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

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6
votes
1answer
263 views

Shortest polygonal path

I'd like to find the shortest distance between some points (every point must be visited), such as between these 3 points: ...
5
votes
0answers
197 views

Strange Integrate behavior (a bug!)

The following two calculations should give the same result. After all, integration is a linear operation. I have pasted the code below in case you want to play with it. ...
0
votes
0answers
61 views

mathematica function autocomplete issue [duplicate]

This is the default function structure prompt from Mathematica 9 This is my own function module ...
4
votes
1answer
1k views

Integral of Lorentzian yields different results depending on when parameter assigments are made

I'm evaluating the integral of a Lorentzian, which I know equals one. First I define the function and evaluate the integral in two slightly different ways. Surprisingly, I do not get the right answer ...
1
vote
0answers
78 views

Decapitating “explicit” and “implicit” heads

This is a follow up to this question. So far, I named "explicit" heads to those that appear explicitly in the expression. For example, f[x] has an explicit head. I ...
13
votes
3answers
2k views

Difference between @ and @@

I am confused by the commands @ and @@. From the documentation, I learnt that @@ is the ...
15
votes
5answers
445 views

Partitioning a list of numbers the Mathematica way

I have two sorted lists, one list will be called the "fences" and the other the "values" Fences could be: $\{1, 5, 9, 14\}$ Values could be $\{-1, 1, 3, 4, 6, 9, 10, 13, 14, 15\}$ I want to ...
2
votes
1answer
99 views

What is the need for function parameters? Many possible inputs

If I have many possible variables related to one another, why do I need to define my function with parameters for plotting? For example, if I have an equation like: ...
1
vote
1answer
227 views

using a Mathematica function to define a new function

I'd like to define a function of three variables which produces a new, named function of a single variable, where this final variable is not a member of the first three. So I'd like something where I ...
2
votes
1answer
91 views

Behavior of ValueQ inside a function

The following code Cases[Function[{x}, x + 1], a_?ValueQ :> Hold[a], ∞, Heads -> True] unexpectedly returns {Hold[x + 1]} According to the manual, ...
1
vote
1answer
153 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 ...
3
votes
1answer
207 views

The UnitStep function and Intervals

For the input UnitStep[Interval[{-4, 5}]] I get Interval[{0, 1}] Why is this not ...
-5
votes
1answer
90 views

Converting function into differential version

I am looking through a journal and I came across a function that I wanted to convert to its differential version using Mathematica. Would anyone be able to get the differential version by using ...
5
votes
1answer
195 views

Reverse engineer a sample value from a CDF

The image below shows the cumulative distribution of a normal distribution with mean = 4 and standard deviation = 1. Notice that if you have a value with a rank of 0.8 (meaning it would be 80th item ...
2
votes
2answers
437 views

Are there Min and Max functions that work properly on Intervals?

Mathematica overloads the Min and Max functions to retrieve the lower and upper bounds of an interval. I need functions that ...
7
votes
1answer
302 views

Understanding FullForm in front end

I want to understand the following effect better (In Mathematica 9) .. Or, maybe, is it a bug? Running the following line FullForm[Subscript[α,β_]] gives as ...
18
votes
1answer
789 views

Two ways of map a function on the list: Which one is faster?

There are 2 ways to make a function listable on the list: Use Map or use SetAttributes. My question is, which one is faster, ...
1
vote
1answer
154 views

DSolve bvfail “For some branches of the general solution, unable to solve the conditions”

I have a problem with the DSolve function and its usage: ...
0
votes
0answers
95 views

creating some smooth density functions

I would like to create some density functions based on some distance measure $D$. As a base density function lets say I have a Gaussian density $f$ with mean $-1$ and variance $1$. I would like to ...
6
votes
1answer
259 views

Iteration process involving several functions

I would like to carry out a following iteration process: Apply function f1[a_,b_,c_,d_] to a starting list l1={a1,b1,c1,d1}, ...
5
votes
1answer
125 views

Why DateDifference returns machine number?

