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32
votes
2answers
1k views

Memoization with pure functions?

Is this possible? If I have a simple function, say: f=If[#>0,1,2]& then for each value of # this will re-evaluate f right? Is it possible to define a ...
27
votes
2answers
2k views

What are the cool kids talking about when they use ##&[]? [duplicate]

All the cool kids are apparently using ##&[] for Unevaluated @ Sequence[] but I have no idea what either means. ...
21
votes
2answers
808 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 ...
17
votes
2answers
463 views

Using several anonymous functions mixed together

This works: list // BarChart[#[[2]], ChartLabels -> DateString @@@ #[[1]], ChartStyle -> "Pastel"] & This doesn't: ...
15
votes
2answers
293 views

What are Root objects with multiple polynomials?

In Mathematica 9 a new flavor of Root object with multiple polynomials was introduced. For example, ...
13
votes
2answers
1k views

What happens when you divide by ##?

I've been playing around with sequences a bit. In particular with using ## with unary and binary operators. Let's start simple, the following all make some kind of ...
12
votes
4answers
940 views

Second level depth pure function?

I have the following working construction: Select[ln125, # == Nearest[ln125, 551.748][[1]] &] Here, ln125 is a one ...
12
votes
1answer
296 views

Pure function with attributes of arbitrary number of arguments: Is it possible?

Mathematica allows to define pure function, like Function[{a, b},Length[Unevaluated@a]{b}][1+2,2+3] (* ==> {0} *) Pure functions in Mathematica can take an ...
12
votes
3answers
218 views

Using Through to evaluate complex expressions

Suppose we're given the expression f*g+h, where f,g,h are all pure functions. How can we evaluate this expression on some ...
10
votes
1answer
291 views

Why does the documentation call functions “pure”?

Clearly, functions in mathematica are not pure functions according to the definition on Wikipedia (no side effects - basically implementabe with table lookups): ...
10
votes
1answer
136 views

What are the scoping rules for function parameters shadowing System` symbols?

Here are some very contrived code snippets, highly unlikely to appear in real code, but still I am curious why they behave like this: ...
8
votes
3answers
338 views

Operate over list of pure functions

I have list of pure functions (All functions are InterpolatingFunction) i.e {{a, b}, {c, d}, {e, f}, ...} and I would like ...
8
votes
3answers
355 views

Have I found a big difference between using the short form and the long form of a pure function?

By referring to the Mathematica documentation, I learned to use ##2 to represent all the arguments but the first one. This is a brief way to represent a pattern ...
8
votes
1answer
286 views

Mma10 mystery: Failure of pure function substitution with Interpretation?

Bug introduced in 10.0.0 and fixed in 10.0.1 I had code to display with subscripts from Displaying index as subscript on output: e.g. C[i] -> C_i with Notation[...] or Interpretation[..]? which ...
7
votes
2answers
649 views

How to programmatically covert a function-like rule to a pure function?

Is there a programmatic way to convert a Mathematica rule that acts like a typical mathematical function of one variable into the equivalent pure function? For example, the code should convert ...
7
votes
3answers
349 views

Functional equivalent of a For loop referring to consecutive elements in a list

I have implemented this function which smooths the values in a list by, if it encounters a zero, replacing this entry by the average of its two neighbours (apart from the first and last values of the ...
5
votes
3answers
279 views

How to use multiple pure functions correctly?

I have used Mathematica for two years.And usually,I can use single pure function(#&) rightly.However,for the use of multiple pure function,I always make all ...
5
votes
1answer
195 views

How can I make a “self-referential” replacement operation self-contained?

Fairly often I find use for replacement rules that call themselves on the right-hand side of the rule, e.g.: ...
5
votes
4answers
142 views

Syntax for Table with a pure function

I have: g = #1^2 + a #2^3 / #1 & Now I wish to make a Table evaluating this from 1 ...
5
votes
1answer
208 views

How to use Compile to efficiently apply a function to every element of a list

Let's say I have a list of random numbers; list = Table[Random[], {100000}]; I want to apply a function f in every element of ...
5
votes
1answer
538 views

nested use of Apply/Map/MapThread in pure functions

1. My main question I have a function with two argument slots. I wan't to apply this function to 2 lists with different length's. I thought in this solution: ...
5
votes
3answers
281 views

Multiply list of pure functions by list of scalars?

I am trying to write a function that returns a list of pure functions. The last step in the function, is to multiply the list of pure functions by a list of scalars (i.e. matrix multiplication). When ...
5
votes
0answers
82 views

Third syntax version of LogitModelFit: unexpected result of “BestFit”

The third listed syntax version of LogitModelFit allows one to specify input in a simple way: Only a design matrix (with a row of values of the explanatory input ...
4
votes
2answers
194 views

Multiplying expressions within a list of pure functions

Let's say I have a list of pure functions that are nice algebraic expressions: say l = {(#1 - 1)&, (#1^2 + #1)&, (#1^3 - 1)&} What's an easy way to ...
4
votes
0answers
45 views

Wrong autogenerated package from notebook containing #key and Part as subscript

Bug introduced in 10.0.0 and persisting through 10.1.0 or later Mathematica v10.1.0, under Windows 8.1 x64 Mathematica v10.0.2, under Windows 1) Define a function in an initialization cell: ...
3
votes
5answers
1k views

Find the slope between adjacent points in a list

I have a list of two dimensional points that are ordered by their x-coordinate. I would like to calculate the slope between all adjacent points. I'm familiar with the use of pure functions in Sort ...
3
votes
3answers
381 views

How to exchange two arguments?

