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

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11
votes
4answers
278 views

Using With to scope over pure functions

Consider this example: given an option for a function func as "x" :> (a&), how can one assign different values to ...
1
vote
0answers
106 views

parameter NDSolve

the question I need to solve is: t x'[t] == -x[t] + y[t], t y'[t] == -5 t^2/x[t]^2 + x[t] - y[t], x[1] == 4, x[b] == 1 in order to solve the coupled ...
2
votes
2answers
365 views

Q-Function representation in Mathematica

I observed that there is no Q-function representation in Mathematica. The definition of Q-Function is: \begin{align} Q(x) &= \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-\frac{u^2}{2}}du \\ ...
3
votes
3answers
170 views

What is the formula for this numerical series?

I'm developing a questions game. My goal is that the score for each correct answer will increase as the user answers more questions. Initially there are 15 points for each correct answer. Every 4 ...
8
votes
0answers
133 views

Limit of sequence of functions behaving strange

I'm trying to determine the limit of the sequence of functions $$f_n(x)=\left(\frac{1}{\pi}\arctan(n x) + 1/2\right)^n. $$ I define ...
2
votes
2answers
163 views

Write 199319989756262759279209 = 5x + y, where x and y are integers

$\frac{199319989756262759279209}{5} $ = $ 3.9864\times 10^{22}$ according to Mathematica, but I would like to see this number exactly in decimal form (not in scientific notation). I'm attempting to ...
6
votes
2answers
104 views

Why is ToRadicals[] not able to handle all cases? Is there a workaround?

The documentation for the function ToRadicals says: ♦ There are some cases in which expressions involving radicals can in principle be given, but ...
1
vote
2answers
193 views

Heron's formula for area of a triangle [closed]

Use the first form of Heron's formula to give a function areah, which gives the area of a triangle. Test your answer on the isosceles triangle ...
5
votes
0answers
81 views

Is there something like MaxProcessorUsed?

For standard procedures it is easy to test if the implementation is better or worse than other by using Timing etc. It does not help us with creating ...
14
votes
1answer
271 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
0
votes
4answers
56 views

Don't understand why Do-loop index is not evaluated in Play expression

So here is some weird behavior: When I create a list inside a loop whose elements are Play functions, with arguments that depend on the counter, it is as if the counter is being stored symbolically, ...
0
votes
1answer
211 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 = ...
1
vote
1answer
179 views

function returning 0

Why is my function returning 0? ...
1
vote
1answer
82 views

Issues with creating functions [duplicate]

Sometimes when I try to create a function inside a function, Mathematica gives me a hard time. I usually just have to play around with the syntax until it gets something it "likes" but I really have ...
3
votes
1answer
66 views

What is the syntax to combine conditions and options? [duplicate]

How can a condition and an option be written on the RHS of a function? I.e. ...
6
votes
0answers
124 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 ...
5
votes
2answers
487 views

How to find the non-differentiable point(s) of a given continuous function?

For example, the non-differentiable point of the function $f(x)=|x|$ is at $x=0$. How to find the non-differentiable points of a continuous function that is defined numerically?
8
votes
3answers
365 views

Create sine function with random increase in phase

I am trying to simulate a signal that randomly increases its phase, so far I have tried two thing but neither worked. I usually use matlab but I want to learn some Mathematica so I thought I would try ...
0
votes
2answers
86 views

Summation limits [closed]

The Sum is a built-in function in Mathematica, so the summation limits must be assigned. What I need to know is how to use a value computed in a separate ...
1
vote
2answers
156 views

How to apply function f for each time value t, to each pixel from image, resulting in t images

I have a 2D array of complex values and I want to apply a function to every entry of the array, for every timepoint t in a list. I know how to apply my function to one entry for every time t in a ...
3
votes
1answer
166 views

Creating a function to simplify WolframAlpha query

When I can't remember an integral I usually just query wolfram and have it show steps. This was my naive attempt at trying to make a simpler function. ...
3
votes
0answers
73 views

Gather dependency on list order?

I get intrigued about Gather behavior on this post. I thought that Gather was invariant under list order? Here is the result I ...
2
votes
1answer
90 views

How to define a function of z[bar], etc

Using Displaying index as subscript on output: e.g. C[i] -> C_i with Notation[...] or Interpretation[..]? I have often ended up wanting to define functions of annotated variables to better match my ...
1
vote
2answers
225 views
5
votes
1answer
144 views

Why does MapIndexed return the index in a list?

MapIndex returns the index in a list instead of as shown in my revised example. I can work with it (or work around it), but what's the design concept? It seems ...
4
votes
1answer
114 views

How hide symbolic definition of a function?

How can the actual definition of a function be hidden from a user? I want the user of a notebook to be able to evaluate a real-valued function f of a real variable at any particular numeric input yet ...
4
votes
4answers
297 views

How to find the maximum of a function on a set of discrete points?

