# Tagged Questions

Questions about Mathematica's functional programming style, including the use of pure functions (Function[], #, &) and functions such as Map, Apply, Nest, and Through.

340 views

### From iterative to functional

How to write this small piece in a functional way (ie. without state variables)?: ...
250 views

### Timing differences between multiple executions of identical code

I have a list of pairs of numbers and I'd like to change the sign of the second element in each pair i.e. $(a,b)\rightarrow (a,-b)$. I'm sure there are many ...
522 views

### How to create a list of variable names to some function of that variable

For example, for a single variable I can write Print[Unevaluated[a], "=", f[a]] But if I try the next thing I'd think of doing, assuming I want a list, it doesn'...
1k views

### How do I convert an argument list to a list of arguments?

I think this is a basic question, but I am having difficulty finding the answer in the documentation. Thread is not what I am looking for, I think. Suppose that I ...
171 views

### How can define a set of nested parameters

I would like to know how I to define a function with a nested set of parameters (or whatever you would like to call it). For example, how would I get the following function ...
402 views

### Thread a function over a list and with a non-atomic 2nd parameter?

From the documentation, Thread's behavior on functions where the first parameter is a List and the second is an atomic expression, is this: ...
2k views

### Map a function across a list conditionally

It seems that this is a really basic question, and I feel that the answer should be obvious to me. However, I am not seeing. Can you please help me? Thanks. Suppose I have a list of data ...
136 views

### About minimizing calculations when using ComposeList

I have a lot of functions to use in a iterative way, and I need some of the calculation results. For example: ...
285 views

### How to nest my own “times” function to get powers

I have a "times" function. I'd like to create a power function using it. It should look like this for an 6th power: ...
126 views

### What are some general strategies to avoid using For loops? [duplicate]

Possible Duplicate: Iterating over lists in Mathematica While there are some cases where a For loop might be reasonable, it's a general mantra – one I ...
2k views

### Using pure functions in Table

I need a table with the elements made of pure functions and list elements. This is a simplified example: I need a list as: ...
227 views

### GatherBy Option to group results?

How can GatherBy be programmed to take an option to group results as follows: ...
192 views

### Using Nest inside NestList

I need results like this: {Cos[Cos[x]], Sin[Cos[Cos[x]]],Cos[Cos[Sin[Cos[Cos[x]]]]], Sin[Cos[Cos[Sin[Cos[Cos[x]]]]]], ... } I've tried to use ...
447 views

### How to keep some of the results of the NestList

I'm using some iterative arithmetics to calculate wave propagation with the help of NestList. I have to use a small step size for iteration to guarantee the accuracy, which lead to too much data (e.g, ...
236 views

### Ways to change an explicit function into a pure function

I'm trying to use FixedPoint to solve a transcendental equations, but the first argument of the FixedPoint should be a pure ...
749 views

### What's the most “functional” way to do Cholesky decomposition?

I can do Cholesky in a procedural style, such as: ...
626 views

### How can I trace a functional expression's evaluation visually?

Ok, so the goal is to visualize the execution of this expression foo /@ {3 + 1, bar /@ {1 + 2, {4 + 7}}} in the following fashion using nested rectangles with ...
779 views

### Prefix operator with low precedence

The question is simple, but I will elaborate on the background as well for those interested in the idea: How to define a new operator with specified precedence value? Background Mathematica was ...
622 views

### Reproducing nested loops using Map?

I keep producing bits of code like the following: ...
210 views

### Composite graphics with Row, Column, data aggregation and layout control

This chromogram shown here represents data (mouse activity patterns during visits) for ~20 physicians in a study, each of which may have a variable number of visits in the study (physicians are color ...
247 views

### 3x+1 on arithmetic chains, tree pruning and NestList

Given the following function Collatz: ...
309 views

### Cases[data,Colon[key,_]] vs. Cases[data,key:_] toward XPath, XQuery

Exploring methods to index and search tree-structured key:value pairs via named-entity index (key paths) as opposed to Position-based indexing. Using Rule as <...
386 views

### Can this code be written in a more functional style

Referencing this question, I wonder if the following code can be written more concisely using a functional style, i.e. without For loops or ...
1k views

### Does every Symbol in Mathematica induce a monad?

From my question about types in Mathematica, I assume that every Symbol in Mathematica is a type if it appears as a Head of some ...
1k views

### Using a list of tuples in a pure function

I want to use a list of tuples within a function to make assignments. Say I want to make assignments of the form value[i,j] = val What I have is a list of ...
384 views

### Explanation on why Compile statement works only if input and output sizes work

I found the following code: Compile[{{m, _Real, 2}}, Fourier[m]][Table[N[i - j], {i, 4}, {j, 4}]] which doesn't work correctly. But the following was posted as a ...
413 views

### Are there advantages to using additional arguments of common functions rather than alternative ways of calculating with lists?

(Apologies for the long question title.) One of the interesting, if sometimes confusing, things about Mathematica is that there is always more than one way to do things. Even intermediate users can ...
2k views

### Can this be written well, without loops?

Inspired by this question I would like to know if the following code can be written without explicit loops (For, While, etc.) in a clean, efficient and non-contrived way. I have been unable to do so. ...
805 views

### Is there a more elegant and efficient way to write brainf*** style loops in Mathematica?

I'm having some fun writing a brainf*** interpreter in Mathematica. See this wiki article for more info. It works nicely but I'd like to find an elegant, preferably functional, way to handle the ...
825 views

### Can someone explain this snippet: (#[#] &)[#[#][#] &]

A friend showed me this snippet of code today: (#[#] &)[#[#][#] &] I can sort of see that we're constructing an anonymous function that takes a function ...