# Tagged Questions

Questions about the use of built-in Mathematica functions, including pure functions.

7k views

### What are the use cases for different scoping constructs?

Mathematica includes three functions that I know of which can be used to effectively (if not actually) define a variable and give it a value within a local scope: ...
10k views

### List of compilable functions

Is there somewhere a list on the functions that Compile can compile, or the cases in which a particular function can be compiled that I haven't found? I'd be glad ...
3k views

### Using a PatternTest versus a Condition for pattern matching

My last question to the site resulted in several answers that involve using pattern matching in Mathematica, a feature I wasn't very familiar with at the time. I am currently reading Mathematica ...
902 views

### Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs

Using global variables the following turns an "expression" into a Function: expr = 2 x; Function[x, Evaluate[expr]] Of course ...
6k views

### What are some useful, undocumented Mathematica functions?

There have already been some questions about some undocumented functionality in Mathematica. Such as (please add to these lists!) How can one find undocumented options or option values in ...
8k views

### What is the difference between Reduce and Solve?

Solve and Reduce both can be used for solving equations. Just by working with them, I know there are some differences between ...
4k views

### How to modify function argument?

Usually in programming languages, function arguments are normal local variables, which can be modified. Is this not true in Mathematica? ...
2k views

### Scan vs. Map vs. Apply

I cannot understand the difference between Apply, Scan, and Map. I have tried to play with ...
2k views

### What is the difference between Set and SetDelayed?

I have a problem with defining a function and most of time I get confused by Set or = and ...
4k views

### What is so special about Prime?

When we try to evaluate Prime on big numbers (e.g. 10^13) we encounter the following issue: ...
3k views

### Flatten command: matrix as second argument

One thing I could never wrap my head around is how Flatten works when provided with a matrix as the second argument, and the Mathematica help isn't particularly ...
2k views

### How to load a package without naming conflicts?

This question applies to any package, but I encountered this problem while working with graphs. There are symbols in the Combinatorica package (such as ...
2k views

### What best practices or performance considerations are there for choosing between Cases, Position, Pick and Select?

Cases, Select,Pick and Position each have different ...
3k views

### Plotting piecewise function with distinct colors in each section

I have a piecewise function that I would like to plot but I was wondering if it is possible that each part of the function that is plotted when its corresponding condition is true be plotted with a ...
2k views

### Automatically generating a dependency graph of an arbitrary Mathematica function?

Has anyone written a function to pull the function dependencies of a function? That is, it would be nice to have a function that returns a list of function dependencies as a set of rules, terminating ...
627 views

### Shorter syntax for Fold and FoldList?

I find it tedious to write out the following: a = {1, 2, 3, 4}; Fold[f, First @ a, Rest @ a] f[f[f[1, 2], 3], 4] It ...
1k views

### Why is the new PositionIndex horribly slow?

This issue has largely been mitigated in 10.0.1. New timings for the final test below are: ...
871 views

### Block attributes of Equal

I answered “Equating matrices (or higher order tensors) element-wise” with: ...
1k views

### Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
958 views

### Evaluating an If condition to yield True/False

I would like to decide whether an option passed to my custom function has the value Automatic or something else. This is my attempt: ...
805 views

### Applying And to lists of Booleans

I'd like to take {True,True,False} and {True,False,False} and apply And to get ...
417 views

### Position function not always returning an answer even with no apparent problems

I'm having some problems with Position. Sometimes it will give an empty list instead of the actual position of the element I am looking for when that element is ...
1k views

### Why is there no PositionFunction in Mathematica?

Too often I have seen the programs of inexperienced users greatly slowed by using Position in an iterative fashion, when far faster would have been to compute a ...
985 views

### DeleteDuplicatesBy is not performing as I'd hoped. Am I missing something?

Déjà vu: a new-in-v10 function should provide a better solution to an old problem, but my enthusiasm is curbed when I run timings. This time the function is ...
2k views

### How Can I use Solve/Reduce Output

Suppose I want x and y to be rationals Solve[ x^2 + y^2 == 1, {x, y}, Rationals] I am ...
158 views

