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

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8
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3answers
306 views

How to write a function-defining function which stores the function arguments in a stack?

I have a function-defining function SetAttributes[DefFn, HoldAll]; DefFn[f_[args___], body_] := f[args] := body; I am trying to modify this function to record ...
8
votes
3answers
170 views

With/Function(/etc) replacement behaviour

Can anyone explain to me this behaviour? I've been having more than a couple of similar doubts these last weeks. For example f[_?NumericQ] := 8; Now, if I do ...
8
votes
3answers
1k views

Keyboard shortcut to evaluate notebook

(If this is entirely trivial, although I couldn't find an answer as much as I searched the archives, I will delete the question.) How could I add a keyboard shortcut to evaluate the entire notebook ...
8
votes
2answers
326 views

Why do I have to put Evaluate[] here

I wanted to draw some contours. I succeeded with this: ...
8
votes
1answer
120 views

How to catch the “Preemptive” evaluations from within the main loop?

When trying to make an optimized version of my plotRange fonction I faced a problem of catching the "Preemptive" evaluations ...
8
votes
2answers
171 views

How to correct this, `f[a_] := FindRoot[eq == 0, {x, 0.5}]`, where `eq` contains a parameter $a$, without using `eq[a]`?

I want to solve an equation with a parameter $a$, and define the result as a function of $a$. It is something like this: ...
8
votes
2answers
3k views

How do you force a decimal output? [duplicate]

I have some very small values such as 2.601519253*10^-8. I'd like to output these values to CSV for another program to work with. I've tried N[value, 50], but Mathematica still insists on producing ...
8
votes
2answers
428 views

Exporting held expressions through JSON

Trying to round-trip expressions through JSON, I'm getting unexpected errors for held expressions, and would be grateful for advice or clues. Consider, first, something that works well ...
8
votes
1answer
180 views

Why is building a table of function values so much slower than just plotting the function?

Here is a function that take some time to evaluate: n = 1000; coeffs = RandomVariate[NormalDistribution[], n]; f[x_] := Sum[coeffs[[k]] Sin[k x]/k, {k, 1, n}]; ...
8
votes
2answers
710 views

Mathematica rule substitution memory

First I present the specific programming question, and then I provide further background details. Given an expression in Mathematica, say f=3x+7y, there are two ...
8
votes
2answers
160 views

Half-delayed evaluation

In a certain wider context, I need to make some delayed definitions, such as x := a + b + c, but within these definitions I want ...
8
votes
1answer
167 views

The Flat Attribute, Unevaluated and the Evaluation Process

To make this question easy to follow let's give some symbols a couple attributes. Attributes[f] = {Flat}; Attributes[s] = {Orderless}; Now consider the ...
8
votes
1answer
519 views

How to properly DumpSave & Get Global`s symbols inside packages while not touching Global context?

For efficiency reasons I prefer to use DumpSave instead of Save. For ease of access I prefer to save symbols in ...
8
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2answers
310 views

Understanding Villegas-Gayley

Temporary message: I have written another question about the behaviour the code by Oleksandr R. . Sadly I clicked "discard" and that was lost. I am a bit demotivated now and in order to not let the ...
8
votes
1answer
196 views

Why does Plot[Hold[x], {x,0,1}] work?

It appears that, counter to my expectation, all of these (and probably many others) seem to work fine: ...
8
votes
1answer
132 views

Prevent Plus from threading InterpolatingFunction

For an InterpolatingFunction $y:\ \mathbb{R}\to\mathbb{R}^2$, Plus is unaware of this, so when I do any modifications to it in ...
8
votes
1answer
144 views

Is it possible to write a function immune to symbol redefinitions in any Block surrounding its invocation?

Normally, semantics of symbols used in a function definition can be changed by their redefinitions in Blocks surrounding the function invocation: ...
7
votes
6answers
200 views

How to join held Lists?

Let's say I have a = Hold@{2+2} b = Hold@{4+4} How can I get Hold@{2+2,4+4} ie join the two held lists ? More ...
7
votes
4answers
229 views

Button's command is not evaluated in iteration

I wish I didn't feel like a newbie after several months, but... If I enter the following: Table[ Button[ "Number: " <> ToString @ i, Print @ i], {i, 1, 5}] ...
7
votes
3answers
278 views
7
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2answers
523 views

How does Mathematica determine that an evaluation should be terminated?

How exactly does Mathematica determine that evaluation of particular expression should be finished and the result should be returned? Here are some examples of unclear behavior which have arisen, ...
7
votes
4answers
1k views

Force function to make assumptions about its input variables in Mathematica

I'm trying to force a Mathematica function to make an assumption about its input variables. In my case, I'm trying to define a function to return the pdf of a Gaussian. But let's use a simple toy ...
7
votes
2answers
253 views

Nothing appears in simple plot

I'm trying to get the following simple code to work. (The code is just supposed to graph the norm of the second derivative of a vector function). ...
7
votes
3answers
217 views

Graphics in Notebook Different from Graphics Expression?

Consider the expression TreeForm[a+b^2+c^3+d] which displays as This is a nice Graphics object, as I can prove by typing ...
7
votes
2answers
182 views

Keywords to find documentation for this syntax

Mathematica allows this syntax, but I cannot find any documentation (or books) that discuss the various uses/advantages of it ...
7
votes
3answers
224 views

Why does Mathematica not seem to know that $i^x$ cannot be equal to $0$?

