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.
15
questions
17
votes
5answers
5k views
Is it possible to have Mathematica move all terms to one side of an inequality?
I have an inequality expression that I would like to express in terms of the relation of the parameters to zero. More simply, I want to have mathematica move all the terms to one side of the ...
5
votes
2answers
259 views
12
votes
7answers
3k views
Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$
As an intermediate step, consider the function:
f[x_] := x Sin[Pi/x]
I want to prove that this function is increasing for $x\ge 1$. This can be done with the ...
5
votes
4answers
1k views
Converting inequalities to intervals
I have an inequality, ie: 1.57116 < g < 14.1405
There will be a large set of similar inequalities, and I want to find the intersection of them all. I figured it would be easier to convert the ...
8
votes
3answers
2k views
Shading a region where an inequality is satisfied
Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later
I'm creating solution sets for a calculus course and need to shade the region in $\mathbb R^2$ such that $x^2 < y < x^4$. ...
1
vote
1answer
144 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 ...
2
votes
1answer
89 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 ...
5
votes
2answers
184 views
Solve for parameters so that a relation is always satisfied
Let's say I have a function parameterized by a number of variables. As a simple example
$$F(x,y) = ax^2 +by^2-cxy+1$$
I want to find some set of values (doesn't really matter what they are) for the ...
3
votes
4answers
2k views
Find the volume of the region defined by $|x|+|y|+|z|<4$
I want to find the volume of the region defined by the following inequality:
$\quad \quad |x|+|y|+|z|<4$
In addition to calculating the volume of this region, I would also like to be able to ...
4
votes
0answers
111 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
1answer
136 views
How to represent in a 3D graph the set of solutions to this system of inequalities?
I am studying this piecewise function:
...
1
vote
1answer
202 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:
...
1
vote
1answer
91 views
How to get solutions for this system of inequalities?
I am new to Mathematica and I am struggling finding the solution for the following problem.
I am studying this piecewise function:
...
0
votes
1answer
134 views
Reduction of an Inequality in $\mathbb{C}$
Reduce[
Abs[-((4 p)/(-1 + Sqrt[1 + 4 p + 4 q])^2)] +
Abs[-((4 q)/(-1 + Sqrt[1 + 4 p + 4 q])^2)] < 1 , Abs[p]]
It is taking lot of time. It is running. Can ...
0
votes
1answer
215 views
Intersection of volumes defined by inequalities
I have 5 inequalities with some parameters like dh, din and thetawhich I intend to vary.
In ...
