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.

48 questions with no upvoted or accepted answers
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45 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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109 views

Inequality involving Quantity stays unevaluated

Bug introduced in 10.1 and solved in 11.1 An expression like this one a < x < b is represented as Less[a, x, b] ...
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43 views

Evaluating inequality involving powers

I want to evaluate an inequality of the form $x^a > x$ under the assumptions $x > 1$ and $a > 1$. I expect this inequality to be true, but ...
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44 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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66 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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85 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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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: ...
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171 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: ...
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2answers
113 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: ...
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26 views

Sign of a determinant based on sign conditions

New user here. I want to sign a determinant, using known qualitative conditions on the components. any help appreciated. dummy example below. thanks. ...
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86 views

problem with solving inequality $x+1/x>-1+1/x$. different answer in Mathematica and Wolfram Alpha

I tried to solve inequality $x+1/x>-1+1/x$ with Wolfram Alpha, and it gave me the answer $(-1,0)\cup(0,+\infty)$. This is correct. But when I try to solve it in Wolfram Mathematica 12.0 (with ...
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2answers
105 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 +...
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25 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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54 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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120 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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67 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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158 views

Error using NMinimize/NMaximize : The initial region specified may not contain any feasible points

Link : Reduce time taken to get feasible solution An example of 18 non linear inequations with 4 variables is given in the image. But I have a set of 32 non linear inequations with 9 variables (I ...
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103 views

Solving an Inequality that contains many unknown variables

So, I'm a beginner in using mathematica, can do only the basic stuff... anyway, I want to find the bound for [pi], that makes this quantity 2 ((n - y)Log[(n - y)]+yLog[ y_]-yLog[n[Pi]] - (n - y) Log[...
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78 views

FullSimplify versus Reduce applied to set of inequalities

I have a complicated expression Expr describing a bunch of inequalities and I am trying to reduce it to a manageable subset that facilitates ready interpretation. I ...
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341 views

Can Mathematica solve Kuhn-Tucker Equations with arbitrary functional form (up to 2nd order derivative)

I am in a business of solving a 5-variables optimization with inequality constraints, and I would like to maintain the functional form as arbitrary as possible. So far, I am assuming that the ...
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104 views

Simplify Integer powers in inequalities

I have a fairly simple expression that I am surprised Mathematica (10.1) won't simplify ...
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62 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. ...
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68 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? ...
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49 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 ...
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37 views

Simplify large equation system, with conditions

I have a large matrix $Q$ where $0≤Q_{ij}≤1$ and $\sum_iQ_{ij}=1$ for $j=1,2,3,4$, and all entries depend on 6 variables $a,b,c,d,e,f$. Is it possible to simplify this huge matrix? ...
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47 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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38 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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2answers
84 views

RegionPlot avoiding some complex terms

I have a system of inequalities given as follows: ...
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44 views

Solving Inequalities: Run time too long

I am trying to solve the following system for d: ...
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77 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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53 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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91 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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85 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 ...
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58 views

Test varying number of inequalities

I want to test a varying number of inequalities ...
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160 views

Drawing convex cone with given vectors

I have vectors in matrix form. By using Mathematica, I want to draw it as convex cone and intersect. Let me explain, my intent is to create a new cone which is created by intersection of a null spaced ...
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50 views

Why does Mathematica take an aeon to solve an inequality?

I gave Mathematica this inequality to solve: ...
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35 views

Solving an inequality with conditions on the values

I have to know if an equation is always negative for the realistic set of values that I'm looking at. The problem is that the equation is way too big. I know I can do it manually if I spend a couple ...
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55 views

Solving Inequality involving Sum of PrimePi's

I am trying to figure out if for each $n$ we have $$\sum_{i=1}^n\pi (2^i)+(1-1/2^n)\Bigg(\sum_{i=1}^{\lfloor n Log2/Log3\rfloor-1}\pi(3^i)+\sum_{i=1}^{\lfloor n log2/log5\rfloor-1}\pi(5^i)+\cdots+\...
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100 views

Verifying inequality with a specific set of parameter restrictions

I would like to have Mathematica check an inequality over a set of parameter restrictions. More in detail, given a function $f(x;a,b)$, where $a$, and $b$ are parameters, I would like to verify that $...
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65 views

Find out if a very complicated function is always $\le 0$

On $\mathbb{R}^4$ put coordinates $x1,y1,x2,y2$ and consider the function $c:\mathbb{R}^4\rightarrow \mathbb{R}$ defined in the following way: ...
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142 views

Inequality Solving

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130 views

How to simplify $x \coth(x) > 1$?

I have the inequality $x \coth(x) > 1$ which is correct for real arguments $x>0$. However, Mathematica does not seem to realize this: ...
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299 views

Solving a set of nonlinear algebraic equations under inequalities constraints

I just started today using Mathematica. I want to solve the following four equations already written in the function "Solve" under four inequalities constraints and one unequal constraint. ...
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99 views

How to solve a quadratic inequality containing parameters?

I have the following inequality to solve for $R$ in terms of $\delta$ and $n$, with assumption that $n \geq 3$ and $\delta>0$: $$-2 < 2 -\frac{16n\delta^{2}}{R^{2}\sin^{2}\frac{\pi}{n}} \left(...
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123 views

How can I make an amateur demonstration to solve absolute value equations and inequalities?

I would like to make a program which can solve absolute value equations and inequalities, but I'm a beginner of using the mathematica. I found amazing good demonstrations at the web-page of ...
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79 views

Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?

In order to solve This problem: What is the maximum value of coefficient fv with the constraint that the matrix is positive semi-definite?, I have used the following code (Determinant is computed by ...
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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'...