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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0
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1answer
33 views

How do I define the following piecewise function?

For 0<=t<=10, if 5t<=n<=5t+2, then f[n]=4n, and if 5t+3<=n<=5t+4, then f[n]=4n+1? I would like then to use the specific values of f[n], for all n between 0 and 54 (t here is any ...
1
vote
2answers
61 views

Theory => practice: constructing a function “functionally”

I've read the Mathematica documentation and am certain there's way to do this with functional programming, but can't quite conceive yet how. I've taken a simple example (stating the series for ...
20
votes
5answers
421 views

Can I make a default for an optional argument the value of another argument?

I'd like to define a function with several optional arguments, some of which default to the value supplied for other arguments. For example, I'd like to be able to write something like ...
3
votes
1answer
81 views

Given a list made up of subsets of an alphabet, how can I use associations to create a Boolean dictionary of the given list

I have a list of 30,000 elements, each of the element is a list in itself {{a, b}, {p, q, r}, {a, p}, ..., {z, x}}. Second one contains unique elements ...
1
vote
1answer
53 views

Table of references

I have a list of variables (say a, b, c, d, e) that I want to assign in a single command. {a,b,c,d,e} = {1,2,3,4,5} would ...
1
vote
1answer
80 views

Changing default behavior of Series to give slightly different SeriesData

I am working with complicated expressions expr that contains the symbolic function f[x] which I know to have a pole at ...
1
vote
1answer
46 views

Summimg peculiar nestings

I have some lists with peculiar nestings: ...
1
vote
1answer
64 views

How in Mathematica, would I define a function that takes arguments much like one would in an object orientated language

I would know how to write a function in object orientated language, just I don't know how to do this in mathematica, in an OOP I would define a function like this: ...
0
votes
2answers
28 views

Retrieve Options from function other than graphics objects

We can retrieve information about used Options for Graphics via: Options[Plot[Sin[x], {x, 0, 1}], "AspectRatio"] (* {AspectRatio -> 1/GoldenRatio} *) even if ...
7
votes
3answers
150 views

Localising OptionValues

The documentation on OptionsPattern leaves me with some unanswered questions. From the example section: ...
2
votes
3answers
88 views

Testing for a vector of reals [closed]

Suppose I define: RealVector[expr_]:=VectorQ[expr,NumberQ[#]&&Head[#]===Real)]; Then: ...
0
votes
0answers
46 views

How to Fold (FoldList) this in a more compact (efficient) way?

Example code: x = Table[something[i], {i, 5}] Table[Fold[f1[#1, f2[#2, a], a] &, x[[i]], {c1, c2, c3}], {i, Length[x]}] This above is just an example. I ...
1
vote
1answer
102 views

Why does Mathematica add Hold to the result of my user defined symbol?

In the code below I have defined a symbol that multiplies two block-matrices (I can't use the builtin Dot since Dot assumes that the matrix coefficients commute): ...
6
votes
1answer
108 views

How to track Part of Symbol or How to symbolize Parts of Symbol without copying data

Let's create simple function: SetAttributes[h, HoldFirst]; h[data_] := Dynamic[Grid[data], TrackedSymbols :> {data}] test = RandomReal[1, {2, 2}]; h[test] ...
2
votes
2answers
118 views

Polynomial expansion of operator

I am new to Mathematica, I am trying to generate the polynomial function of a operator. So for example, the operator $L $ is $\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y} $, and I want ...
4
votes
1answer
92 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 ...
0
votes
0answers
70 views

Numerical Integration/Function

I have a problem with a function defined numerically through an integral of the form: ...
0
votes
1answer
43 views

Defining solutions to FindRoot as a function of parameters in Mathematica

This works: f[a_] := x /. FindRoot[x^2 - a == 0, {x, 1}] f[3] (* 1.73205 *) I need this to work, but it doesn't: ...
3
votes
2answers
67 views

Forward function arguments to built-in Plot[]

Suppose I need to write a function to plot the real and imaginary part of some function (just an example). I want to define a function foo so that ...
1
vote
0answers
44 views

How to input a dynamically changing parameter in NDSolve? [closed]

I am trying to solve a system of DEs with additional conditions, and one condition depends on a parameter. Let us consider the following example: ...
2
votes
1answer
97 views

Inverse gradient operator

I found a nice paper about inverse vector operators here. I have successfully implemented a Mathematica function for most of them, however I can't figure out how to do inverse gradient (page 7 in the ...
3
votes
3answers
405 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: ...
1
vote
1answer
88 views
6
votes
4answers
217 views

