# [Mathematica 6.0+] Preserving order of variables

• Mathematica
• Hepth

#### Hepth

Gold Member
Is there a way to set Mathematica so that it preserves the order of variables.
i.e. I put:

F[x_] = A B x
F[a]
output : aAB

where I would want it: ABa

Thanks.

I am having the same problem.
The best solution I have found in general is using NonCommutativeMultiply:
F[x_] := A ** B ** x
although you usually have to define lots of other stuff to get everything working out as you want.
In some cases (like where A and B are explicitly defined matrices) you can use matrix multiplication
F[x_] := A . B . x
or a function
F[x_] := AB[x]

Do you have anything specific in mind?

I just have a long string of things that could either be matrices or vectors or scalars or tensors or etc. I'm trying to do some simplifications and then use the output. Its nothing special, I just need to preserve order. I'm not doing any REAL products (like inner, outer, contractions, etc) just representative products. If I define everything as matrices/vectors etc then it'll try to simplify it which i don't want. It needs to stay symbolic, yet perform basic distribution multiplication.

I guess I'll try the noncommutative, that should work.
Thanks!

If you want distributivity, you probably want to define something like
Code:
ExpandNCM[x_] := x //. {
NonCommutativeMultiply[a__, b_ + c_, d__] :> a ** b ** d + a ** c ** d
}

So that, for example,
Code:
a ** (b + c) ** d // ExpandNCM
gives
Code:
a ** b ** d + a ** c ** d
.

By the way, you can also try
Code:
ClearAttributes[Times, Orderless]
but I don't think it's the best solution because the Orderless attribute gets re-set seemingly at random.

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