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
2answers
80 views

Assigning function values in a memoized recursive module

I have a complicated recursive module which I have memoized. I realised that certain isomorphs of inputs to this function will give the same output. Therefore I decided to memoize all such ...
3
votes
1answer
61 views

Prevent expression from evaluation in function when using `ToString `

I defined function fhold Clear[fhold] SetAttributes[fhold, HoldAll] fhold[para_List] := ToString[para]; What I want is that ...
6
votes
4answers
237 views

Recursive piecewise integral relation with piecewise base case?

How is this recursive formula $$ f_{n+1}(z) = \int_0^1 f_{n}(z-y)\,{\rm d}y $$ implemented in Mathematica? The base case is $$ f_1(z) = \begin{cases} 1 & 0\leq z\leq 1 \\ 0 & ...
2
votes
1answer
117 views

How to properly define this function of function

I encountered real problem at first, and here is the toy example variable argument stored some expression that is generated from other parts of the program. I ...
2
votes
0answers
68 views

Automating game simulation, using previous results [closed]

Based on this question on MSE, I would like to simulate a game whereby player $2$ enters a number, so as to test the strategy. The basis for this is the factor game online here. ...
9
votes
1answer
149 views

Why there is only `HoldFirst` but no `HoldSecond`, `HoldThird`, …`HoldN`?

I feel that this must be a duplicate. But I just can't find such a post. Mathematica has HoldFirst, HoldRest, ...
3
votes
1answer
98 views

How to get name of “named row” in Dataset for function applied to each row

After some calculations and a GroupBy I have a Dataset that is structured like this. ...
4
votes
1answer
214 views

How to tame the wild MMA?

MMA is a free country. But TOO free sometimes. Just as an example: Clear[a] a[x_] == a[y_] ^:= Round[x] == Round[y] {a[3] == a[3.01], a[3] == a[4]} is {True, ...
3
votes
0answers
55 views

Memoized function with function parameter [duplicate]

I have some code that takes a function and uses the function to do some complicated computation. Thus, I wish to store this so I don't have to repeat this. Below, it is more simple than my real ...
1
vote
1answer
138 views

How to find period of a discrete sequence?

For example, {1,2,3,4,5,6,7,8} has period 1, the base is {1} {1,2,4,5,7,8,10,11} has period 3, the base is {1,2} I ...
3
votes
1answer
58 views

Setting a One Dimensional Function Equal to a Constant over a Specific Range

I am trying to take the output from NDSolve and create a variable equal to the solution except for a certain range of values. Here is the code I am trying to use ...
0
votes
0answers
47 views

Improving numerical stability of the Goldstein-Price Function

Goldstein-Price Function is a two-dimensional test function for optimization, defined as $$f(y,z) = \left(\left(3 y^2+2 y (3 z-7)+z (3 z-14)+19\right) (y+z+1)^2+1\right) \times \left(\left(12 y^2-4 y ...
1
vote
1answer
101 views

How to write or extend operators like $*\!\!*$

I'm stuck on trying to define simplification rules for NonCommutativeMultiply, much like ExpandNCM found in Documentation Center, under Applications. For example, I'd like ...
0
votes
1answer
41 views

Construct a function whose definition depends on the values of its arguments and evaluates a Section

I have defined a function that returns different output according to the values of the axes of an ellipsoidal. If none of the Which statement cases is satisfied then the function evaluates the ...
3
votes
2answers
197 views

Pollard's Rho algorithm

I'm working in Mathematica and I'm trying to implement the [Pollard's Rho Algorithm for the Discrete Logartihm Problem][1].
2
votes
1answer
49 views

Defining function [duplicate]

ver1 = 2 x verf[x_] := ver1 verf[3] Result : 2 x Expected Result : 6 In the above code ...
1
vote
1answer
26 views

Evaluate function entrywise on high dimensional array [closed]

I have defined a function $f$ from number to number. I want to tell Mathematica to apply that function to each entry of a high dimensional array $A$, to get a new array $f(A)$ in the same form of $A$. ...
1
vote
1answer
80 views

Defining function from table [closed]

I have a table of values of the form Table[{i1,j1}, {i2,j2}...] and I want to define a function like f[i] to take the values ...
5
votes
0answers
78 views

Does Compilation option “InlineExternalDefinitions”/“InlineCompiledFunctions” lead to unnecessarily complicated nesting?

Question: When an external (possibly complicated) definition f is used inside a compiled function with ...
1
vote
2answers
55 views

Find function to relate two lists of values

I know Mathematica has the FindFit function to determine the parameters of a known function that fits a sequence of points, but what if you do not know the relationship (linear, log, quadratic, etc)? ...
4
votes
3answers
222 views

How to tell Mathematica that the argument of a function is real?

