Questions tagged [sets]
For questions pertaining to sets in the set-theoretical sense. Use "assignment" for questions about the use of the Mathematica functions Set or SetDelayed.
121
questions
2
votes
1
answer
104
views
1
vote
2
answers
100
views
How to make a list be skipped if it is an empty set when it is being iterated over
Could you give me some advice?
There is a box[a,b] in which the number and number of lists are randomly generated.
For example as follows.
...
- 220
1
vote
1
answer
120
views
Fixing code for a combinatorics problem
The problem I am solving is:
Determine all possible values of positive integer $n$, such that there are $n$ different $3$-element subsets $A_1,A_2,...,A_n$ of the set $\{1,2,...,n\}$, with $|A_i \cap ...
- 6,744
1
vote
1
answer
251
views
Enumeration of a sequence involving closure operators
Let us call a collection $\mathcal{F} \subseteq \mathcal{P}(X)$ special if it satisfies the following two conditions:
$\emptyset, X \in \mathcal{F}$
For all $U, V \in \mathcal{F}$, it holds that $U \...
- 75
5
votes
3
answers
201
views
How can I remove and keep the elements of this set?
I have a list
list = {{1, 3, 7, 1, 2, 1, 4, 7}, {6, 2, 7, 9, 4, 3, 6, 7}, {2, 8, 8, 2, 3, 2, 4, 6}, {5, 7, 7, 5, 2, 1, 2, 4}, {8, 10, 10, 8, 2, 1, 2, 4}}
Consider ...
- 527
3
votes
2
answers
125
views
How to create a GroupBy function that is better aligned with relational algebra?
I want a GroupBy function that behaves more in alignment with relational algebra principles.
I can get what I want if I do it in 2 steps:
Preparation:
...
- 918
4
votes
1
answer
142
views
Displaying Hasse diagram (directed edges in graph pointing upwards)
I use the following code to display a Hasse diagram of a graph.
...
- 1,596
8
votes
3
answers
188
views
How to do integer interval arithmetic?
How to calculate union, intersection and complement of integer intervals without actually generating all integers in the range and perform set-arithmetic (Union, <...
- 46.5k
1
vote
0
answers
35
views
Is there a nice way to deal with sets in an abstract/symbolic way?
For instance, if I wanted to
declare $A$ to be the set of all finite subsets of $\mathbb{Z}$, and
declare $B$ to be a set comprising all finite subsets of $\mathbb{Z^{-}}$, and then
declare $C$ to be ...
- 753
1
vote
1
answer
94
views
Speed up random set partition code
I have managed to construct code for randomly generating a set partition of size n with k parts. Note that the total number of such objects is counted by a Stirling number of the second kind.
The code ...
- 2,364
3
votes
1
answer
260
views
Enumeration of a certain sequence III
Let’s call a collection $\mathcal{F} \subseteq \mathcal{P}(X)$ satisfying:
$\emptyset, X \in \mathcal{F}$
For all $U, V \in \mathcal{F}$ it holds that $U \cap V \in \mathcal{F}$.
special.
We can ...
- 75
2
votes
1
answer
140
views
formations of union of sets
How do I get the formations generated by the union of sets?
Practical example
As an example of this calculation,if we denote the four sets:
...
- 732
3
votes
4
answers
304
views
Verifying a combination problem using subsets
The question is shown below. The handwritten answer is one of the methods of the mark scheme.
This method "seemed" ok, but we are not so convinced about the Total of 140 ways.
Also, there is ...
- 1,460
6
votes
3
answers
156
views
How to define variables $a$,$b$,$c$,$d$ are all elements of set $\{2,3,5,7\}$?
I would appreciate it if somebody could help me with the following problem:
I want to create a Wolfram Language expression that states that all $a$,$b$,$c$,$d$ variables are elements of the set $\{2,...
- 259
5
votes
2
answers
571
views
Maps between finite sets
With SageMath, one can do FiniteSetMaps(["a", "b"], [3, 4, 5]) to get all maps from {a,b} to ...
- 395
0
votes
0
answers
119
views
Global assumption non zero
I would like to define globally an assumption stating that I have a nonzero real vector $v$.
For now, I put :
$Assumptions = Element[v,Vectors[{100},Reals]]
but $v$ ...
- 592
4
votes
4
answers
686
views
How to generate Venn diagram from a universe and 3 random sets?
Given a universe u with random numbers between 1 and 50
and three sets a,b,c, that have random numbers
a between 3 and 30, b between 2 and 40 and c between 4 and 49
How can I represent the sets a, b ...
