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copied!<p><strong>The below only works if you remove the Flat attribute of NonCommutativeMultiply</strong> (Which is something I did by mistake during testing... a rookie mistake!)</p> <p>The simplest thing to do is</p> <pre><code>Unprotect[NonCommutativeMultiply]; NonCommutativeMultiply[a___, 1, b___] := a ** b NonCommutativeMultiply[___, 0, ___] := 0 NonCommutativeMultiply[a_] := a Protect[NonCommutativeMultiply]; </code></pre> <p>The final expression is needed so that <code>a**1</code> simplifies to <code>a</code> instead of <code>NonCommutativeMultiply[a]</code>. You might also need <code>NonCommutativeMultiply[]:=1</code> so that expressions like <code>1**1</code> simplify properly (*). The only problem with all of this, is for large expressions, the pattern is checked against everything and this gets really slow.</p> <p>The above two definitions for 0 and 1 can be combined and generalized to</p> <pre><code>NonCommutativeMultiply[a___, n_?NumericQ, b___] := n a ** b </code></pre> <p>which factors out any numerical terms inside the expression. But this slows down things even more in large expressions, since each term is checked to see if its numerical.</p> <p>To simplify your <code>a**a</code> to <code>a^2</code>, you need something like</p> <pre><code>NonCommutativeMultiply[a___, b_, b_, c___] := a ** b^2 ** c </code></pre> <p>or more generally</p> <pre><code>NonCommutativeMultiply[a___, b_^n_., b_^m_., c___] := a ** b^(n + m) ** c </code></pre> <hr> <p>(*) Note that this is only because the default order that Mathematica puts its <code>DownValues</code> in is not necessarily the best in this case. Change the order so that <code>NonCommutativeMultiply[a_]</code> comes before <code>a___ ** n_?NumericQ ** b___</code> then <code>NonCommutativeMultiply[]</code> won't be generated by the rules, and you won't need that last pattern (unless you produce <code>NonCommutativeMultiply[]</code> some other way).</p>

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