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
1answer
138 views

Multiple down-values with exactly the same lefthand side

I was working on an answer to this question, when I was sidetracked by what I bring up here. I wanted a function, which when given a string representing a binary number, would convert the string to a ...
4
votes
2answers
247 views

How can I create a class of matrices programmatically?

I am trying to figure out how to create a function that can create the matrix pattern below, where: f[1] returns {{1}} ...
4
votes
4answers
238 views

Speed up replace all

I have large list of rules, I would like to use list/.rule, but assume that rule is a set of rules rule 1, rule2 rule...I want ...
4
votes
1answer
118 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: ...
4
votes
2answers
308 views

Returning Replacement Rules in a function and using it later on

I would like a function which returns replacement rules as some internal mathematica functions are doing and use the results in other functions. I could not find any information on that and I'm ...
4
votes
1answer
109 views

Map at a subsequence of a list

I'm trying to construct a function somewhat similar to MapAt. A basic usage example should look like this: ...
4
votes
1answer
96 views

How can I implement this recurrence equation in Mathematica?

I asked a similar question yesterday but today I realized that I was implementing the wrong function. I have tried changing the implementation but I can't get it to work. Problem: There is a river ...
4
votes
2answers
80 views

How to sum values in the list that belongs to same week

I need to sum values that belongs to same week. For example, I have the list x with one column and n rows. Format: ...
4
votes
1answer
251 views

Defining the Moyal Product in Mathematica

What would be the best way to define the Moyal Product, $f(x,p)\star g(x,p)$, in Mathematica? $f(x,p)\star g(x,p)$ may be written as $f\star ...
4
votes
1answer
218 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 ...
4
votes
2answers
91 views

Creating functions from output of other calculations

Apologies in advance if the title is vague, I'm not really sure what to call this. I have a function (call it 'foo') that generates a largeish polynomial, and it is natural to make the variables be ...
4
votes
4answers
332 views

Differentiating space curves

I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by ...
4
votes
1answer
280 views

How do I use the result of Solve in a function definition?

I'm trying to adapt the following piece to the part where PowerF is a function of amax. ...
4
votes
2answers
124 views

Nested mapping of a function

If I use the construct f[#] & /@ f[#] & /@ f[#] & /@ {a, b, c} my function works, but if I use ...
4
votes
1answer
101 views

Display level of recursion of a recursive function during execution

Given a recursive function, is there some simple way to display or store the value of recursion or "how many levels deep" the function is at a given time? For instance, if we wrote the recursive ...
4
votes
1answer
207 views

Find lengths of contours in a ContourPlot

I am trying to find the lengths of different contours in the following plot: It is a complicated piecewise function evaluated on the unit disk. I am hoping there is an easy, generalized way to ...
4
votes
1answer
175 views

Feedback on my Subscript code

I have written a code, and I need a little feed back.. I want to make the Subscript distributive across (1) addition and (2) multiplication to mimic short-hand for ...
4
votes
1answer
236 views
4
votes
2answers
71 views

Count the number of element repeats at various distances

I have a function of x: f[x_] := Abs[Extract[list, x + n] - Extract[list, x]] I then apply this: ...
4
votes
2answers
92 views

Function pattern to support listed and non-listed arguments [duplicate]

I often want to write functions that take as an argument either a) a rule or b) a list of rules. As an example, when using Replace with just one rule, it does not ...
4
votes
1answer
176 views

Finding mappings between expressions

Suppose we have an expression of the form: $j=\frac{A\left(t\right)}{B\left(t\right)}=\frac{C\left(s\right)}{D\left(s\right)}$ That is, $j$ can be expressed either as a function of $t$, or as a ...
4
votes
1answer
208 views

What's the most intelligent way to store the information of a selfmade graph?

I have a very long list of element, say $a1,a2, a3$,..., and they are all connected in that each is the child of many parents. E.g. $a74$ is associated with $a2,a55,a71$, and also contains ...
3
votes
9answers
2k views

How to find palindromic numbers (Project Euler #4)?

I'm trying to solve the fourth Project Euler's problem with this: ...
3
votes
3answers
417 views

Alternatives pattern in a function definition

I thought that I remembered a way to write a function definition using "|", but can't find documentation for it. So for example, I'd want to define: ...
3
votes
2answers
409 views

Write a function that returns the logarithmic derivative

How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
3
votes
4answers
230 views

How to create a composite function from a variable number of components?

