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
1
vote
1answer
201 views

Wrong root when using numerical values

I have the following inequality: $$ \sqrt{\frac{a}{2x}}+ \frac{b}{1-\frac{a}{a+\sqrt{a(2bx + a)}}} + \frac{a}{2x\frac{a}{a+\sqrt{a(2bx + a)}}\left(1-\frac{a}{a+\sqrt{a(2bx + a)}}\right)} < f $$ on ...
0
votes
0answers
49 views

Tips on finessing Reduce[] with inequalities

Reduce[] sometimes solves inequalities I give it, sometimes it doesn't. Is there some general principles I'm missing or some common pitfalls I'm falling into? For example, here is easy problem I can'...
4
votes
1answer
189 views

How to reduce/simplify an inequality involving Abs[]?

Can Mathematica reduce this inequality into a domain of z, where {z, r1, ...
3
votes
1answer
140 views

Using TrueQ with conditions

Say I want to ask Mathematica whether $|x| = x$ for all $x > 0$. Obviously, if I try TrueQ[Abs[x] == x], I get False, ...
0
votes
1answer
307 views

Plot absolute value inequalities - number line

I'd like to ask you about the way to draw the number line for absolute value inequalities. Is there any built-in tool? In this case the input was $|x-6| > 3$. My point is to achieve something ...
0
votes
2answers
117 views

Evaluating a list of inequalities with random numbers [closed]

I have a list of inequalities, which include in total four parameters, that I would like to test by feeding the four parameters with random numbers. The goal is to find the best values of the ...
7
votes
0answers
232 views

How does Mathematica resolve symbolic systems of inequalities? [closed]

Before getting into my question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A major part of the ...
0
votes
1answer
133 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 ...
1
vote
0answers
104 views

Simplify Integer powers in inequalities

I have a fairly simple expression that I am surprised Mathematica (10.1) won't simplify ...
3
votes
1answer
190 views

Solve an inequality involving a sum with a parameter

Good day. I am new to Mathematica and I am looking for advice. Is it possible to solve $$\sum_{k=0}^{n} \frac{p^k}{k!}>0$$ for $n$ where $p$ is a parameter? When I do ...
6
votes
1answer
125 views

How to simplify expressions by closing open inequalities?

Recently I have often acquired results which consist of combinations of 0, 1 and 2-dimensional (in)equalities. For instance, consider a very simple case with ineq1 ...
0
votes
0answers
51 views

Need help with solving inequality under assumptions [duplicate]

I seriously need help for my research. I need to solve an inequality with several assumptions. I tried many times with Reduce but it did not work out properly. Sometimes the results I get are simply ...
-1
votes
1answer
202 views

Find a minimum value which satisfies an equation

I have to find a minimum value of "a" which makes x=-a+b+c, y=-a+b+c^2 positive where a>1, 0 ...
0
votes
1answer
119 views

Trouble in finding instances of values of variables that satisfy an inequality

Consider the following mathematical expression with complex numbers (phasor) and two variables (lambda and ia2): ...
4
votes
1answer
526 views

How to solve a conditional inequality?

I am trying to use Mathematica to solve a conditional inequality. Find all (real) numbers $a$ and $b$ such that $|a| + |b| \ge 2/ \sqrt{3}$ and for any real $x$ the inequality $ |a\sin x + b \sin ...
4
votes
1answer
240 views

Does `Reduce` give complete and necessary conditions?

I want to obtain a solution for a system of five inequalities. For instance, ...
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 ...
2
votes
0answers
62 views

How to speed up geometric Resolve query involving $\exists$ and $\forall$?

I would want to test connectedness of semialgebraic sets with naive code like this: ...
0
votes
2answers
163 views

Proving simple inequality

I have a simple function and want to make sure that it satisfies an inequality over a certain range of parameters. My approach is: ...
-1
votes
3answers
154 views

Filtering the output from Table and export it into excel

I have the following functions ...
2
votes
2answers
94 views

Reduce and roots of an irrational inequality

I use command Reduce to solve an inequality. First, I used Reduce[Sqrt[4 x + 5] - Sqrt[-6 x + 10] <= Sqrt[2 x - 1], x] and ...
5
votes
2answers
381 views
2
votes
1answer
381 views

Replacing Logic operator List and generate combination of variables

so I'm trying to do the following starting from a list of inequalities: ...
2
votes
0answers
172 views

Proving large inequality in 6 variables

I have arrived at a very large inequality in 6 variables that I would like to prove is true. The command I have tried is the following: ...
1
vote
0answers
63 views

Simplifying an inequality inside an answer by parts

I have the following piece of code where I'm evaluating a probability of a variable v being greater than some threshold under a Uniform distribution. ...
0
votes
2answers
108 views

Why Mathematica cannot tell if Sqrt[Abs[u0^2 + v0^2/b^2]] is positive?

In the code below I was careful to declare all variables as real and to use Refine. Still, Mathematica cannot tell that a sum of squares is a positive number. What am I missing? Thanks to ...
3
votes
4answers
565 views

Solving puzzles with Mathematica

I would like to be able to solve logic puzzles such as the one described here using Mathematica. I have copied & pasted the listed example below to save on jumping about with hyperlinks: The ...
3
votes
3answers
251 views

Remove all “not equal” clauses from an expression

I am banging my head against the following question: how can I have Mathematica take cond = 2 a >= 3 b && 70 a >= 19 && 20 a != 13; and ...
2
votes
2answers
889 views

Given a system of inequalities, how to make Solve find out that two variables should be equal?

Given two boolean variables x1 and x2 (in the sense that they are in the range [0,1]), if I try to solve the following equation system with Solve: ...
4
votes
1answer
2k views

How to find the integer solution number of a linear system with inequalities?

I have the following system with mixed equality and inequalities defined as: ...
6
votes
3answers
598 views

How to count the integer grid numbers defined by inequalities?

I have the following code to show a red area defined by inequalities: ...
4
votes
3answers
319 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
0
votes
1answer
494 views

Finding maximum/minimum value of system of inequalites

How would I get the maximum values for x1 and x2 given that I have plotted the region governed by the following system of ...
6
votes
1answer
951 views

Is there a way to check inequalities in Mathematica given restrictions?

Sorry if I'm still a noob, but is there a way to check inequalities in mathematica given some restrictions? For example how could one go about checking whether: Given $a,b,c\in\mathbb{R}$ and $a,b,...

1 2 3 4
5