Tagged Questions

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.

1answer
350 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: ...
1answer
249 views

Implementing Bilinear Products

Consider a real, vector space $V$ with basis $B=\{v_1,v_2,\dots\}$, and let $\star:V\times V\to\mathbb R$ be a bilinear product on $V$. I would like to implement this product in Mathematica by ...
0answers
103 views

creating some smooth density functions

I would like to create some density functions based on some distance measure $D$. As a base density function lets say I have a Gaussian density $f$ with mean $-1$ and variance $1$. I would like to ...
1answer
233 views

Writing NDSolve-like functions

I've been using Mathematica for a while now, and there are multiple common tasks that I end up doing. I'd like to learn how to convert them into functions so that I can store them in some file and ...
1answer
298 views

Defining commutation relations with Flat functions

Here is a minimal example of the problem I am having. ...
3answers
217 views

Using PatternTest and/or Condition to detect equal list lengths as well as list element formats

On searching Mathematica.SE for information about overloading functions, I came across several threads about PatternTest and ...
0answers
41 views

Get pattern from rising numbers [duplicate]

I am no mathematician or math star, yet wondering if there is a formula or a way to calculate what follows: I have series of numbers: ...
2answers
2k views

Q-Function representation in Mathematica

I observed that there is no Q-function representation in Mathematica. The definition of Q-Function is: \begin{align} Q(x) &= \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-\frac{u^2}{2}}du \\ &...
2answers
155 views

bulk initialization of associative array/hash implemented with function pattern matching?

I see that we can do associative arrays in Mathematica using functions that have implicit pattern arguments, as in ...
3answers
189 views

Declare local variable when defining a function to mimic Table[]

The problem: I want to define a function tab to replace the long line Table[f[i,j,k,l],{i,3},{j,3},{k,3},{l,3}] by a shorter ...
1answer
103 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 ...
2answers
359 views

Plotting a defined function gives different results from plotting the function directly

Consider the following piece of code: function[t_]:=Exp[-9 t^2]; LogLogPlot[{function[t],Exp[-9 t^2]},{t,.01,100}] I expect the two plots to exactly overlap each ...
2answers
184 views

How to optimize computing a product?

Problem description Write a function to caculate the formula My solutions Solution 1: ...
3answers
2k views

Implementing Newton's method

I have this question on coding Newton's method in Mathematica. I have some code to go by but I have no clue if it's computing the functions in the right order. The book is the numerical methods ...
2answers
576 views

Recursive formula involving a piecewise function

I am trying to construct a recursion, g[t], where g[t] = a[t] if g[t-1] = 1 ...
2answers
102 views

Elegant way to transform formula with sum into code

I have this formula, and many other which contains sum, I am perfectly able to do the computation over a list, however to do this I need to do it in several manual steps. Therefore, I wonder if there ...
1answer
95 views

Calculations in sequence

I have a this calculation, as you can see it is doing a calculation on each list, from list 1 to list 4 of the datafile. My problem is that using Mapthread to do this calculation does not work because ...
1answer
617 views

How can I define a Listable function only apply to a vector?

Consider the function f which should behave as f[{{1, 2}, {3, 4}, {5, 6, 7}}] ...
2answers
191 views

Using mathematical notation

Is it possible to write this function in mathematica exactly as shown, and then run the expression on a dataset? Please note I know that there are several other ways to do this. I am only ...
1answer
170 views

Logic behind Flatten and Append to in Module

I have a list(kicks), and a function(fix). I am aware of the problem using Loop and Append or AppendTo. My question is why does the Flatten produce the desired output. List: ...
2answers
512 views

Force Mathematica not to reduce a fraction

I am interested in a function which would stop Mathematica reducing fraction. If my input is 50/100, Mathematica outputs 1/2, I ...
2answers
2k views

How to find the non-differentiable point(s) of a given continuous function?

