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

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0
votes
1answer
52 views

Does Mathematica always return a rational number in its simplified form? [closed]

If I enter: 1/RandomInteger[10^200]+1/RandomInteger[10^200] I get (instantly) an exact fraction. Is this fraction in simplified (reduced) form? In other words is ...
0
votes
1answer
50 views

FindRoot over a function with some constant variables

I would like to perform the FindRoot command over the function func. Suppose: ...
7
votes
2answers
648 views

How to programmatically covert a function-like rule to a pure function?

Is there a programmatic way to convert a Mathematica rule that acts like a typical mathematical function of one variable into the equivalent pure function? For example, the code should convert ...
2
votes
1answer
50 views

How do I make Mathematica nest argument changes?

I want something like Nest[f,x,n], but what where f is an argument change like a pushforward and x[t] is a function, for example, symbolically, and not in any sort of code: $$ F{x[t]} \equiv x[2t + ...
1
vote
1answer
109 views

Quantum Physics question [closed]

I'm not sure if anyone here would be able to help me. But if you know a more appropriate place where I could ask for help, please let me know. So here's the question: And here's my attempt at ...
3
votes
1answer
83 views

Why is left NumberPadding always applied in NumberForm?

I would like to display numbers like 9.0001 and 10.0001 in the fixed-width form of xx.xxxx. ...
17
votes
2answers
312 views

Why doesn't a Composition[] hold its arguments and what can be done about it?

Now that Composition (also RightComposition) has shorthand syntax I am more inclined to use it, however what I feel should be ...
14
votes
1answer
197 views

Why won't SparseArray let me store values with the head List?

When you attempt to define a SparseArray with elements that have the head List it complains: ...
5
votes
1answer
127 views

Why do functions defined with SetDelayed and Function behave differently in callbacks?

It seems to me that functions defined using a simple pattern and SetDelayed (the usual way to define a "function") should be equivalent in all respects to functions ...
0
votes
0answers
37 views

How can I get the covariance result cumulatively?

I am trying to derive the covariance results for n x 4 matrix where n is an arbitrary number. I am trying to derive the covariance for each row cumulatively. For example, I am trying to derive the ...
-2
votes
1answer
76 views

plot sum of two function

I am trying to illustrate sum of functions. I have one function x*x - 8*x + 7 and another Log[2*x + 4.5] I understand that I ...
6
votes
2answers
181 views

Built in function without Attributes Listable works as if it has Attributes Listable

Can Built-in function works as if it has Attributes Listable even if it doesn't have that ...
1
vote
4answers
73 views

NestWhileList, control to show the second sequence

For example,each number will end up with 89 or 1, however , How can I generate a sequence with two sub sequence. f[n_] := IntegerDigits[n]^2 // Total One sub ...
17
votes
2answers
1k views

Sum or Product with Exclusions

Is there a built-in feature for handling things like: $$\sum_{\substack{i=0\\i\ne j}}^n\frac{a-a_i}{a_i-a_j}$$ and $$\prod_{\substack{i=0\\i\ne j}}^n\frac{a-a_i}{a_i-a_j}$$ or should I work out some ...
3
votes
1answer
163 views

Creating the Nabla operator as a operator

How can I define the nabla-operator as a an operator, acting on everything to the right of the operator! Also taking \[Del]^2 would give the second derivivates. I wish to be able to write ...
1
vote
1answer
51 views

little problem of Thread, List head of second argument

Thread[f[{a, b, c}, 0]] (* {f[a,0],f[b,0],f[c,0]} *) Thread[f[{a, b, c}, pp[0]]] (* {f[a,pp[0]],f[b,pp[0]],f[c,pp[0]]} *) Howerver, the head of pp ...
2
votes
3answers
115 views

Finding minimum of a list of pairs

Sometimes I need to find the Min of a list, whose elements are lists (say of two elements, a pair). Given that Min does not have the option to indicate a sorting function like Sort, I elaborated the ...
1
vote
1answer
51 views

Changing Function Domain of Fourier Series

If I write FourierSinSeries[x, x, 10] Mathematica will output the first 10 terms of the Fourier Sine Series f(x) = x defined for 0 < x < Pi. How do I output the the Fourier Sine Series for ...
12
votes
1answer
322 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 ...
6
votes
3answers
239 views

How to build a matrix from a set of vectors and other matrices using ArrayFlatten

I want to build a 6 by 3 matrix, from the following: one vector is 3 by 1, then a matrix, which is 3 by 2. These will go to the top 3 rows. Now the bottom 3 rows, I'll have 3 vectors each is 3 by 1. ...
2
votes
2answers
170 views

Plotting difference between a function and its inverse function

I would like to plot the difference a function and its inverse function. (1/27)*(x^4-6x^3+12x^2+19x) (* where 0<x<5 *) I tried the following: ...
90
votes
8answers
8k views

List of compilable functions

Is there somewhere a list on the functions that Compile can compile, or the cases in which a particular function can be compiled that I haven't found? I'd be glad ...
1
vote
1answer
48 views

Function taking arbitrary number of arguments

I have a very similar function to that which a solution was provided by kguler, but am unsure as to how to adapt the solution that was given there. That post can be seen here. The adaptation is only ...
3
votes
1answer
98 views

Listable on first level [duplicate]

I have some function which take List as input. f[l_List]:=someActions[l] I need apply this function to a list of lists. Now I ...
1
vote
1answer
90 views

How to find and verify relationships between functions?

