Questions about how Mathematica evaluates expressions, tracing evaluation (Trace*), handling expressions in unevaluated form (Hold*, Unevaluated), nonstandard evaluation, etc.

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70
votes
5answers
46k views

Get a “step-by-step” evaluation in Mathematica

Is it possible in Mathematica to get a step-by-step evaluation of some functions; that's to say, outputting not only the result but all the stages that have led to it? If so, how does one do it? ...
51
votes
4answers
3k views

Plot draws list of curves in same color when not using Evaluate

This example comes from the Mathematica documentation for Plot under Basic Examples. Can someone please explain why these are each plotted as a different color in ...
40
votes
8answers
2k views

Injecting a sequence of expressions into a held expression

Consider the following toy example: Hold[{1, 2, x}] /. x -> Sequence[3, 4] It will give Hold[{1, 2, Sequence[3, 4]}] ...
40
votes
4answers
2k views

How do I evaluate only one step of an expression?

I am looking for a simple, robust way to evaluate an expression only one step, and return the result in a held form. The definition of a single step is ambiguous, and this itself is probably worthy ...
39
votes
3answers
1k views

The clearest way to represent Mathematica's evaluation sequence

WReach has presented here a nice way to represent the Mathematica's evaluation sequence using OpenerView. It is much more clear way to go than using the standard ...
37
votes
1answer
1k views

How to compare power towers in Mathematica?

First I tried it directly, but it overflowed: ...
27
votes
2answers
2k views

What are the cool kids talking about when they use ##&[]? [duplicate]

All the cool kids are apparently using ##&[] for Unevaluated @ Sequence[] but I have no idea what either means. ...
26
votes
1answer
793 views

How do you set attributes on SubValues?

SubValues, as discussed in a previous question, are declared as follows ...
25
votes
2answers
807 views

Block attributes of Equal

I answered “Equating matrices (or higher order tensors) element-wise” with: ...
22
votes
2answers
389 views

Evaluation of OptionValue[]

I have a function that takes an OptionsPattern and I want to access several options, say a, and ...
22
votes
1answer
434 views

How does Return work?

It is not completely clear to me how Return[] works. The documentation says: Return[expr] returns the value expr from a ...
20
votes
5answers
587 views

Reassign values to symbols

I've got a situation where I have, say 4 symbols, a, b, c and ...
20
votes
5answers
888 views

How do you programatically load data into symbols?

I am trying to convert a list of string names into symbols, which will then be used to store data. I have 24 files (where the name of each file is a member of the list mentioned above) that I need to ...
20
votes
2answers
963 views

Mathematica for Computer Scientists

Background I've coded in C/Scheme for 10 years. I have a BS CS. I've recently become very interested in pattern-matching (lisp's match macro), and term rewriting systems, which brought me to ...
20
votes
2answers
474 views

Context unique to each group at a specified level

Are there any new tools in v10 that might be applicable to this problem? Recent versions of Mathematica provide the option of having a unique $Context for each ...
19
votes
5answers
2k views

How to pass a symbol name to a function with any of the Hold attributes?

Given a function with the attribute HoldFirst, HoldAll or similar, and a variable, list, how ...
19
votes
2answers
483 views

Implementing a safe ValueQ that does not evaluate its argument

Mathematica has a built-in function ValueQ. Quoting the docs, ValueQ[expr] gives True if ...
19
votes
1answer
214 views

How to get Cases to wrap results in an arbitrary head?

A number of functions provide for results to be wrapped in an arbitrary head. This is very important in cases where the results should not be evaluated. Take ...
18
votes
3answers
626 views

How can I completely ban usage of some functions in output and mandate use of others?

For example, I hate that Mathematica uses Pochhammer symbol in outputs and prefer all the expressions in Gamma function. How can ...
18
votes
4answers
416 views

Function that caches when it returns unevaluated

How would you go about implementing a function that caches not the result but the fact that it didn't match a pattern? So that it doesn't waste time recomputing a complex time-consuming pattern ...
18
votes
3answers
1k views

Asynchronous evaluation: Is it possible?

Currently we have a limited number of ways to perform asynchronous evaluation. The most common is through Dynamic and ...
18
votes
1answer
852 views

How can I set a keyboard shortcut to run a command?

I want to use this to add a keyboard shortcut to an undo function I wrote. The basic problem is the following: I have a command, let's say x=1, and I want to run ...
18
votes
1answer
491 views

Incorrect result from Integrate

I attempted to calculate the following integral: ...
17
votes
2answers
2k views

Difference between AbsoluteTiming and Timing

I need to evaluate the efficiency of my code. Therefore I would like to evaluate the time the code need for some calculations. Mathematica gives me two possibilities for this kind of evaluation: ...
17
votes
4answers
685 views

Making a symbol's new definitions be tried before all previously defined ones

Is there any way to "close" a package (or a symbol, or a context) in that if a user of the package adds definitions to the symbol they will be tried before the package defined ones, just like what ...
17
votes
2answers
312 views

Why doesn't a Composition[] hold its arguments and what can be done about it?

