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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2
votes
1answer
230 views

Defining Piecewise Functions [duplicate]

I'm having trouble defining piecewise functions. What I have so far is a function that outputs something in a suitable format for Piecewise: ...
5
votes
3answers
415 views

How to define the Poisson bracket in Mathematica

If $f,g$ are functions of the independent variables $\{q_1, q_2, ..., q_N, p_1, p_2, ..., p_N\}$, then the Poisson bracket is defined as: \begin{equation*} [f, g] = \sum_{i=1}^N \left(\frac{\partial ...
9
votes
1answer
217 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
101 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
35 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
155 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 ...
3
votes
1answer
101 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
104 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
154 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
165 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
46 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
73 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 ...
1
vote
2answers
222 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
294 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. ...
1
vote
1answer
89 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 ...
3
votes
1answer
108 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: ...
19
votes
3answers
370 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
5answers
94 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: ...
4
votes
1answer
163 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
139 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
117 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
176 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
114 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
179 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
81 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
175 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
80 views

Need to run evaluation 2 times

Why does this only work after running the evaluation 2 times? ...
8
votes
2answers
236 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
96 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 ...
5
votes
2answers
237 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 ...
3
votes
3answers
215 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
171 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
776 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 ...
8
votes
3answers
196 views
3
votes
0answers
57 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
177 views
0
votes
2answers
143 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
99 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
114 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 ...
3
votes
2answers
327 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
102 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
132 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 ...
18
votes
1answer
286 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
368 views

Equivalent Nested Loop Structure

Consider the following examples: ...
1
vote
1answer
200 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
190 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
212 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
204 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: ...