For questions on writing functions (pure or using Set/SetDelayed) for any purpose, including the features that may be incorporated in those functions, such as options, patterns and conditions.

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7
votes
2answers
157 views

Change some option of a function when calling it [duplicate]

Say I have defined some function like f[p_] := Plot[Sin[p*x], {x, 0, 2 Pi}] Now in most cases, I just need to specify the value of ...
7
votes
1answer
231 views

FullDefinition and Module local variable

I have a question about FullDefinition and how it interacts with the local variables of Module. I've created a few functions ...
7
votes
1answer
102 views

Context-dependent functions

TL;DR warning! My question is not about getting the length of the ticks correct (although if someone has good suggestions, that would be welcomed). My question is about constructing functions that ...
7
votes
2answers
160 views

How to track Part of Symbol or How to symbolize Parts of Symbol without copying data

Let's create simple function: SetAttributes[h, HoldFirst]; h[data_] := Dynamic[Grid[data], TrackedSymbols :> {data}] test = RandomReal[1, {2, 2}]; h[test] ...
6
votes
5answers
1k views

Find function inverse

I'm trying to find the inverse of a function: (30*x^2 (1 - x)^2) (* where 0<x<1 *) I tried all the following options: 1. ...
6
votes
2answers
859 views

Number of digits for factorial of 12345678987654321

A hard math problem What is the number of digits (IntegerLength) of the factorial of 12 345 678 987 654 321? The number of zeros at the end of this factorial was calculated and it is huge: exactly 3 ...
6
votes
3answers
608 views

How can I rewrite this with NestList or FoldList?

The original code used For: ...
6
votes
3answers
1k views

How do I designate arguments in a nested map?

Say I have two lists, list1 = {a, b, c} list2 = {x, y, z} and I want to map a function f over them to produce ...
6
votes
3answers
301 views

How can I create currying functions using pure function syntax?

For example how can I write In: pureFunctionSyntax[myF] /@ {7, 3} Out: {myF[7, Log[7]], myF[3, Log[3]]}
6
votes
2answers
516 views

Passing unquoted strings (poor man's enumeration)

I would like to be able to pass an unquoted string as a parameter to a Mathematica function [that I am writing] and have it show up without evaluation if the string happens to be defined. Thus I would ...
6
votes
2answers
353 views

Calculating extreme spread with a Do loop [closed]

I am trying to model what is called the extreme spread of a series of shots at a target. Each shot is from a normal distribution with mean 0 and variance 1. For this example there are three shots per ...
6
votes
3answers
420 views

Using function with multiple definitions in Manipulate

I'm trying to use Manipulate to visually try out different values of lambda in a Box-Cox transformation. I've created a boxcox ...
6
votes
2answers
272 views

What evaluation mechanism is behind Mathematica support for multiple definitions of a function? What is the benefit of this?

I am studying the question What are the most common pitfalls awaiting new users? Up to now, I have fulfilled some of the parts but yet don't understand which this problem is related to? Consider the ...
6
votes
2answers
2k views

How to find the non-differentiable point(s) of a given continuous function?

For example, the non-differentiable point of the function $f(x)=|x|$ is at $x=0$. How to find the non-differentiable points of a continuous function that is defined numerically?
6
votes
4answers
722 views

Function argument to default under certain condition

Inspired by this and this question (and how I handle this in practice), what is the best way to default a function value when a certain condition is met? For example, if a function is defined as: ...
6
votes
2answers
172 views

Using a held option

Woud there be an elegant way to use a held option ? For example if I need to pass by reference several variables but I don't always need all of them, it can be useful. For example if I want to append ...
6
votes
3answers
516 views

Function with zero or one arguments

Is there a neat way to define a function with a single optional argument that defaults to an empty sequence? For example, suppose I want to define a wrapper for ...
6
votes
3answers
212 views

Using PatternTest and/or Condition to detect equal list lengths as well as list element formats

On searching Mathematica.SE for information about overloading functions, I came across several threads about PatternTest and ...
6
votes
2answers
224 views

How to understand the process of ListCorrelate when it in two-dimensional condition?

Toady,I learn a function ListCorrelate,and I can understand process of execution his result in one-dimensional. However,the ...
6
votes
3answers
240 views

How to get “Signature” of each element of “Permutation” output

I need to sum over all possible permutations, multiplied by the Signature of each permutation of a given list of symbols. But, I don't know how to determine the ...
6
votes
3answers
136 views

Explicit use of Evaluate not behaving the way I expect it to

I discovered a strange behavior of the Evaluate function. Case 1: ...
6
votes
2answers
2k views

How to define a polynomial/function from an array of coefficients?

I have the coefficients of my desired polynomial in an array CoefArr (I'm new to mathematica, so I think of everything as arrays, it is actually a list I believe) starting with the constant at index ...
6
votes
2answers
285 views

How can I create a class of matrices programmatically?