How to find the maximum of a function on a set of discrete points? For example, what is the best way to find the maximum of ...
4
votes
1answer
131 views

Simplifying polynomials in non-commutative variables

I would like to be able to simplify a polynomial in two non commuting variables, the desired result being that in every term one variable occurs to the left of the other variable. An example would be ...
5
votes
2answers
183 views

Obtaining the name of a variable as a string

Suppose that I have an arbitrary variable myVariable. Is there some function fun -- either built-in or one that I can define -- ...
0
votes
1answer
94 views

Nested function problem [closed]

I have trouble defining the following function in Mathematica sp[M_, u_] := 1/Sum[u^k M!/(M - k)!, {k, 0, M}] After defining it Mathematica displays an error. ...
15
votes
8answers
376 views

Is it possible to use RandomChoice to choose without other choices being evaluated?

I'm trying to do this: i1 = 1; i2 = 1; RandomChoice[{ (i1 = i1 + 1), (i1 = i1 - 1), (i2 = i1 + 1), (i2 = i2 - 1)}] In order to chose randomly which ...
0
votes
1answer
73 views

Log is not being evaluated inside Grid [closed]

My command is: Grid[{{N, logN!, N log N - N}, {10, Log[10!], 10 Log[10] - 10}}, Frame -> All] In the second row of the grid, the function ...
2
votes
2answers
475 views

How to enter an equation into FindFit?

I have the equation ...
0
votes
2answers
146 views

Apply a function to a matrix of vectors [closed]

I have a matrix containing on each position a pair of numbers $(a,b)$. I would like to compute the norm of each vector $(a,b)$ and keep the result in form of a matrix. So basically, I need to apply ...
1
vote
1answer
120 views

Using NMinimize Properly

I'd like to find the point on a Bezier curve that's closest to some other point. The tricky thing is that because Bezier curves can loop around, the distance function can have multiple local minima ...
2
votes
1answer
93 views

Why the EuclideanDistance of these 2 exact points generates the warning N::meprec?

The two points are: pts = {{1/4 (-1 - Sqrt[5]), Sqrt[5/8 - Sqrt[5]/8]}, {1/4 (-1 - Sqrt[5]), -Sqrt[5/8 - Sqrt[5]/8]}}; EuclideanDistance @@ pts ...
2
votes
2answers
72 views

How to make a function work on symbols in a specific context

Let us say we have two sets of symbols $(x, y, z)$ with the same names that live in two different contexts: ...
3
votes
3answers
201 views

How to find the numbers $a$, $b$, $c$, $d$ of the function?

I want to find four numbers $a$, $b$, $c$, $d$ of the function $f(x)= \dfrac{a x + b}{c x + d}$ satisfying the conditions $f(-6)=4$, $f(-5)=5$, $f(1)=3$ and $f(2)=2$. I tried ...
17
votes
1answer
174 views

How to get Cases to wrap results in an arbitrary head?

A number of functions provide for results to be wrapped in an arbitrary head. This is very important in cases where the results should not be evaluated. Take ...
0
votes
0answers
41 views

Phase Unwrap List Of Points: Implementing continuous phase/Arg function for List of Points [duplicate]

I am looking for a function to unwrap phase of a list of points as done here for the continuous case. I have the Re/Im data as my input and would like the unwrapped phase as the output. Does anyone ...
10
votes
5answers
443 views

How to find first list element that differs from average of N previous elements by more than a given amount?

Given a list of real numbers, I need to write a function that returns the value of the first element in the list that differs from the mean of the previous $N$ elements by greater than $P$ standard ...
9
votes
3answers
535 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 ...
3
votes
1answer
201 views

NestList with a list inside?

I'm new to Mathematica, and was looking for more efficient ways to implement the Do loop below. a, ...
1
vote
1answer
77 views

User-defined Distance Functions with extra parameters [duplicate]

The Nearest function accepts a customized distance function. For example, a simple case that works well is ...
1
vote
1answer
62 views

Why is a function I defined in a package not visible when I load the package? [duplicate]

I made a package containing some functions in the following way. ...
6
votes
2answers
206 views

Not FullDefinition for Save. MachineID not Protected?

Is there a way to set what symbols's definitions I do not want to store? Consider the following code: ...
1
vote
1answer
174 views

Map a function conditional on elements at multiple relative positions in a list

I figure this question has many solutions, and if an answer already exists it would be nice just to be referred to it. I need a function that 'maps' over my list and produces a list of equal length ...
0
votes
1answer
59 views

Errors in evalauting an expression

I have the following: Constants: b3b = 2; G = (1/eps^2); a1 = 3; a3 = 4; xc = 0.3; Functions: ...
7
votes
3answers
161 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 ...