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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Inequality problem [migrated]

What are the values ​​of $B_1, B_2$, and $B_s$ so that the following inequality is satisfied with any value of $U1$ and $U2$? $ B_1 U_1^2 + B_2 U_2^2 < B_s (U_1-U_2)^2 $
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111 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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1answer
145 views

Reduce with for all and implies

I have the following question. p1 = a (1 - c + a) p2 = b (1 - c - b)/((1 - b)^2) v1 = (x^1.5 - 3*x)*p1 v2 = x*p2 I want to find x ranges which makes v1>v2 under ...
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1answer
38 views

This system cannot be solved with the methods available to Reduce [closed]

I get the error message in the Title, which is not very helpful. Situation: Reduce[ForAll[{x,y,z},Implies[x<=y&&y<=z, x<=z]]] evaluates to True, ...
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2answers
80 views

RegionPlot avoiding some complex terms

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

Setting the tolerance for `Equal[]` [duplicate]

I would like to control how Equal[] works and allow a certain error associated with it. I would like numerical values which are, say, within one-thousandth of one ...
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0answers
30 views

Tackling variational problem with constraints [closed]

I need to minimize (preferably symbolically) functional with constraints: $$ F = \int_{0}^{\pi/2} f(x)cos{x}dx\,\\ 1.1 \geq f(x) \geq 0\\ 2.\int_{0}^{\pi/2} f(x)dx=Const\\ 3. f(0) =1\\ 4.f(\pi/2) = 0\...
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1answer
74 views

How to plot a graphic with solution of some inequality?

I defined the function $z(n)$ by z[n_] := Catch[Do[i; If[Mod[Fibonacci[i], n] == 0, Throw[i]], {i, 100000}]] and now, I would like to plot the graphic (n,z(n)) ...
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1answer
157 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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1answer
65 views

How to verify an inequality?

I'm working with an expression that seems to be non-positive, but I'm having a hard time verifying it: ...
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2answers
66 views

Positiveness of two variable inequality

How to show that the function g[a_, n_] = -4 a^2 + 8 a^3 - 4 a^4 + 16 a n - 24 a^2 n + 8 a^3 n - 12 n^2 - 4 a n^2 + 12 a^2 n^2 + 12 n^3 - 8 a n^3 of ...
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1answer
101 views

Can Mathematica Resolve this inequality?

I want Mathematica to Indicate this inequality is (hopefully) true for all values that meet the initial conditions: a+b+c=1 and a,b,c are positive real numbers ...
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1answer
177 views

How to visualize and solve darboux-like sum taking average of function $P$ defined on domain dense in its’ infinite limit points?

Consider $P:A\to[0,1]$ where $A\subseteq[0,1]$. Suppose $$A=\left\{\frac{1}{2^x}+\frac{1}{2^y}+\frac{1}{2^z}:x,y,z\in\mathbb{Z}\right\}\cap[0,1]$$ and the partition of $[0,1]$ is a sequence $x_i$ ...
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3answers
48 views

Replace inequality to equation

I have a region of inequalities from a RegionPlot[]: ...
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1answer
182 views

Summation with inequalities

How can I perform this function with Mathematica? $$\sum_{1\le j<k\le N}\frac1{\left(r_{jk}\right)^\alpha}$$ where n = 5.
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2answers
58 views

Solving a big system of equations using certain conditions

I have the following problem: I want to solve a big system of equations for a certain number of variables which I call $a_k$, the variables need to satisfy the following conditions: all $a_k\in\mathbb{...
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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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1answer
58 views

RegionPlot with four parameters

I will try to illustrate my question with an example: Let us define the RegionPlot for b and ...
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1answer
19 views

Putting a Count function for a matrix, in a loop

previously i had a doubt on how to assign different rows with certain values using a special function, which i later figured out by using the far more superior "DO" Loop. At present i have two ...
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0answers
25 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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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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1answer
61 views

Finding a Numerical Solution to a Linear Combination Inequality [closed]

Can I use Mathematica to find a value for $\alpha$ that satisfies the below linear combination inequality? If so, how? $$ \begin{bmatrix} -1 \\ -1 \\ -1 \end{bmatrix} < \begin{bmatrix} g_1 \\ \...
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0answers
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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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1answer
75 views

Solving a coupled system of inequalities over integers

! tried to solve $ \frac{999999}{1000000}<a+\sqrt{2} b\land a+\sqrt{2} b<1$ over the integers through ...
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3answers
131 views

Is there a way to speed up the following calculation Table[If[TrueQ[],k,Nothing],{k,10^5,10^7}]

I've the following code: Table[If[TrueQ[2+3^k>2^k+(-1+2^k)*Floor[(3/2)^k]],k,Nothing],{k,10^5,10^7}] Is there a way to speed the calculation up in Mathematica ...
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1answer
107 views

Simplifying integer inequalities to equality

I try (in Mathematica 10) FullSimplify[l >= l1 + l2, {l <= l1 + l2, Element[l | l1 | l2, Integers]}] But that gives back ...
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1answer
52 views

Numerical results for Reduce on an inequality

I am trying to determine the regions parameters (a, b) must belong to for a function to be negative for any argument x greater than zero. I have tried using Resolve ...
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3answers
181 views

Solving inequality with logarithmic expression

I am trying to solve the following inequality 2 y(Log[1 + (y-1)x] - x Log[y]) - x(1 - x)(y - 1)^2 < 0 where ...
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0answers
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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1answer
50 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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2answers
302 views

Using Mathematica to confirm Bernoulli's inequality

I have several challenges that I want to confirm is true. I have chosen this one because it is rather simple (proof by induction). There are times when I do not want to spend ages trying find proofs. ...
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7answers
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Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

As an intermediate step, consider the function: f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the ...
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1answer
2k views

Proving inequalities with Mathematica

Question summary: I would like to learn some tips and tricks on how to prove inequalities with Mathematica. I'm studying various inequalities in triangle that have the form $R+ar + bs\geq 0$, where $...
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0answers
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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0answers
24 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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3answers
76 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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2answers
82 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 ...
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1answer
80 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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0answers
37 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
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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
148 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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0answers
41 views

Solving Inequalities: Run time too long

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

Inconsistent region plot?

If I do a region plot of the following inequality, ...
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0answers
34 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
71 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
76 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
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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2answers
49 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
54 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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