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5038761
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2011-02-18T07:39:02.767
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2011-02-18T08:08:17.393
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2011-02-18T08:08:17.393
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The key to doing this is to realize that Mathematica represents <code>a-b</code> as <code>a+((-1)*b)</code>, as you can see from <pre><code>In[1]= FullForm[a-b] Out[2]= Plus[a,Times[-1,b]] </code></pre> For the first part of your question, all you have to do is add this rule: <pre><code>NonCommutativeMultiply[Times[-1, a_], b__] := - a ** b </code></pre> or you can even catch the sign from any position: <pre><code>NonCommutativeMultiply[a___, Times[-1, b_], c___] := - a ** b ** c </code></pre> Update -- part 2. The general problem with getting scalars to front is that the pattern <code>_Integer</code> in your current rule will only spot things that are manifestly integers. It wont even spot that <code>q</code> is an integer in a construction like <code>Assuming[{Element[q, Integers]}, a**q**b]</code>. To achieve this, you need to examine assumptions, a process that is probably to expensive to be put in the global transformation table. Instead I would write a transformation function that I could apply manually (and maybe remove the current rule form the global table). Something like this might work: <pre><code>NCMScalarReduce[e_] := e //. { NonCommutativeMultiply[a___, i_ /; Simplify@Element[i, Reals],b___] :> i a ** b } </code></pre> The rule used above uses <code>Simplify</code> to explicitly query assumptions, which you can set globally by assigning to <code>$Assumptions</code> or locally by using <code>Assuming</code>: <pre><code>Assuming[{q \[Element] Reals}, NCMScalarReduce[c ** (-q) ** c]] </code></pre> returns <code>-q c**c</code>. HTH
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