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

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0answers
33 views

Analog of GeneratingFunction for Newton series [duplicate]

GeneratingFunction gives the generating function for Maclauren series. I wonder if there a similar function for Newton series. If $$g(x)=\sum_{k=0}^{\infty}\frac{x^k}{k!}f(k)$$ Then g(x) is ...
23
votes
3answers
1k views

Visualisation of a recursive function

Is there a way to nicely visualize recursive functions? (diagrams/plots) More specifically I'm looking for a way to make contrast (visually) between e.g. the cosine function which if continuously ...
8
votes
2answers
202 views

Is there a way to revert to the built-in function after overwritting it using Unprotect

When using Unprotect, we can overwrite a functions definition: Unprotect[Sqrt] Sqrt[x_]="blahblah" Protect[Sqrt] Once this is done, can we revert to the built-in ...
14
votes
3answers
2k views

Fitting ellipse to 5 given points on the plane

Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ...
5
votes
5answers
259 views

Replacing columns of a matrix with zeros

I am to create a function that replaces columns 'm' through till 'n' with zeros. Here is what I have so far: ...
3
votes
1answer
149 views

How do I format Compile[] correctly?

My Mathematica skill is still rusty, so kindly bear with me. I'm having problem formatting expression to compile the function correctly: $\sum _{g=1}^G \sum ...
2
votes
3answers
143 views

Function to Expand exponentials

Is there a function similar to PowerExpand which expand exponentials? This would, for example, take Exp[5(a + b)] and ...
6
votes
5answers
1k views

Find function inverse

I'm trying to find the inverse of a function: (30*x^2 (1 - x)^2) (* where 0<x<1 *) I tried all the following options: 1. ...
6
votes
2answers
412 views

Modifying parameters: Set::setps in the part assignment is not a symbol [duplicate]

Ok, this will probably be a silly question, but I can't get my head around it. I'm making a simple module that, given a list and two integers, will swap the position of the elements in the ...
2
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1answer
95 views

JordanDecomposition in Mathematica

I'm trying to find the Jordan Decomposition in Mathematica for $$ A=\left( \begin{matrix} 2& -5& 8&-12\\ 1& -2& 4&-8\\ 0&0&2&-5\\ 0&0&1&-2 \end{matrix} ...
70
votes
2answers
3k views

Flatten command: matrix as second argument

One thing I could never wrap my head around is how Flatten works when provided with a matrix as the second argument, and the Mathematica help isn't particularly ...
1
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1answer
184 views

StreamPlot in Mathematica

A $2\times 2$ linear ODE system can be visualized by StreamPlot in Mathematica. For example: ...
3
votes
1answer
120 views

Ted's explanation for the 3rd argument of ListCorrelate doesn't apply to the {1, -1} case?

I was reading Ted Ersek's explanation for the usage of ListCorrelate(.nb version can be found here) and noticed something confusing. It's the third example of ...
14
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2answers
826 views

Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
38
votes
2answers
1k views

Why is the new PositionIndex horribly slow?

This issue has largely been mitigated in 10.0.1. New timings for the final test below are: ...
4
votes
0answers
230 views

Strange behaviour of MMA in derivatives of some standard functions

There are some peculiar things to be discovered in derivatives of some standard functions in MMA: Strange behaviour Example 1: Abs We have ...
1
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1answer
48 views

Strange behaviour of Set and Part when given a sequence

Consider this example: lis1 = {a, b, c}; lis1[[2]] = Sequence[e, f]; lis1 (*{a, e, f, c}*) lis1[[2]] (*e*) lis1[[2]] = Sequence[g, h]; lis1 (*{a, g, h, c}*) It ...
6
votes
2answers
312 views

Is there a built-in function which detects singularities in a function?

Given a function f[x] and a region M in the complex x-plane, how can I find singularities of f in this region, i.e., issue a ...
3
votes
0answers
152 views

Generating function for Newton series?

The function GeneratingFunction gives generating function for Taylor series. Is there a similar function for Newton's series? $$f(x) = \sum_{k=0}^\infty \binom{x}k \Delta^k [f]\left (0\right)$$
5
votes
2answers
162 views

Strange Behavior when making Equal Listable in Pick

While trying to make this problem more efficient I tried different methods and dabbled with making Greater and Equal ...
1
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1answer
97 views

How can I export numerical data in a calculation-favorable format?

I am exporting some data into the txt file but since the values exported to this txt file expresses 10^6 to be *^6, I cannot use these numbers in calculations in other programs.. For instance, when I ...
3
votes
2answers
114 views

Wrapping Interval Notation for Take

I'm trying to implement the solution to a math problem in Mathematica, but my code can't handle a particular boundary case. I think that I could implement a function that would do what I want it to, ...
0
votes
1answer
192 views

Finding real roots for an eigth-degree polynomial

The context for this problem is identical to my first question. Unfortunately my previous result for $L$ was inexact since it was a relatively simple approximation. This time I have managed to produce ...
7
votes
4answers
733 views

Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
3
votes
2answers
214 views

Get domain for a given function (including e.g. singularities)

I am new to Mathematica and this is probably a simple question, but I can't figure it out at the moment... f[x_]:=1/(x-3) Clearly the vertical asymptote is at ...
3
votes
2answers
251 views

What would be the inverse function for the following condition?

