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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How to solve a problem with inequality

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How to find a set of solution of the inequality?

There exists a,b,c,d,e such that ...
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How to get a solution of this inequality?

I used ...
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Solving a set of trig inequalities

I have a set of inequalities Cos[a]Cos[b]>=Cos[t-a]Cos[b]&&Cos[a]Cos[b]>=Cos[t/2]&&Cos[a]Cos[b]>=Sin[t/2]&&a<=t<=Pi How to ...
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How to prove or disprove an inequality with Mathematica?

I mean there exist $\lambda>0, x\in \mathbb R$ s.t. the inequality $$ \frac{3^{\lambda } e^x+e^{3 x}+1}{2^{\lambda } e^{2 x}}<\frac{1}{10^{100}}$$ is valid. Here are my unsuccessful attempts. <...
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Why does MMA fail to find a solution but WA does?

I am looking for $n$, where $$\dfrac{2^{-3 n-2} \pi ^{n+1}}{(n+1)!}<\dfrac{1}{10000000000000000}$$ We can just test values of $n$ and find the smallest $n = 13$, or any $n \gt 13$ or can use ...
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While Loop inside a Do loop and the usage of a break

I am struggling with using a While loop inside a Do loop and using the break to break the loop. In this code, I would like to use the While loop for the value of i and the Do loop for the value of h, ...
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Reduce works for simple inequalities in Reals but not in Integers

In the domain of Reals Reduce correctly reduces the system to True: ...
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Reduce an inequality

I have this inequality I don't know why it is not working?! ...
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Solutions to systems of linear inequalities

I want to obtain canonical representations of solutions to sets of linear inequalities. For example, $x \ge y \ge z \ge 0, x - y - z < -1$ and at least one of $z > 0$, $-1 \ge x - y$ and $x - y \...
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Intersection of a set of structurally homogeneous inequalities and extracting a combination of numbers to fully satisfy it

There are a number of structurally homogeneous inequalities: $\begin{array}{l} \left| s_1\right| \leq \sqrt{4 s_2} \\ \left| s_2\right| \leq \sqrt{4 s_4} \\ \left| s_3\right| \leq \sqrt{4 s_6} \\ \...
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How to prove the inequality of undefined function?

For example, how to prove the following inequality? ...
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How to find constrains on variables that make a system of inequalities not have a solution

My problem is as follows: How do I ask Mathematica the following question. Let $f(x,y,z,a,b)$ be a 5 variable polynomial. I want to find all values of $a,b$ for which $f$ has no zeros in the region $...
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Challenges and Opportunities of `FindInstance` Command

I'm testing the FindInstance capabilities and ran into one problem that behaves similarly with different types of inequalities. I calculate two points satisfying ...
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Formalization of one optimization problem or solution of inequalities - Part №2

Continuing the question: Formalization of one optimization problem or solution of inequalities Let's consider a more complex problem. We have two polynomial: $p_1=A_2t^2+A_1t+A_0$ $p_2=B_2t^2+B_1t+B_0$...
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Formalization of one optimization problem or solution of inequalities

I have polynomial: $p=A_2t^2+A_1t+A_0$ $A_0=(x^2-y^2)+xz$ $A_1=x^2+y^2+z^2+\sin(x)$ $A_2=x^4+y^3+z^2$ $x,y,z$ - parameters, moreover $z$ - the value of which varies in the range $[0,1]$. Polynomial $p$...
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InverseFunction of ArcTanh and Log [closed]

I solved an equation and one solution was this: ...
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Find the $z$ such that $|z + a| \leq |z| + |a|\cos(\arg(z))$

Find the $z$ such that $|z + a| \leq |z| + |a|\cos(\arg(z))$. My approach is to use Resolve: ...
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How to find an instance of this inequality?

I am trying to show that a given inequality is true for some triple but I am having trouble finding anything. Here is a tiny version of what I am working with: We define the following polynomials <...
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NMaximize - global maximum fail - How to?

Problem : Let x,y,z be non-negative real number whose sum is 1. Find maximum of 0.2x + 0.2y + x^2*z + y*z^2 What I did first was reducing variable. ...
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Tips to help FindInstance with a lot of complicated inequalities

I'm trying to find a numerical instance (I don't need arbitrarily high precision) of solution to 7 relatively complicated inequalities (plus the region specification) involving 8 variables. The ...
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How to "read" the solution of an inequality?

The solution of fun[x,y]>0 leads to the following output ...
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Obtain Data Points (x,y) from a 2D region plot generated from an inequality

I have a code that generates a region plot modeling an aperture. I would like to generate a table of ordered pairs (x,y) for a given u that manipulates my inequality. When I attempt to great a table ...
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Why isn't this expression returning true to being positive when it is clearly positive?

Consider: ...
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Plot the region given by inequaities

How can one visualize the regions of intersection of the following ...
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FindInstance: How does it work for linear inequalities?