### Expressions containing globally undefined symbols inside a function where they are defined

Consider the following code. f[a_,b_]:=x; Clear[a,b]; x=a+b; f[1,2] It returns a+b. However, from a certain viewpoint, one ...
3k views

### Implementing continuous phase/Arg function

In MATLAB there's a function called phase that is just like our Listable friend Arg, but ...
390 views

### How to create a dynamic expanding DisplayForm's styled like the ones in v10?

The display forms for objects like ClassifierFunction are nice clickable boxes I like this, and now I'm trying to create my a custom version of this for my ...
708 views

### How can the behavior of InterpolationOrder->0 be controlled?

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
4k views

### How to plot periodic function's graphic?

How to plot periodic function's graphic? For example, $f(t) = t$ when $-5<t<5$ and $f(t+10) = f(t)$. ...
2k views

### Prevent Part[] from trying to extract parts of symbolic expressions

If you have a list, e.g. {1, 2, 3} then you can extract the $k$th part using Part (...
6k views

### Pass function or formula as function parameter

I can write either Integrate[x^2, {x,0,3}] or f[x_] = x^2 Integrate[f[x],{x,0,3}] and get the same computation. Suppose I ...
1k views

### Will Version 9 functions all work in Version 10?

Having developed a substantial code base in Mathematica 9, leads me to ask these important questions prior to downloading and installing Mathematica 10. Will any Mathematica functions from the ...
967 views

### How to plot several functions without jumping? (multiple eigenvalues of a system as functions of 2 parameters)

I've been working on this research problem for months with some success by no global/proper solution to the problem. So I have square, Hermitian matrices of various sizes ($8,20,38$ dimensions) with ...
466 views

### Manipulating slots in a pure function

How does one manipulate the slot numbers in a pure function? Some trick with Evaluate or Hold? I'm aiming for something along ...
2k views

### Are there “All” and “Any” functions in Mathematica?

In Python, there is a function all which returns true if all of its arguments are true, and any which returns true if at least ...
1k views

### Pure Functions with Lists as arguments

Assuming I have two function: example 1: add[{x_, y_, z_}] := x + y - z add[{1, 3, 5}] If use pure function,I know I can write it as : ...
418 views

### How to check the style and number of arguments like the built-in functions?

Given that I have a function sqrt[x] that I must check the style and number of argument x. I can do like this: ...
500 views

### Using several anonymous functions mixed together

This works: list // BarChart[#[[2]], ChartLabels -> DateString @@@ #[[1]], ChartStyle -> "Pastel"] & This doesn't: ...
2k views

### How do I find the elements in a list that return the highest value for a function?

Suppose we have a list of values and a function f. I want to find which of the elements maximizes the return value of the function in Mathematica. Let call the ...
470 views

### Function with custom Options and modified Options for built-in Symbols

I couldn't find a more descriptive title, but I guess an example will explain my problem. I set up some customized Grid function including some additional ...
3k views

### Solve trigonometric equation

I'm looking for a solution (graphic, numeric or analytic) for a function of the form: $$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$ preferably using Mathematica. Any advice?
332 views

Sometimes you need to check for the type of an expression. You use Head[data] to get answers. Some data: ...
820 views

### How to make a function that evaluates an expression?

I'm trying to make a function where the input is an expression, but somehow it just won't be evaluated. For example, this little function doesn't work: ...
1k views

### Output of plots from within Do[ ] Command

I am wondering why the following does not plot the way it's written and exactly how does the Do[] function operate? I think I could be using it incorrectly. ...
847 views

### Why does Expand not work within a function?

I'm writing this fairly simple function: ...
775 views

### Parentheses in pure functions: # & vs. ( # &)

I've been using Mathematica for years, and over time I have developed the habit of using: Select[data, (# == 1 &)] instead of ...
507 views

### Why does list assignment with a packed array result in unpacked values?

Bug introduced in 5.2 or earlier and fixed in 10.1.0 This is another question on the design choices in Mathematica. I understand that without direct reply from the developers it may not be ...