I tried the problem but i couldn't take above condition in question in terms of f(x)
4
votes
3answers
175 views

How to Nest a Function with three Arguments?

I have two functions with three arguments $f_x(a,b,t)$ and $f_y(a,b,t)$. And i need a nesting like this ...
6
votes
4answers
2k views

Use Mathematica to calculate the area enclosed between two curves

use mathematica Hence, calculate the exact area enclosed by these curves using Mathematica. $f(x)=x^3$ and $g(x)=x^5 - 2 x^3 - 3 x$ i have got the graph...now I'm stuck with finding the area
11
votes
4answers
554 views

Set of integers not divisible by smaller set of primes

Let $p_n$ be the sequence of prime numbers, and $s(x,n)=$ the set of integers less or equal than $x$ that are not divisible by $p_1,\dots,p_n.$ I can define it as follows: ...
10
votes
5answers
580 views

What is my problem with MeshFunction?

I want plot the max value in a sine plot. We can use the following code ...
12
votes
4answers
1k views

How do I plot Thomae's function in Mathematica?

I wanted to plot this function $$f(x) =\begin{cases} 1 & \text{if } x= 0 \\ \tfrac1{q} & \text{if } x = \tfrac{p}{q}\\ 0 & \text{if } x \in \mathbb{R}-\mathbb{Q} ...
9
votes
2answers
901 views

Can you apply the Cellular Automata function to a grid containing numbers?

Im attempting to simulate a simple evacuation model using cellular automata theory.My study aims to determine whether Cellular Automata can effectively represent how people would behave in a fire ...
18
votes
5answers
8k views

How to find the domain and range of a function with Mathematica?

I'm studying calculus and in some exercises I am asked to find the domain and range of a function. Does Mathematica have already a built-in function for this? I can imagine some ways of doing so, ...
1
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1answer
96 views

Attaching functions to movable locators

I'm trying to create a manipulate plot showing the electric field due to a collection of point charges. At the moment I've created such a plot which allows the x and y positions of each charge to be ...
12
votes
2answers
262 views

Why isn't Lookup treated like other symbols?

With Mathematica 10, I wanted to overload Lookup using TagSetDelayed, but it doesn't work. For instance, if I define two objects ...
1
vote
1answer
151 views

How to apply a tensor to a list of arguments

The problem I have is the following: Let C be a list of coordinates, say, C = {x1, x2, ..., xn} and ...
2
votes
1answer
196 views

RegionPlot3D run forever when plotting 3D ParametricRegion

when working with 2D, RegionPlot works fine with ParametricRegion as can be seen in this example: ...
1
vote
2answers
138 views

How to define logical expressions for platonic solids?

A more general question would be: How to find logical expressions for 3D-objects described by closed polygon sets? Finally a simple question is more prolific, therefore: How to define logical ...
3
votes
5answers
408 views

How to add periodicity to condition?

Is it possible to set the following function f[a], where a can be any real number? $$ f(\alpha) = \begin{cases} 1 ...
0
votes
2answers
425 views

$RecursionLimit::reclim: Recursion problem

Please, find bellow my original question. Here is all my code: ...
2
votes
1answer
275 views

Finding average error of the data

Considering I have some data, and I want to fit the data to a linear fit and find the average error from the linear fit, how can I do that using Mathematica? I have ...
0
votes
0answers
39 views

How to prevent function from substituting the part of the parameter name if it has a subscript? [duplicate]

I have the following problem, when defining and using a function, that's supposed to have an outside parameter xmin: A[x_] := Exp[-x/Subscript[x, min]] A[5] ...
5
votes
1answer
201 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
0answers
186 views

How do I choose only one branch of ArcTan?

I have a problem concerning ArcTan drawing a graph using ListPlot. I import a table of data: ...
3
votes
0answers
64 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
2
votes
1answer
108 views

How to explain the behavior of Rule inside these functions [duplicate]

I'm trying to define a function that takes an expression and spits out a pure function involving a replacement rule of that function's variable. An example would be a function ...
0
votes
0answers
30 views

Use FindRoot solution as number in function [duplicate]

I would like to save a number that I gain with FindRoot so that I can use it in another function. I tried: ...
1
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1answer
800 views
2
votes
1answer
201 views

Finding the minimum of a function

I asked this question Mark Minimum Value in DensityPlot. Another question has come up, or better said, a task: Find the minimum of a function. I haven't been able to write the needed code for that, ...