MMa gave me a complicated result involving Hypergeometric0F1's. It was much less complicated after I discovered this identity: ...
0
votes
1answer
43 views

Calling a function on a variable with parameters [duplicate]

I have an equation that contains parameters. I want to use it in a function like NDSolve, but I can't seem to figure out how to do so. Here's an example: I define ...
1
vote
0answers
86 views

Incorrect output from InverseFourierTransform

Bug introduced in 8.0.4 or earlier and fixed in 9.0.1 or earlier I am trying to compute the inverse Fourier transform of this expression ...
0
votes
1answer
53 views

Permanently fixing a variable in the function

I need to define a function let's say f[x_, y_] := x^2 + y^2 such that I need to fix one variable (let's take y = a) and to ...
0
votes
2answers
60 views

Supply a function as an argument to another, and find its minimum

I would like to minimize a function, which is supplied as an argument to another function, and report back the estimates of the values of the variables that result in its minimum. In specific, I would ...
18
votes
3answers
738 views

Can someone explain this snippet: (#[#] &)[#[#][#] &]

A friend showed me this snippet of code today: (#[#] &)[#[#][#] &] I can sort of see that we're constructing an anonymous function that takes a function ...
1
vote
1answer
143 views

General function taking general number of arguments

The following is an edit of this post, for which a working solution was provided by John McGee. I have a different function and am not sure how to adapt the solution for it: I want to construct a ...
6
votes
1answer
234 views

How trustworthy is NMaximize?

Suppose I solve a constrained optimisation problem using NMaximize. How confident can I be of the accuracy of the result? For concreteness, suppose that F,G are ...
0
votes
2answers
69 views

Function that creates a table from two lists

I have two lists shown below: list1 = {(0,0,0,0),(0,0,0,1),(0,0,1,0),...,(1,1,1,1)} list2 = {1,5,5,5,...,5} How can I construct a function that outputs a table similar to this: $$\begin{array}{c|c} ...
0
votes
1answer
94 views

Help with functions in Mathematica

Still learning how to do things in Mathematica. I want to make a function that has many parts. Doing this in something such as Java, which I am familiar with, would be simple. In Mathematica I have ...
-1
votes
1answer
221 views

Find minimum function value in data and give coordinates of minimum

I create with Table an array containing the function value of some function and the n1and ...
0
votes
2answers
56 views

Fitting data in form $f = f_0 + c A^x$

The Fit[] function in Mathematica can fit data in form of $f = f_0+c_1x+c_2x^2+...$ ($f_0$ and $c_i$ are unknown constants), is there a function can fit date in ...
0
votes
2answers
90 views

Is there a function that filter positive values x = f(x), and return zero for all negative values? [closed]

I'm searching for f that will comply this definition : x = f(x) where x is natural >= 0 0 = f(x) where x is natural < 0
0
votes
1answer
76 views

How to create a line due to requiriements?

Considering we have three lines, and know the intersection points (How to find intersection points of lines?) How can I draw a line that will cross the intersection point of the two lines and will be ...
1
vote
3answers
371 views

How to find intersection points of lines?

Considering I have three functions f1 = -x + 1; f2 = x - 1; f3 = x + 3; How can I find the intersection points of this functions? Thanks. This didn't work ...
0
votes
0answers
65 views

What is the product of 1+1/p^2 over all primes p? [duplicate]

Can Mathematica Sum or Multiply over the set of all primes? I can get an estimate of my question in the title with: ...
4
votes
3answers
240 views

Problem about an ant walking up a hill

An ant is walking up a hill given by $f(x)$. At what point can it see a blade of grass. I've been working on this problem with Mathematica and by hand. Help with either would be fantastic. The ...
1
vote
1answer
55 views

Using Inner to calculate a log likelihood

I am trying to use the function Inner to calculate the sum of log likelihoods of a custom probability distribution 'custom' applied to a vector of data 'vData'. The custom distribution changes ...
-2
votes
2answers
92 views

Plotting self-made functions [closed]

EDITED AS SUGGESTED I have defined a function, which takes two values and returns a function n(x), like so ...
0
votes
1answer
40 views

Summation of functions

I want to define a function that is a sum of other functions. For this, I define functions of the form ...
2
votes
1answer
93 views

Dirichlet convolution of two lists [closed]

The Dirichlet convolution of two arithmetic functions f,g is defined by $f*g(n) = Sum_{d|n} f(d)*g(n/d)$ How can I get the Dirichlet convolution of two lists? For example: Input: ...
0
votes
1answer
41 views

How to set a shared variable Power (a modified one)?

Unprotect[Power]; Power[0|0., 0|0.] = 1 ; Protect[Power]; Table[0^0, {i, 5}] No problem at all. ParallelTable[0^0, {i, 5}] ...
0
votes
0answers
59 views

subtlety of self-defined function and its evaluation [duplicate]

I wrote a simple code as follows f[x_,y_]:=NIntegrate[x+z,{z,0,1}]; g[x_,y_]:=NIntegrate[y+z,{z,0,1}]; VectorPlot[{f[x,y],g[x,y]},{x,0,1},{y,0,1}] then ...
0
votes
1answer
64 views

Mathematica function to generate a different 4 digit number [closed]

I m looking for a function that permit me to generate a different 4 digit number (>0) each time (to 4^10 possibilities) corresponding to a parameter that will never be the same (like current ...
16
votes
7answers
597 views

Enumerating tuples from a larger space such that all pairs of values are present at least once

I am trying to write a function that will accept a list of N lists and returns a list of N-tuples that represent all pairs of values from the original N lists at least once. To illustrate with an ...