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.
Overview
Questions tagged [inequalities]
386 questions
10
votes
5 answers
What does `{x,y}<0` mean?
In[1]:= Simplify[x<0, x<0]
Out[1]= True
In[2]:= Simplify[x<0, {x,y}<0]
Out[2]= x < 0
In[3]:= $Version …
user1722
7
votes
1 answer
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 $a,b,c>0.5+\sqrt{5/4}$, is $abc(a+b+c)>3abc+ab+bc+ca$…
user18875
- 71
- 2
4
votes
1 answer
How to reduce/simplify an inequality involving Abs[]?
Can Mathematica reduce this inequality into a domain of z, where {z, r1, r2} are all complex?
Reduce[Abs[z^2 - r1] > Abs[z^3 - r2], z]
The line never returns a result. I also tried just calculating the boundary:
Simplify[Abs[z^2 - r1] == Abs[z^3 -…
Jerry Guern
- 4,602
- 18
- 47
4
votes
2 answers
Solving inequalities involving floor function
Why mathematica doesn’t solve this simple inequality ?
Reduce[Floor[x/2]<10,x,Integers]
It returns the error:Reduce::nsmet
Is it related to floor function?How to fix it?
Lophotro
- 41
- 1
4
votes
3 answers
Solving inequality with logarithmic expression
I am trying to solve the following inequality
2 y(Log[1 + (y-1)x] - x Log[y]) - x(1 - x)(y - 1)^2 < 0
where
y > 1 && x < 1/2 && x > 0.
RegionPlot can handle my description but any other command (Reduce, Solve) can not. I would like Mathematica…
mathastri
- 51
- 3
4
votes
1 answer
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 what was the value of a. But I was quite surprised to find out that the same behavior…
Daniel
- 163
- 6
4
votes
3 answers
Restrictions on variables of two functions in order to be larger and smaller relative to each other
I have two functions
f1[x_, y_] := -1 + x - Sqrt[8 + x^2 + (1 - x) (1 + x)];
f2[x_, y_] := -1 - x - Sqrt[8 y^2 + (1 - 3 x) (1 - x) + x^2];
I am searching the restriction and the relation between x and y in which f1 > f2. Also other condition in…
Unbelievable
- 4,847
- 1
- 20
- 46
3
votes
4 answers
How to to solve inequality $(a+b\cos x)^2+(c \sin x)^2\leq 1$ for any $x$?
Does Mathematica have the ability to solve this inequality:
(a + b * Cos[x])^2 + (c * Sin[x])^2 <= 1
for any x ∈ [0, 2*Pi]?
The answer should contain conditions/inequalities for a, b and c.
Aerterliusi
- 353
- 1
- 5
3
votes
1 answer
How to use conditions with Reduce?
I am solving a simple inequality with Reduce:
Reduce[r^2-d^2>0,d]
I get a correct solution, but I would like to impose the condition r>0 in order to simplify the result, how can I do that?
mattiav27
- 6,677
- 3
- 28
- 64
3
votes
2 answers
How to run co-ordinates through inequalities
I want to run the y-coordinates of this graph through a set of inequalities and store only those values which satisfy them. I thought of using For loop with TrueQ but the y co-ordinates have three solutions corresponding to a particular x. I did…
Lost
- 226
- 1
- 7
3
votes
2 answers
How to get the set of solutions of linear systems of inequations in Mathematica?
I would like to solve the following system of equations:
$$y < -3 + 2x$$
$$y \ge 1-x$$
So I tried the following:
Solve[{y < -3 + 2 x, y >= 1 - x}, {x, y}]
But the following message appears: "The solution set contains a full-dimensional component;…
Joshua Salazar
- 733
- 4
- 12
3
votes
2 answers
Solving an inequality involving the Fibonacci function
How can I solve an inequality that involves the Fibonacci function? For instance, say I want to determine for which values of $n$ we get that $$F_n\leqslant 1000.$$
I tried to use Solve and Reduce, like this,
Reduce[(Fibonacci[n] < 40) && n…
Workaholic
- 133
- 5
2
votes
2 answers
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 got
x < -(5/4) || 1/2 <= x <= 1
I put
f[x_] := Sqrt[4 x + 5] - Sqrt[-6 x + 10] - Sqrt[2 x - 1]
and found $f[-2]$,
I…
minthao_2011
- 4,503
- 3
- 31
- 46
2
votes
1 answer
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 of parameter $a$?
I have calculated both solution sets as…
csn899
- 3,953
- 6
- 13
2
votes
2 answers
Solve inequality with parameter
I want to solve the inequality
$m<700000log((m-1)a)+3 $
Where $a$ is a positive integer i know the command when there is no parameter in the inequality but I don't know for the case of parameter .(a is the parameter )
I want the command for…
Abdo
- 23
- 4