Re: How to evaluate parts of an expression, but not other parts?

*To*: mathgroup at smc.vnet.net*Subject*: [mg122697] Re: How to evaluate parts of an expression, but not other parts?*From*: "David Park" <djmpark at comcast.net>*Date*: Sun, 6 Nov 2011 05:56:49 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <32289202.13251.1320484280567.JavaMail.root@m06>

I'm sure that you will obtain some answers to do this with plain Mathematica, but the Presentations package does have routines that allow selective manipulation of expressions. Along with HoldForm your can use EvaluateAt or EvaluateAtPattern to do selective evaluations of held expressions. You can also use CreateSubexpression, OperateSubexlression and ReleaseSubexpressions to tag and group things together to prevent Mathematica from mixing there elements with other elements outside the subexpressions. Tagged Subexpressions also show the tag in a tooltip when the mouse hovers over the Subexpression. We also have MapLevelParts that allows an operation to be performed on selected level parts in an expression (usually a sum, product or list). So, as a simple example we could do: <<Presentations` a = 1; b = 2; c = 3; d = 4; HoldForm[a + b] + HoldForm[c + d] % // EvaluateAt[{1, 1}] % // EvaluateAt[{2, 1}] % // ReleaseHold (a+b)+(c+d) 3+(c+d) 3+7 10 Using tagged Subexpressions we could do the following. We can also specify that a subexpression should always show parentheses. a = 1; b = 2; c = 3; d = 4; CreateSubexpression[HoldForm[a + b], True, tag1] + CreateSubexpression[HoldForm[c + d], True, tag2] % // OperateSubexpression[ReleaseHold, tag1] % // OperateSubexpression[ReleaseHold, tag2] % // ReleaseSubexpressions[All] (a+b)+(c+d) (3)+(c+d) (3)+(7) 10 If we want to show the individual values before they are combined in a Subexpression we could use nested Subexpressions and the following more complicated construction. Clear[a, b, c, d] step1 = Plus @@ MapThread[ CreateSubexpression[#1, #2] &, {HoldForm /@ {a, b, c, d}, {taga, tagb, tagc, tagd}}] a = 1; b = 2; c = 3; d = 4; step2 = step1 // MapLevelParts[CreateSubexpression[#, tagcd] &, {{3, 4}}]; step3 = step2 // MapLevelParts[CreateSubexpression[#, tagab] &, {{1, 2}}] step4 = Fold[OperateSubexpression[ReleaseHold, #2][#1] &, step3, {taga, tagb, tagc, tagd}] step5 = Fold[ReleaseSubexpressions[#2][#1] &, step4, {taga, tagb, tagc, tagd}] FixedPoint[ReleaseSubexpressions[All], step5] (a)+(b)+(c)+(d) ((a)+(b))+((c)+(d)) ((1)+(2))+((3)+(4)) (3)+(7) 10 David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Julian Francis [mailto:julian.w.francis at gmail.com] Dear all, I'd like to use the TreePlot function to visualise the expression of a dynamic programming problem I am working on. If I have something like: ( (a+b) + (c+d ) Mathematica helpfully simplifies this to: a + b + c + d But I'd prefer it to be in the original form. I can't write Hold[ ( (a+b) + (c+d) )] because I do want a,b,c & d to be evaluated. I want to write something like: Hold[ ( (Evaluate[a]+Evaluate[b]) + (Evaluate[c]+Evaluate[d]) ) ] But this just leaves the Evaluate expressions unevaluated. Any help greatly appreciated. Thanks, Julian.