Questions tagged [inequalities]

Questions about handling with inequalities with, e.g., Reduce, Solve, FindInstance etc., their application in defining Regions, and ways to incorporate them into other computations, e.g. integration.

Filter by
Sorted by
Tagged with
2
votes
1answer
263 views

Inequalities/extracting data from RegionPlot

I've searched everywhere for this but can't seem to find a simple way to do this. I have defined a function of two variables and am able to plot a 2D region in the domain space - the endpoints of the ...
1
vote
0answers
161 views

Plotting, NDSolve, initial conditions from range, inequalities [closed]

I will do my best to describe the simplest version of my problem as clearly as I can. Please bear with me: We have a,b and c which are functions of x and y, and their t-evolution is given by coupled ...
2
votes
1answer
83 views

Make Reduce produce nicer output

I am trying to reduce a bunch of inequalities using the Reduce command in Mathematica. But the output is very convoluted and I am wondering if there's a way to systematically organize it so that I can ...
1
vote
1answer
138 views

Speedup of reduce function?

I tried to run this $15$ variable feasibility linear programming to see what the solution looks like. Unfortunately it is taking too much time on my laptop. Is there a way to speed it up? Any tips ...
4
votes
1answer
508 views

How to draw a tropical surface?

By definition, a tropical surface in $\mathbb R^3$ is the set of points $(x,y,z)$ where the maximum $f=\max(f_1,f_2,\dots,f_n)$ is attained at least twice, here $f_i$ stand for some linear functions ...
0
votes
5answers
411 views

Find all the closest positive integer solutions within a bound for a simple linear equation

Suppose I have a linear equation/inequality like $$xA+yB \leq C,$$ with $x,y \in \mathbb{Z}^{+}_{\neq 0}$ and $A,B,C \in \{x | x = 0.01\mu, \forall \mu \in \mathbb{Z}^+_{\neq0}\}$. I want to find ...
2
votes
1answer
95 views
0
votes
0answers
58 views

Test varying number of inequalities

I want to test a varying number of inequalities ...
0
votes
1answer
173 views

Solving a system of inequalities

I'm trying to solve a system of inequalities with $6$ variables using Reduce but it's taking a long time (at least 30 mins) and has not yet finished. ...
3
votes
2answers
250 views

Plot surface defined by inequality

I have an inequality which looks like 5 < x < 25 && 5 < y < 25 && z == 3 And I would like to plot this surface. However, ...
10
votes
5answers
2k views
5
votes
2answers
345 views

Volume of a 3D implicit region

To find the volume of the following region: ...
0
votes
5answers
128 views

Solving inequalities

I would like to solve this problem: ...
3
votes
1answer
1k views

Restrict 3D plot to region specified by an inequality

I would liked to plot a piece of the unit sphere surface within the region defined by $$x \geq y \geq z \geq 0$$ Plotting the region (RegionPlot3D) and the ...
0
votes
1answer
150 views

Unable to solve an inequality

I wanted to solve the inequality -1 < 3/2 π*Sin[αa]/αa + Cos[αa] < 1 for αa in range ...
0
votes
2answers
105 views

Solving an inequality with many parameters [closed]

I need to solve the below inequality for x. I am very new to Mathematica. Below syntax does not give me any output. Please help. ...
0
votes
0answers
160 views

Drawing convex cone with given vectors

I have vectors in matrix form. By using Mathematica, I want to draw it as convex cone and intersect. Let me explain, my intent is to create a new cone which is created by intersection of a null spaced ...
1
vote
1answer
220 views

Drawing polytope

Consider the $10 \times 3$ matrix ${\bf A}$ and the inequalities ${\bf A}{\bf x} \leq {\bf b}$: $$ \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 &1 \\ 1 & 0 & 0\\ 0 & 1 & 0\\ ...
0
votes
0answers
50 views

Why does Mathematica take an aeon to solve an inequality?

I gave Mathematica this inequality to solve: ...
0
votes
0answers
35 views

Solving an inequality with conditions on the values

I have to know if an equation is always negative for the realistic set of values that I'm looking at. The problem is that the equation is way too big. I know I can do it manually if I spend a couple ...
0
votes
1answer
373 views

Resolve, Solve, Refine, etc., do not work, but Wolfram|Alpha does

As a teacher, I am trying to show some step-by-step execution. (Any help with tools would be most appreciated.) Related, I cannot get the following to work: ...
0
votes
0answers
130 views

How to simplify $x \coth(x) > 1$?

I have the inequality $x \coth(x) > 1$ which is correct for real arguments $x>0$. However, Mathematica does not seem to realize this: ...
1
vote
1answer
139 views
1
vote
0answers
160 views

Error using NMinimize/NMaximize : The initial region specified may not contain any feasible points

Link : Reduce time taken to get feasible solution An example of 18 non linear inequations with 4 variables is given in the image. But I have a set of 32 non linear inequations with 9 variables (I ...
1
vote
1answer
140 views

Reduce time taken to get feasible solution [closed]

I have such a set of nonlinear inequalities with m variables, Please suggest some good method to get some feasible solutions, where a[i]'s belong to [-5,5].So please suggest an approach, to get ...
0
votes
1answer
59 views

How to help Mathematica to determine whether or not there is a solution to a system of inequalities?

