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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3
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2answers
50 views

Solving inequalities involving floor function

Why mathematica doesn’t solve this simple inequality ? Reduce[Floor[x/2]<10,x,Integers] It returns the error:Reduce::nsmet Is it related to floor function?How ...
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1answer
33 views

Find the condition under which an inequality holds

I've got an inequality of 8 non-negative parameters (arising from a 5x5 matrix) and would like to find a condition under which my inequality holds. The condition would be an inequality too of these ...
3
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1answer
73 views

Solving Inequalities using Mathematica

How can I solve this inequality using Mathematica? Sqrt[B^2 + J^2] Cosh[(2 J)/T ] < J Sinh[ (2 Sqrt[B^2 + J^2])/T] where T, J, and B are reals and they are >...
3
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3answers
64 views

Plotting a function with the domain restricted. Basic question

I'm trying to Plot a simple function on a restricted domain. I tried ListLinePlot[Table[x^2, {x, x>-3, x<3, 1}]]. This doesn't work. I'm not sure how to take ...
6
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3answers
138 views

Verify an inequality of many parameters

I've got an inequality of 10 non-negative parameters (arising from a 5x5 matrix) and would like to verify whether it holds. I tried the following, which doesn't seem to work: ...
0
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1answer
46 views

Define a Region where a disequation is satisfied for all values of a variable

I'm having a problem with Mathematica. I have a large and complicate system of 3 inequalities in 3 variables, let's call them x,y,z. Now, I can't use reduce to solve it exactly. There is a way to ...
0
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1answer
56 views

LinearModelFit with the dependent variable given in intervals instead of exact values

I have data of the form $\{x_{i1},...,x_{ik},\{a_i,b_i\}\}$, $i=1,...,N$, and I want to find a function $f(x_1,...,x_k)$ (say, linear) such that violation of $a_i\le f(x_{i1},...,x_{ik})\le b_i$ for ...
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1answer
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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0answers
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 ...
0
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1answer
42 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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0answers
32 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
31 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
52 views
0
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1answer
67 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
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: ...
2
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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 ...
0
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2answers
69 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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3answers
51 views

Replace inequality to equation

I have a region of inequalities from a RegionPlot[]: ...
1
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1answer
180 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 $x_i$ ...
1
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2answers
61 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{...
0
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0answers
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? ...
1
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1answer
59 views

RegionPlot with four parameters

I will try to illustrate my question with an example: Let us define the RegionPlot for b and ...
1
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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
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. ...
1
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1answer
82 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)) ...
1
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1answer
65 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 \\ \...
5
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1answer
186 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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0answers
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 ...
1
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2answers
111 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 +...
2
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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 ...
3
votes
3answers
145 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 ...
1
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1answer
54 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 ...
3
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3answers
186 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 ...
2
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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 ...
0
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1answer
51 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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0answers
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 ...
0
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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 ...
0
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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 ...
2
votes
1answer
87 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 ...
0
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3answers
77 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 ...
0
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0answers
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 \...
1
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0answers
47 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. ...
0
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2answers
153 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: ...
0
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2answers
84 views

RegionPlot avoiding some complex terms

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

Solving Inequalities: Run time too long

I am trying to solve the following system for d: ...
0
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1answer
39 views

Inconsistent region plot?

If I do a region plot of the following inequality, ...
0
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0answers
35 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: ...
1
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1answer
76 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, ...
0
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0answers
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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