Background of the problem: A patient takes a drug every $X$ hours with a half-life of $Y$ hours. How much of the drug will be (exactly) in his system after $h$ hours? For $X=24$, and $Y=24$ I made the ...
3
votes
3answers
434 views

How to pull scalars out of a function that should act on lists?

Suppose I have A = a vecA B = b vecB where a and b are supposed to be arbitrary scalars ...
3
votes
2answers
518 views

Defining a function using Series? [duplicate]

Possible Duplicate: General::ivar is not a valid variable when plotting - what actually causes this and how to avoid it? I need to define a function using the output of series, i.e. ...
3
votes
5answers
221 views

Define a function with variables linked implicitly

I would like to define a function $f(x,y)$, with the variables x and y linked by an equation implicitly, so $f(x,y)=f(x(y),y)=f(y)$. Eventually I would like to draw a graph with $f(x(y),y)$ being the ...
3
votes
4answers
168 views

Pack Solve results into a vector

I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace: ...
3
votes
2answers
125 views

How to define multiple functions using a for command

Let's say I want to plot 10 graphs of those following functions. Since they are recursive functions, I cant make a table with 10 different initial conditions because Mathematica stores each value ...
3
votes
2answers
175 views

Improve timings for calculating coeficients

Is there a quicker way of finding ther coefficients of something like $$(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2}+x_{9}^{2}+x_{10}^{2})\times\\ ...
3
votes
3answers
268 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).) ...
3
votes
1answer
94 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 ...
3
votes
2answers
233 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 ...
3
votes
1answer
221 views

Evaluation of self-defined functions

I defined a function that I call disc which I want to minimize later. The function is defined as ...
3
votes
3answers
180 views

Function that prints a different value than it returns

I want to create a function something like this: test[x_] := (Print[1]; Return[2];) Except it prints 1 when executed as ...
3
votes
2answers
448 views

Differential operator squared

I defined a one-dimensional momentum operator $\hat{p}=-i\hbar\frac{\partial}{\partial{x}}$ in Mathematica p = -I * h * D[#, x]& and I want to get the ...
3
votes
2answers
347 views

Why does the first derivative of a piecewise continuous function have discontinuities?

I have this piecewise continuous function which is also continuously differentiable over time : ...
3
votes
1answer
147 views

Function that returns the second argument of Reap

I'm trying to create a function that returns only the second argument of Reap. Here's my naive guess of how it would go : Reap2[x_]:= Flatten[Reap[x][[2]],1] ...
3
votes
5answers
317 views

How to add periodicity to condition?

Is it possible to set the following function f[a], where a can be any real number? $$ f(\alpha) = \begin{cases} 1 ...
3
votes
2answers
235 views

Multiplicative partition function

I am trying to create a multiplicative partition function that would generate something like ...
3
votes
1answer
209 views

Extracting function calls from an expression

I have an expression like this: expr = F[0, 1] + 2 F[0, 0] - 17*F[2, 0] and I want to transform it to a list consisting of all function calls with its arguments: ...
3
votes
2answers
592 views

Ways to plot interpolating functions more economically?

I am interpolating a lot of data over geographic coordinates obtained via GPS, and frequently I need to plot these interpolated functions together. For example, I may have an interpolated elevation ...
3
votes
3answers
141 views

How to identify patterns in a tensor-polynomial and replace appropriate symbol?

I want to write a function tensorReplace[input] that takes a tensor polynomial in $r_i$ such as $r_i r_j r_k+r_i q_j q_k +q_i q_j q_k$ , and replaces each monomial ...
3
votes
2answers
152 views

Apply UpValues before Listability

I'm trying to modify Plus but am running into trouble with it being Listable: ...
3
votes
5answers
97 views

How can I convert a Piecewise into a nested If?

For later conversion into a programming language where if is the only conditional construct, I would like to convert a Piecewise ...
3
votes
3answers
91 views

Defining a function that that evaluates a function to obtain a value not supplied as an optional argument

I have a function like this CentralDifferentMethod[α_, β_, α1_, α2_, λ_, v0_, dt_, t_] Now, I want to add a new parameter ...
3
votes
1answer
140 views

Extract data from WeatherData as a list of associations

Given weather data for 2013 and 2014 as follows: ...