Recently, I have being using Mathematica to write my undergraduate paper. I want to use two pattern lists such as { A -> a, B -> b, c -> C, ....} and ...
3
votes
4answers
157 views

Correct slot assignment when mapping from different lists using pure function

Given expr = u == a1 + a2 x + a3 y; and uRep = {u1, u2, u3}; xyRep = {{x1, y1}, {x2, y2}, {x3, y3}}; I'd like to generate ...
3
votes
2answers
160 views

Generating a list of pure variables

I want to pass a list of pure variables to a function, in which the ordering of the variables matters. For instance, if I want a palindrome, my function might be: ...
3
votes
5answers
184 views

Algebraic expressions on pure functions

I would like to know how to perform algebraic operations with pure functions. Simple version: Here's a silly toy model: I want to transform the algebraic expression Sin*Cos into the function ...
3
votes
2answers
97 views

Conflict with variables in pure functions

Consider the following snippet of code. Clear[f, g] f[x_] := Function[{i}, x]; g[h_] := Module[{Z}, Z[i_] := Print[h]; Print[h]; Z[1]; ]; When ...
3
votes
1answer
110 views

Recursion when randomizing elements in a list

I want to randomize certain elements of a list; Since the code list = {a, b, c, d, e, f, g}; list[[{1, 3, 5}]] = RandomSample@list[[{1, 3, 5}]]; list works fine, ...
3
votes
1answer
111 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 ...
2
votes
2answers
189 views

Using DeleteCases and Map together

Given: list1 = {{"a",1},{"b",2},{"c",3}} I would like to delete any pair in list1 that does not have a first element that belongs to list2. Example 1: If ...
2
votes
3answers
101 views

How to make a symbolic vector into a pure function?

As part of a set of functions to implement a steepest descent algorithm I created my own n dimensional gradient function. It is defined as follows: ...
2
votes
1answer
72 views

Why is Chop ignored in Plot?

I want to plot multiple functions with the same settings side-by-side, so I use the pure function construct (for clarity, I only use one function in this example) ...
2
votes
1answer
82 views

Need to run evaluation 2 times

Why does this only work after running the evaluation 2 times? ...
2
votes
1answer
74 views

Use of parenthesis and pure function

I had read that when using a pure-function it was a good general practice to enclose the function and the associated ampersand in parenthesis. (#^2 &)[a] I ...
2
votes
1answer
516 views

Why is either Listable or HoldFirst not working?

Starting with a fresh kernel, I evaluate the following: ...
2
votes
1answer
54 views

Expressing a definite integral as pure function with the upper-bound as it argument

Suppose i have an integral which has a closed form, $\quad \quad \int_{a}^{b} f(x) dx=F(a,b)$ I want to use output function $F$ as a pure function, like ...
2
votes
1answer
77 views

Patterns for destructuring “Function” function arguments

I want to define a function for finding a Jacobian matrix of pure vector function of vector argument. I try ...
1
vote
4answers
224 views

How to find all symbols in an expression and perform an operation on them?

========== motivation =========== Suppose, for example, I have an incoming expression like m = (3-I)x + 4(x y)/(Cos[y]) I want to find all the symbols in ...
1
vote
4answers
139 views

Pure function, one slot refers to List-position

I used all my google-fu trying to find how to make this work; read the docs as well. What have I missed? I feel sure this can't be a new question, but I can't find anything Here is is: ...
1
vote
1answer
97 views

How to input pure function to package?

I would like to input a pure function into a custom written package, but am running into a variety of errors. The package I have created is as follows: ...
1
vote
1answer
63 views

How-to implement iteration over a result of an iteration in a functional way

I have a pure function f:= #1 * #2 * #3 &; Which I can invoke in a following way: f[#,2,3]& /@ {1,2,3} Which ...
1
vote
1answer
108 views

What is happening in Map[Function[x, x^2], a + b + c] from the Pure Function tutorial

The Pure Function tutorial gives an example: Map[Function[x, x^2], a + b + c]. I would expect the output to be (a + b + c)^2, ...
1
vote
2answers
147 views

`Slot` (#) interfering with evaluation

In the following I am using one function makeFunc to assemble two functions a[t] and b[t] to ...
1
vote
2answers
83 views

How to construct a new list made from a function that operates on two lists

I need to take two lists (each list contains the number of moles of a chemical). I have a function calledFraction that takes the each entry of the list and then calculates the mole fraction of ...
1
vote
2answers
310 views

How do I create matrices with arbitrary list restrictions?

I want to randomly generate a square matrix of dimension n with entries in the list StartingEntries, and also satisfying that for any such matrix M, the matrix Inverse[IdentityMatrix[n] - M] has ...