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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9
votes
1answer
264 views

How to define function that can change patterns

Given time series data as follows: data = {{{2011, 1, 13}, 10}, {{2011, 2, 14}, 17}, {{2011, 3, 15}, 20}, {{2012, 1, 16}, 30}, {{2012, 2, 17}, 40}}; ...
0
votes
1answer
161 views

Holding Input Windows

I am creating a Mathematica document which contains a list of proofs in various fields of Mathematics so that I can easily review whenever I would like. First, I create a large set I call 'proofs' ...
0
votes
0answers
39 views

Varying number of function arguments [duplicate]

I have a function of six arguments: ffit[q1_, q2_, q3_, q4_, q5_, q6_] := (a1*q1^2 + a2*q2^2 + a3*q3^2 + a4*q4^2 + a5*q5^2 + a6*q6^2) ...
7
votes
3answers
169 views

Checking through an expression

I am writing a code that manipulates expressions that contains functions with an arbitrary number of arguments. An example expression is ...
4
votes
1answer
220 views

How to Override the Head of a Symbol

I was wondering if it is possible to override the head of symbols/operators. As a motivating example if I run: Then Ket will be returned. But lets say I want Bob to be returned instead of Ket. Is ...
1
vote
3answers
129 views

Difficult parametric function

I've got this strange parametric function and I want to implement it on Mathematica. I know that I could use Excel and calculate it, but my database is quite large and I want to do some reproducible ...
2
votes
2answers
281 views

Find partial derivatives when the number of variables is unknown

The idea is that I have a defined function of $n$ variables. I want to find out $n$ and get partial derivation for each of variables, Suppose you have a function ...
0
votes
1answer
197 views

Please explain this code (contains Append, Do, Coefficient)

I am a graduate student using a past student's Mathematica program. Will someone please explain to me exactly what this piece of code is doing? Specifically the ...
1
vote
1answer
54 views

How to substitue local variables into expression with free variables?

I'm wondering how to do the following: expr = L + R; foo[L_, R_] := expr; foo[1, 2] (* L + R *) and have it substitute the function variables ...
-1
votes
1answer
96 views

How to specify a specific range for a loop?

I'm having trouble with setting up a particular range in a loop for my programming. Now I have a defined range of data (not continuous numbers) that needs to be applied in a loop. Since the aim for my ...
3
votes
2answers
1k views

Define function using variable list

I have a list of variables variables={a,b} and a list with values values={1,2}. I'd like to define a function using the ...
4
votes
2answers
657 views

Can Mathematica functions have static variables?

In C, one can have variables that are declared static. These are not re-initialized every single time a function is called. I.e.:...
1
vote
1answer
147 views

Possibility of evaluating the expression within a NestList at each iteration?

I want to rotate iteratively a triangle about the same point, increasing for each iteration the length of its side in the same proportion and change the color of its sides. I came up with the solution ...
6
votes
1answer
151 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: ...
21
votes
3answers
449 views

Why x = x doesn't cause an infinite loop, but f[x_] := f[x] does?

If I execute: In[1] := x = x Out[1] = x and then I evaluate the symbol x: ...
1
vote
4answers
115 views

Question about sum and list in a function

I have a list of this form: $ lst =\left\{\left\{q_1,x_1,y_1,z_1\right\},\left\{q_2,x_2,y_2,z_2\right\},\text{...},\left\{q_n,x_n,y_n,z_n\right\}\right\} $ I want to use this list in the function: $...
6
votes
1answer
363 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 ...
3
votes
3answers
185 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 {0.5,...
0
votes
2answers
246 views

A function generating particle-in-a-box eigenfunctions

This function sequence is defined over $\left[-\frac{L}{2},\frac{L}{2}\right]$ (all elements are valued 0 outside this interval): $$\psi_n(x)=\begin{cases}\sqrt{\frac2{L}}\sin{\left(\frac{n\pi x}{L}\...
1
vote
3answers
249 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
140 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 ...
1
vote
1answer
308 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 ...
2
votes
2answers
102 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 ...
4
votes
2answers
215 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
83 views

Need to run evaluation 2 times

Why does this only work after running the evaluation 2 times? ...
8
votes
2answers
310 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: ...
1
vote
1answer
166 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 ...
6
votes
2answers
1k 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 $q[t]$...
5
votes
3answers
380 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
275 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 ...
5
votes
3answers
3k 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 ...
10
votes
3answers
322 views

How to exit from the innermost enclosing pure function?

Here is what I tried to do: Scan[Function[x, Scan[Function[y, If[y == 2, Return[]]; (* Do something useful *) Print[y]], x]], {{1, 2, 3}, {4, 5, 6}}] ...
3
votes
0answers
85 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
324 views
0
votes
2answers
617 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
128 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
273 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 x_{1}(\tau)+\mu^{2}x_{2}(\tau)+\...
1
vote
1answer
224 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 S\...
6
votes
1answer
79 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
1k 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 \left(\textstyle{\int}v\...
0
votes
2answers
214 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: ...
5
votes
1answer
637 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 ...
21
votes
2answers
363 views

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

Bug introduced in 9.0 and fixed in 10.0.2 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 ...
12
votes
4answers
411 views

Equivalent Nested Loop Structure

Consider the following examples: ...
1
vote
1answer
335 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 ...
8
votes
2answers
289 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
335 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
349 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: ...
5
votes
1answer
249 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
103 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 ...