# 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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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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### 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] ...
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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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 ...
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 ...
104 views

### Simplify Integer powers in inequalities

I have a fairly simple expression that I am surprised Mathematica (10.1) won't simplify ...
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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### 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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### Solving inequality

I am trying to solve this inequality for $\eta$, where B, J, $\eta$, and $\beta$ are reals and $\beta$>0. I used ...
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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### 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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### 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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### 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: ...
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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### 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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### 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 ...