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 can I solve this inequality? Can I provide extra information when doing Solve?

I am new to Mathematica so I could really use your help. I am hoping to figure out the condition that the following function is larger than 0. I tried to FullSimplify it and to simplify it myself ...
C. K's user avatar
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2 answers
119 views

Simplifying a logical expression with multivariate polynomials

I have several expressions similar to a (a b + c d) != 0 || b (a b + c d) != 0 || c (a b + c d) != 0 || d (a b + c d) != 0 and I would like to reduce them ...
მამუკა ჯიბლაძე's user avatar
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Get limits of values from inequalites

My code above as below; ...
Soon's user avatar
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2 answers
135 views

How to numerically find complex non-real roots of a function?

Using Mathematica, how can we numerically find only complexes, but not real roots, of a function? For example, if we have f:C->C, and we have roots like, R1,R2,...,Rn (real roots, without imaginary ...
GarouDan's user avatar
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2 votes
1 answer
108 views

Equation different plots

I have this equation to plot. f[x]*g[x] >= 310 the problem is how should it be converted? should I write ...
lia's user avatar
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0 answers
102 views

Solving simple inequality gets MMA into an infinite loop [closed]

I was solving inequalities and here is a very simplified version of what I am seeing. When you do the following, all is well. Reduce[3^n < 250, n, Integers] ...
Moo's user avatar
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Transforming a set of conditions with both equalities and inequalities using linear transformations

I wish to Transform a set of conditions, containing both equalities and inequalities, by using a kind of "change of variable" on the constrained variables. The change is straightforward (it ...
sg1234's user avatar
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How to transform the regions in which a piecewise function are defined?

I have a function f[x,y,z] that has a piecewise definition, i.e., its values depends on the ranges of the arguments. Now suppose I have a coordinate transformation <...
user1620696's user avatar
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Range of values which not satisfy an equation?

Let $$x+5=z\tag1$$ 1. How can i obtain all the values of $0<x<10$ which don't satisfy the given relation. Edit: of course $x$ and $z$ are positive integers. 2. What command should i use to find ...
Mathix's user avatar
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2 answers
86 views

`Reduce` is running forever

I'm trying to solve the last inequality in Reduce in the code below in terms of rmax under the parameter conditions included in <...
ppp's user avatar
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Solving multiple inequalities

I am new to Mathematica and I want to know if there are solutions to the following 4 coupled inequalities. Note that the inequalities are long and cumbersome with many variables with subscripts (I ...
Monty's user avatar
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Find the condition under which an inequality is satisfied

I need to find the conditions among the variables under which the inequality est-tru>0 holds. ...
Dotman's user avatar
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Parametric Plotting 6D Dimensions to 3D for Visualizing a Solution

I am trying to find out when: $$f(x,y,z,α,β,γ):= z\cos(β)\cos(γ)+y(\cos(γ)\sin(α)\sin(β)+\cos(α)\sin(γ))+x(−\cos(α)\cos(γ)\sin(β)+\sin(α)\sin(γ)),$$ where $α,β, \text{and } γ$ can be any value in $[-2\...
Teg Louis's user avatar
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3 votes
3 answers
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Computation time unexpectedly long for a Volume

The command is Volume[Region[ImplicitRegion[{Sqrt[x^2+y^2]<=Abs[Sin[z]],0<=z<=2Pi},{x,y,z}]]] The computation time is exceeding my expectation. The ...
Jowo's user avatar
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2 answers
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How to show a region defined by an inequality within the specified domain?

Firstly, I wrote the following code to specifiy the domain of the variables a and x: ...
Ya He's user avatar
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How to get the range of analytical solution of inequalities?