- 480
2
votes
2
answers
199
views
How can I subtract and calculate the complement of a pair of sets? [closed]
I cannot properly implement these operations. How can I do it?
This is a reduced example:
A={2,3,4}
B={2,4,6}
C={1,2,3,4}
Find
...
- 417
6
votes
1
answer
175
views
Can Solve[...] be used for set math? If so, how? If not, how else?
I'm a recreational user who loves using the product.
I'm looking for a strategy to solve the following question using Mathematica.
The question is from a sample actuarial exam. I can solve this with ...
- 83
3
votes
1
answer
140
views
Mathematica code for q-Stirling numbers
In the paper [A new $q$-Analog of Stirling Numbers],(https://hal.archives-ouvertes.fr/hal-01372920/document)[PDF] J. Cigler defined $q$-Stirling numbers of the second
kind as the following:
He ...
- 143
0
votes
1
answer
60
views
Part of array as a blank variable [duplicate]
I have a little question.
Let me define the function:
f[k_]:=k
So 'k' in the argument of 'f' is a blank variable.
Is there a way to define a part of array as a ...
7
votes
1
answer
137
views
What Does Compile`SetIterate Do?
The list of compilable functions (given by Compile`CompilerFunctions[] // Sort) shows one of the more interesting- and core-sounding functions: ...
- 1,597
3
votes
2
answers
235
views
How to draw 3D sets in Mathematica given inqualities
I would like to draw a 3D set ($E$) given the following conditions:
$E=\{(x, y, z)\in\mathbb R^3: x, y, z \in [0, 1], x+2y-1\leq z\}$
I have seen in the Mathematica documentation that there are ...
1
vote
3
answers
70
views
How to ask Mathematica to do the given operation for a set of parameters?
I have a set of numbers like this
s = {a, b, c, d, e, f, ..., g, h}
and I would like to ask Mathematica to do the following operation (to sum the subtractions of ...
user67849
3
votes
2
answers
323
views
Most efficient way to find equivalence classes of an equivalence relation
This is a most basic thing and is probably just built-in but I am ignorant of it, so...
I've got some set S={a,b,c,...} and a function ...
- 1,770
5
votes
1
answer
58
views
Is there an argument to MemberQ so that it will always return TRUE?
Is there an argument for the first input to MemberQ which will result in MemberQ always returning TRUE? It would basically be a constant for the set of everything, I suppose.
- 5,340
1
vote
0
answers
106
views
How to determine the domain (intersection and disjoint set) of two functions define on a set? [closed]
Suppose I have two multivariate functions $f(x,y,z)$ and $g(x,y,z)$ such that $0<x<1,0<y<1,0<z<1$. $f(x,y,z)$ is defined on values satisfying $\{0<x<1,0<y<1/2, z>y\}$ ...
- 147
0
votes
1
answer
56
views
How do we express set theoretic extensionality in Mathematica for instance I want it to see {2,1} as equal to {1,2)
I think the title pretty much covers it
- 465
4
votes
2
answers
189
views
7
votes
2
answers
167
views
How to decompose a list of n-tuples into a union of Cartesian products
I have a list with all elements at the same level
{
{a, d}, {a, e}, {a, f},
{b, d}, {b, e}, {b, f},
{c, d}, {c, e}, {c, f},
{x, t}, {x, q}
}
How ...
- 73
3
votes
0
answers
63
views
Symbolic Set Difference
Suppose I have two symbolic set containing 2-points like
A={(m,n)| for m,n belonging to whole numbers}. So m,n=0,1,2,...
and I have another set containing 2-points ...
- 1,122
0
votes
1
answer
39
views
Generalizing previous question: Partition $[a,b]$ into $m$ sub-intervals and count number of sub-interval intersecting $A_1\subseteq[a,b]$?
In my previous question, How to partition $[a,b]$ into $m$ equal sub-intervals and count the number of sub-intervals that intersect with a subset of $[a,b]$?, I was given an answer to my specific ...
- 29
1
vote
1
answer
112
views
How to partition $[a,b]$ into $m$ equal sub-intervals and count the number of sub-intervals that intersect with a subset of $[a,b]$?
Suppose we have a subset of $[a,b]$, where $a=0$ and $b=1$, such as
$$A_1=\left\{\frac{1}{2^x}+\frac{1}{2^y}+\frac{1}{2^z}:x,y,z\in\mathbb{Z}\right\}\cap[0,1]$$
Which is a subset of $[0,1]$
If we ...