I am trying to figure out how to create a function that can create the matrix pattern below, where: f[1] returns {{1}} ...
6
votes
2answers
774 views

Manipulation of InterpolatingFunction

Suppose that $q[t]$ is obtained by NDSolve as an InterpolatingFunction, and I want to define $Q[t]$ to be some function of ...
6
votes
2answers
105 views

Force evaluation of the right-hand side of a local variable definition

One can do expression = a + 1; f[a_] := Evaluate[expression] but how would one do something like this ...
6
votes
2answers
127 views

Optional arguments with lists as function parameter

I'm developing a function f which should support optional arguments {x_, y_} in list form. A simple example looks like this: ...
6
votes
1answer
193 views

Parentheses for negative integers

Trying to standard create prime factors presentation, but can't seem to remove the parentheses: ...
6
votes
1answer
144 views

Graphics Function Definition Style (Using SubValues vs. DownValues)

I am going through some of the items in "Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition". An example of the style used by these authors is: ...
6
votes
1answer
331 views

What does it mean when a function is defined with two pairs of brackets

I have noticed a function defined as such: f[x_][y_] := expr; How is the argument y in 2nd pair of brackets being used? What is the difference from defining a ...
6
votes
1answer
1k views

Nesting multiple functions of multiple variables

I was wondering how one would go about nesting multiple functions of, say, two variables. The problem comes from trying to implement the Chirikov standard map without using "for" cycles. I found a ...
6
votes
3answers
82 views

How to organize expression by symbols (like Collect), but apply different functions to each coefficient

I want to mimic the functionality of Collect[expr, {vars}, func], but with the following modification: The function f that is ...
6
votes
1answer
83 views

How to delay the definition of a function from the time of package initialization to when it is first called

I am writing a package where a couple defined functions take a very long time define at initialization time (because they are large CompiledFunctions). However ...
6
votes
1answer
208 views

How can a function know in which function it was evaluated?

Hello my second question here might be very hard. I am asking for something "magical", if i define a function g and i call it inside a function f, how can g have information about the outer function ...
6
votes
3answers
243 views

How to define a nested function like this?

For example, I want to calculate the limit of $\frac{1}{1+\frac{2}{1+\frac{3}{1+\ldots}}}$. So I want to define: $f(1)=1$ $f(2)=\frac{1}{1+2}$ $f(3)=\frac{1}{1+\frac{2}{1+3}}$ Then I calculate ...
6
votes
2answers
275 views

How to write complex function definitions at run time?

(Posting as a self-answered question to share a technique I discovered) In a certain project, I have many function definitions in which all parameters should be optional and come with default values. ...
6
votes
3answers
181 views

What is the recommended way to define numeric function with special cases?

What is the recommended way to define a purely numeric function with special cases? Should I define many special cases with pattern matching? ...
6
votes
1answer
295 views

Compiling a function that takes lots of optional arguments

I have a function that takes lots of optional arguments (basically some design parameters, about 10 of them) and performs some basic algebraic calculations involving complex numbers with the options. ...
6
votes
1answer
113 views

A question about two ways to use Default

Usually we define a function with default values by the syntax x_:default, but there is another technique to do this by registering a global default value with ...
6
votes
1answer
199 views

Property assignment on a graph vertex using PropertyValue does not work inside a function

I created this function: AddStone[board_Graph, v_, s : white | black | empty] := PropertyValue[{board, v}, VertexState] = s This function should change the ...
6
votes
1answer
234 views

Functional-Style Partial Application and the Accumulator Pattern?

Following up on Functional-style Fixed-Length Queue Object?, I want to generalize it to a functional-style accumulator pattern. Lots of things look like accumulators, loosely defined as binary ...
6
votes
1answer
78 views

How to bail out from a non-applicable transformation function?

I provide a custom function in TransformationFunctions options of FullSimplify that can do a transformation only for some values ...
6
votes
2answers
288 views

How to implement a formal expectation operator over an unknown distribution?

I need to do some simplification of an expression involving averages over a stochastic variable (in order to verify a long analytical calculation). The easiest way to do that, I figured, were if I ...
6
votes
1answer
193 views

Creating a Block from a list of rules

How can I create a function which works like Block but takes a list of rules as its first argument, rather than a list of assignments? The function needs to be ...
6
votes
1answer
275 views

Pattern definition for replacing plus and subtract

Suppose I have two functions $h_1(x)$ and $h_2(x)$, for which we know their sum and their difference: $$ h_1(x)+h_2(x) = d(x) \qquad h_1(x)-h_2(x) = i f(x) $$ I have a complicated expression, in ...
6
votes
1answer
125 views

Is there an elegant way of delaying evaluation of `A==B` when calling a function that uses this pattern

Suppose I wanted to define a number of functions that accepts expressions of the form: ...
6
votes
0answers
134 views

Fine tuning compiled code that computes dilogarithm function

As an exercise of writing a good Compile function, I want to do the simple task of coding a routine that outputs the real part of the dilogarithm function ...
5
votes
3answers
2k views

Make a differentiable smooth sawtooth waveform

So, I am trying to understand the effect of sawtooth waveform on a mechanical system model. For example, a system of a plate and a box on it. And then we try to oscillate the plate. In order to do ...
5
votes
4answers
1k views

Swap two entries in a matrix

Is there a nice, simple script one can use to swap two entires in a matrix? For example, suppose we have the matrix below: $A=\begin{pmatrix}2 & 4 & 1\\ 3 & 1 & 2\\ 4 & 3 & 1 ...
5
votes
3answers
235 views

Creating a nonperiodic function in mathematica

I want to create a non-periodic square wave with values of 1 and -1(not necessarily alternating). For e.g. I want to convert an arbitrary array like {1,-1,-1,1,-1,1,-1} into a function. I tried ...
5
votes
4answers
193 views

Make second argument same as first when only one argument passed to function [duplicate]

Clear[f] f[n_, k_: n] :={n, k} f[x] {x,n} Actually I would like to get: {x,x} The following is one wrong definition, I'm showing that I need the ...