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
105 views

How can I find the domain of $x$ for which the function $g(x)\geq0\;$?

I have this function ($x>0$) $$f (x)=\frac{\sqrt{g (x)}+4 x \left(x^2+1\right) \sin (\pi x) \cos ((3+\pi ) x)}{x^4+2 x^2+1+\left(4 x^2+\left(x^2-1\right)^2 \cos (2 \pi x)\right)}$$ ...
1
vote
2answers
129 views

Validating an inequality

I want to show That: $$ 1+a^{2017}+b^{2017} \geq a^{10}b^7+a^7b^{2000}+a^{2000}b^{10} \\ a,b\in \mathbb{R}^+_0$$ I used Simplify and then Resolve That is taking forever: ...
9
votes
5answers
496 views

How do I find complex values that satisfy multiple inequalities?

I want to find $a,b \in \mathbb{C}$ such that $$|1-2a-2b| < 1 \quad \text{&} \quad |1-2a+2b| < 1$$ using mathematica. I tried to use ...
4
votes
1answer
41 views

How to use conditions with Reduce? [closed]

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 ...
1
vote
2answers
158 views

Fast way to check if $f(x)>x$ for what value of $x$

In order to find the value $x$ for which $f(x)>x$, I tried it using the following code: ParallelTable[If[TrueQ[f[x]>x],x,Nothing],{x,0,10^9}] For some ...
0
votes
0answers
22 views

Reduce function returns error

I am trying to prove the inequality below for the given condition stated, but I get a warning result. ...
2
votes
2answers
66 views

Reduce inequality does not finish

I am trying to show general cases of symmetry of regions. However, for the following, Reduce does not finish: ...
0
votes
2answers
32 views

Isolate variable in inequality

I'm having the most stupid of problems. Suppose I have a simple inequality like $$ |2-x|>2.$$ The solution to this is $$ x<0 , \,x>4.$$ This is pretty obvious, though Mathematica insists on ...
0
votes
1answer
57 views

Two inequalities with Mathematica [closed]

How can I prove these two statements: For any $x,y \in \mathbb{R}$ and $p \geq 2$ the inequality $\left(|x|^{p-2}x-|y|^{p-2}y\right)(x-y) \geq 0$ holds and the second inequality $\left(|x|^{p-2}x-|y|^{...
1
vote
3answers
149 views

Solve inequalities and find parameters

Let $$S=4 (\alpha -2) \beta -58 (\alpha -2)^2-\beta ^2-8 c_6 \left(7 \alpha +2 c_6-13\right)$$ $$T=-\frac{\left((\alpha -4) (\alpha -2) (\alpha (3 \alpha +4 \beta -27)-18 \beta +60)+4 c_2 (\alpha +...
2
votes
3answers
326 views

How can I write in Mathematica that 2*x is an integer? [closed]

I have to maximize $h/k^2$, where $h/k^2 < 0.1974$ and $k$ is an integer, and $2\cdot h$ is an integer, $h>0$, $k>0$. How can I write this problem in Mathematica?
-1
votes
3answers
73 views

Inequalities having inconsistent InputForm [closed]

I'm having a tough time dealing with inequalities. ...
5
votes
1answer
39 views

Plotting regions with 1D and 2D components

I am trying to plot a region defined by an inequality which contains both a 2D square and a 1D segment. My issue is that RegionPlot only shows the square and ignores the line. I noticed that if I use ...
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 ...
0
votes
1answer
75 views

Solving an exponential inequality in two ways

I would like to solve the following inequality E^x/x^1000 >= 2 without Reduce. Then I would like to solve it with ...
0
votes
1answer
130 views

LinearSolve and LeastSquares giving different results on system with a solution

So I'm working on a program for my PhD which is supposed to do the following: Take a polynomial f, build a matrix A with ...
3
votes
1answer
98 views

Need help with a linear programming problem

Consider $1\rightarrow{}x+2y\leq{500}$, $2\rightarrow{}2x +y \leq{520}$, $3\rightarrow{}2x+5y \leq{}1200$, $4\rightarrow{}x \geq{}0$, $5\rightarrow{}y \geq{}0$, The above is the set of inequalities ...
1
vote
0answers
58 views
1
vote
1answer
58 views

Obtaining the intersections of 3-D regions using loop?

I am trying to take intersections of several three-dimensional regions by using the regionplot3d command. Currently thinking about how to use looping to take intersections for several 3-D regions. <...
0
votes
1answer
35 views

how to solve system of polynomials restricted to positive reals?

I'm new to Mathematica and would like to use it to solve a system of polynomials. In this system, every variable (and every solution I'm interested in) is a positive real number. I tried this: ...
0
votes
2answers
98 views
1
vote
1answer
53 views

System of inequalities with Max command

I'm trying to use both Max and Reduce function but Mathematica seems not able to find any solution. I put the code below and I hope one can tell me what's wrong in my coding. Thanks in advance for ...
0
votes
0answers
27 views

Why a complementary inequality for function values does not simplify to False?

I have a general assumption of a function to be positive. The direct inequality (f[x]>0) does simplify to True, but a complementary one (f[x] < 0) does not simplify at all despite the fact that ...
0
votes
1answer
28 views

How to plot the solution region of system of inequalities with slack variables?

