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

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9
votes
2answers
212 views

Held keys in associations

Jacob Akkerboom commented: Note that PositionIndex does work correctly with held expressions, whereas this is a bit painful to implement using ...
9
votes
3answers
166 views

Implement settable properties

I am looking for advice on implementing the following. (It is possible that the answer is that it is simply not a good idea to do this.) I would like to have an object similar to ...
9
votes
1answer
135 views

Is it possible to use the global definition of a symbol as part of its new local definition set in a Block?

Consider the following expression: Block[{Print = CopyToClipboard}, doSomething[]] Now all calls to Print from ...
9
votes
1answer
116 views

Why does $Failed have attribute HoldAll?

Why does $Failed have attribute HoldAll? Are there typical situations where $Failed is ...
9
votes
2answers
336 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 ...
9
votes
2answers
165 views

A notebook created on demand from a main document showing executable input along with output cells

I would like to make Mathematica documents with hidden calculations, such that they can be visualized on demand. In general it can be done in several forms and I actually use some. I would like to ask ...
9
votes
1answer
675 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 ...
9
votes
1answer
319 views

Performance of Dispatch and lists of Rules

The issue outlined here seems to be no longer present in version 10, if you use a Dispatch table! This because a Dispatch table ...
9
votes
1answer
162 views

Comparing exact expressions for equality — is it really OK if I get wrong answer?

Bug introduced in 7.0 or earlier and fixed in 10.2.0 I found an unexpected behavior (that I think of as a bug) in evaluation of the equality operator applied to mathematical functions with exact ...
8
votes
2answers
285 views

Unexpected behavior of rule matching a pattern

I am a beginner exploring the world of Mathematica. I expected the following code T[6, 5, 4, 1, 2, 3] /. {T[a___, 1, b___] -> Length[List[b]]} should return ...
8
votes
2answers
222 views

Why does the name of a pattern affect the result of a transformation rule?

I was playing a little dirty, trying to get a template for defining a Curl[] operator. I wrote the following rule, which I knew was going to spit out a few ...
8
votes
4answers
2k 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 ...
8
votes
3answers
233 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 ...
8
votes
2answers
663 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, ...
8
votes
3answers
737 views

Why are functions called first-class objects in Mathematica?

I've heard lots of people say a function is a first-class object in Mathematica. "Everything is an expression, including function." "There is no distinction between functions and data." Having read ...
8
votes
3answers
334 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
2k 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
788 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 -- ...
8
votes
3answers
172 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
2answers
148 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 ...
8
votes
1answer
129 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
525 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
228 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
1answer
221 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 ...
8
votes
2answers
759 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
183 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
330 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 ...
8
votes
1answer
176 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
614 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
votes
1answer
238 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
141 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
156 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
4answers
6k 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: ...
7
votes
6answers
211 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
246 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
323 views
7
votes
2answers
194 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
2answers
462 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
5answers
209 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 ...
7
votes
3answers
234 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
298 views

Using up-values and down-values

I have a problem I'm trying hard to find a solution for, although I don't know if a solution exists. The following rules produce the result e[2].f[] ...
7
votes
2answers
206 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
6k 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 ...
7
votes
2answers
184 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
4answers
467 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 ...
7
votes
2answers
198 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: ...
7
votes
3answers
133 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
263 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
403 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
1answer
109 views

Unevaluated @ {args} versus Unevaluated /@ {args}

Working my way through Robby Villegas's lovely notes on withholding evaluation, I almost got Polish Notation on my first try. Here is my final solution, which seems to work well enough: ...