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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.

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48 views

Solve multivariable inequlity and read the output correctly

Hi I need to solve an inequality for multiple variables, and I do not understand in a good manner the results. The inequality that I tray to obtain is $$ a+b+(2*c)+\sqrt{(-2\,c-b-a)^2-4\,(2\,c\,b+b\,...
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1answer
21 views

Inequality in RegionPlot with LogLinear scale

I want to plot a RegionPlot in LogLinear scale. If I try with a simple linear scale, ...
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1answer
21 views

Trying to apply Jensen's inequality to a complicated symbolic expression

I have a somewhat complicated inequality expression like this: ...
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2answers
41 views

How to manipulate sequences of inequalities?

I am trying to write some symbolic inequality proofs in Mathematica. What would be a clean way to make the inference that a >= b and ...
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1answer
30 views

Testing which expression is greater

I have two expressions: expr1 = e^2/(8 + 4*e + e^2) and expr2 = (d^2 - 2*d*e + e^2)/(8 + d^2 - 2*d*2 - 2*d*e + 4*e + e^2) ...
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0answers
38 views

Verifying an inequality

I want to verify an inequality in mathematica but I don't know where I'm mistaken. Please help me out, thanks in advance. $\psi(t):\to[0,\infty)$ and $\phi(t):\to[0,\infty)$ where; $\psi(t)=3/2*t^2$...
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1answer
69 views
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0answers
37 views

Export system of inequalities in MPS format

I am interested in the .MPS format, usually used in Linear Programming problems (see here). When importing a file in the .MPS ...
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2answers
130 views

RegionIntersection not returning what I expected

Consider the following implicit region defined on one variable reg = {x > 0 && x < 0} If I Reduce this system, ...
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0answers
39 views

Wrong output of RegionPlot

I think Mathematica goes wrong if asked to plot this very simple region: Region2 = ImplicitRegion[x < -1 && y < -1/x, {{x, -3, 0}, {y, 0, 1}}] by ...
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2answers
69 views

Region plot in the $xy$-plane of $f(x,y,z) < 0$

I want to plot the region in the $xy$-plane which satisfies $f(x,y,z) < 0$, where $z$ can take values in the range [-1, 1]. How do I do this in Mathematica?
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1answer
42 views

Strange behaviour of RegionIntersection

Consider this list of inequalities ...
2
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2answers
300 views

=== not working properly [closed]

I've been trying to check the identity using wolfram Mathematica and I've found the following ...
6
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3answers
296 views

Calculating the width of the interval defined by an inequality

I am looking for a Mathematica function that takes an inequality as the input and gives back the width defined by upper bound - lower bound: Example: ...
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3answers
380 views

Can Mathematica prove inequalities involving complex numbers?

I am given two complex numbers $z$ and $w$ that satisfy the following constraint $$ |z - \overline{z}w| + |w|^2 < 1. $$ I want to see if the following inequality is true $$ z^2 \overline{w} + \...
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2answers
44 views

Get the set of points from constant function

I have a function f defined by points: finput = {{0, 1/5}, {1/5, 1/5}, {1/2, 1}, {1, 0}}; ListLinePlot[finput, PlotRange -> {{0, 1}, {0, 1}}] Then I create a ...
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1answer
61 views

How to judge whether a relation is true or false

$x$ is a real number, how to judge $x+1>x$ is true using Wolfram.
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2answers
116 views

Remove legend if a plot in an array of plots is empty

In an array of plots of regions (inequalities) p[..] which are eventually combined using Show, how do I suppress the legend of ...
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1answer
103 views

How to simplify $ a^n > -1$ ($\forall$ Integer $n >0$) to $ a > -1 $?

Assume $ a $ is real, and $ a^n > -1 $ for all positive integers $n$. It follows that $ a > -1 $. How can I do this simplification? More generally, I would like to find restrictions on $a$ ...
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4answers
157 views

How to generate repetitive graphs?

I need to create several graph for different values of a parameter $h$. The code is the following ...
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1answer
53 views

Trying to obtain a numeric solution to an inequality. Code might be not working as intended

I need to check whether an inequality can have solutions in the real numbers, given some extra constraints on the variables. I suspect that no solutions exist but I would like some verification of ...
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0answers
74 views

An optimization problem

I have the following two quantities denoted by $LHS$ and $RHS$: ...
2
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1answer
62 views

Why is Reduce in Mathematica giving solution in other symbols that don't exist in original equation [closed]

Here is an example: Reduce[P/Q < (P - X)/(Q - X) && X > 0 && P > 0 && Q > 0 && P > Q, {X}, Integers] The solution ...
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1answer
49 views

Reducing system of 10 inequalities

I have the following system of inequalities of real variables ...
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2answers
364 views

How to prove that $(1 - x)^y \leq 1$, When $1 > x > 0 \wedge y \geq 1$?

