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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9
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1answer
139 views

Is it possible to use the global definition of a symbol as part of its new local definition set in a Block?

Consider the following expression: Block[{Print = CopyToClipboard}, doSomething[]] Now all calls to Print from ...
9
votes
1answer
111 views

Maximizing a recursive functional equation

I would like to maximize a recursive functional equation but I am struggling with setting up the problem correctly. The equation I am interested in captures the nature of a decision process over time ...
9
votes
1answer
176 views

Finding large prime gaps

I am using basic searches for prime gaps as follows: ...
9
votes
1answer
144 views

Why there is only `HoldFirst` but no `HoldSecond`, `HoldThird`, …`HoldN`?

I feel that this must be a duplicate. But I just can't find such a post. Mathematica has HoldFirst, HoldRest, ...
9
votes
2answers
211 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 ...
8
votes
4answers
2k views

Turn expression into function

I'm new to Mathematica and I spent the last hour trying to make the expression ...
8
votes
4answers
230 views

How to inject unevaluated list of Unique into a RuleDelayed?

I am writing a function that constructs a rule which has Unique[] in the RHS. Here is a simplified segment of code ...
8
votes
2answers
547 views

Generating a position lookup function for an arbitrary list of integers

In my code, I generate a list of integers called numlist. Here is an example numlist: ...
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 ...
8
votes
2answers
279 views

Composition of functions using slots

Apolgies if this has been asked and answered, but I'm not even sure what to search for. I have two functions defined as follows: ...
8
votes
2answers
3k 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 ...
8
votes
2answers
144 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 ...
8
votes
4answers
193 views

Identify the independent variable in an expression [duplicate]

Suppose that you write something like this for your students. This is just the beginning of something I would like to write to help them with the formal definition of a limit, but I am puzzled by the ...
8
votes
2answers
231 views

Error computing sum of sum of digits

I've defined a function that computes the sum of the base-b digits of n: DigitSum[n_, b_] := Total[IntegerDigits[n, b]] Then I defined a function that computes ...
8
votes
2answers
291 views

Automatically compute r[1] = r1; r[2] = r2; …

I have three variables like this, r1 = 4; r2 = 3; r3 = 1; and I want to insert them into a function use them in a function definition like so: ...
8
votes
3answers
279 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 ...
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
2answers
630 views

Mapping data on Archimedes' spiral

I would like to map my data on Archimedes' spiral and preserve the distance between points on the curve. The test data consists of 20 evenly spaced {x,y} ...
8
votes
2answers
168 views

Possible to scope an anonymous function within Module?

This is my first question. I'm fairly new to Mathematica and completely new to SE, so I apologize if this question is trivial. I'm working on a problem that requires a function to be redefined ...
8
votes
2answers
148 views

using memoization with conditional statement

I would like some advice about the use of memoization in conjunction with conditional statements. Let me try to explain my problem: I am constructing a function depending on a number of parameters. ...
8
votes
1answer
83 views

How to make `D` apply chain rule on user-defined symbols as it does on `Dot` and `NonCommutativeMultiply`

I have my own version of Dot called mydot, and it behaves quite similar to the built-in version in that it represents the ...
8
votes
3answers
132 views

Defining a custom Plus for a specific class of arguments

I'm trying to develop an domain-specific language with Mathematica. I want to define a customized behavior for the Plus function when applied to my data. For ...
8
votes
1answer
157 views

Is it possible to write a function immune to symbol redefinitions in any Block surrounding its invocation?

Normally, semantics of symbols used in a function definition can be changed by their redefinitions in Blocks surrounding the function invocation: ...
8
votes
1answer
116 views

Maximum number of literal values for SetDelayed?

Under what circumstances should I expect Mathematica to turn a delayed assignment into an immediate assignment? I have put together a minimal example (available here) which demonstrates this behavior. ...
8
votes
1answer
320 views

Two identical functions give different answers

I am new to mathematica and I hope this is a simple problem. I have two identical functions that only differ by the variable names: ...
7
votes
7answers
627 views

Can my color function be written more simply?

