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PONoncommutative Multiplication and Negative coeffcients at the Beginning of an Expression in Mathematica
 

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  1. PONoncommutative Multiplication and Negative coeffcients at the Beginning of an Expression in Mathematica
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    <p>With the help of some very gracious stackoverflow contributors <a href="https://stackoverflow.com/questions/5023863/redefine-noncommutative-multiplication-in-mathematica">in this post</a>, I have the following new definition for <code>NonCommutativeMultiply (**)</code> in Mathematica: </p> <p><code> Unprotect[NonCommutativeMultiply];<br> ClearAll[NonCommutativeMultiply]<br> NonCommutativeMultiply[] := 1<br> NonCommutativeMultiply[___, 0, ___] := 0<br> NonCommutativeMultiply[a___, 1, b___] := a ** b<br> NonCommutativeMultiply[a___, i_Integer, b___] := i*a ** b<br> NonCommutativeMultiply[a_] := a<br> c___ ** Subscript[a_, i_] ** Subscript[b_, j_] ** d___ /; i &gt; j :=<br> c ** Subscript[b, j] ** Subscript[a, i] ** d<br> SetAttributes[NonCommutativeMultiply, {OneIdentity, Flat}]<br> Protect[NonCommutativeMultiply];</code> </p> <p>This multiplication is great, however, it does not deal with negative values at the beginning of an expression, i.e.,<br> <code>a**b**c + (-q)**c**a</code><br> should simplify to<br> <code>a**b**c - q**c**a</code><br> and it will not. </p> <p>In my multiplication, the variable <code>q</code> (and any integer scaler) is commutative; I am still trying to write a <code>SetCommutative</code> function, without success. I am not in desperate need of <code>SetCommutative</code>, it would just be nice. </p> <p>It would also be helpful if I were able to pull all of the <code>q's</code> to the beginning of each expression, i.e.,:<br> <code>a**b**c + a**b**q**c**a</code><br> should simplify to:<br> <code>a**b**c + q**a**b**c**a</code><br> and similarly, combining these two issues:<br> <code>a**b**c + a**c**(-q)**b</code><br> should simplify to:<br> <code>a**b**c - q**a**c**b</code> </p> <p>At the current time, I would like to figure out how to deal with these negative variables at the beginning of an expression and how to pull the <code>q's</code> and <code>(-q)'s</code> to the front as above. I have tried to deal with the two issues mentioned here using <code>ReplaceRepeated (\\.)</code>, but so far I have had no success. </p> <p>All ideas are welcome, thanks...</p>
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    1. COFor the SetCommutative part I suggest you have a look at the grassmanOps package I mentioned in an earlier question. There they have operations to define variables as "fermionic" (anti commuting) and "bosonic" (commuting) and have a modification to NonCommutativeMultiply that checks this grading and takes all bosonic variables out in front.
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