Mathematica: subscript simplification under non-communicative multiplication.

• To: mathgroup at smc.vnet.net
• Subject: [mg116416] Mathematica: subscript simplification under non-communicative multiplication.
• From: Cantormath <cantormath at gmail.com>
• Date: Mon, 14 Feb 2011 04:27:08 -0500 (EST)

```Using Subscript[variable, integer] in Mathematica 7.0+, I have
expressions of the following form:

a_-4 ** b_1 ** a_-4 ** b_-4 ** a_1 ** c_-4 ** c_1 ** c_5

I would like to simplify this expression.
Rules:
Variables with the same subscript to don't commute,
variables with different subscripts do commute.

I need a way to simplify the expression and combine like terms (if
possible); the output should be something like:

(a_-4)^2 ** b_-4 ** c_-4 ** b_1 ** a_1 ** c_1 ** c_5

The most important thing I need is to order the terms in the
expression by subscripts while preserving the rules about what
commutes and what does not. The second thing (I would like) to do is
to combine like terms once the order is correct. I need to at least
order expressions like above in the following way:

a_-4 ** a_-4 ** b_-4 ** c_-4 ** b_1 ** a_1 ** c_1 ** c_5,

that is, commute variables with different subscripts while preserving
the non-communicative nature of variables with the same subscripts.

All Ideas are welcome, thanks.

```

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