The code shown below works well, but I think the pure function I'm supplying to the ColorFunction option could be more elegant. How can I simplify it? ...
7
votes
3answers
236 views

Generating date ranges

How can I, in one line, generate all the dates with a constant day difference from one date to another? For example, if I'm interested in dates in the interval staring from 24.4.2012 till 2015 and a ...
7
votes
3answers
178 views

Localising OptionValues

The documentation on OptionsPattern leaves me with some unanswered questions. From the example section: ...
7
votes
3answers
459 views

Composition of mappings not working as expected

I have two functions $f,g:\mathbb{R}^2 \to \mathbb{R}^2$ and I define a third one $h:\mathbb{R}^2 \to \mathbb{R}^2$ as the composition $$h(x,y) = g(f(x,y))$$ I'm trying to get this function into ...
7
votes
5answers
250 views

How to write an operator that acts on pure function (to give another pure function)

I would like to write an operator oper that acts on a pure function f with an undetermined number of arguments, with the syntax ...
7
votes
3answers
2k views

Simulate MATLAB's meshgrid function

Here is MATLAB's meshgrid. I came up with these implementations in Mathematica: ...
7
votes
2answers
554 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 ...
7
votes
4answers
581 views

How can I shorten this code to rotate a line segment around its center?

I have a list of line segments stored in the form: { {{x11,y11},{x12,y12}} , {{x21,y21},{x22,y22}} , ... , {{xn1,yn1},{xn2,yn2}} } Now I want to rotate all of ...
7
votes
3answers
848 views

Composition of functions

I have a number of rotations computed by rot = RotationTransform[theta, point], and I would like to compose them to produce one function that is the composition of ...
7
votes
4answers
96 views

Problem with handling a factor of $1$ in pattern matching

I am trying to implement the creation and annihilation operators $\hat{a}$ and $\hat{a}^{\dagger}$ of quantum mechanics with the following code, but alas, there is a problem with the pattern matching ...
7
votes
4answers
2k views

“do … while” loop equivalent in Mathematica [closed]

Have I missed something or is there no built-in which mimics the behaviour of do ... while loop? I am looking for a construct that evaluates procedure once and ...
7
votes
1answer
355 views

How can I define a function that can accumulate its parameter?

For example, write a function add: add[3] return 3 add[4] return 7 add[10] return 17
7
votes
5answers
158 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 ...
7
votes
3answers
563 views

Problems using hand-made transformation functions

I experience difficulties when using custom transformation rules. Below I give two concrete problems. I am interested in fixing each of them and in understanding what is wrong with my attitude to the ...
7
votes
1answer
126 views

Can one specify a “computed optional value”?

I would like to write a function with an optional argument, which if absent should not be a default value, but rather a computed value. What I mean is the following [warning this code does not work, ...
7
votes
3answers
272 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 ...
7
votes
2answers
220 views

How to correct this, `f[a_] := FindRoot[eq == 0, {x, 0.5}]`, where `eq` contains a parameter $a$, without using `eq[a]`?

I want to solve an equation with a parameter $a$, and define the result as a function of $a$. It is something like this: ...
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 ...
7
votes
2answers
4k views

Building matrices by attaching vectors (columns) and matrices

Having the need to attach a column to a matrix or to join matrices to make longer rows is an operation that I use very frequently and I find the Join function ideal ...
7
votes
2answers
185 views

Account for powers of 0 and 1 when defining function

I have a function that I am defining as (assume m,n,a,b are non-negative integers): myfcn[x_^m_ p_^n_, x_^a_ p_^b_] := basefcn[m, n, a, b]; and then extending to ...
7
votes
3answers
169 views

Checking through an expression

I am writing a code that manipulates expressions that contains functions with an arbitrary number of arguments. An example expression is ...
7
votes
3answers
77 views

TagSetDelayed on a function with a delayed value

I'm trying to automatically optimize cases when the user evaluates Length[returnsList[x_]] to instead use returnsLength: ...
7
votes
1answer
174 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 ...
7
votes
2answers
156 views

Change some option of a function when calling it [duplicate]

Say I have defined some function like f[p_] := Plot[Sin[p*x], {x, 0, 2 Pi}] Now in most cases, I just need to specify the value of ...
7
votes
1answer
231 views

FullDefinition and Module local variable

I have a question about FullDefinition and how it interacts with the local variables of Module. I've created a few functions ...