For example, the non-differentiable point of the function $f(x)=|x|$ is at $x=0$. How to find the non-differentiable points of a continuous function that is defined numerically?
1answer
154 views

How to define a function of z[bar], etc

Using Displaying index as subscript on output: e.g. C[i] -> C_i with Notation[...] or Interpretation[..]? I have often ended up wanting to define functions of annotated variables to better match my ...
2answers
443 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 ...
2answers
1k views

Mapping function onto two lists, simultaneously [duplicate]

I have this function ...
1answer
248 views

Use of StringExpression as argument

Is it possible to use a StringExpression as a pattern for an argument? I.E. something like foo[chars__~~ WordCharacter.. ~~ num:NumberString] := {chars, num}; At ...
4answers
3k views

Turn expression into function

I'm new to Mathematica and I spent the last hour trying to make the expression ...
1answer
201 views

Creating a Block from a list of rules

How can I create a function which works like Block but takes a list of rules as its first argument, rather than a list of assignments? The function needs to be ...
1answer
224 views

Issue with Coefficient command [closed]

I'm trying to used the Coefficient command to extract the numerical values in front of a Chebyshev polynomial. I know that there is a numerical way to do this, presented in numerical recipes, which I ...
2answers
196 views

How can one write a robust ListableQ function?

I would like to have a test that determines if a particular function is Listable. In the case of Symbols this is merely a matter of checking Attributes. ...
2answers
3k views

Run entire notebook

I have created a notebook, with functions. The only thing that I want to change in the notebook later is the input file. I therefor want to have a button that runs every input step-by-step so that I ...
1answer
420 views

NestList with a list inside?

I'm new to Mathematica, and was looking for more efficient ways to implement the Do loop below. a, ...
12answers
2k views

Pick elements of largest absolute value

For example, given list = {{1, -3, -5}, {2, 1, 6}, {0, 2, 4}, {-9, 2, 6}} should return: {-5, 6, 4, -9} Updated I found ...
1answer
228 views

User-defined Distance Functions with extra parameters [duplicate]

The Nearest function accepts a customized distance function. For example, a simple case that works well is ...
3answers
308 views

How can I break through Function's HoldAll attribute to force evaluation of a body element?

The question concerns creating a function. Let consider the following code With[{f = Function[t, Cos[t]]}, {First[#], f'[#]} & ] which returns ...
3answers
3k views

Simulate MATLAB's meshgrid function

Here is MATLAB's meshgrid. I came up with these implementations in Mathematica: ...
4answers
242 views

How to avoid writing $K$ loops?

I want to evaluate a mathematical function of $K$ variables each of variables varying between 1:N. One way to do this is writing $K$ loops and varying variables accordingly, as shown below: ...
2answers
345 views

Writing a function that returns a (usable) function

I am trying to create a function that returns Arnold's Cat Map of size n iterated k times. I can get something out of the Function command, but I can't figure out ...
0answers
292 views

Positive integrand giving negative answer

I'm integrating a positive function f(t) times sin(t) from 0 to pi/5 and get -38. Actually f is slightly negative for a short time (smallest value ~ -0.0005), but far from enough to explain this. ...
0answers
37 views

Detecting a more general pattern [duplicate]

I need a function that, given 2 patterns, determines if the first pattern is more general than the second (i.e. that any expression successfully matched by the second, will be successfully matched by ...
1answer
119 views

How to make InverseFunction work on function defined with restriction on arguments

This example works to define InverseFunction on the first argument of a function ...
2answers
497 views

Collatz Tool Box — any speed ups possible?

I have created a tool box for experimenting with the Collatz conjecture. Info here: Wolfram MathWorld and here: Wikipedia The patterns I have found allow us to make the conjecture jump through some ...
2answers
1k views

Is there any way to define pure functions with optional arguments?

For example consider the following function: Function[{u,v},u^2+v^4] Is there anyway to define default values for the variables ...
2answers
803 views

How to define a function based on the output of DSolve? [duplicate]

I would like to define a function based on the output of the following DSolve call: ...
1answer
182 views

Specifying optional arguments with variables

Perhaps this is poor programming on my part, but I would like to create a function that uses a variable as an optional parameter: var = 2; f[a_:var] := {a} The ...
1answer
139 views

How can I define a function taking two distinguishable sets of options?

It commonly happens that one wants to define some function foo which in turn calls some other function (e.g., Plot) that can ...
0answers
151 views

How to insert a function into OptionsPattern?

I’ve written a function TableauForm to draw a standard Young Tableau. This problem is related to this one, however, the difficulty is that, a function has to be applied to the list in my case. This ...
1answer
1k 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 ...
6answers
642 views

Constructing symbol definitions for With

I would like to be able to define two arrays, one containing symbol names and one containing the values of those symbols, for use in constructs such as With. For ...
4answers
549 views

Recurrence relation in a table

I am trying to generate a list of x-values for a function using a module, where my x-value must increase by 'a' if the term ...