Re: What is the difference Between MakeBoxes and ToBoxes

*To*: mathgroup at smc.vnet.net*Subject*: [mg106754] Re: [mg106684] What is the difference Between MakeBoxes and ToBoxes*From*: "David Park" <djmpark at comcast.net>*Date*: Fri, 22 Jan 2010 05:41:55 -0500 (EST)*References*: <713167.1264068057720.JavaMail.root@n11>

George, MakeBoxes is very useful if you want to have specially formatted output display but use standard Mathematica input. Standard input is often more convenient than a special input (using the Notation package or MakeExpression) because you don't have to bring up a special box structure or tab around when entering information. Here is a simple example taken from one of my Presentations package essays. MatrixExp has no special formatting. MatrixExp[\[Theta] J] % /. J -> ( { {0, -1}, {1, 0} } ) // MatrixForm Perhaps we would want MatrixExp to format as an exponential when it doesn't evaluate. We can do it with the following MakeBoxes definition: MakeBoxes[MatrixExp[x_], form : StandardForm | TraditionalForm] := InterpretationBox[#1, #2] & @@ {SuperscriptBox["\[ExponentialE]", MakeBoxes[x, form]], MatrixExp[x]} Now evaluate the same statements above. (It is the first statement that is formatted.) Notice the structure of the rhs of the MakeBoxes definition. InterpretationBox has the Attributes HoldAll, but we can circumvent this by making it a pure function that we apply to a List. The first item in the list is the formatted structure and the second item is the internal representations. The list could be replaced by a Module that did some calculations to determine the display structure. Notice also that the rhs uses MakeBoxes on x because we don't know if it might have its own formatting definitions. InterpretationBox also has an option SyntaxForm that can be used to determine the precedence grouping of the formatted expression, and hence whether Mathematica adds parentheses in various cases. However, this is not fully integrated into Mathematica, and in my experience causes FrontEnd crashes. That is a flaw in Mathematica that I don't like, but usually you can get by without SyntaxForm. Instead of writing the displayed form entirely with low level box structures, you might be able to write all or part of it with high level Mathematica expressions and then use ToBoxes to generate the box structures. It depends on whether the format you want fits into regular Mathematica formatting, or is just too special. Here we could write the MakeBoxes definition above as: MakeBoxes[MatrixExp[x_], form : StandardForm | TraditionalForm] := InterpretationBox[#1, #2] & @@ {ToBoxes[Superscript["\[ExponentialE]", x], form], MatrixExp[x]} We also have the high level Interpretation statement and I've used this successfully in some cases, but it is not as versatile as InterpretationBox. There is also the Format statement. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: George [mailto:gtatishvili at gmail.com] May you please advise me what is the difference between "ToBoxes" and "MakeBoxes"? I read in Mathematica manual and unerstood that the only differerence is that "MakeBoxes" generates boxes without evaluation of input...So is that all the difference? I saw also some examples where on lhs is "MakeBoxes" and on rhs is "ToBoxes" when I just changed "MakeBoxes" into "ToBoxes" (and vice versa) the Mathematica gave me some errors.... So could anybody explain me with a simple practical example with explanation? Thank you very much George