Re: A function to evaluate only parts matching a pattern

*To*: mathgroup at smc.vnet.net*Subject*: [mg25645] Re: A function to evaluate only parts matching a pattern*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Wed, 18 Oct 2000 02:52:21 -0400 (EDT)*References*: <8se9n3$6ps@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Ted, ReplaceAll, /., causes a problem with EvaluatePattern[expr_,pattn_]:= expr/.Pattern[p,pattn] :> With[{eval =p}, eval /; True] Thus: EvaluatePattern[Hold[2 + 3 + Hold[2 + 3]], _Plus] Hold[5 + Hold[2 + 3]] We can't solve this by using ReplaceRepeated, insead of ReplaceAll : EvaluatePattern2[expr_, pattn_] := expr //. Pattern[p, pattn] :> With[{eval = p}, eval /; True] EvaluatePattern2[Hold[2 + 3 + Hold[2 + 3]], _Plus] Hold[5 + Hold[2 + 3]] because the second use of ReplaceAll sees 5+Hold[2+3] and does not move on to 2+3. Here is a different approach to the problem of evaluating in place, based on position rather than pattern. This will appear in Mathematica in Education and Research 9.1 together with an analysis and variations on the Micheal Trott, Adam Strzebonski idea. EvaluateAt[expr_, pos_, f_:Identity] := Module[{pos1},(*normalize pos*) pos1 = Switch[pos, _Integer, {{pos}}, {__Integer}, {pos}, _, pos]; Fold[ReplacePart[#1, Extract[#1, #2, f], #2] &, expr, Reverse[Sort[pos1]]] ] EvaluateAt[expr, Position[expr, _Plus]] Hold[5 + Hold[5]] EvaluateAt[expr, 1] Hold[5 + Hold[2 + 3]] EvaluateAt[expr, {1, 3, 1}, #^2 &] Hold[2 + 3 + Hold[25]] Programming note 1. Reverse is used in Reverse[Sort[pos]] to arrange the position lists in decreasing length so that the later positions still refer to the same part of the modified expression 2. Fold is used so that later replacements replace with parts of the previously modified expression, not parts of the original expression. -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Ersek, Ted R" <ErsekTR at navair.navy.mil> wrote in message news:8se9n3$6ps at smc.vnet.net... > The function below evaluates all parts of a held expression that match a > certain pattern. This is based on some code Robby Villegas of Wolfram > Research discussed at the 1999 Developer Conference. There Micheal Trott and > Adam Strzebonski of Wolfram Research are mentioned as the inventors of this > trick discussed by Robby Villegas. > > In[1]:= > EvaluatePattern[expr_,pattn_]:= > expr/.Pattern[p,pattn] :> With[{eval =p}, eval /; True] > > > I made it into a function and added (Pattern[p,pattn]). The nice part > is that there is no need to use Module[{p}, _] > > ----------- > The next cell creates a held expression and evaluates all sub expressions > with the Head Plus but nothing else evaluates. In this example > Erf[Infinity]+5, 1+3, 5+4, Sqrt[36]-Sqrt[16] evaluate to 6, 4, 9, 2 > respectively since they each have the head Plus. > > In[2]:= > > demo=HoldForm[(Erf[Infinity]+5)*Sin[Pi/(1+3)]*Sqrt[5+4]/(Sqrt[36]-Sqrt[16])] > ; > EvaluatePattern[demo,_Plus] > > Out[3]= > HoldForm[(6*Sin[Pi/4]*Sqrt[9])/2] > > > Isn't that slick! Now this function doesn't work if any of the definitions > below are used. Why is the definition above the only one that works? > > > EvaluatePattern[expr_,pattn_]:= > expr/.Pattern[p,pattn]:>(p/;True) > > EvaluatePattern[expr_,pattn_]:= > expr/.Pattern[p,pattn]:>With[{eval=p},eval] > > EvaluatePattern[expr_,pattn_]:= > expr/.Pattern[p,pattn]->p > > > -------------------- > Regards, > Ted Ersek > > Down load Mathematica tips, tricks from > http://www.verbeia.com/mathematica/tips/Tricks.html > > >