I have a set of linear inequalities, rational coefficients. When FindInstance returns {}, does that really mean there is no ...
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How plot the domain of multivariable function? [closed]

I want to get and plot the domain of the following function with mathematica : $$Arccos(xy)$$ Any idea ?
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How to determine values of parameters such that an inequality is satisfied?

Given inequality f[x, y]>0 where f[x, y]=1/16 (-1 + x (2 - x + x^3 (-1 + y)^2 y^2)), how can one find the values ...
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Can't this inequality really not be solved with Reduce?

Taking $\alpha$ as given, I am trying to understand/know under which restrictions on $n$, the following holds: $$ 0 \leq n+\alpha W\left(-e^{\frac{-n}{\alpha}} \right) \leq 1.$$ i.e I want to solve ...
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Find smallest instance satisfying certain inequalities

I need a "clean" way to find the smallest solution to some (in)equalities given by Reduce and containing only one variable ...
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3 votes
1 answer
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Solution for inequality equation - "Cannot be solved with the methods available to Reduce"

I am trying to solve the following inequality for $v$: $b>e^{\frac{-v}{\alpha}}\cdot \alpha + v$. (Where I know: $b>0$, $v \in [0, 1]$, and $\alpha >0$). However the following doesn't work: <...
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How do I generate a random permutation of a (long [millions-length]) list of symbols? [closed]

I have a list of length twelve: p = {t[1, 1], t[1, 2], t[1, 3], t[1, 4], t[2, 2], t[2, 3], t[2, 4], t[1, 5], t[3, 3], t[3, 4], t[1, 6], t[4, 4]} and a set of ...
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What is the proper way to solve inequalities in WL?

I often have to transform inputs of trigonometric functions which involve finding the new domain. The inequalities themselves are trivial to solve but they get tedious. ...
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Why can't this set of inequalities be solved with the methods available to Reduce?

Take the following set of inequalities: ...
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Using Simplify and Reduce with Assumptions when the inequality is already one of the assumptions

I am using the Simplify and Reduce functions to reduce inequalities, but somehow the function Simplify does not consistently give "True" when the inequality happens to be one of the ...
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5 votes
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Why does Reduce give False on SameQ with its copy-pasted result?

If I evaluate Reduce[#, x] & /@ {{4 x > 1, 2 x < 5}, {5 x > 1, x < 5}, {4 x > 1, x < 5}} the result is ...
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Can Mathematica solve this exponential equation

My version (12.1.0.0 Student Edition) does not solve this equation: Solve[Exp [-n^2/(2 m)] <= 3/4, m] WolframAlpha finds the solutions, but only for integer n? ...
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How to solve this inequality with Reduce or Solve?

I need to solve this inequality: ...
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Why doesn't Reduce work?

I try to solve an inequality with parameters using Reduce. The answer i get is : This system cannot be solved with the methods available to Reduce. Here is the inequality: ...
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Reduce not working

I am trying to check some inequality with Reduce function, but Mathematica doesn't work. The code I am using is: ...
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3 votes
1 answer
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Solve system of trigonometric polynomials

I am trying to solve a real system of trigonometric polynomials, which contain 7 symbols {b[1],b[2],b[3],b[4],a[2],a[3],a[4]} between 7 equations: ...
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Solving equation for specified parameters

I have a long expression which depends of several parameters ...
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Condition of existence while solving inequalities

I would like to have solutions of inequalities where condition of existence are included, but Reduce doesn't work like this, it would simplify the denominators ...
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plotting an inequality [closed]

Can anyone help in plot an inequallity Abs[[x/[1 + x]] - [y/[1 + y]]] <= Abs[x - y]/[1 + 0.01 Abs[x - y]] where 0 < x< 1 and 0 < y< 1 When I tried with Plot command as well as Plot3D ...
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Finding the joint domain for a couple of functions of three variables

I have two functions $f_{1}(x,y,z)$ and $f_{2}(x,y,z)$ defined respectively as ...
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2 votes
3 answers
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How to solve this inequality correctly?

Find the value range of real number a, so that for any real number x and $\theta \in\left[0, \frac{\pi}{2}\right]$, make $(x+3+2 \sin \theta \cos \theta)^{2}+(x+a \sin \theta+a \cos \theta)^{2} \...
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Regarding validity of expressions involving inequalities

This expression is valid: $$\left|\log(1+x) - \log(1 - x)\right| \leq \frac{\left|x-y\right|}{1+|x-y|},\ \ 0<x<1, \ 0<y<1 $$ How we can prove using Mathematica (either graphically or ...
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How to simplify one side of an inequality with a lot of square roots that are the same

Mathematica seems to refuse to simplify the following inequality, even though it is obvious there are things that can be done ...
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3 votes
1 answer
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RegionPlot edges with different BoundaryStyles?

I executed this command: RegionPlot[x > 2 && x < 3 && y > 2 && y < 3, {x, 0, 4}, {y, 0, 4}] I would like the top and right sides of the square to be dashed lines ...
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9 votes
5 answers
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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 ...
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