Questions about how Mathematica evaluates expressions, tracing evaluation (Trace*), handling expressions in unevaluated form (Hold*, Unevaluated), nonstandard evaluation, etc.
32
votes
3answers
9k 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?
Example : Let's say I want to ...
28
votes
1answer
509 views
24
votes
9answers
780 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]}]
...
24
votes
4answers
900 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 ...
23
votes
2answers
684 views
Block attributes of Equal
I answered “Equating matrices (or higher order tensors) element-wise” with:
...
22
votes
3answers
725 views
Difference in Plot when using Evaluate vs 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 ...
19
votes
2answers
646 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 ...
18
votes
2answers
188 views
Evaluation of OptionValue[]
I have a function that takes an OptionsPattern and I want to access several options, say a, and ...
17
votes
3answers
403 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 ...
17
votes
2answers
357 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 ...
16
votes
5answers
326 views
16
votes
1answer
354 views
How do you set attributes on SubValues?
SubValues, as discussed in a previous question, are declared as follows
...
16
votes
3answers
447 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 ...
16
votes
2answers
280 views
Context unique to each group at a specified level
Recent versions of Mathematica provide the option of having a unique $Context for each cell group, via:
Evaluation > Notebook's Default Context > Unique to Each ...
15
votes
5answers
677 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 ...
15
votes
4answers
277 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 ...
15
votes
1answer
346 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
...
15
votes
1answer
198 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 ...
13
votes
3answers
176 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 ...
13
votes
2answers
224 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 ...
13
votes
2answers
303 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 ...
13
votes
1answer
396 views
Unique[] symbol not properly tracked
In a nutshell, why does this work (change y and see how the value updates)
...
12
votes
2answers
385 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:
...
12
votes
4answers
467 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 ...
12
votes
1answer
107 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 ...
12
votes
1answer
226 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 ...
12
votes
2answers
323 views
Preventing Numerical value from being evaluated
I have searched stackoverflow (and comparable pages) for quite a while now (got redirected from there to this specialized stack), and I surrender. I am trying to evaluate an expression that is small ...
11
votes
3answers
219 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 ...
11
votes
5answers
454 views
How to determine how much of a table is generated?
If I'm generating a table from a slow function, like this:
foo = Table[SuperSlowExpression, {1000}]
is there a way to determine after submission (so it is too ...
11
votes
3answers
208 views
Numbers in alternate bases transcend the evaluator?
It looks to me like a number in a base other than base 10 gets evaluated before the evaluator ever gets a chance to be tweaked.
For example, FullForm[16^^abcdef] ...
11
votes
3answers
241 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 ...
11
votes
3answers
230 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 ...
11
votes
3answers
290 views
Labeling plots without evaluation
This is my first question here so please excuse my mistakes.
Let us consider a rather contrived example:
...
11
votes
2answers
213 views
can a ColorFunction have side effects?
Can anyone explain this (to me) odd behavior. If I run this code once (fresh kernel) it works as intended.
...
11
votes
1answer
320 views
Get the current iteration count
I would like to be able to get the current iteration count, the one that if exceeds $IterationLimit makes the evaluation stop.
After not finding a magical variable ...
10
votes
7answers
256 views
Question about evaluation control
I want to make a function that takes a function as a parameter and prints an integral with the function inside. I've tried this:
...
10
votes
4answers
152 views
How do I evaluate the terms in an expression, but not the expression itself?
I am trying to write a set of homework questions.
I would like the output to evaluate the constants but not the sum, so that I may present the homework question as something like this:
...
10
votes
2answers
177 views
Make a button that evaluates a function over and over
I would like to have a command "RedoButton" which would make a button (or whatever control is suitable) that when clicked would print the value of a certain function over and over in the same place. ...
10
votes
3answers
191 views
Arguments to If[] are not evaluated
I got bitten by the following:
f[x_] := 3*x;
g[x_] := If[Log[f[x]] < 0, f[x], 0];
g[x]
Out[11]= If[Log[3 x] < 0, f[x], 0]
where I thought the call to ...
10
votes
4answers
272 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
...
10
votes
3answers
232 views
How can I hold UpValues but evaluate other expressions?
Consider these definitions:
own = "OwnValue";
down[_] = "DownValue";
sub[_][_] = "SubValue";
N[n] = 3.14;
_[___, up, ___] ^= "UpValue";
The attribute ...
10
votes
3answers
267 views
Why does ++++x return an increment of 2 when the value of x is only incremented by 1?
This line returns 3:
x = 1; ++++x
However, the value of x after the increment is only ...
10
votes
2answers
337 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 ...
10
votes
2answers
186 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?
10
votes
2answers
260 views
Unexpected differences with various uses of NormFunction
I would expect all of the following to give the same answer (2.12467) but only half of them give this answer. The others seem to be using the default ...
10
votes
2answers
131 views
Subtle difference in conditional rules placement
I had gotten used to thinking of the placement of a condition in a rule definition as logically immaterial. In my specific example, namely
...
10
votes
2answers
264 views
DSolve cannot solve for certain branches of the solution
Could somebody please tell me, why I am always getting an error message when trying to run the following code:
...
10
votes
1answer
145 views
Old values are not freed/garbage collected when you re-evaluate an assignment
For this code:
(* Cell 1 *)
generate := Module[{x}, x = Range[100 * 1000 * 1000]; x];
(* Cell 2 *)
g = generate[];
MemoryInUse[]
If I evaluate cell 2 ...
10
votes
1answer
261 views
Manipulate evaluation sequence
Manipulate doesn't always evaluate in the order I expect it to. What is the evaluation sequence for Manipulate and other ...
10
votes
1answer
137 views
Evaluation indicator for a notebook
I have a GUI with a number of TabView and other Manipulate controls. Sometimes clicking from one Tabview to the other can take a while, and I would like to have a global "Please wait" indicator.
So ...
