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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4
votes
3answers
495 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
480 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, ...
18
votes
2answers
245 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
106 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
115 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
374 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
77 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 ...
0
votes
1answer
79 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
181 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
62 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
459 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
85 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
339 views
3
votes
1answer
101 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
186 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
173 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
158 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
136 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
144 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
101 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
65 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
129 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
76 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
563 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
101 views

Defining commutation relations with Flat functions

Here is a minimal example of the problem I am having. ...
6
votes
3answers
140 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
289 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
89 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
103 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
76 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: ...
2
votes
2answers
221 views

Recursive formula involving a piecewise function

I am trying to construct a recursion, g[t], where g[t] = a[t] if g[t-1] = 1 ...
5
votes
2answers
492 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?
0
votes
2answers
86 views

Elegant way to transform formula with sum into code

I have this formula, and many other which contains sum, I am perfectly able to do the computation over a list, however to do this I need to do it in several manual steps. Therefore, I wonder if there ...
-2
votes
1answer
82 views

Calculations in sequence

I have a this calculation, as you can see it is doing a calculation on each list, from list 1 to list 4 of the datafile. My problem is that using Mapthread to do this calculation does not work because ...
17
votes
3answers
311 views

Nested definition: How can I define a function with a passed-in expression?

Here's a simplified version of what I'm trying to do: ...
1
vote
2answers
138 views

Using mathematical notation

Is it possible to write this function in mathematica exactly as shown, and then run the expression on a dataset? Please note I know that there are several other ways to do this. I am only ...
5
votes
1answer
167 views

How can I define a Listable function only apply to a vector?

Consider the function f which should behave as f[{{1, 2}, {3, 4}, {5, 6, 7}}] ...
3
votes
2answers
165 views

Force Mathematica not to reduce a fraction

I am interested in a function which would stop Mathematica reducing fraction. If my input is 50/100, Mathematica outputs 1/2, I ...
0
votes
1answer
89 views

Logic behind Flatten and Append to in Module

I have a list(kicks), and a function(fix). I am aware of the problem using Loop and Append or AppendTo. My question is why does the Flatten produce the desired output. List: ...
3
votes
2answers
162 views

How to declare a function that uses local variables of a module outside this module?

I have the following code Module[{f,x=0}, f[t_] := x + t; ..........; ...f[1]...; ..........; ] My aim is to put the declaration of the function ...
2
votes
1answer
90 views

How to define a function of z[bar], etc

Using Displaying index as subscript on output: e.g. C[i] -> C_i with Notation[...] or Interpretation[..]? I have often ended up wanting to define functions of annotated variables to better match my ...
19
votes
1answer
359 views

How can I make threading more flexible?

Threading automatically with Listable functions requires the argument expressions to have the same length (or for one of them to be atomic). For nested lists the ...
3
votes
1answer
70 views

Use of StringExpression as argument

Is it possible to use a StringExpression as a pattern for an argument? I.E. something like foo[chars__~~ WordCharacter.. ~~ num:NumberString] := {chars, num}; At ...
6
votes
4answers
350 views

Turn expression into function

I'm new to Mathematica and I spent the last hour trying to make the expression ...
17
votes
2answers
279 views

Pattern that matches colors

Suppose I'm writing a function that takes a color as a parameter; for example: drawShape[color_] := Graphics[{Style[Disk[], color]}]; But if the caller inputs an ...