Now that Composition (also RightComposition) has shorthand syntax I am more inclined to use it, however what I feel should be ...
16
votes
1answer
561 views

Wagner's trick to monitor FindRoot no longer works in Mathematica version 8

I recently learned that we can use Print as a monitoring tool. My favorite is Ted Ersek's example ...
16
votes
1answer
278 views

Exclude Sections/Subsections/… from evaluation

I'm working on a large notebook and I want to exclude some sections and subsections from being evaluated when I evaluate the whole notebook. Is there a way to exclude specific sections or ...
16
votes
1answer
330 views

Quit the Kernel and start new session automatically

The question is how to quit the kernel, start a new session automatically, and to be able to run such procedure from e.g. Button. This is especially useful when ...
15
votes
8answers
409 views

Is it possible to use RandomChoice to choose without other choices being evaluated?

I'm trying to do this: i1 = 1; i2 = 1; RandomChoice[{ (i1 = i1 + 1), (i1 = i1 - 1), (i2 = i1 + 1), (i2 = i2 - 1)}] In order to chose randomly which ...
15
votes
4answers
312 views

Result about Context is inconsistent with the description of “Power Programming with Mathematica”

x = 5; temp`x = 6; Begin["temp`"] {x, Global`x, temp`x} The result in my Mathematica session is {5,5,6}, but it's ...
15
votes
4answers
597 views

HoldForm doesn't hold form

Bug introduced in 10.0.0 and fixed in 10.0.1 In Mathematica version 10, HoldForm no longer produces the same results as in version 8 (edit: I only have versions ...
15
votes
4answers
380 views

Prevent graphics render inside held expression

Assuming each odd line is input I would like the even lines to be the output of the following lines. In the above the Graphics are inside ...
15
votes
4answers
624 views

Recovering intermediate results from a Table after an interruption

I am interested in knowing if it is possible to recover intermediate results from a Table after an interruption. Let us say I want to produce a really useful table ...
15
votes
3answers
524 views

Comparing Mathematica expressions like diff

I am looking for a way to compare (or "diff") two Mathematica expressions, similarly to how to diff utility can compare two text files and report the differences. Has anyone already written such a ...
15
votes
2answers
280 views

How can I access a variable in one evaluator from another evaluator?

I have two notebooks, each with a different kernel. Is there a way to grab the value of a variable in KernelA from KernelB?
15
votes
2answers
936 views

Why do certain values in ArcSin not fully evaluate?

This is a continuation of: Why do certain fractional values in TriangleWave not evaluate? The analysis by R.M and rasher revealed that problem to reduce to the behavior of: ...
15
votes
1answer
468 views

Using Evaluate and Evaluated -> True in Plot

A few use cases: (1) This, as expected, returns (almost) immediately: f[x_?NumericQ] := Evaluate[(Pause[1]; x)] Plot[f[x], {x, 0, 1}] (2) This takes ...
15
votes
1answer
312 views

Polynomial expectations of generic distributions

Summary Polynomial expectations depend only moments and cross moments of a multivariate distribution. I would like to use Expectation to compute polynomial ...
14
votes
4answers
660 views

Returning an unevaluated expression with values substituted in

Let's say I have a function formula[x_List] := (x[[1]] - x[[2]]) + (x[[3]] - x[[4]]); and I want to pass it a variable and get back the unevaluated formula with ...
14
votes
3answers
240 views

How can I test properties of a symbol from the string name without the symbol completely evaluating

Suppose I have a few symbols, one of which has a value: {abc1, abc2 = 5, abc3}; I can use Names to get the list of names, as ...
14
votes
2answers
340 views

How to make use of NumericQ[x] = True (and use it safely)?

Basic Issue: I'm trying to understand the proper use of NumericQ's "magical" capabilities. Please consider the examples below. Actual question and some links are ...
14
votes
2answers
177 views

How to find out what files are touched when Get is called?

Is there a way to capture all package files touched whenever a package is called via Get, Needs, ...
14
votes
1answer
433 views

What is the real default CellEvaluationFunction?

The default CellEvaluationFunction is Identity but one can quickly see that this is handled specially as an equivalent function, ...
13
votes
3answers
492 views

Does AbsoluteTiming slow the evaluation time?

I've started using AbsoluteTiming to discriminate between similar function constructs, but I sometimes feel like it takes substantially more time to evaluate a ...
13
votes
5answers
955 views

How are parameters evaluated for a Plot in Manipulate

I am trying to get my head around how Manipulate evaluates functions in a Plot. I have read the introduction to Manipulate, and introduction to Dynamic, but I still ...
13
votes
2answers
136 views

Why the Block command does not forget the $ContextPath variable

I do not understand this behavior: ...
13
votes
3answers
234 views

Can't inject EncryptedObject

Here are minimal examples: ...
13
votes
2answers
323 views

Clever use of DownValues, or failure to understand the “Mathematica Way.”

I needed to look at the changes in the values of about 4000 items from one year to the next. I have a table with identifiers and values for each year. Not all of the items are in each list. The ...
13
votes
2answers
444 views

How to REALLY Hold arguments and capture FullForm?

I'm trying to write an expression deconstructor or FullForm-capturer; might even call it a parser, maybe, but that might be too glorious a word. I got some great ...