The statement in the question is obviously true. But when I tried FullSimplify[(1 - x)^y <= 1, 1 > x > 0 && y >= 1] I got ...
3
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1answer
127 views

Generate convex-hull of a 15 dimensional space

This question follows my last post. I have a function $ \vec{f}: S^6 \times S^6 \rightarrow \mathbb{R}^{13} $ defined on two 6-dim hyperspheres. We will denote the function $ \vec{f}(\vec{x},\vec{y}) ...
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1answer
34 views

Inequality with assumptions

I would like to find 2D region formed by $(a,c) \in \mathbb{R}^2$ such that the inequality $f(a,c,x,y) \geq 0$ holds for all $x,y \in [0,1]$. If I solve this inequality with reduce of the form ...
2
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1answer
49 views

FindInstance for all real values satisfying a condition

I seek at least one instance of positive fractions $p,q,r$ where $p,q,r \in \mathbb{Q}^+$, for which $$\frac12 (a - 2 b + c)^2 \ge pa^2 + qb^2 + rc^2\quad \forall\ a,b,c \in \mathbb{R}.$$ I used this ...
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0answers
86 views

Solving a recurrence relation with variable coefficients

I am trying to solve this recurrence inequality for $ a_n $, hopefully in terms of $ a_0,a_1,c $ and $ x $, $$(1-x)a_{n+1} \le xa_n + (1+x)a_{n-1} + c\quad\forall\ n\ge1$$ What I tried: RSolve. But ...
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0answers
49 views

Simplify (or Reduce) a system of inequalities intelligently

I have the following system of inequalities of 4 real variables 3 (a + b) + 4 (d + c) > 0 && 2 (a - d) + 3 (b - c) > 0 The system can be written as ...
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0answers
62 views

Connectivity of semi-algebraic set

I am given the following semi-algebraic set: $$ \{ x= \begin{bmatrix} x_1,x_2,x_3,x_4,x_5 \end{bmatrix} ^T\in\mathbb{R}^5| -2 \leq (1 - x_2x_3)x_5 - 2x_4x_3x_1 \leq 1.5,\\ ~ -1 \leq x_1 \leq 30,...
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1answer
98 views
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1answer
83 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: ...
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0answers
80 views

Is it possible to solve following question about integer programming using mathematica?

Consider a $5$-uple $(r,a,b,c,s)$ with $a,b,c\in\mathbb{Z},s\in\mathbb{Q}_+,r\in\mathbb{Z}_+$, denote $\frac{1}{2}(a^2-b^2-c^2)-\frac{s}{r}$ by $\Delta(\mathbf{v})$. Let $A$ be a positive real number....
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0answers
39 views

How to find ranges of values where specific conditions are true?

I'm trying to get Mathematica to solve a particular inequality in terms of the variables (and constants) of interest to find where the inequality holds as true. Specifically, I have three functions of ...
3
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1answer
64 views

Determining the absence of Truth value of an inequality given assumptions

I have a set of assumptions, say, $x > 0$ and $y > 0$. So I specified the $Assumptions = x > 0 && y > 0 Now the inequality $x - y/2 > 0$ ...
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1answer
49 views

FindInstance with a symbolic constant

Please consider FindInstance[m >= 0 && x >= 0 && x <= m, {x}] for which, I would like a parametric answer ...
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1answer
80 views

Numerical Integration with Inequality Condition [closed]

I need to solve the following definite integral: $$\int_0^1 \mathrm{d}s \int_0^{2\pi} \mathrm{d}\phi \int_0^{2\pi} \mathrm{d}\phi' \int \mathrm{d}\theta\,'\sin{\theta\,'} \text{,}$$ such that $$\...
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0answers
34 views

Determine if nonlinear function can be positive subject to nonlinear constraints [closed]

I am trying to determine if a certain nonlinear function can be positive when the variables have to satisfy multiple nonlinear constraints. Currently my code looks like ...
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1answer
25 views

Finding smallest domain within which variables can satisfy inequality

Given an arbitrary number of variables $\epsilon_i$ that can be picked from a domain $[0, W]$ and some inequality relation between all the variables $G(\epsilon_1, \epsilon_2, ...)$, is there some way ...
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0answers
71 views

inequalitysolution [closed]

I have a function for which I would like to solve an inequality and find a range of r with respect to other quantities. I am not well familiar with Mathematica, ...
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1answer
66 views

How can I solve this inequality?

How can I find the answer to this inequality for Lambda? ...
2
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1answer
70 views

FindInstance within a range

I am trying to find particular solutions to my inequality for two positive integers $a$ and $b$: FindInstance[a<f[etc...]*b,{a,b},Integers] However I want $a$ ...
2
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1answer
106 views

Inequalities/extracting data from RegionPlot

I've searched everywhere for this but can't seem to find a simple way to do this. I have defined a function of two variables and am able to plot a 2D region in the domain space - the endpoints of the ...
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0answers
92 views

Plotting, NDSolve, initial conditions from range, inequalities [closed]

I will do my best to describe the simplest version of my problem as clearly as I can. Please bear with me: We have a,b and c which are functions of x and y, and their t-evolution is given by coupled ...
2
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1answer
65 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 ...
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1answer
114 views

Speedup of reduce function?

I tried to run this $15$ variable feasibility linear programming to see what the solution looks like. Unfortunately it is taking too much time on my laptop. Is there a way to speed it up? Any tips ...
2
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1answer
92 views
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0answers
58 views

Test varying number of inequalities

I want to test a varying number of inequalities ...
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5answers
247 views

Find all the closest positive integer solutions within a bound for a simple linear equation

Suppose I have a linear equation/inequality like $$xA+yB \leq C,$$ with $x,y \in \mathbb{Z}^{+}_{\neq 0}$ and $A,B,C \in \{x | x = 0.01\mu, \forall \mu \in \mathbb{Z}^+_{\neq0}\}$. I want to find ...