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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7
votes
2answers
605 views

Define a function with a function for an input

I want to create the functions $even[f]$ and $odd[f]$ which will apply the formula $even[f(x)] = \frac{f(x)+f(-x)}{2}$ and $odd[f(x)]=\frac{f(x)-f(-x)}{2}$ for an arbitrary $f$. I tried using ...
6
votes
2answers
573 views

Passing unquoted strings (poor man's enumeration)

I would like to be able to pass an unquoted string as a parameter to a Mathematica function [that I am writing] and have it show up without evaluation if the string happens to be defined. Thus I would ...
4
votes
1answer
211 views

How can I overload a function with multiple bracket-slots so f[a][b] and f[a] can coexist?

Maybe this is not even possible: I want to create a function f that can have two input brackets like: f[a_][b_:1]:= a*b and ...
3
votes
3answers
3k views

Passing a matrix as a function argument

I am trying to do the following: ...
2
votes
1answer
310 views

Finding average error of the data

Considering I have some data, and I want to fit the data to a linear fit and find the average error from the linear fit, how can I do that using Mathematica? I have ...
0
votes
1answer
157 views

iterative programming

i have 3 equations with 3 variables and two constants(to be substituted repeatedly). the value of the variables we got by applying nsolve on the system of 3 equations assuming some initial value for ...
0
votes
1answer
380 views

Function to marginalize a table over given parameters

Let us say I have generated a table tab with entries {p1,..,pd,chi2[p1,..,pd]} of dimension ...
9
votes
1answer
264 views

How to define function that can change patterns

Given time series data as follows: data = {{{2011, 1, 13}, 10}, {{2011, 2, 14}, 17}, {{2011, 3, 15}, 20}, {{2012, 1, 16}, 30}, {{2012, 2, 17}, 40}}; ...
6
votes
2answers
110 views

How to define a complicated function inside the body of Compile?

I want to compile a function in a way to keep its memory footprint down. In the example below, I am trying to compile a function f that makes three calls to ...
3
votes
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 ...
3
votes
3answers
595 views

Generating pairs of additive and multiplicative factors for integers

Given an integer $n$, I want to get two lists: a) the set of pairs of the divsors $a,b$ into exactly two factors $n=a\cdot b$, b) the set of pairs $a,b$ of two summands $n=a+b$. The code I ...
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: ...
2
votes
1answer
174 views

General function taking general number of arguments

The following is an edit of this post, for which a working solution was provided by John McGee. I have a different function and am not sure how to adapt the solution for it: I want to construct a ...
2
votes
3answers
105 views

Testing for a vector of reals [closed]

Suppose I define: RealVector[expr_]:=VectorQ[expr,NumberQ[#]&&Head[#]===Real)]; Then: ...
2
votes
1answer
161 views

Passing function as argument

I've been mucking around with passing functions as arguments to other functions and via trial and error seem to have something that works. I was wondering if someone could have a quick look at some ...
2
votes
1answer
196 views

Requiring NumericQ in Pure Function

Potential duplicate, but doesn't seem to solve my problem: Using patterns in pure functions I have a function that returns an InterpolatingFunction, and it works ...
2
votes
0answers
470 views

Generating a function which outputs possible chemical reactions

I want to make a list of chemical reactions and I write them down in a $\require{mhchem}\LaTeX$ format. They are of the following form $$NA_n^i+MB_m^j \rightarrow \hat NA_{\hat n}^{\hat i}+\hat ...
0
votes
1answer
98 views

How to calculate the pseudo-remainder and pseudo-quotient of two multivariate polynomials

I have fixed some code, but it always gives me errors. Can anybody tell me its right code? ...
0
votes
2answers
80 views

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

I have to evaluate the components of a 6x6 matrix $S$. This matrix depends upon the semi-axes of an ellipsoid $a1$, $a2$ and $a3$. For various specific cases (sphere, prolate spheroid, oblate ...
0
votes
1answer
136 views

A problem with set values

The following code is just an example to clearly explain my problem. Assume that : ...
0
votes
1answer
121 views

Defining functions from expressions of variable lengths

I have a list of symbols that I have defined using d = Table[Symbol["d" <> ToString[i]], {i, 1, n}] giving ...
19
votes
1answer
254 views

What is the difference between defining a function and specifying the type of argument, versus applying a test to that argument?