Function for a series of joined slopes

I need a function for a series of joined slopes and my solution feels a bit kludgy. Is there a better way? A list of pairs of transition points and slopes: ...
27
votes
1answer
562 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
8
votes
1answer
119 views

How to assemble and disassemble a function into steps

I've watched many programmers (both novice and expert) write functions in Mathematica and have observed a common behavioral pattern. This pattern has many elements that would be automated and thus ...
1
vote
2answers
79 views

Expressions containing globally undefined symbols inside a function where they are defined

Consider the following code. f[a_,b_]:=x; Clear[a,b]; x=a+b; f[1,2] It returns a+b. However, from a certain viewpoint, one ...
1
vote
0answers
61 views

The problem (time) caused by ?NumericQ

In here, I asked a related (similar) question. Using ?NumericQ seems have slowed down the entire calculation. But I now have a more serious problem: ...
1
vote
1answer
594 views

Computing the fundamental matrix and its monodromy matrix

Assume $\dot x(t)=v(x,t)$ is a $T$-periodic, with respect to $t$ dynamical system. That is: $x\in\mathbb R^n,\quad t\in\mathbb R,\qquad v(x,t+T)=v(x,t)$. Let $x_0$ be a smooth periodic solution in ...
0
votes
0answers
61 views

How to define a two-variable sequence?

I would like to define the following function but I am having a problem. I would like Mathematica to "understand" what I mean by writing "+...+". For example, for large values for $n$ and $m$ it takes ...
2
votes
1answer
52 views

How to protect function variables [duplicate]

I am sure this has been asked before, but I can't seem to find the right solution. I want a function to be the solution to a differential equation ...
3
votes
1answer
144 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] ...
1
vote
1answer
112 views

Piecewise smooth rectangle pulse

I am wondering how to create a single rectangle pulse with nonlinear riding and falling edges on both sides. I don't know whether it is better to do it piecewise or to mathematically transform the ...
3
votes
1answer
37 views

How shortening argument test when declaring functions?

When defining some functions which depend in many arguments sometimes we need to include question Q constraints to diminish processing time. My question is simple, there is a way to shorten a long ...
4
votes
2answers
170 views

A better way of handling Module output?

I am sure this has been asked before in a way or another. I need to Save or DumpSave some symbols that contain the result of ...
0
votes
0answers
77 views

How to conveniently stop a programme without aborting the computation

I have a programme that will have to run for a few days. However, I would like the user to have the option of stopping the computation of the code, without aborting it, when he desires, without ...
1
vote
1answer
101 views

Quantize a real-valued function?

I'm wondering if there's a built-in way in Mathematica to take a function whose output values are continuous, and quantize it to produce a step function. For example, I have the function ...
0
votes
1answer
54 views

Defining a function with algebraic parameters

I am trying to define and use a function to represent the eigenstates of a Quantum Harmonic Oscillator, which have the general form: $$\psi_{n}(x) = \frac{1}{\sqrt{2^{n} n!}}\left(\frac{m \omega}{2 ...
1
vote
1answer
93 views

Why doesn't Thread work in this case?

The following function is supposed to pick the element of the list with highest weight, i.e., with Thread [f[{{a,1},{b,2}}]] it should make the variables ...
6
votes
3answers
187 views

How to define a nested function like this?

For example, I want to calculate the limit of $\frac{1}{1+\frac{2}{1+\frac{3}{1+\ldots}}}$. So I want to define: $f(1)=1$ $f(2)=\frac{1}{1+2}$ $f(3)=\frac{1}{1+\frac{2}{1+3}}$ Then I calculate ...
3
votes
1answer
106 views

Define and plot a piecewise function with parameters [closed]

I have this function , but i do not know how to define it in mathematica \begin{equation} f_t(x)=% \begin{cases} i& \text{$\frac{1}{1+i}<|x-t|\le \frac{1}{i}$} \\ ...
2
votes
3answers
79 views

How to test a condition for a list and output all the expression that is true?

Suppose that I have a list lis={x-y,x+y,x*y}; and a function f[a_,b_]:=#/.{x->a,y->b}& I want to output all the ...
2
votes
1answer
249 views

How to make a function from body with variable number of arguments?

Suppose I have an UNKNOWN function, which generates formulas with given number of x[i]. ...
1
vote
1answer
47 views

Composition of Multivariable function

I am trying to compose functions of xleft, maybe like xleft[xleft[f]] or even higher order. And here is my function: ...
0
votes
0answers
45 views

Question about treillis structures

I have difficulties finding a command to plot multiple segments connected in nodes in Mathematica. Ultimately, my goal is to modelise something like this by entering nodes coordinates. Also, the ...