There are already related questions to this one, but I could not transfer these solutions to my problem. I have the system $\sqrt{t_1^2+u_1^2}+\sqrt{t_2^2+u_2^2}\leq 1$, $x=2t_1-u_1+2t_2+u_2$, $y=...
0
votes
0answers
37 views

Testing Matrix inequalities

I was wondering how one might check whether matrix inequalities are true/false the same way it can be done for scalar variables (like in this post). Say I want to test the obvious inequality A,B are ...
3
votes
2answers
96 views

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 ...
1
vote
2answers
112 views

How should I prove that this inequality is always true?

When $e<a<b<e^{2}$, $ \ln ^{2} b-\ln ^{2} a>\frac{4}{e^{2}}(b-a)$ should always hold. ...
1
vote
1answer
42 views

How can I determine the behavior of a certain inequality? [closed]

Consider the expression $\qquad 2(1-2c)/(c-1)^2$ where $c < 0$. I would like to know if it is bigger than 1 anywhere in its domain. 2(1-2c)/(c-1)^2
1
vote
2answers
63 views

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 ...
0
votes
2answers
81 views

Mathematica is saying both inequality are false [closed]

I'm trying to ask Mathematica to compare 2 different values in inequality but it keeps saying "False". I put the code I'm running below. Thanks in Advance for any hint on what is problematic ...
0
votes
0answers
37 views

Can we use Max function inside Reduce function

I'm having a hard to find how to use the function max[.] and I'm almost sure the problem comes from this but I don't know what to do. I'm putting the code just below. Thanks in advance for any comment!...
1
vote
0answers
38 views

Solving a system of inequalities where some of the variables are integer-valued, and some are real-valued [closed]

I'd like to know how to ask the Reduce command to solve over one domain for certain variables, and another domain for other variables. For example, I'd like to solve the system of inequalities $$ 2 a +...
2
votes
1answer
67 views

matching Inequalities

Consider the following list list={0 < x < 1/12, 0 < x < 1/4} I wish to find the intersection of the two ranges of x ...
0
votes
0answers
32 views

Mathematica does not stop running when trying to reduce a inequality

I have a problem when running the command as Mathematica never stops running. I wonder if it's because there are too many solutions or just because I wrote something wrong. Thanks for your help. The ...
1
vote
1answer
76 views

Solve inequalities

I use FindInstance to find a set of real parameters to satisfy the following inequality $-3 c_{11}-k_4^2-k_7^2-k_9^2>0$, $$ -4 \alpha^6+84 \alpha^5-721 \alpha^4+3228 \alpha^3-7924 \alpha^2+10080 \...
0
votes
1answer
83 views

How to Solve this specific inequality

I want to solve this inequality for l. I have tried to use Reduce and Solve and its not worked out. How can I solve this? ...
3
votes
2answers
57 views

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 ...
1
vote
1answer
46 views

Find the condition under which an inequality holds

I've got an inequality of 8 non-negative parameters (arising from a 5x5 matrix) and would like to find a condition under which my inequality holds. The condition would be an inequality too of these ...
6
votes
3answers
165 views

Verify an inequality of many parameters

I've got an inequality of 10 non-negative parameters (arising from a 5x5 matrix) and would like to verify whether it holds. I tried the following, which doesn't seem to work: ...
3
votes
1answer
81 views

Solving Inequalities using Mathematica

How can I solve this inequality using Mathematica? Sqrt[B^2 + J^2] Cosh[(2 J)/T ] < J Sinh[ (2 Sqrt[B^2 + J^2])/T] where T, J, and B are reals and they are >...
3
votes
3answers
75 views

Plotting a function with the domain restricted. Basic question

I'm trying to Plot a simple function on a restricted domain. I tried ListLinePlot[Table[x^2, {x, x>-3, x<3, 1}]]. This doesn't work. I'm not sure how to take ...
0
votes
1answer
53 views

Define a Region where a disequation is satisfied for all values of a variable

I'm having a problem with Mathematica. I have a large and complicate system of 3 inequalities in 3 variables, let's call them x,y,z. Now, I can't use reduce to solve it exactly. There is a way to ...
0
votes
1answer
57 views

LinearModelFit with the dependent variable given in intervals instead of exact values

I have data of the form $\{x_{i1},...,x_{ik},\{a_i,b_i\}\}$, $i=1,...,N$, and I want to find a function $f(x_1,...,x_k)$ (say, linear) such that violation of $a_i\le f(x_{i1},...,x_{ik})\le b_i$ for ...
0
votes
0answers
60 views

Solving inequality

I am trying to solve this inequality for $\eta$, where B, J, $\eta$, and $\beta$ are reals and $\beta$>0. I used ...
1
vote
1answer
85 views

How to plot a graphic with solution of some inequality?

I defined the function $z(n)$ by z[n_] := Catch[Do[i; If[Mod[Fibonacci[i], n] == 0, Throw[i]], {i, 100000}]] and now, I would like to plot the graphic (n,z(n)) ...
1
vote
1answer
68 views
2
votes
1answer
146 views

Reduce with for all and implies

I have the following question. p1 = a (1 - c + a) p2 = b (1 - c - b)/((1 - b)^2) v1 = (x^1.5 - 3*x)*p1 v2 = x*p2 I want to find x ranges which makes v1>v2 under ...
0
votes
1answer
49 views

This system cannot be solved with the methods available to Reduce [closed]

I get the error message in the Title, which is not very helpful. Situation: Reduce[ForAll[{x,y,z},Implies[x<=y&&y<=z, x<=z]]] evaluates to True, ...

1
2 3 4 5 6