I am experiencing a curious behaviour of Simplify when handling expressions involving powers of $\mathbf{i}$, such as $\mathbf{i}^x$ where $x$ is unknown. For ...
7
votes
2answers
205 views

Is there a way to show the details of a numerical computation?

I have recently started using Mathematica as a calculator while teaching (definitely overkill, but I try to use as few tools as possible). I would like my students to be able to trace simple numerical ...
7
votes
2answers
128 views

Obtain input expression from history without evaluating

I typed and evaluated an expression, but deleted it from the notebook. For instance, suppose it was In[1]:= Round@SessionTime[] Out[1]= 2 I now want to retrieve ...
7
votes
2answers
177 views

“A number in base b” and pure functions: why doesn't b^^# & work?

Why do the following not work (in Mathematica 7)? 2^^ # & /@ {1000, 1101} and 2^^ # & @ 1101 This does work: ...
7
votes
3answers
124 views

How to stop a single function to be evaluated?

See this example: AA = {x} \[Function] Normalize[x] BB = {x} \[Function] Evaluate[AA[x]*5] I need BB to be Normalize[x]*5. Some context:I call evaluate because ...
7
votes
1answer
266 views

How to force an evaluation to use only one core?

There are some evaluations which are automatically parallelized or multithread if there are cores available.( for example, Eigenvalues) But I don't want the ...
7
votes
1answer
252 views

Module variable scoping in Scheduled Tasks?

I ran across a scoping puzzle while experimenting with ScheduledTasks, and I'd be grateful for an explanation from the sages here. I found a workaround by intuitive horse sense, but was unable to ...
7
votes
1answer
214 views

How do I write a ValueQ function that only returns True if there exists an OwnValue?

Reading the comments in this answer has motivated me to request a full solution to part of this problem. What I'd like is an efficient solution that returns True ...
7
votes
1answer
322 views

Changing the plot variable inside Plot [duplicate]

Possible Duplicate: Difference in Plot when using Evaluate vs when not using Evaluate Assume one has vector of functions (e.g., vec={x,x^2}). The ...
7
votes
2answers
162 views

Menu item “Interrupt Evaluation…” missing in V10

The menu item “Interrupt Evaluation…” seems to have disappeared in Mathematica 10 on OS X. Well, this is a bummer. I personally use Mathematica for very long calculations, and I was using this ...
7
votes
1answer
266 views

Can Mathematica do two evaluations at the same time?

When one evaluation is running, if I want do another evaluation, Mathematica will put the second one in the queue and run it after the first evaluation finish. However, the first evaluation may take ...
7
votes
1answer
191 views

How can I have interruptible computations inside a manipulate?

Here's a perfect example of my problem: Manipulate[Pause[n], {n, {1, 10}, ContinuousAction -> False}, SynchronousUpdating -> False] It is illustrated by ...
6
votes
4answers
4k views

Mapping multiple parameters of a function to specific values

I am a little bit confused by the documentation for Apply (@@). I want to define a list of parameters, for instance: ...
6
votes
3answers
836 views

Keep function range as a variable

Plot[2*x^2 - x + 2, {x, -1, 1}] plots a function of x from -1 to 1. As far as I can see, I cannot "save" this range in a variable: ...
6
votes
2answers
492 views

Obtaining the name of a variable as a string [duplicate]

Suppose that I have an arbitrary variable myVariable. Is there some function fun -- either built-in or one that I can define -- ...
6
votes
4answers
165 views

Generate list of strings from a list of assigned variables

How do I generate a list of strings from a list of assigned variables? Eg. Convert ...
6
votes
2answers
5k views

Simple ways to evaluate a derivative at a point?

The contrast in behavior between, say, f[x_] = Sin[x^2]; f'[2] vs. u[x_, y_] = Cos[x + y^2]; has always bothered my ...
6
votes
2answers
277 views

Why is CityData[All, “Coordinates”] failing?

When I evaluate CityData[All, "Coordinates"] Mathematica returns {Missing["NotAvailable"], Missing["NotAvailable"]} ...
6
votes
4answers
397 views

Attaching persistent assumptions to symbol definition

Is it possible to attach assumptions to a symbol? This relates to this question. Most of my work involves physical equations, i.e. there are basic assumptions on variables that will always hold true ...
6
votes
2answers
464 views

How Can Notebook Know When it Called by Another Notebook?

I would like a notebook to behave slightly differently depending on whether it is evaluated from another notebook; i.e., ...
6
votes
2answers
198 views

Why does Mathematica appear to change the head of certain expressions?

I don't know if the question trivial or not (if so I will delete it), but here is what I have: I know that x x (* x^2 *) Looking at the full form gives ...
6
votes
2answers
198 views

Evaluation in lambda function

If I have a function, that returns a function, for example: f[a_] := a^2 * # & then f[3] == 3^2 # & Is there a way ...
6
votes
2answers
123 views

Partial result of aborted evaluation of FullSimplify

When FullSimplify invoked on a large expression, it can run for hours. If I do not have time to wait, and abort the evaluation, I get no result, although, ...
6
votes
2answers
487 views

How do I make NotebookEvaluate work inside Button?

The following creates a button to select a notebook to run. When the button is pressed it seems that Mathematica finds the notebook but cannot evaluate it. The following error occurs Could not ...
6
votes
3answers
114 views

Explicit use of Evaluate not behaving the way I expect it to

I discovered a strange behavior of the Evaluate function. Case 1: ...