I want to define the following function in mathematica: $$R(\psi)=\begin{bmatrix}1&0&0\\0&\cos 2\psi & \sin 2\psi\\0&-\sin 2\psi & \cos 2\psi\end{bmatrix}\qquad,\psi\in\mathbb ...
6
votes
1answer
97 views

How to delay the definition of a function from the time of package initialization to when it is first called

I am writing a package where a couple defined functions take a very long time define at initialization time (because they are large CompiledFunctions). However ...
2
votes
1answer
173 views

How to define functions with a list of arguments

I wante to define several functions, all of them with the same arguments, for example: f[a_, b_, c_]:= ... g[a_, b_, c_]:= ... h[a_, b_, c_]:= ... How can I do ...
1
vote
1answer
293 views

How to define a periodic function from an interval to Play (monotonic) sound

I would like to define a function on an interval and then duplicate it on other intervals of the same length in order to define a (generally discontinuous) periodic function, from which I could get a ...
3
votes
1answer
128 views

Programming a MaxMin Linear Optimization

I want to program a function for a two-player game. Basically it's like this: . Each player has an array of options, and the result of the game is based on both players choices. So heres my most ...
8
votes
2answers
170 views

Name rewriting for Function fails in closure

At its heart, Mathematica is a dynamically scoped language. While the choice of dynamic scope for Mathematica is very much a defensible one, lexical scope is too useful to do without, and Mathematica ...
1
vote
4answers
205 views

How to define a conditioned function that returns one when x is integer and zero otherwise? [closed]

What is the simplest way to define a conditioned function that returns one when x is integer and zero otherwise? I'm doing it wrong: ...
3
votes
1answer
73 views

Using functionals in Mathematica [duplicate]

I recently installed Mathematica and I wanted to define a functional in it. This is what I did: ...
15
votes
4answers
425 views

Skipping “middle” Optional Arguments

Is there a way to call a function where the "middle" arguments should use their default value while specifying values for the "right-most" arguments? For example, given this function: ...
4
votes
1answer
66 views

Create a function for $\Pi^{-1}(n)$

Is it possible to create a function that gives the inverse of pP[x_] := Sum[PrimePi[x^(1/k)]/k, {k, 1, Floor[Log2[x]]}] i.e., a function that plots ...
0
votes
1answer
49 views

Checking the solution of a differential equation with a boundary condition depending on an arbitrary function

I have the partial differential equation: $\qquad U_{x} - 4 x^{2} U_{t} = x U, \qquad U(x,0)=f(x), \qquad x \in (- \infty, \infty), \qquad t \in (0, \infty)$ Where $U_{x} = \frac{\partial ...
6
votes
2answers
356 views

Calculating extreme spread with a Do loop [closed]

I am trying to model what is called the extreme spread of a series of shots at a target. Each shot is from a normal distribution with mean 0 and variance 1. For this example there are three shots per ...
16
votes
3answers
280 views

Is it possible to change the order that symbol definitions are checked? (DownValues vs UpValues)

Suppose I have the function f with the following definition assigned to it: ...
6
votes
2answers
283 views

What evaluation mechanism is behind Mathematica support for multiple definitions of a function? What is the benefit of this?

I am studying the question What are the most common pitfalls awaiting new users? Up to now, I have fulfilled some of the parts but yet don't understand which this problem is related to? Consider the ...
10
votes
1answer
238 views

Question about Rules and Pattern (The operator patt/;test)

Maybe this question is so trivial but it has confused me. I'm studying the What the @#%^&*?! do all those funny signs mean? and in the Rules and patterns under ...
0
votes
1answer
89 views

Optimization of a voxel projection function

I implemented a function to check if a voxel (3D pixel) is well projected on the space of a image (black and white silhouette) through a perspective camera. The function does the work but It need more ...
2
votes
3answers
192 views

data manipulation in log-log scale

Say that I have the following: y[t_] := 2 + (2/10)*(1 - Exp[-t/11]) timedat = N[Table[{t, y[t]}, {t, 0, 10, 1/1000}]]; How is it possible to construct an ...
4
votes
2answers
109 views

Unsure how to nest / fold this power tower factorisation

Not quite sure how to nest this. What I would like is power tower of integer factored until all powers are primes. eg desired output for f[3*125^4] would be ...
0
votes
1answer
70 views

a function that evaluates a Section

I have defined a function that returns different output according to the values of the axes of an ellipsoidal. The function is given below: ...
2
votes
0answers
36 views

Unexpected behavior from Return called in a Block [duplicate]

I like to write functions that dispose of failure cases early, before they do the main calculation, but I don't like to write cascading If statements. Here is a toy ...
1
vote
1answer
70 views

Writing a function with two functions as arguments

I am trying to write a function of two functions. A function of one function works as in h[f___, x_, y_] := Integrate[f, x] h[x^2 + y, x, y] and this ...
2
votes
3answers
94 views

Making a list of functions

Suppose I have the following equation system to solve: x(t_):={x1(t),x2(t)}; DSolve[x'(t)==x(t),x(t),t] This code works fine, but now suppose that instead of 2 ...
9
votes
1answer
178 views

Finding large prime gaps

I am using basic searches for prime gaps as follows: ...
12
votes
4answers
219 views

Distributing function arguments with function compositions. How to compute $(f + g^2)(x) = f(x) + g(x)^2$?

Suppose I have two functions f and g. To compute $f + g$ evaluated at a point $x$, I know that one can use ...
0
votes
1answer
79 views

Working with functionals [closed]

I am trying to work with functionals in Mathematica, this means that I want to define a function of a function. I defined my function of a function as: ...
1
vote
2answers
53 views

Replace function with multiple functions while respecting the inputs

I want to replace a function with either one or two functions and also combine their arguments. Say I have an original expression expr = u[i + 1] r[i] r[i-1] ...
3
votes
5answers
307 views

Function involving For loop

I've written the following function (the code includes the output): ...
1
vote
1answer
105 views
17
votes
3answers
471 views

Improving speed of code computing number of nonrepeating partitions

I need to answer the following for a number of parameters: How many ways can the integer $k$ be written as a sum of $n$ different integers ranging from $1$ to $m$? My initial attempt was the ...