question about 'factor_out'

Question

In my recent study, I encounter the following problem:

{A,B,C,D}::NonCommuting.
ex:=A B (a-b)+B A (b-a)+A C (a-c)+C A (c-a)+B C (b-c)+C B (c-b);

How to simplify the expression above? i.e. get the result $$ (AB-BA)(a-b)+(AC-CA)(a-c)+(BC-CB)(b-c) $$

Answer 1

Remember that you need to write either a space or a * character to indicate products. Also, NonCommuting is spelled with a single t.

What do you want to do with this? You can distribute(_) this, but there isn't much else you can simplify given that the capital symbols do not commute with each other.

Comments

Sorry for my typo. I want to extract the scalars in the following expression (the matrices outside the brackets are noncommuting)

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I have written following code

substitute(_,$A?? (B??)+ C?? (D??)|B??+D??=0->(A??-C??) B??$);

but it's useless.

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I don't understand what you want to do. Can you write down the expression that you would like to end up with?

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OK, just like this https://yadi.sk/i/EzNCxFW_mStnFQ

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I have known how to solve it. Only need to combine multiply_through ,zoom and factor_out.

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Hi @Eureka, Could you please port your answer? So we can all benefit from it. Thx.

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For example:

{a,b}::SortOrder.
{A,B}::NonCommuting.
ex:=A B (a-b)+B A (b-a);
import cdb.core.manip as manip
zoom(_,$B A A??$);
distribute(_);
manip.multiply_through(_,$-1$);
factor_out(_,$A,B$);
manip.multiply_through(_,$-1$);
sort_sum(_);
unzoom(_);
factor_out(_,$a-b$);

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But I have no ideas how to solve my practical problem simply. .