Questions about the use of built-in Mathematica functions, including pure functions.

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8
votes
3answers
600 views

Why are functions called first-class objects in Mathematica?

I've heard lots of people say a function is a first-class object in Mathematica. "Everything is an expression, including function." "There is no distinction between functions and data." Having read ...
4
votes
3answers
547 views

Simplify function notation

I have some calculations with arbitrary functions. In the output, Mathematica always shows the functions with its arguments. I would like to tidy the notation a bit, by hiding the arguments in the ...
8
votes
8answers
666 views

Finding maximum or minimum of implicit functions

is there any built in function that can be used to find maximum or minimum of implicit functions? For example, if we have the equation $$x^2 + y^2 = (2 x^2 + 2 y^2 - x)^2,$$ then we can visualize the ...
11
votes
1answer
267 views

Overloading second argument of CountryData

For convenience I'm trying to add an extra property to CountryData ...
10
votes
4answers
685 views

How to find the domain and range of an implicit function?

For example, we have this curve: $$ x^2 + y^2 = 1 $$ Is there a function in Mathematica for finding out that the ranges for $x$ and $y$ are both [-1, 1]? What ...
1
vote
2answers
105 views

Define the square of a function [closed]

Is there any good way to define the square of a function in M9? Usually one can write e.g. f[z_] = 3*Sin[z] etc etc. But is it possible to define ...
2
votes
2answers
76 views

Funny behavior of Ellipsoid function

From its description I thought that the normalizations of the directions d_i of the semi-axes did not matter when using the ...
-1
votes
3answers
116 views

Creating Do loop that cycles back to earlier values

I need to create a Do loop that distributes letters in a list of lists. I also need to be able to cycle back through to the beginning of the list. For example, I ...
0
votes
0answers
93 views

Which functions automatically generate new functions?

In his video http://www.wolfram.com/broadcast/video.php?channel=362&video=1643, Wolfram gives the following example: the output from ...
0
votes
1answer
64 views

Laplacian in D Dimensions

Is it possible to compute $\Delta F=\nabla^2 F$ for $F=F(x^1,x^2,…,x^D)$ with $D$ finite? I seem to be only able to specify spherical coorindates, for example, if I want to leave standard ...
13
votes
4answers
397 views

How to make a function with its own options as well as passing options to other functions [duplicate]

I have a function with many of its own options, but I would also like to pass options to subfunctions using the FilterRules function. Here's a simple example: ...
0
votes
1answer
61 views

Cannot solve equation

I just started using mathematica and I'm facing a problem that I just can't solve. I want to solve the following equation: Code: ...
1
vote
1answer
96 views

How can I define a function that takes a list of reals?

I'm trying to define a function f which takes a list of reals. My purpose is to build a function which I can give a list of reals, integers or strings and have it ...
0
votes
2answers
84 views

Defining a function as a sum of several Gaussians

I have a function that is a summation of several Gaussians. Working with a 1D Gaussian here, there are 3 variables for each Gaussian: A, ...
0
votes
0answers
79 views

Problem With NDsolve trying to simulate n-body-gravity problem

Im Trying to model a cloud of point masses that act according to gravity, what im strugeling with is the exclusion of cases where euclidian distance = 0, If I try to do it with an If statement in my ...
2
votes
3answers
246 views

Tracking iterations of a function

I'm learning MMA with Wagner's book. On page 41, he uses this to display the iterative steps of a FindRoot. However, I can't seem to replicate this (code at end), perhaps due to the difference in MMA ...
6
votes
1answer
265 views
0
votes
3answers
88 views

Create polynomials from Series

This question actually doesn't have quite a lot to do with the Series function, but I don't know how to describe my problem. So here's the thing. I'm trying to ...
0
votes
1answer
58 views

Integrating function can't be epressed? [closed]

Hi I have a function in a form of $$\frac{a}{x}exp(\frac{b}{\sqrt{3}-x})$$ The code is Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}] But it can't work ...
9
votes
3answers
2k views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
2
votes
1answer
91 views

Define function that counts recursive fibonacci

If I write count=0; fib[0]:=(count=count+1; 0); fib[1]:=(count=count+1; 1); fib[n_] := (count = count+1; fib[n-2] + fib[n-1]); Then I can ...
2
votes
4answers
305 views

How to completely delete the head of a function expression

Is there any way to completely remove the head of an expression function? For example, how would I remove the head Cos from ...
1
vote
0answers
61 views

Expression for evaluating multiple functions?

I am constructing 3D data points for a plot and corresponding to specific conditions "manually". I define the values of five parameters [these I always have to define myself]. From those, I evaluate ...
4
votes
3answers
187 views

Counting number of inversions

Is there an inbuilt method to find the number of inversions in a set of numbers? I found Inversions in Combinatorica but when I ...
0
votes
1answer
42 views

Switching the ordinate and abscissa causes problem in `ParametricPlot`

I have a function that plots properly in PolarPlot, but I'd like to plot it in ParametricPlot and then switch the y and x ...
0
votes
1answer
86 views

Getting “Null” output from package?

