# 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.

376 questions
Filter by
Sorted by
Tagged with
66 views

### Find the condition under which an inequality is satisfied

I need to find the conditions among the variables under which the inequality est-tru>0 holds. ...
1 vote
37 views

### Parametric Plotting 6D dimensions to 3D for Visualizing a Solution

I am trying to find out when: $$f(x,y,z,α,β,γ):= zcos(β)cos(γ)+y(cos(γ)sin(α)sin(β)+cos(α)sin(γ))+x(−cos(α)cos(γ)sin(β)+sin(α)sin(γ)),$$ where $α,β, \text{and } γ$ can be any value in $[-2\pi,2\pi]$ ...
195 views

### Computation time unexpectedly long for a Volume

The command is Volume[Region[ImplicitRegion[{Sqrt[x^2+y^2]<=Abs[Sin[z]],0<=z<=2Pi},{x,y,z}]]] The computation time is exceeding my expectation. The ...
123 views

### How to show a region defined by an inequality within the specified domain?

Firstly, I wrote the following code to specifiy the domain of the variables a and x: ...
80 views

### How to get the range of analytical solution of inequalities?

Is there a way to get the range of analytical solution of inequalities? Such as: ...
1 vote
80 views

### Trying to use Linear Optimization to solve inequalities

I am trying to use Mathematica to get bounds on some quantities using a certain procedure which is called conformal bootstrap. For the users who don't come with a background in HEP, I am basically ...
85 views

### Finding parameter range from two solution sets

Let the solution set of the following system of two inequations $$x^2 - 4 x + 3 < 0 \\ x^2 - 6 x + 8 < 0$$ be a subset of the solution set of $$2 x^2 - 9 x + a < 0.$$ How can I find the range ...
1 vote
239 views

### Solving inequation with parameter

Let the following inequality $$4^xa - 2^x + 1 > 0$$ hold for any $x$. How can I find the range of parameter $a$? The following method doesn't work: ...
40 views

### Finding parameter range of inequation with no solution

Let the solution set of the following inequation $$6 k - 2 x + k x^2 < 0, \quad k \neq 0$$ be an empty set. How can I find find the range of parameter $k$? The following code gives an answer: ...
422 views

### Calculating union of two sets of reals

Given the following two sets of reals: -(1/4) < x <= 0 || 0 < x <= 1/2 || x > 1/2 x <= -1 || -1 < x < 0 how can I calculate their union? ...
1 vote
68 views

### Solving inequation with a solution set from another inequation

Given that the solution set of inequation $$ax ^ 2-bx-1>0$$ is $-1/2<x<-1/3$, I want to calculate the solution set of inequation $$x ^ 2-bx-a\geq 0.$$ I have used the following code, but is ...
1 vote
64 views

### Why can't the range of this inequality parameter be determined?

How can I accurately find the range of $t$? Reduce seems to be unable to find it: ...
44 views

...
50 views

### How to simultaneously determine the range of x and base a when an inequality with logarithms holds?

Log[a, x + 1] > Log[a, x - 1] the inequality above is equation holds good under all circumstances You can see the range of x ...
77 views

The following code draws the intersection of a surface N: eqNcar=0 with three other surfaces defined by eq1=0, ...
61 views

### Possible ranges of variables that are defined by inequalities

There are the following inequalities 0.09 <=(a1*a2)/(a1 + a2) <= 0.2 and 1 >= a1/a2 >= 0.5 How can all possible ...
56 views

1 vote
118 views

115 views

### Permutations with inequalities constraint

In how many ways can I arrange the first $6$ positive integers such that this inequalities chain will hold? $a < b > c < d < e > f$ One of these arrangements is $\{5, 6, 1, 2, 4, 3\}$, ...
67 views

### Reducing an inequality with a complicated Log term?

I am trying to symbolically Reduce the following (admittedly complicated) inequality: ...
1 vote
87 views