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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4
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1answer
109 views

What is the difference in pattern matching

Here is some pattern code: ...
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1answer
140 views

Using Solve for Objective function max/min [closed]

I have an objective function z = 4 x + 2 y with constraints of ...
0
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1answer
187 views

Intersection of volumes defined by inequalities

I have 5 inequalities with some parameters like dh, din and thetawhich I intend to vary. In ...
1
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1answer
479 views

Volume of a Region defined by Inequalities [duplicate]

I am trying to compute the volume of a 3-dimensional region defined by 5 inequalities. Mathematica takes too long to compute it. In fact, I haven't ever seen it complete the execution of the below ...
0
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2answers
213 views

Verifying inequality in Mathematica

I am trying to verify the following inequality Mathematica. This I wrote the fillowing code: ...
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2answers
54 views

Chains of approximate numeric equalities

Mathematica considers two numbers equal if "at most their last seven binary digits" differ. For example: ...
2
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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 ...
0
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0answers
98 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(...
4
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2answers
214 views

Checking inequalities: How can $x>0,y>0$ yet $x+y$ indeterminate?

I have the following: ...
3
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1answer
428 views

Reduce a complex inequality

Reduce[Abs[1/(1 + I/Sqrt[α])] < 0.5, {α}] It is taking long time to run. Can any one help me to get the reduced condition in terms of $\alpha$ or its modulus. ...
0
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2answers
100 views
3
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1answer
94 views

Numerical testing of Hardy's inequality

I want to check the following, Hardy's most fundamental inequality, by using Mathematica: $$\sum_{n=1}^\infty \left(\frac{A_n}{n}\right)^p<\left(\frac{p}{p-1}\right)^p\sum_{n=1}^\infty a_n^p$$ ...
3
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1answer
550 views

Way to simplify an inequality with many variables

my problem is the following: I have three inequalities in five variables $x,u,a,b,c\in \mathbb{R},x>0 $: ...
2
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2answers
147 views

Ask Mathematica if there exists a value that satisfies conditions

I would like to build a function that returns true if there exists even one value of xg1 such that having as inputs Mtot, PL, xg2, mac, xga, and defining ...
3
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2answers
184 views

Problems with integrating over a region

Following the example of this answer: Find the volume of the region defined by $|x|+|y|+|z|<4$ I tried to compute the following integral over a region by using ImplicitRegion. However, when I ...
0
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2answers
320 views

Solving several inequalities in Mathematica

I am a very beginner of Mathematica and the following will probably be a very stupid question. I have a bunch of inequalities in 6 unknowns and I want to find the set of values satisfying them. Can I ...
0
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1answer
80 views

Reduce unable to solve simple inequalities with quantifiers

I have try to solve following inequalities using Mamthematica. But it unable to solve that. ...
3
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2answers
102 views

Solving an inequality involving the Fibonacci function

How can I solve an inequality that involves the Fibonacci function? For instance, say I want to determine for which values of $n$ we get that $$F_n\leqslant 1000.$$ I tried to use ...
1
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0answers
335 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 ...
5
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3answers
277 views

Relational operators on vectors

How do I use relational operators on vectors? {1, 2, 3} > {0, 1, 2} (*outputs {1, 2, 3} > {0, 1, 2}*) More generally, I want ...
6
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2answers
97 views

Strange behavior with Inequality and pattern matching

An expression like this one a < x < b is normally represented as Less[a, x, b] while an expression like ...
0
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1answer
116 views

How can I graph this inequality on the x-y plane?

I'd like to graph the following inequality on the x-y plane: $$ P(y): (\forall x\in [0,y))\left(\frac{x - \epsilon(1+a)}{a} \leq y \leq \frac{x + \epsilon(1+a)}{a}\right) $$ This is the set of ...
1
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1answer
85 views

Create large system of inequalities by substituting coefficients from intervals

I have given statements for example: $ax + by < c_1$ $cx + by + dz < c_2$ And I want to create larger system of inequations in such a way (suppose variables $x,y,z$ from intervals): I replace ...
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2answers
117 views

How can I make a command to write out the solution of the absolute value inequality?

