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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1
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1answer
92 views

Using a table as a variable in a function

I have a bunch of arrays and need to extract specific rows and columns of these that obey certain criteria. So for one table I'd do like this ...
1
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1answer
37 views

Please explain this pattern/Message related issue and help with finding workaround

I attempted to clean up my code and also add messages to functions if they are called with wrong arguments. This introduced some error which I tracked down to the following: ...
2
votes
1answer
47 views

How to make Simplify (and FullSimplify) give a default output if $Assumptions are contradictory

I have a function (deep inside my package) that looks like ...
2
votes
2answers
73 views

Function where variable is integration bound

Lets say I have a function of the form: $f(T) = T^4 \int_0^{1/T} \frac{x^3 dx}{e^x-1}$ This is an example of the situation I am describing not a unique problem. I want to define it as a numerical ...
2
votes
1answer
45 views

combine two definitions into one [closed]

Suppose I have two definitions of a function such as ...
4
votes
3answers
186 views

Make own rule for multiplication

I'm new to mathematica, so I still cannot use it properly. I want to do symbolic programming. My question is : is there any way to define our own multiplication. Suppose $a,b$ are arbitrary ...
1
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1answer
72 views

Define recursive function over two indices

I have $x_i=(i-1)/50$ for $i=1,\ldots,51 $. Given a function $ f(x) = x^2 $, I want to find $y_i^k$ given by \begin{eqnarray} y_i^1 &=& f(x_i) \\ y_i^{k+1} &=& ...
6
votes
3answers
301 views

How can I create currying functions using pure function syntax?

For example how can I write In: pureFunctionSyntax[myF] /@ {7, 3} Out: {myF[7, Log[7]], myF[3, Log[3]]}
3
votes
1answer
73 views

InverseFunction: how can I extract the function inside?

This is probably a trivial question. But I could not find an answer. Given the explicit expression for ft in te assignment ...
1
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0answers
46 views

Mapping over two indices with a condition

How can I use Map over two indices with a condition? I am trying to calculate second derivative of an eigenvalue, $\lambda_i(x)$, of $n \times n$ matrix $M(x)$ ...
2
votes
1answer
83 views

Why must I specify the Global context for a symbol in a private package?

I have written two versions of the function below in a package. When I load the package and call the function, Why does the first version where the variable s has no explicit Context return the long ...
1
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0answers
31 views

Piecewise in 2D with quadrants as conditions

I am trying to define a piecewise vector field. Can the condition be of the form I am using (i.e. a quadrant)? I can't also make Piecewise work with more than two ...
4
votes
3answers
132 views

List of functions to list of parameters

I am working in a Dataset and I need to create a function for a ChartStyle option of a ...
4
votes
2answers
74 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
52 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 ...
5
votes
4answers
202 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
104 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
67 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
144 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
84 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
206 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
54 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
103 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
54 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
41 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
99 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
38 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
152 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].
11
votes
2answers
257 views

How to build a function object like the built-ins such as Interpolation?

There are many built-in functions that return a function object, such as Interpolation[], BSplineFunction[] ,...
2
votes
1answer
44 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
23 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
66 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
62 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
52 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
198 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
83 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
121 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
82 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
125 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
144 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
198 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: ...
14
votes
4answers
385 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
65 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
43 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
353 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
271 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
272 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
231 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
87 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 ...