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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11
votes
2answers
591 views

How to plot a barycentric line

I want to plot a barycentric function on an equilateral triangle (ternary plot). For example f1 = {Abs[Sin[x]], Mod[x, 2], Abs[Cos[x]]}; At the moment I evaluate ...
37
votes
6answers
2k views

How can I create a function with optional arguments and options?

Is it possible to create a function with optional arguments that also takes options? Here is a simple example. I have a function f with option "g". It also has ...
3
votes
1answer
148 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 ...
2
votes
3answers
137 views

How to generate a series of bisection points of a given line segment?

I want to get the coordinates of the bisection points for a given line segment to a specified resolution. For example, when the line is given by {0,0} and {1,0}, the output coordinates should be ...
0
votes
1answer
109 views

A function generating particle-in-a-box eigenfunctions

The function sequence is defined over $[-\frac{L}{2},\frac{L}{2}]$ (all elements are valued 0 outside this interval): $$\psi_n(x)=\begin{cases}\sqrt{2/L}\sin{(\frac{n\pi x}{L})} & n \space even ...
1
vote
3answers
164 views

professionalize/optimize my code that calls a function

I have the following construction, which defines a function that I subsequently call in a loop multiple times. I use this very often, but I have never looked into if there is a more professional way ...
1
vote
1answer
112 views

Module that finds the sum of digits of any given positive integer

How can I make a module that finds the sum of digits of any given positive integer? I use this command F[x_]:= Apply[ Plus, IntegerDigits[x] ] Is there another ...
2
votes
2answers
79 views

`PrimeNu` counting function

Building on this question, what is the most efficient counting function for distinct prime factors? It would obviously be more efficient if Prime and ...
1
vote
1answer
152 views

Part::pspec error returned when using a ListLinePlot ColorFunction variable as list index

In ListLinePlot, I'm attempting to construct my own ColorFunction for coloring points differently based on a third dimension of data not plotted to a specific axis. However, ColorFunction only uses ...
4
votes
2answers
174 views

Is it possible to `Protect` a dynamic programming process?

I wrote a function using dynamic programming to speed up the evaluation. For safety, I also want to protect this function. Take factorial for example: ...
2
votes
1answer
79 views

Need to run evaluation 2 times

Why does this only work after running the evaluation 2 times? ...
8
votes
2answers
224 views

Automatically compute r[1] = r1; r[2] = r2; …

I have three variables like this, r1 = 4; r2 = 3; r3 = 1; and I want to insert them into a function use them in a function definition like so: ...
5
votes
2answers
218 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 ...
1
vote
1answer
92 views

Linearity of a function in Mathematica

I have a function which has something like myFunc[q,a state[c,d]] a could be anything, and I want to tell Mathematica that ...
3
votes
3answers
199 views

Prime factor counting function

Is there any way I can speed up this prime factor counting function? (I am looking for all numbers in a range with 3 prime factors (counted with multiplicity).) ...
1
vote
3answers
160 views

Pure function inside another pure function

I have the following working expression: In[15]:= Length[Select[IntegerPartitions[10],First[#1]==5&]] Out[15]= 7 But, instead of using the constant 5 I want ...
4
votes
3answers
671 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 ...
15
votes
2answers
516 views

Constructing functions with variable number of output arguments

In Mathematica, you can construct a function f to have different definitions based on its input arguments. For example, ...
19
votes
2answers
261 views

Plotting a defined function gives different results from plotting the function directly

Consider the following piece of code: function[t_]:=Exp[-9 t^2]; LogLogPlot[{function[t],Exp[-9 t^2]},{t,.01,100}] I expect the two plots to exactly overlap each ...
-4
votes
1answer
110 views

Programming Multipolar Expansions in Spherical Tensors

We have that a density matrix can be written in a basis of spherical tensors: $\rho =\sum _{K=0}^S\sum_{q=-K}^K \rho _{\text{Kq}}^{(S)} T_{\text{Kq}}^{(S)}$ for example for a 3x3 matrix, $S=1$, ...
0
votes
2answers
134 views

How to insert trigonometric functions into matrices' vector components? [closed]

Is it possible to insert a trigonometric function into a matrix which will be able to be used dynamically, as an element of one of the vectors of the matrix? I'm trying to perform an operation like ...
2
votes
2answers
470 views

Q-Function representation in Mathematica

I observed that there is no Q-function representation in Mathematica. The definition of Q-Function is: \begin{align} Q(x) &= \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-\frac{u^2}{2}}du \\ ...
0
votes
1answer
93 views

Is it possible to define a function in terms of a power series?

