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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2
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0answers
43 views

Cannot simplify or reduce a region

I have a region specified by a rather short expression, and the same region by a longer one, and cannot seem to reduce the size of the longer one. A simple example is ...
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1answer
46 views

How can I solve this inequality for every $n$ in Mathematica?

I am trying to find the solution to the inequality $t^{-1/n}<1$ when $n$ is an integer and $t$ is positive, however when using Reduce[t^(-1/n) >= 1, t] it ...
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22 views

Inequalities in the context of stability analysis

I find for the study of the active control of a system with 2 dofs to study the stability conditions. For that purpose, i use the Routh criteria and look when all the coefficients of the first row ...
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45 views

Verifying simple inequality involving FactorialPower function

It is obviously true that FactorialPower[k, m] <= k^m when k and m are both positive ...
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2answers
79 views

Verifying that a functions attends values below something

After plotting the graph of $$f(x)=\frac{π}{3\sqrt{2 π}} (\frac{e^{\frac{-x^2}{18}}}{3} + \frac{e^{\frac{-(x - 5)^2}{2}}}{1} +\frac{e^{\frac{-(x - 15)^2}{8}}}{2} ) (1 + x^2)$$ I would like to ...
2
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1answer
40 views

Inequality plot like Wolfram Alpha

I'd like to reproduce in Mathematica the output of this Wolfram Alpha query. Of course I can just use WolframAlpha but I'd like to manipulate the graphics (add ...
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3answers
59 views

How would I plot the inequality lines together with the intersection plot of the inequalities?

For example, I've got the following code: Plot[{x >= 5, y >= 8, x + 2y <= 64, x + y <= 40}] This would plot: Now, this is fair enough. It shows me ...
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35 views

How to find the value in which an expression becomes greater than another

I have the following expressions: $\Delta \sigma_1=\frac{2 \gamma ^2 \left(\text{$\sigma $Y} \log \left(\frac{\gamma }{\alpha }\right)+\text{pe}\right)}{\left(\gamma ^2-1\right) \rho ^2}$ $\Delta \...
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0answers
43 views

FindInstance Returns “Aborted” [closed]

Edit: Apologies, the question needs to be reworked, because I cannot reproduce the original problem using this code. I don't delete the question, in case someone is preparing an answer at the moment. ...
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2answers
109 views

How to plot all the points which satisfy equation/inequality in two variables?

I am new to Mathematica and I have two questions that I really appreciate if you can help me to solve them. 1) I want to plot all the points (x, y) which satisfy the following equation: ...
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1answer
29 views

RegionPlot avoiding some complex terms

I have a system of inequalities given as follows: ...
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0answers
40 views

Solving Inequalities: Run time too long

I am trying to solve the following system for d: ...
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1answer
26 views

Inconsistent region plot?

If I do a region plot of the following inequality, ...
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0answers
32 views

Translate Mathematica Output to Latex type font [duplicate]

In solving the inequality $2d^2\ge -(2(1+d)+\frac{4d^3}{1-d})(d-1)$, Mathematica returns something using Slots and Functions: ...
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1answer
51 views

Reduce all pairwise comparisons in a list

I have a list of 37 values, like $2d^2$ and $2d(1-d^2)$. I know I can use Reduce[] to solve an inequality of the values. For example, ...
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0answers
71 views

How to make ternary Plot 3D in a different situation?

Owing to xzczd, I could make ternary plot with the following code: ...
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0answers
51 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
39 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
25 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
45 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
36 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
61 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
71 views

Reduce not handling 0 == a properly

Consider ...
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0answers
46 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
161 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
43 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 ...
2
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2answers
89 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
47 views

Strange behaviour of RegionIntersection

Consider this list of inequalities ...
2
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2answers
313 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
307 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
397 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
64 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
140 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
117 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
170 views

How to generate repetitive graphs?

I need to create several graph for different values of a parameter $h$. The code is the following ...
0
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1answer
69 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 ...
2
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1answer
65 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 ...
1
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1answer
57 views

Reducing system of 10 inequalities

I have the following system of inequalities of real variables ...
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2answers
474 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
136 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}) ...
0
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1answer
51 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
52 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
106 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 ...
2
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0answers
59 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
63 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
109 views

How to represent in a 3D graph the set of solutions to this system of inequalities?

I am studying this piecewise function: ...
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1answer
85 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: ...
1
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0answers
83 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
67 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 ...