I have a system of inequalities and I am wondering wether or not there exists a solution. With these definitions ...
0
votes
1answer
49 views

How do I find analytical apexes of a region? [duplicate]

I have a set of inequalities that plot to the region given below, how do I find the analytical apexes that shape this region? ...
1
vote
1answer
190 views

Evaluating an Inequality

I am evaluating a parametric inequality conditional on some assumptions on the parameters. In the simplest form, here, I am assuming the numerator and the denominator are positive: ...
0
votes
1answer
67 views

“x + b < constraint” for “domain_start < x < domain_end”. Solution for “b” only according to the set “x” domain

I am giving a really simple example that describes my problem really clear. Example: "x + b < 50" for "3 < x < 6" i need a solution set for my coefficient (e.g. for "b") that satisfies ...
1
vote
1answer
233 views

Solving systems of differential inequalities and differential equations

This question is motivated by another one I recently asked: Obstacle problem for the heat equation. It seems to me that DSolveValue does not work for ...
2
votes
1answer
83 views

When Reduce yields False for a system of inequalities, can I take this as a formal proof? [closed]

As part of the proof of a proposition in an economics paper, I need to show that a system of inequalities in four variables is inconsistent. Because the system is complicated, I cannot show this ...
1
vote
2answers
130 views

true/false of an inequality

I would like to check whether the expression is always positive or not with certain assumptions on variables. I have tried this approach but it doesn't solve the purpose. Any other way to resolve this?...
1
vote
1answer
137 views

Help with using RegionPlot3D to plot output of Reduce

Is there a simple way to take this output from Reduce: ...
2
votes
1answer
204 views

Region bounded by the curve [duplicate]

How to colour the region "under" the curve? Given that $0<x<3$, $-4<y<4$, $0<z<4$ ParametricPlot3D[{3/2, y, Abs[y]/(3/2)^(1/4)}, {y, -4, 4}]
0
votes
0answers
55 views

Solving Inequality involving Sum of PrimePi's

I am trying to figure out if for each $n$ we have $$\sum_{i=1}^n\pi (2^i)+(1-1/2^n)\Bigg(\sum_{i=1}^{\lfloor n Log2/Log3\rfloor-1}\pi(3^i)+\sum_{i=1}^{\lfloor n log2/log5\rfloor-1}\pi(5^i)+\cdots+\...
3
votes
4answers
341 views

Patching removable singularities of a function

How can I make FunctionDomain include removable singularities? For instance, FunctionDomain[Sinc[x], x] == True But ...
2
votes
1answer
226 views

Unable to solve a simple inequality [duplicate]

I want to find the solutions for $$(4k+1)(2k)!\ge 10^6$$ I tried the expressions ...
3
votes
2answers
165 views

Get the inequalities from answers

I have two inequality. x1 >= x2 x1 >= x3 x1,x2,x3 ∈ {0,1} the answer of the Inequalities is (x1,x2,x3) ∈ {(0,0,0),(1,0,0),(1,1,0),(1,0,1)} How to get the Inequalities from our ...
1
vote
1answer
67 views

Why does my inequality require “AssumptionsMaxNonlinearVariables” -> 14?

I have the following code for simplifying an inequality: ...
1
vote
1answer
246 views

Reduce or Solve to solve 3 simultaneous equations/inequalities

I've tried both ways, and maybe it justtakes Mathematica a long time to solve this system of equations, but I can't tell if it is hung up or crunching. So, I'm wondering im y approach with ...
2
votes
1answer
112 views

Visualising set of inequalities

Is there any way to visualise a set of inequalities when there are 4 variables at play? Context: if we have inequalities involving two variables only, one can highlight the ensemble of points that ...
0
votes
0answers
102 views

Verifying inequality with a specific set of parameter restrictions

I would like to have Mathematica check an inequality over a set of parameter restrictions. More in detail, given a function $f(x;a,b)$, where $a$, and $b$ are parameters, I would like to verify that $...
3
votes
0answers
95 views

Solve a system of many inequalities with varying coefficients [closed]

I have to solve the following problem concerning a system of inequalities: Distinguish two groups of real variables: the first composed by the following 15 real variables ...
2
votes
1answer
78 views

Sums of Solutions of a Linear System

I have a system of equations/inequalities involving 36 numbers $p_{11},p_{12},...,p_{16},p_{21},...,p_{66}$. I have some equations/inequalities, such as (i) $0\le p_{i,j}\le 1$ for all $i,j$. (ii)...
0
votes
1answer
64 views

minimization problem with integer variables and constraints

My question is this: Find l,m,k (l,m,k are integers $>$0 and l is odd) which minimize: $M(l,m,k)=m^2(1-\gamma)+\frac{l^2}{4}\gamma-k^2$ (Where $0<\gamma<1$ and $\gamma$ is a known rational ...
0
votes
2answers
70 views

Reduce applied to large inequality doesn't work

I want to solve the next inequality : ...
4
votes
0answers
109 views

Inequality involving Quantity stays unevaluated

Bug introduced in 10.1 and solved in 11.1 An expression like this one a < x < b is represented as Less[a, x, b] ...
1
vote
0answers
103 views

Solving an Inequality that contains many unknown variables

So, I'm a beginner in using mathematica, can do only the basic stuff... anyway, I want to find the bound for [pi], that makes this quantity 2 ((n - y)Log[(n - y)]+yLog[ y_]-yLog[n[Pi]] - (n - y) Log[...
3
votes
0answers
43 views

Evaluating inequality involving powers

I want to evaluate an inequality of the form $x^a > x$ under the assumptions $x > 1$ and $a > 1$. I expect this inequality to be true, but ...
4
votes
1answer
102 views

Equalities, inequalities and fractions

Today I was surprised by the following treatment of equations in Mathematica. I understand, for example, the following In: a*b/a Out: b and nobody cares about ...