Say I want to create a function that evaluates differently based on what type of argument is given. I've found two ways of doing this, ...
17
votes
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 ...
9
votes
2answers
5k views

How to define a differential operator?

I have a linear differential operator, for instance, $L\left (\partial _{t} \right )=\partial _{tt} - 3\partial _{t} + 2$. I use it in 2 different ways: apply the operator to a function: $L\left ...
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 ...
16
votes
2answers
275 views

Clean and handy Options management/filtering

the case I want to be able to create a function with some default options but also without need to add full explicit list of options available for it. And then inside I want to be able to filter ...
9
votes
1answer
169 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: ...
22
votes
4answers
325 views

Is there a GraphicsPrimitiveQ (or a complete list of Heads of graphics primitives)?

For various reasons related to workflow associated with creating figures for journals, I am creating functions that will accept graphics primitives and a set of options and spit out a ...
14
votes
3answers
1k views

Passing down arguments

In R, one can use ... to pass arguments down to another function. For example ...
12
votes
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. ...
12
votes
2answers
1k views

NestList on a function of several arguments

I'd like to know if it is possible to use NestList on a regular function of several arguments, such as: ...
8
votes
3answers
296 views

Why these ways of defining a function with variable number of arguments fail?

First: I know about the correct way to define a function with variable number of arguments: Clear[f] f[s__] := Plus[s] f[1, 2, 3, 4] (* 10 *) BUT I ...
8
votes
1answer
1k views

Stereographic Projection

Say I want to represent points of the complex plane in the sphere $\Bbb S^2$ using stereographic projection. That is, the Riemann sphere: Specifically, it would be nice to be able to: Given the ...
8
votes
4answers
2k views

Force function to make assumptions about its input variables in Mathematica

I'm trying to force a Mathematica function to make an assumption about its input variables. In my case, I'm trying to define a function to return the pdf of a Gaussian. But let's use a simple toy ...
7
votes
2answers
184 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] ...
6
votes
2answers
173 views

Using a held option

Woud there be an elegant way to use a held option ? For example if I need to pass by reference several variables but I don't always need all of them, it can be useful. For example if I want to append ...
5
votes
2answers
266 views

Optimising coefficient finding functions

I'm seeking a generalisation to this question, where I am looking to list the coefficients (without repetition) to monomials of the form ...
5
votes
1answer
217 views

How to Override the Head of a Symbol

I was wondering if it is possible to override the head of symbols/operators. As a motivating example if I run: Then Ket will be returned. But lets say I want Bob to be returned instead of Ket. Is ...
15
votes
4answers
420 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: ...
13
votes
0answers
176 views

func::usage needs to be run twice? [duplicate]

There is an annoying problem that I can't figure out why it's happening. I have defined a usage for a my function tensorA: ...
10
votes
2answers
329 views

Manipulating OptionsPatterns[]

How do you combine OptionsPatterns? For example, I would like to have a function that can take both options that I specify, and options for all graphs: ...
7
votes
3answers
1k views

How do I designate arguments in a nested map?

Say I have two lists, list1 = {a, b, c} list2 = {x, y, z} and I want to map a function f over them to produce ...
7
votes
1answer
1k views

How to find the smallest root

I have a continuous, differentiable, monotonic, bounded function called F[t]. If t -> Infinity then ...
6
votes
3answers
251 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 ...
6
votes
2answers
306 views

How to write complex function definitions at run time?

(Posting as a self-answered question to share a technique I discovered) In a certain project, I have many function definitions in which all parameters should be optional and come with default values. ...
5
votes
2answers
167 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
3answers
207 views

How to re-parse (or re-map) character '.' to user-defined function

The default behavior of the character . between two non-numeric characters is to be interpreted as the infix of the Mathematica function ...
4
votes
2answers
497 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 ...
3
votes
2answers
157 views

How to deal with the condition that a function own many options?

Assming that I have a function myFunc which has some options. ...