Questions about how Mathematica evaluates expressions, tracing evaluation (Trace*), handling expressions in unevaluated form (Hold*, Unevaluated), nonstandard evaluation, etc.
31
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
490 views
23
votes
9answers
755 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]}]
...
23
votes
4answers
841 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
681 views
Block attributes of Equal
I answered “Equating matrices (or higher order tensors) element-wise” with:
...
21
votes
3answers
677 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
633 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
181 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
397 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 ...
16
votes
1answer
345 views
How do you set attributes on SubValues?
SubValues, as discussed in a previous question, are declared as follows
...
16
votes
3answers
425 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
279 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
4answers
271 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
2answers
305 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 ...
15
votes
1answer
343 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
194 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
5answers
276 views
13
votes
2answers
222 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
302 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
395 views
Unique[] symbol not properly tracked
In a nutshell, why does this work (change y and see how the value updates)
...
12
votes
2answers
365 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
431 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
104 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
222 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
317 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
218 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
442 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
205 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
5answers
624 views
How to pass a symbolname to a function with any of the Hold attributes?
Given a function with the attribute HoldFirst, HoldAll or similar, and a variable, list, how ...
11
votes
3answers
237 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
2answers
212 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
315 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
252 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
149 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
176 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
189 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
3answers
226 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
264 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
330 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
167 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
256 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
128 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
255 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
144 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
3answers
279 views
Labeling plots without evaluation
This is my first question here so please excuse my mistakes.
Let us consider a rather contrived example:
...
10
votes
1answer
259 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
132 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 ...
9
votes
4answers
207 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 ...
9
votes
4answers
267 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
...
9
votes
2answers
174 views
Bags and non-standard evaluation
What can internally be happening here? Is the evaluator just messing with us and going non-standard because it's a Bag? Or am I just not seeing how something like ...
