or is
>> it obtained by vector algebraic operations on vector expressions. I assume
>> e0, e1, and e2 are arbitrary vectors.
>>
>> On Mon, Feb 27, 2017 at 12:04 PM, Nico Schlömer <[email protected]>
>> wrote:
>>>
>>> I have a somewhat large expression in inner products,
>>> ```
>>> zeta = (
>>> - <e0, e0> * <e1, e1> * <e2, e2>
>>> + 4 * <e0, e1> * <e1, e2> * <e2, e0>
>>> + (
>>> + <e0, e0> * <e1, e2>
>>> + <e1, e1> * <e2, e0>
>>> + <e2, e2> * <e0, e1>
>>> ) * (
>>> + <e0, e0> + <e1, e1> + <e2, e2>
>>> - <e0, e1> - <e1, e2> - <e2, e0>
>>> )
>>> - <e0, e0>**2 * <e1, e2>
>>> - <e1, e1>**2 * <e2, e0>
>>> - <e2, e2>**2 * <e0, e1>
>>> )
>>> ```
>>> and the symmetry in the expression has me suspect that it can be further
>>> simplified. Is sympy capable of simplifying vector/dot product expressions?
>>> A small example that, for example, takes
>>> ```
>>> <a, c> + <b,d> - <b,c> - <a, d>
>>> ```
>>> and spits out
>>> ```
>>> <a-b, c-d>
>>> ```
>>> would be great.
>>>
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>>
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