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copied!<p>The following is a bit wasteful, but it works: The idea is to simply watch for cases where the <code>Listable</code> attribute of <code>Plus</code> has put the same <code>pt</code> into all elements of a list (i.e. a raw point) -- and then pull it back out. First, define a function for adding pt objects: </p> <pre><code>SetAttributes[ptPlus, {Orderless}] ptPlus[pt[pa : {_, _}], pt[pb : {_, _}], r___] := ptPlus[pt[pa + pb], r]; ptPlus[p_pt] := p; </code></pre> <p>Then we make sure that any <code>Plus</code> which involves a <code>pt</code> is mapped to <code>ptPlus</code> (an associate the rule with pt). </p> <pre><code>Plus[h___, a_pt, t___] ^:= ptPlus[h, a, t]; </code></pre> <p>The above rules means that: <code>{x0,y0}+pt[{x1,y1}]</code> will be expanded from <code>{x0+pt[{x1,y1}],y0+pt[{x1,y1}]}</code> to <code>{ptPlus[x0,pt[{x1,y1}]],ptPlus[y0,pt[{x1,y1}]]}</code>. Now we just make a rule to transform this to <code>pt[{x0,y0}]+pt[{x1,y1}]</code> (note the deferred condition which checks that the <code>pt</code>s are equal): </p> <pre><code>{ptPlus[x__], ptPlus[y__]} ^:= Module[{ ptCases = Cases[{{x}, {y}}, _pt, {2}]}, ptCases[[1]] + pt[Plus @@@ DeleteCases[{{x}, {y}}, _pt, {2}]] /; Equal @@ ptCases] </code></pre> <p>A more opaque, but slightly more careful version which is easier to generalize to higher dimensions:</p> <pre><code>ptPlus /: p : {_ptPlus, _ptPlus} := Module[{ptCases, rest, lp = ReleaseHold@Apply[List, Hold[p], {2}]}, ptCases = Cases[lp, _pt, {2}]; rest = Plus @@@ DeleteCases[lp, _pt, {2}]; ptCases[[1]] + pt[rest] /; And[Equal @@ ptCases, VectorQ@rest]] </code></pre> <p>This whole approach will of course lead to horribly subtle bugs when <code>{a+pt[{0,0}],a+pt[{0,b}]} /. {a -> pt[{0,0}]}</code> evaluates to <code>pt[{0,0}]</code> when <code>c==0</code> and <code>{pt[{0,0}],pt[{0,c}]}</code> otherwise...</p> <p>HTH -- said the guy to himself...</p>

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