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0
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2answers
56 views

How to make a density plot with composed functions [closed]

I want to create a monochromatic density plot of the E-field around an optical vortex. To do this I've written ...
0
votes
1answer
87 views

What does the expression “Total[funca[a,#] & /@ #] & /@ {x,y}” possibly mean?

Can the expression be simplified as "Total[funca[a,#]] & /@ {x,y}"? What does the double of "& /@" mean? Where can I find some reference? Updated According to Mr.Wizard's answer, I now know ...
10
votes
1answer
240 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): ...
0
votes
1answer
97 views

Why is `B /. h -> #2 &` not a pure function?

I am trying to plot the energy surface of the mean field Ising model, but I am running into a problem with setting the MeshFunctions for the plot. ...
8
votes
3answers
311 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 ...
0
votes
0answers
41 views

How can I mix // with a function of two arguments? [duplicate]

I often find myself using // when playing around with expressions, but it is always cumbersome to have to switch to the full notation just to apply a function of ...
5
votes
4answers
125 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 ...
3
votes
5answers
157 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 ...
5
votes
1answer
188 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.: ...
2
votes
1answer
190 views

Why is either Listable or HoldFirst not working?

Starting with a fresh kernel, I evaluate the following: ...
8
votes
1answer
275 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 ...
1
vote
1answer
48 views

How can I change the scoping of a pure function returned by a function in a package?

I have written a small Mathematica package that contains a module that solves some differential equation with initial conditions. Suppose that the solution to this differential equation defines some ...
5
votes
3answers
246 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 ...
1
vote
4answers
193 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 ...
3
votes
4answers
146 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 ...
2
votes
1answer
62 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) ...
1
vote
1answer
92 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 ...
5
votes
0answers
75 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 ...
0
votes
1answer
86 views

Define a function that returns a function with a variable number of arguments

Previously, I've defined a function with a variable number of arguments with the following method. ...
3
votes
3answers
361 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 ...
1
vote
1answer
97 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
124 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
1answer
93 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: ...
0
votes
1answer
119 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...
0
votes
1answer
80 views

Can I make a function which depends on several arguments which are not independent?

Here's a simple example Suppose have the permanent relation that z is proportional to xy^2, for real numbers s. z = s x y^2 Now, we are interested in ...
3
votes
1answer
104 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, ...
2
votes
1answer
81 views

Need to run evaluation 2 times

Why does this only work after running the evaluation 2 times? ...
0
votes
1answer
87 views

Pure function in Nest

I can't figure out what I'm doing wrong here: Table[Nest[# + 0.1 * -i * #^2 &, 2, 1] , {i, 0, 0.5, 0.1}] (* {2., 1.96, 1.92, 1.88, 1.84, 1.8} *) The problem ...
5
votes
1answer
192 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 ...
1
vote
0answers
119 views

Defining an operator

Let s be a positive integer and let DifferenceDelta be this function with step = 1. Define ...
1
vote
1answer
118 views

Defining a function of a distribution

I have a discrete- time and space markov process that I want to evolve given an initial distribution. To that, I defined ...
0
votes
1answer
220 views

How to combine two usages of # into one and speed up the code?

I have a function num with two variables, matf and matg. How can I combine the last two lines of code below into one? The code is aimed to find out the maxiaml count bel when we give each $i3 = ...
0
votes
2answers
270 views

How combine pure functions of several slots? [duplicate]

How can one define in a functional way a 1st-order linear differential operator involving several independent variables that can then be applied to a function of that many variables? Consider an ...
1
vote
2answers
273 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 ...
3
votes
1answer
106 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 ...
3
votes
5answers
847 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 ...
21
votes
2answers
677 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 ...
9
votes
1answer
236 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 ...
-5
votes
1answer
229 views

Split dataset based on the first column [duplicate]

I have a dataset which I want to split based on the first column. The data looks like this ...
4
votes
2answers
160 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 ...
11
votes
3answers
193 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 ...
0
votes
3answers
96 views

How can I generate a generalized product to two lists in a special way? [duplicate]

Let's say I have two lists, and I'd like to generate a "cartesian product" from these two. Specifically Inputs: A = {{{1}}, {{2}}, {{1}, {2}}}; B = {8, 9}; ...
9
votes
1answer
128 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
291 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 ...
-1
votes
1answer
243 views

How to define a pure function with a Module?

I was not able to use a self defined (using Module and For loops) piecewise function to fit data. It seems that the problem is that I have to define a pure function. I would like to learn how to ...
15
votes
2answers
249 views

What are Root objects with multiple polynomials?

In Mathematica 9 a new flavor of Root object with multiple polynomials was introduced. For example, ...
3
votes
2answers
136 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: ...
5
votes
1answer
441 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: ...
1
vote
2answers
79 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 ...