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

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98
votes
8answers
8k 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 ...
125
votes
7answers
5k 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: ...
55
votes
4answers
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 ...
24
votes
4answers
622 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 ...
52
votes
2answers
6k 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 ...
10
votes
1answer
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 ...
14
votes
4answers
2k 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? ...
63
votes
2answers
2k 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 ...
42
votes
2answers
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 : ...
18
votes
2answers
1k views

Scan vs. Map vs. Apply

I cannot understand the difference between Apply, Scan, and Map. I have tried to play with ...
62
votes
3answers
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 ...
23
votes
3answers
1k 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 ...
21
votes
1answer
510 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 ...
35
votes
2answers
922 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: ...
19
votes
8answers
692 views

Applying And to lists of Booleans

I'd like to take {True,True,False} and {True,False,False} and apply And to get ...
6
votes
2answers
768 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: ...
55
votes
4answers
2k views
32
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 ...
25
votes
2answers
819 views

Block attributes of Equal

I answered “Equating matrices (or higher order tensors) element-wise” with: ...
18
votes
3answers
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 ...
5
votes
1answer
1k 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 ...
2
votes
2answers
293 views

Position function not always retuning 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 ...
22
votes
3answers
833 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 ...
30
votes
4answers
526 views

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

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
15
votes
6answers
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 ...
6
votes
5answers
931 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 (...
26
votes
2answers
2k views

Implementing continuous phase/Arg function

In MATLAB there's a function called phase that is just like our Listable friend Arg, but ...
27
votes
5answers
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 ...
17
votes
2answers
467 views

Using several anonymous functions mixed together

This works: list // BarChart[#[[2]], ChartLabels -> DateString @@@ #[[1]], ChartStyle -> "Pastel"] & This doesn't: ...
13
votes
2answers
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 ...
15
votes
2answers
397 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 ...
9
votes
3answers
190 views

How to deal with the condition $u_i=u_{i+1}$ in B-Spline basis function?

The defintion of B-Spline basis function as shown below: Let $\vec{U}=\{u_0,u_1,\ldots,u_m\}$ a nondecreasing sequence of real numbers,i.e, $u_i\leq u_{i+1}\quad i=0,1,2\ldots m-1$ $$N_{i,0}(u)= ...
3
votes
2answers
416 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 ...
13
votes
1answer
293 views

Is there a summary of answers Head[] can give?

Sometimes you need to check for the type of an expression. You use Head[data] to get answers. Some data: ...
2
votes
3answers
782 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. ...
29
votes
3answers
716 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 ...
22
votes
1answer
457 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 ...
8
votes
5answers
346 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: ...
28
votes
2answers
875 views

Strange ::usage behavior in v9

Bug fixed in 9.0.1 Something has gone wrong with usage in Mathematica 9. Would someone tell me how to fix it? I define a function ...
12
votes
2answers
528 views

Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
8
votes
3answers
685 views

FullSimplify does not work on this expression with no unknowns

I can't reproduce this simple example from Habrat, 2010 ("Mathematica : a Problem-Centered Approach"). It is supposed to demonstrate the functionality of ...
7
votes
5answers
357 views

Is it possible to insert arguments into functions when they're used like Function@ or //Function?

Is it possible to insert arguments into functions when they're used like Function@ or //Function? Sometimes I need to do this, but then I have to return to the standard function usage: Function[] ...
4
votes
2answers
714 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: ...
1
vote
2answers
114 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 ...
9
votes
3answers
779 views

Inverting a function in a certain region

InverseFunction works well for globally invertible functions, like f = 2*# + 2 &; InverseFunction[f] ...
6
votes
2answers
749 views

Why does Expand not work within a function?

I'm writing this fairly simple function: ...
11
votes
2answers
3k 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 ...
19
votes
4answers
798 views

Accessing list elements by name

First, a bit of a long introduction to my problem: I only have a few weeks of Mathematica experience. I am creating a mathematica application that calculates some material properties of steel based ...
8
votes
2answers
2k 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. ...
6
votes
1answer
221 views

Does pass-by-value affect the performance of function calls?

I only have a little coding experience in C, and I remember I was told that pass by reference is more efficient than pass by value since the parameters don't need to be copied. Since there is no pass ...