I have a script written to test a package as follows: ...
0
votes
1answer
71 views

Is there a way to make the MemberQ function apply to a list?

Is there any way to ask a boolean question if the elements of the list {2,5} are in the list {1,2,3,4,5}?
0
votes
1answer
61 views

How I can define a new function as a function argument?

I need to pass a function with t as independent variable as a function parameter and want to create a new function of the same through this provided the argument of another function. Here is my code. ...
2
votes
3answers
301 views

find connectivity

Imagine a chain of 20 rings, labeled by 1-20 sequentially. We want to make random size sets of numbers randomly chosen from these 1-20 rings. No duplicate numbers are allowed. Example of a set: ...
0
votes
2answers
168 views

How to pass a list as function argument?

I have the following function lFreqPhylo[a_, Q_, b_, p_] := Sum[Log[freqFunction[r[[p]][[i]], L[[p]][[i]], a, Q, b, {i, 1, nbranches[[p]]}]; The objects L, r ...
1
vote
0answers
51 views

How to find matrix exponential using RootSum?

From what I've been able to deduce, Mathematica uses a root sum scheme to determine the exponential of a matrix. Can someone please explain to me the theory behind this? I've searched, but have had no ...
2
votes
2answers
174 views

Restarting an Animate animation after variable in Manipulate changes

I've been trying to restart an animation after variables change from Manipulate PopUpMenus. My animation takes the form: ...
6
votes
0answers
144 views

Finding hidden treasure (aka finding undocumented functions) [duplicate]

I was searching for a way to determine if a point is within a polygon and stumbled upon rm -rf's answer. (actually, I really wanted to find a point within a ...
0
votes
1answer
66 views

Apply function to output of previous function

I am trying to write a function that takes 3 tuples. Each tuple contains two lists which are first divided. This results in 3 lists. Then I want to take the Mean of all the columns. I can do this ...
2
votes
1answer
75 views

Can Do-Loops iterate backward? [closed]

If I create a Do statement, Do[expr, {i, imin, imax}] is there a way to make the statement evaluate from ...
0
votes
1answer
48 views

ToExpression and Fortran notation

ToExpression["9.0E-03"] interprets String as 9*e - 3 instead of what I am expecting ...
1
vote
1answer
103 views

What is the formula Mathematica uses for ZetaZero?

What is the formula/algorithm Mathematica uses for the ZetaZero command?
0
votes
1answer
123 views

Discrete peaks to curve via Voigt summation

I have two data sets. One is an experimental recording of an absorption spectrum, composed of regularly spaced (wavenumber, intensity) coordinates with a fine wavenumber resolution, thus making ...
2
votes
2answers
82 views

Graphical solution of a a two-variable system containing an equation and an inequality

I'm currently studying atmospheric-gravity waves and their dispersion relations. I want to have look at values of $(x,y)$ that solve the following system : \begin{equation}\label{}(1) \left\{ ...
0
votes
1answer
52 views

Inverse functions - how are they calculated?

Mathematica is able to calculate InverseFunction[LogIntegral] and InverseFunction[RiemannR] (and many other inverse functions). ...
1
vote
1answer
47 views

VertexSize with GraphPlot [closed]

I'm constructing a graph using GraphPlot and I want some vertices to have a different size than others, like this: ...
1
vote
0answers
67 views

Find eigenvalues without filling the matrix

Is it possible to find eigenvalues of a matrix without filling it? The matrix elements are given by a known function f[p1,p2]. This is relevant for a matrix too ...
1
vote
1answer
49 views

Get subgraphs: communities of graph g

I have a graph g. I want a set of graphs c which holds the community subgraphs of g. I ...
3
votes
0answers
78 views

Why does Part behave like it transposes lists? [closed]

From the documentation of Part: Part[expr,i,j,...] is equivalent to expr[[i]][[j]]... ...
2
votes
1answer
73 views

Why evaluation doesn't fail if arguments are invalid? [duplicate]

Sorry for a noob question, but this is something that I wonder about each time I work with Mathematica. Coming from standard programming languages (Python and Java), I expect my functions to fail ...
1
vote
1answer
76 views

How to study the sign of an expression including a function, with conditions on the function?

I'm trying to study the sign of an expression, having information on some of my parameters. I don't know how to code these conditions. For example, I want to know when this expression: ...
0
votes
1answer
57 views

function of derivative of a function

I know a similar question is answered somewhere, but it doesn't work for my case for some reason. I have the following problem in Mathematica. I want to compute f[h[x]]= x^2 + D[h[x],x]. Here, h[x] ...
1
vote
1answer
70 views

Sort lists of vertices {indegrees, outdegrees} by indegree

in = VertexInDegree[F]; out = VertexOutDegree[F]; I want both in and out to be ordered by in. Example: graph has nodes a,b,c with indegrees 1,2,0 and outdegrees ...
0
votes
1answer
36 views

Defining arbitrary order derivatives function [duplicate]

I have a function $\phi(t)$ and I want to define a function $\phi D(t,r):=\phi^{(r)}(t)$, in other words evaluate the $r$'th derivative of $\phi$ at $t$. The naive code that I have is: ...