- 29
4
votes
3
answers
246
views
How can I solve a Set Cover problem in Mathematica
I have $n$ non-empty possibly non-disjoint sets $S_i$, each having a cost $c_i$, and the union $\Omega=\bigcup_{i=1}^{n}S_i$. How can I find a selection of $S_i$ such that the union is also $\Omega$ ...
- 23.1k
1
vote
4
answers
178
views
How can one expand an arbitrary boolean combination into the $2^n$ atoms of the associated boolean algebra of size $2^{2^n}$?
The answer of user250938 to Can one usefully apply the Boolean functions of Mathematica to measurable Boolean sets? and the second comment of
Monroe Eskew to the answer to https://mathoverflow.net/...
- 2,315
0
votes
1
answer
121
views
Can one usefully apply the Boolean functions of Mathematica to measurable Boolean sets?
This is something of an attempted succinct/pointed rephrasing of an earlier question Given measures on sets and on certain Boolean combinations of the sets, can one check their consistency and/or ...
- 2,315
4
votes
3
answers
103
views
every set intersection for every set in a family with another family of sets
I want to find for each list within a list of lists what intersections occur when taking set intersection for each list in another list of lists.
Hopefully that makes sense.
I have tried
...
- 475
10
votes
5
answers
700
views
Delete sublist when sub-sublists contain same element
Given
lis={{{a},{b,c,d}},{{a,b},{b,c}},{{b,c},{a,b,c}},{{b},{d}},{{a,b},{c,d}}}
I want to delete sublists which have one or more elements in common. So that I ...
- 2,304
3
votes
2
answers
1k
views
How to stretch this Venn diagram?
I am trying to duplicate (approximately) the following Venn diagram in Mathematica:
I have used the top of this page as a guide, which showcases the following Venn diagram triplet:
...
- 3,095
1
vote
1
answer
299
views
ArgMin over intervals and discrete sets
I was playing with ArgMin but I'm not sure how to use it for constrained optimization.
For example,
ArgMin[x^2, x]
returns <...
- 133
1
vote
1
answer
137
views
Possible way to plot the solution density of diophantine equations
Well, I'm trying to investigate the density of solutions to Diophantine equations. What is a general method to describe that density?
I've two functions:
$$\varphi\left(\text{a},\text{b},\text{c}\...
- 1,941
3
votes
1
answer
130
views
Why doesn't DeleteDuplicates do what I want
First off. I am not a mathematician I am a linguist, a syntactician who is trying to say something about semantics, which in the case at hand can be largely understood to reduce to set theory. That ...
- 151
0
votes
2
answers
89
views
Making a function that takes as an input a list not care about the order of the elements of the list
I would like a function f, that takes as input a list, not care about the order of elements of the list. So,for example:
f[{3,2}]=f[{2,3}]
Is this possible? Or is it necessary to convert the list ...
- 141
3
votes
2
answers
211
views
How to find the positions of replaced elements in a list
I have two sets of elements
a={3, 4.8, 5, 4.2, 3.6, 2.3, 4.5, 3.7}
b={2.8, 4.7, 5.3, 3.5, 4.7, 2.8, 4.2, 3.4}
and I create ...
- 93
2
votes
1
answer
115
views
Creating pairs of non-intersecting set from a given set
Let's say I have a set {a,b,c,d} and I want to create a list of pairs {{a,b,c,d},{}},{{a,b,c},{d}},{{a,b,c},{}},... such that there is no intersection between each pair, and they do not need to use ...
- 21
4
votes
1
answer
167
views
Non-flat partitions of a set
A non-flat partition of a set is one where, when the elements of the set are on a grid, the partition does not contain subsets with elements from the same row. When the set is more irregular the same ...
- 1,937
0
votes
1
answer
76
views
How to find disjoint subsets such that union of the sets give the motherset or main set?
Let us define a set $\mathcal{S}=\{1,2, 3,\cdots,67\}$. I have a list of 132 subsets.
I want to obtain 16(or 17) mutually exclusive subsets such that union of such 16(or 17) is equal to $\mathcal{S}$...
- 565
7
votes
5
answers
499
views
Efficient deletion of specific list entries
It is sometimes useful to remove exactly the amount of specific entries on one list from another.
Consider:
...
- 18.6k
2
votes
1
answer
93
views
Calculate plausibility in Dempster-Shafer theory
I want to use Mathematica to show which subsets of a power set are required to calculate the plausibility for a given set in a power set. This has lead me to compute a summation with a ...
- 437
0
votes
2
answers
571
views
Summation over an index and a set
I have an index CC and a set of values CM, and c is an element of CM and ...
- 5,303