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copied!<p>OK, writing rules that play nice with the attributes of <code>NonCommutativeMultiply</code> is sometimes a hassle. Here's an alternate method which introduces a helper <code>NCM</code> that does not have the rules and attributes of <code>NonCommutativeMultiply</code> associated with it.</p> <p>The following code also incorporates the last couple of your questions. <a href="https://stackoverflow.com/q/4988323/421225">(1)</a> <a href="https://stackoverflow.com/q/5001368/421225">(2)</a></p> <pre><code>Unprotect[NonCommutativeMultiply]; Clear[NonCommutativeMultiply] (* Factor out numerics -- could generalize to some ScalarQ *) nc:NonCommutativeMultiply[a__]/;MemberQ[{a},_?NumericQ]:=NCMFactorNumericQ[NCM[a]]/.NCM->NonCommutativeMultiply (* Simplify Powers *) b___**a_^n_.**a_^m_.**c___:=NCM[b,a^(n+m),c]/.NCM->NonCommutativeMultiply (* Expand Brackets *) nc:NonCommutativeMultiply[a___,b_Plus,c___]:=Distribute[NCM[a,b,c]]/.NCM->NonCommutativeMultiply (* Sort Subscripts *) c___**Subscript[a_, i_]**Subscript[b_, j_]**d___/;i>j:=c**Subscript[b, j]**Subscript[a, i]**d Protect[NonCommutativeMultiply]; Unprotect[NCM]; Clear[NCM] NCMFactorNumericQ[nc_NCM]:=With[{pos=Position[nc,_?NumericQ,1]},Times@@Extract[nc,pos] Delete[nc,pos]] NCM[a_]:=a NCM[]:=1 Protect[NCM]; </code></pre> <p>Note that <code>NCMFactorNumericQ</code> is fast because it works in a single pass, but the rule associated with it <code>nc:NonCommutativeMultiply[a__]/;MemberQ[{a},_?NumericQ]</code> is slow, because the Flat attribute means that it does a stupid number of checks using <code>NumericQ</code>. If you really want more speed and have large expressions, then you should just manually apply the <code>Sort</code> and <code>Factor</code> routines, so that Mathematica does less pattern checks.</p>

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