Questions tagged [functions]

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

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218
votes
8answers
13k 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: ...
155
votes
8answers
17k 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 ...
171
votes
20answers
12k 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 Mathematica?...
47
votes
4answers
2k 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 ...
30
votes
2answers
2k views

Plot Option Precedence while combining Plots with Show[]

I like to build sophisticated plots by combining simpler ones with Show[]. Typically this involves setting non-default Plot-Options with the different Plot-Commands,...
73
votes
4answers
5k 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 ...
90
votes
2answers
20k 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 ...
48
votes
2answers
5k views

Scan vs. Map vs. Apply

I cannot understand the difference between Apply, Scan, and Map. I have tried to play with ...
33
votes
4answers
9k 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? ...
5
votes
4answers
390 views

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

Consider the following code. f[a_,b_]:=x x=a+b; f[1,2] (* a + b *) From a certain viewpoint, one might expect it to return 3 ...
51
votes
1answer
2k views

What are SparseArray Properties? How and when should they be used?

A strange undocumented form of SparseArray is increasingly used in answers on this site: ...
56
votes
2answers
5k 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: ...
22
votes
5answers
6k views

Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
95
votes
4answers
3k 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 ...
43
votes
5answers
1k views

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

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
26
votes
4answers
5k 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 ...
49
votes
4answers
1k views

How to create expanding summary boxes like the ones displayed for InterpolatingFunction, NearestFunction, etc.?

The display forms for objects like ClassifierFunction are nice clickable summary boxes I like this, and now I'm trying to create my a custom version of this for my ...
47
votes
3answers
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: ...
23
votes
1answer
866 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 ...
14
votes
5answers
8k 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 $f(t+10) = f(t)$. ...
33
votes
3answers
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 ...
81
votes
4answers
4k 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 ...
43
votes
5answers
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 ...
28
votes
2answers
988 views

Block attributes of Equal

I answered “Equating matrices (or higher order tensors) element-wise” with: ...
22
votes
8answers
1k views

Applying And to lists of Booleans

I'd like to take {True,True,False} and {True,False,False} and apply And to get ...
37
votes
2answers
3k views

What are some common issues with fitting functions to data?

Mathematica has numerous functions designed to, or capable of, fitting known functions, and finding unknown functions to match data sets. What are some common issues that come with finding those fits?
43
votes
1answer
838 views

What does Internal`InheritedBlock do?

What does the function Internal`InheritedBlock do? How is it different from the regular Block?
13
votes
6answers
4k 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 (...
42
votes
4answers
6k views

Implementing continuous phase/Arg function

In MATLAB there's a function called phase that is just like our Listable friend Arg, but ...
24
votes
2answers
15k 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 ...
35
votes
3answers
1k 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 ...
40
votes
3answers
1k views

Is there a name for #1@#2&?

Why does the pure function # @ #2 & have no name? I'm asking because sometimes I find inelegant to write expressions like ...
13
votes
2answers
4k views

Finding all partitions of a set

I'm looking for straightforward way to find all the partitions of a set. IntegerPartitions seems to provide a useful start. But then things get a bit complicated. ...
4
votes
2answers
1k views

Derivative of conjugate multivariate function

I have a problem with Mathematica, taking the derivative of the conjugate of some function. I know that a similar question has been posed before here, but the solution did not work for multivariate ...
14
votes
4answers
983 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: ...
45
votes
1answer
944 views

Is FullGraphics an abandoned function? Is there an alternative?

FullGraphics hasn't worked entirely for a long time and the situation appears to be getting worse instead of better. In Mathematica 10.0, 10.1 up to 11.3 a simple ...
24
votes
1answer
1k views

More Ticks::ticks errors in AbsoluteOptions in v10

Bug introduced in 7.0 or earlier and persisting through 11.3 While the specific bug affecting Plot described in AbsoluteOptions prints error messages in V10 has ...
7
votes
3answers
2k 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 ...
6
votes
1answer
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 ...
6
votes
2answers
610 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 ...
7
votes
2answers
799 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 ...
18
votes
4answers
2k 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 : ...
34
votes
3answers
46k views

How to tell Mathematica that certain variables are real/imaginary, integer-valued, etc

I'm trying to expedite some quantum mechanical calculations (expectation values etc.) by running them through Mathematica. When I say, for example, ...
34
votes
0answers
849 views

Performance problems in new Sequence functions

The new-in-10.1 Sequence* family of functions should provide newly optimized methods for handling sequence problems. Happily in some cases they do! For example ...
30
votes
3answers
1k views

Is there a “precedence table” for the canonical Sort ordering?

This answer in which I wrote about the Operator Precedence Table was unexpectedly popular. That got me thinking about similar things, and I am wondering: Does an "ordering table" exist for the ...
17
votes
1answer
1k views

Get the name of a symbol passed to a function

I'm trying to get the name of a symbol passed to a function with this: f[x_] := {SymbolName[x], x} SetAttributes[f, HoldFirst] x = 5; f[x] But ...
7
votes
2answers
1k views

Why does Expand not work within a function?

I'm writing this fairly simple function: ...
18
votes
1answer
1k views

How do I create a triangulated surface from points?

I have a set of points in a nx3 matrix and I would like to convert them into a surface, so that I may calculate its surface area. The function ListSurfacePlot3D creates the surface how I want it. ...
20
votes
2answers
658 views

Using several anonymous functions mixed together

This works: list // BarChart[#[[2]], ChartLabels -> DateString @@@ #[[1]], ChartStyle -> "Pastel"] & This doesn't: ...
4
votes
2answers
2k views

Permanently rounding numbers/values to a given number of significant figures

I am searching for a simple way of rounding and setting an input to a desired number of significant figures. There are a vast number of posts that discuss similar problems, but none address this issue....