Is there any specific reason why DateDifference cannot give an exact number in this case? ...
2
votes
1answer
123 views

Function to differentiate between date pattern and specific string format

I'd like to write a function that behaves one way when the argument is a Mathematica date, such as {2013,12,15}, or with added hours, minutes and seconds if ...
3
votes
2answers
334 views

Selecting for 2D points that are within a threshold distance of an upper- and lower-bound number of points

I have a very large set of 2D points: numberOf2DPoints = 10^6; pointList = RandomReal[{0, 1000}, {numberOf2DPoints, 2}]; I'd like to find a way to quickly ...
1
vote
1answer
211 views

Passing a joined list of symbols for Module or Block to treat as its own local symbols

The Question I'd like to write a function which itself takes a list of symbols, e.g. Foo[{x, y, z}] to pass to Module ...
6
votes
1answer
506 views

How to express an expression with only ArcTan and ArcTanh?

I have an expression which is simply (j/k) x^(j/k) LerchPhi[x,1,j/k)] where 0 < j < k. Manually I have been able ...
6
votes
1answer
184 views

The third argument of the Root function

Consider the roots of an arbitrary indecomposable polynomial: sol = Solve[x^5 + 2 x + 1 == 0, x] The returned expression is ...
0
votes
1answer
96 views

Is there any automatic method for rating function arguments importance?

If I have a function: y = 2a + 5b + c It can be easily seen that b is the most important parameter, next ...
0
votes
1answer
100 views

Stop function evaluating input at time of definition [duplicate]

I would like to create a function that acts on whether the input is even or odd, e.g.: In[644]:= f[a_] = If[EvenQ[a], 2 a, 3 a]; f[2] Out[645]= 6 I've ...
3
votes
2answers
315 views

Generation function of recurrence sequence

I'm trying to find generation function of recurrence sequence ...
8
votes
1answer
138 views

Strange behaviour of Internal`InheritedBlock

I was going to post an answer for fast way to replace all zeros in the matrix. I was even quite happy because timings were the same order of magnitude as others. The idea was to overwrite ...
5
votes
2answers
424 views

Random Matrix with integer coefficients and inverse also having integer coefficients

I'm trying to build a function that gives me matrices such that each: Has integer coefficients. Is non singular. Has inverse which also has integer coefficients. I have some code that one of my ...
4
votes
3answers
2k views

ArcTan[z] and ArcTan[x,y], Restriction and Conversion

In Mathematica there are two different forms for the arctangent (inverse tangent), namely ArcTan[x,y] which gives the arc tangent of $y/x$, taking into account ...
1
vote
0answers
37 views

Pattern matching list elements in pure functions [duplicate]

Pattern matching here is a functional programming term, but it might be called differently in Mathematica, I'm not sure. It is possible to match the elements of the list in a regular function ...
13
votes
1answer
366 views

Is everything in Mathematica ultimately stored as a rule?

My current understanding about Mathematica is that everything, at the lowest level, ends up as replacement rules. First question: is this true? Second question: does Mathematica "gloss over" these ...
5
votes
2answers
163 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
vote
1answer
139 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 ...
1
vote
1answer
238 views

Split Lingustic(IPA) at Words Unique Sounds

How might I split a word at each IPA of each unique sound. For example {"pray", "wade"} (* {{"p","r","ˈeɪ"}, {"w","ˈeɪ","d"}} *) ssch answered a question here ...
12
votes
4answers
356 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
150 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 ...
1
vote
2answers
2k 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
224 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 ...
2
votes
2answers
172 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
158 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 ...
5
votes
0answers
87 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 ...
0
votes
4answers
75 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
227 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
242 views

function returning 0

Why is my function returning 0? ...
1
vote
1answer
94 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
94 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. ...
7
votes
0answers
168 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 ...