I've written this source code, but I can't finish it yet. ...
0
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0answers
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 ...
0
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0answers
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 ...
1
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1answer
201 views

Wrong root when using numerical values

I have the following inequality: $$ \sqrt{\frac{a}{2x}}+ \frac{b}{1-\frac{a}{a+\sqrt{a(2bx + a)}}} + \frac{a}{2x\frac{a}{a+\sqrt{a(2bx + a)}}\left(1-\frac{a}{a+\sqrt{a(2bx + a)}}\right)} < f $$ on ...
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0answers
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'...
0
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1answer
289 views

Check an inequality if one condition holds

A = Abs[-1 + 1/(1 + β)] + Abs[-((1 + 2 α + Sqrt[1 + 4 α + 4 α β])/(2 α + 2 α β))] Is A <1 if ...
4
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1answer
182 views

How to reduce/simplify an inequality involving Abs[]?

Can Mathematica reduce this inequality into a domain of z, where {z, r1, ...
3
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1answer
136 views

Using TrueQ with conditions

Say I want to ask Mathematica whether $|x| = x$ for all $x > 0$. Obviously, if I try TrueQ[Abs[x] == x], I get False, ...
0
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1answer
306 views

Plot absolute value inequalities - number line

I'd like to ask you about the way to draw the number line for absolute value inequalities. Is there any built-in tool? In this case the input was $|x-6| > 3$. My point is to achieve something ...
0
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2answers
114 views

Evaluating a list of inequalities with random numbers [closed]

I have a list of inequalities, which include in total four parameters, that I would like to test by feeding the four parameters with random numbers. The goal is to find the best values of the ...
8
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3answers
2k views

Shading a region where an inequality is satisfied

Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later I'm creating solution sets for a calculus course and need to shade the region in $\mathbb R^2$ such that $x^2 < y < x^4$. ...
0
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1answer
133 views

Reduction of an Inequality in $\mathbb{C}$

Reduce[ Abs[-((4 p)/(-1 + Sqrt[1 + 4 p + 4 q])^2)] + Abs[-((4 q)/(-1 + Sqrt[1 + 4 p + 4 q])^2)] < 1 , Abs[p]] It is taking lot of time. It is running. Can ...
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0answers
104 views

Simplify Integer powers in inequalities

I have a fairly simple expression that I am surprised Mathematica (10.1) won't simplify ...
2
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1answer
188 views

Solve an inequality involving a sum with a parameter

Good day. I am new to Mathematica and I am looking for advice. Is it possible to solve $$\sum_{k=0}^{n} \frac{p^k}{k!}>0$$ for $n$ where $p$ is a parameter? When I do ...
0
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0answers
51 views

Need help with solving inequality under assumptions [duplicate]

I seriously need help for my research. I need to solve an inequality with several assumptions. I tried many times with Reduce but it did not work out properly. Sometimes the results I get are simply ...
1
vote
1answer
135 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 ...
-1
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1answer
199 views

Find a minimum value which satisfies an equation

I have to find a minimum value of "a" which makes x=-a+b+c, y=-a+b+c^2 positive where a>1, 0 ...
0
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1answer
116 views

Trouble in finding instances of values of variables that satisfy an inequality

Consider the following mathematical expression with complex numbers (phasor) and two variables (lambda and ia2): ...
4
votes
1answer
521 views

How to solve a conditional inequality?

I am trying to use Mathematica to solve a conditional inequality. Find all (real) numbers $a$ and $b$ such that $|a| + |b| \ge 2/ \sqrt{3}$ and for any real $x$ the inequality $ |a\sin x + b \sin ...
4
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1answer
239 views

Does `Reduce` give complete and necessary conditions?

I want to obtain a solution for a system of five inequalities. For instance, ...
6
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1answer
125 views

How to simplify expressions by closing open inequalities?

Recently I have often acquired results which consist of combinations of 0, 1 and 2-dimensional (in)equalities. For instance, consider a very simple case with ineq1 ...
4
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0answers
107 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] ...
3
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4answers
2k views

Find the volume of the region defined by $|x|+|y|+|z|<4$

I want to find the volume of the region defined by the following inequality: $\quad \quad |x|+|y|+|z|<4$ In addition to calculating the volume of this region, I would also like to be able to ...
2
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0answers
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: ...
4
votes
1answer
504 views

How to draw a tropical surface?

By definition, a tropical surface in $\mathbb R^3$ is the set of points $(x,y,z)$ where the maximum $f=\max(f_1,f_2,\dots,f_n)$ is attained at least twice, here $f_i$ stand for some linear functions ...
0
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2answers
158 views

Proving simple inequality

I have a simple function and want to make sure that it satisfies an inequality over a certain range of parameters. My approach is: ...
-1
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3answers
153 views

Filtering the output from Table and export it into excel

I have the following functions ...