Is it at all possible to define a function in Mathematica in terms of a power series? For a specific example, I wish to write $x(\tau)$ as $x(\tau)=x_{0}(\tau)+\mu ...
1
vote
1answer
108 views

Orthogonalizing polynomials with inner product depending on parameters

I need to orthogonalize the polynomials $h_n(x)=x^{2n}(1+x^2)^{-4S}$ with $x\in\textbf{R}$, $2S\in\textbf{N}$ and $n\in\{1,3,5,\ldots, 4S-1\}$ over the inner product $\langle h_n,h_m\rangle=32\pi ...
2
votes
2answers
279 views

Algorithm for parts integration

Sorry if this is a duplicate, I've searched how to do this to no avail. What I'd like to do is a function that integrates by parts $n$ times, i.e $$ \int u(x) v(x) dx = u ...
5
votes
1answer
65 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 ...
7
votes
3answers
510 views

Composition of functions

I have a number of rotations computed by rot = RotationTransform[theta, point], and I would like to compose them to produce one function that is the composition of ...
0
votes
2answers
98 views

A function that (also) changes a replacement rule

I'd like to write a function operating on a list, returning a list, but also changing a replacement rule. Let's say I have a list of replacement rules: ...
12
votes
4answers
364 views
3
votes
1answer
122 views

Define a function with the condition that it must be positive

I have a function f(x) and I want to define a new function g(x) that is equal to f(x) only ...
6
votes
2answers
205 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 ...
1
vote
1answer
193 views

Gram Schmidt inner and outer products

I know the Gram-Schmidt orthogonalization generates an orthonormal basis from an arbitrary basis. I need help with: Write a program that inputs a list $\{b_1,\dotsc,b_n\}$ of linearly independent ...
6
votes
2answers
185 views

Composition of functions using slots

Apolgies if this has been asked and answered, but I'm not even sure what to search for. I have two functions defined as follows: ...
4
votes
1answer
155 views

Implementing Bilinear Products

Consider a real, vector space $V$ with basis $B=\{v_1,v_2,\dots\}$, and let $\star:V\times V\to\mathbb R$ be a bilinear product on $V$. I would like to implement this product in Mathematica by ...
0
votes
1answer
187 views

How to define a function with different types of arguments by setting conditions on function's domain?

I need help in order to properly define a function of $4$ variables. Given that: ...
3
votes
1answer
104 views

How to make InverseFunction work on function defined with restriction on arguments

This example works to define InverseFunction on the first argument of a function ...
0
votes
0answers
73 views

creating some smooth density functions

I would like to create some density functions based on some distance measure $D$. As a base density function lets say I have a Gaussian density $f$ with mean $-1$ and variance $1$. I would like to ...
1
vote
1answer
143 views

Writing NDSolve-like functions

I've been using Mathematica for a while now, and there are multiple common tasks that I end up doing. I'd like to learn how to convert them into functions so that I can store them in some file and ...
0
votes
2answers
80 views

I want to define a function that has integer power [closed]

I am defining this function: f[x_] = kr*g[x] + (c^l*x^l)/(KIR + c^l*x^l) But I want to make l bigger than 0, so if I evaluate ...
10
votes
2answers
649 views

NestList on a function of several arguments

I'd like to know if it is possible to use NestList on a regular function of several arguments, such as: ...
1
vote
1answer
121 views

Defining commutation relations with Flat functions

Here is a minimal example of the problem I am having. ...
6
votes
3answers
157 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 ...
1
vote
0answers
40 views

Get pattern from rising numbers [duplicate]

I am no mathematician or math star, yet wondering if there is a formula or a way to calculate what follows: I have series of numbers: ...
3
votes
3answers
399 views

Implementing Newton's method

I have this question on coding Newton's method in Mathematica. I have some code to go by but I have no clue if it's computing the functions in the right order. The book is the numerical methods ...
2
votes
2answers
105 views

bulk initialization of associative array/hash implemented with function pattern matching?

I see that we can do associative arrays in Mathematica using functions that have implicit pattern arguments, as in ...
1
vote
3answers
107 views

Declare local variable when defining a function to mimic Table[]

The problem: I want to define a function tab to replace the long line Table[f[i,j,k,l],{i,3},{j,3},{k,3},{l,3}] by a shorter ...
2
votes
1answer
83 views

Is it possible to use a mathematical expression as function name?

This might seem as a silly question, but is it feasible to use a mathematical expression as the name of a function? For example, I'm studying the cross section of Compton scattering and there is a ...
5
votes
2answers
169 views

How to optimize computing a product?

Problem description Write a function to caculate the formula My solutions Solution 1: ...