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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8
votes
3answers
182 views
3
votes
0answers
56 views

How to combine DifferenceRoot objects for odd and even-indexed terms

I'm trying to analyze a certain infinite sequence $S$, indexed by positive integers starting from $1$. It can be split into two subsequences: $S^{odd}$ by removing all even-indexed elements and ...
1
vote
2answers
159 views
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 ...
-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
1answer
95 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 ...
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 ...
2
votes
2answers
284 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 ...
0
votes
2answers
100 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: ...
3
votes
1answer
123 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 ...
16
votes
1answer
257 views

Kernel inexplicably hangs if I define a pure function without suppressing output

Save any unsaved work before trying as it may crash Mathematica and other programs by filling up the memory! In v9.0.1.0 on OSX 10.8.5, if I start a new session and define two functions ...
12
votes
4answers
364 views

Equivalent Nested Loop Structure

Consider the following examples: ...
1
vote
1answer
195 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: ...
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 ...
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: ...
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
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 ...
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
158 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: ...
2
votes
2answers
481 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 \\ ...
2
votes
2answers
107 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 ...
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 ...
14
votes
1answer
289 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
5
votes
2answers
169 views

How to optimize computing a product?

Problem description Write a function to caculate the formula My solutions Solution 1: ...
3
votes
3answers
404 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
254 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 ...
0
votes
2answers
89 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
85 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 ...
6
votes
1answer
205 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}}] ...
1
vote
2answers
142 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 ...
0
votes
1answer
99 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
192 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 ...
5
votes
2answers
553 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?
2
votes
1answer
101 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 ...
3
votes
2answers
175 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 ...
1
vote
2answers
333 views
3
votes
1answer
84 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 ...
7
votes
4answers
466 views

Turn expression into function

I'm new to Mathematica and I spent the last hour trying to make the expression ...
6
votes
1answer
123 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 ...
1
vote
0answers
125 views

Issue with Coefficient command

I'm trying to used the Coefficient command to extract the numerical values in front of a Chebyshev polynomial. I know that there is a numerical way to do this, presented in numerical recipes, which I ...
12
votes
2answers
170 views

How can one write a robust ListableQ function?

I would like to have a test that determines if a particular function is Listable. In the case of Symbols this is merely a matter of checking Attributes. ...
1
vote
2answers
354 views

Run entire notebook

I have created a notebook, with functions. The only thing that I want to change in the notebook later is the input file. I therefor want to have a button that runs every input step-by-step so that I ...
3
votes
1answer
224 views

NestList with a list inside?

I'm new to Mathematica, and was looking for more efficient ways to implement the Do loop below. a, ...