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# Questions tagged [function-construction]

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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### How to make a custom Echo

I usually check my intermediate variable by Echo.Like Table[Echo@x, {x, 10}] But when the intermediate variable have too much ...
2k views

### How does a Pringle lose its curvature?

Nom! As part of a bigger project, I've was writing some code to calculate the scalar curvature of surfaces of the form $z = f(x,y)$. This uses a general calculation of the scalar curvature to produce ...
232 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. ...
4k views

### Recursive function with if-statement

I am trying to represent the following function definition in Mathematica: \begin{align*} f(1)&=1 \\ f(2n)&= \begin{cases}f(n) & \text{if}\space n\equiv0\pmod{2} \\ 2f(n) & \text{if}...
603 views

### Optional argument that can be completely omitted?

I am writing a simple function return similar words. Clear[similarWords] similarWords[string_]:=Nearest[WordList[],string] I want to add another argument ...
2k views

### Building a Noisy Function

Here's a nice function with a nice plot: f[t_] := Exp[-Abs[t]] Sin[t]; Plot[f[t], {t, -10, 10}, PlotRange -> All] What I would like to do is to make it noisy.....
3k 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 ...
441 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: ...
787 views

### How to pass a list of arguments into HoldAll

I have a list of arguments (which in reality is lengthy): arguments = {a, b, c} arguments2 = {a_, b_, c_} f[Sequence@@arguments2] := a + b + c Note: It seems ...
281 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 ...
713 views

### How to check the validity of an option value

I have a user-defined function, func, which takes the following form: func[arg1, arg2, options] Here is the actual code ...
459 views

### Equivalent Nested Loop Structure

Consider the following examples: ...
181 views

### Is it possible to set multiple type to a variable?

Consider this f[x_Real] := 2 x f f f[1.0] 2.0 I want ...
1k views

### How to plot a barycentric line

I want to plot a barycentric function on an equilateral triangle (ternary plot). For example f1 = {Abs[Sin[x]], Mod[x, 2], Abs[Cos[x]]}; At the moment I evaluate ...
830 views

### Safe way to put a pattern on the right hand side of a rule

I'm interested in creating a function or rule that generates its own set of rules. For instance, it would take as an input the expression h[m, n] and the indices <...
310 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] ...
310 views

### Implement settable properties

I am looking for advice on implementing the following. (It is possible that the answer is that it is simply not a good idea to do this.) I would like to have an object similar to ...
211 views

### Set Attributes -> Orderless for only some variables in a function? [duplicate]

I have the following function: ...
399 views

### Is there a concise form of Which or similar conditional?

Suppose that I want to write a function fun that takes an Integer num as input, and returns <...
1k views

### Number of sign flips in list?

Given a list of signs: list={1,1,-1,1,-1,-1,1,1,1,-1}; how to most conveniently and quickly determine the number of sign flips in the sequence? I have this ad-...
1k views

### Number of digits for factorial of 12345678987654321

What is the number of digits (IntegerLength) of the factorial of 12 345 678 987 654 321? The number of zeros at the end of this factorial was calculated and it is huge: exactly 3 086 419 746 913 569 ...
675 views

This function finds n given the nth prime: findPrime[n_] := If[PrimeQ[n], i = 1; While[Prime[i] < n, i = i + 1]; i, False]; This works: ...
542 views

### Where in the documentation can I find a list of function argument types?

Recently, I learned that it is possible to assign "types" to function arguments in the definition of a function. Suppose I have a function stringFun that does some ...
4k views

### Gram-Schmidt Process for Polynomials

I want to implement the Gram Schimdt procedure to the vector space of polynomials of degree up to 5, i.e. I want to find an orthogonal basis from the set of vectors $v=(1,x,x^2,x^3,x^4,x^5)$. The ...
145 views

### Left-associative Apply

Often I want a version of @ that is left-associative (might not be using that term correctly). What I mean is I'd like some operator ...
260 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 ...
555 views

### How to set a TraditionalForm output for a symbol

How do I set a TraditionalForm output for a particular symbol/function? In particular I would like my user-defined symbol ...
404 views

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512 views

### How to get the parameter number of inbuilt function

I want to make a custom function parameterNumber,which can return the parameter number of inbuilt function,as the Plot's ...
537 views

### Using predefined expressions as free variables in a pure function [duplicate]

I want to have a function value of an expression where some variables are solutions to some set of equations, with some values of parameters. I had an idea to use pure functions for that. However, ...
1k views

### Reverse Polish Notation

Is there a way to evaluate a string containing RPN in Mathematica? SE thinks this question is too short, so let me expand on it. Do you know of any function, that provides the following functionality?...
474 views

### How to build private function with built-in function's option

Since this code work well: ...
239 views

### Simplifying a reverse Fold for a Query

Is there a simpler way to parametrize this tail-recursive expression to be applied as a Query (for processing a nested ...
193 views

### Is there a built-in function to inverse Thread?

Namely, while Thread @ f[{a, b}, {x, y}] gives {f[a, x], f[b, y]} the InverseThread (if it existed) should reverse the ...
557 views

### Inheriting Options?

This question is an extension of Passing down arguments. To help clarify my question, I will be referring to another recent post of mine Making Quartile Plots from a Dataset, the code to which can ...
176 views

### Syntax information for pure functions

Mathematica's help on SyntaxInformation does not rule out syntax information for pure functions. SyntaxInformation[f] gives information used to generate syntax coloring and other advisories when f[…...
476 views

### Combining pure functions

Is there an easy way to combine pure functions into a single pure function? For example, say I have f = #1^2 &; g = #1 - 2 &; and I want to define a new ...
236 views

### Copy Built-in function to new name

It is know that some built-in functions are system function and changing their properties may cause trouble. Suppose for example I want to change features of Cases: ...
300 views

### can a ColorFunction have side effects?

Can anyone explain this (to me) odd behavior. If I run this code once (fresh kernel) it works as intended. ...
909 views

### How to construct the RHS of Wick's theorem

I've been trying this for a few days now, but I just can't seem to find an efficient (speed-wise) functional way to code the following task. Context: I would like to construct an expressions that is ...
333 views

### Fine tuning compiled code that computes dilogarithm function

As an exercise in writing a good Compile function, I want to do the simple task of coding a routine that outputs the real part of the dilogarithm function ...
413 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: ...
719 views

### intersection between two 2D arrays with labeled data is slow

Here is how to Generate data the function is below with two images to generate data img1 img2 ...
752 views

### Functions that remember their values

Can someone explain what is going on with the following ... func[y_] := func[y] = (Print["Hello world !!!"];) func Hello world !!! ...
452 views

### How to exit from the innermost enclosing pure function?

Here is what I tried to do: Scan[Function[x, Scan[Function[y, If[y == 2, Return[]]; (* Do something useful *) Print[y]], x]], {{1, 2, 3}, {4, 5, 6}}] ...
401 views

### Combinations of multiple matching patterns

I wonder if there is any nice way to combine DownValues (or any other suitable rule-/pattern-/function -based Mathematica construct) when multiple patterns match an expression. Let me explain what I ...
417 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 ...
6k views

### How to define a polynomial/function from an array of coefficients?

I have the coefficients of my desired polynomial in an array CoefArr (I'm new to mathematica, so I think of everything as arrays, it is actually a list I believe) starting with the constant at index 1....