Is there a way to get the range of analytical solution of inequalities? Such as: ...
Y. zeng's user avatar
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Trying to use Linear Optimization to solve inequalities

I am trying to use Mathematica to get bounds on some quantities using a certain procedure which is called conformal bootstrap. For the users who don't come with a background in HEP, I am basically ...
QFTheorist's user avatar
2 votes
1 answer
89 views

Finding parameter range from two solution sets

Let the solution set of the following system of two inequations $$x^2 - 4 x + 3 < 0 \\ x^2 - 6 x + 8 < 0$$ be a subset of the solution set of $$2 x^2 - 9 x + a < 0.$$ How can I find the range ...
csn899's user avatar
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2 votes
4 answers
251 views

Solving inequation with parameter

Let the following inequality $$4^xa - 2^x + 1 > 0$$ hold for any $x$. How can I find the range of parameter $a$? The following method doesn't work: ...
csn899's user avatar
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1 answer
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Finding parameter range of inequation with no solution

Let the solution set of the following inequation $$6 k - 2 x + k x^2 < 0, \quad k \neq 0$$ be an empty set. How can I find find the range of parameter $k$? The following code gives an answer: ...
csn899's user avatar
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2 votes
5 answers
438 views

Calculating union of two sets of reals

Given the following two sets of reals: -(1/4) < x <= 0 || 0 < x <= 1/2 || x > 1/2 x <= -1 || -1 < x < 0 how can I calculate their union? ...
csn899's user avatar
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1 answer
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Solving inequation with a solution set from another inequation

Given that the solution set of inequation $$ax ^ 2-bx-1>0$$ is $-1/2<x<-1/3$, I want to calculate the solution set of inequation $$x ^ 2-bx-a\geq 0.$$ I have used the following code, but is ...
csn899's user avatar
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1 vote
1 answer
68 views

Why can't the range of this inequality parameter be determined?

How can I accurately find the range of $t$? Reduce seems to be unable to find it: ...
csn899's user avatar
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How to merge the solution sets of inequality involving Trigonometric functions?

...
csn899's user avatar
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2 answers
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How to simultaneously determine the range of x and base a when an inequality with logarithms holds?

Log[a, x + 1] > Log[a, x - 1] the inequality above is equation holds good under all circumstances You can see the range of x ...
csn899's user avatar
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4 votes
1 answer
97 views

Understanding the MeshShading options

The following code draws the intersection of a surface N: eqNcar=0 with three other surfaces defined by eq1=0, ...
Smilia's user avatar
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2 votes
1 answer
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Possible ranges of variables that are defined by inequalities

There are the following inequalities 0.09 <=(a1*a2)/(a1 + a2) <= 0.2 and 1 >= a1/a2 >= 0.5 How can all possible ...
Mam Mam's user avatar
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Solving system of inequalities and equations with Reduce

I want to the use Reduce to solve a system of equations and inequalities. In particular, I am looking for the conditions for which: $$ \left(\alpha\frac{B-K_R}{p_e}\...
bubuteo's user avatar
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1 answer
50 views

How to solve this inequality? [closed]

This inequality: -1 + a E^x > 0 ...
csn899's user avatar
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1 vote
2 answers
97 views

Generate family of linear inequalities from vector variable for use in `FindInstance`

Suppose that I have a vector variable xvec = Array[x, 10]. How do I generate the family of linear inequalities $$F = \{ {x\in\mathbb{R}^{10}:x_1\geq x_2,\ldots,x_9\...
rrrrr's user avatar
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How to estimate whether the objective expression has a global minimum value?

I have an expression concerning $x$ as follows (from my friend). $f(x)=x^4-2 a d x^3-2 b d x^3-2 c d x^3-2 d x^3+a^2 d^2 x^2+b^2 d^2 x^2+c^2 d^2 x^2+4 a d^2 x^2+2 a b d^2 x^2+3 b d^2 x^2+2 a c d^2 x^2+...
licheng's user avatar
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3 votes
2 answers
84 views

How to check the simultaneous positivity of two multivariable functions in Mathematica? [closed]

Given two functions of several real variables, say f[x1_, x2_, x3_, x4_] := x1 + 3 x2^2 - 5 x3 - 7 x4; and ...
Zilch's user avatar
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1 vote
1 answer
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Unable to apply Reduce to a variable number of inequalities (obtained by InputFields)

I'm new to Mathematica and I'm stuck on this piece of code. The code is supposed to let the user choose how many inequalities (in a number between 1 and 5) they want to be evaluated. ...
Gbekss's user avatar
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1 vote
1 answer
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Solving the inequality equation in Mathematica

I am trying to solve the following inequality equation in Mathematica: 12 Sin[300 t] >= 8 I want to find the values of t ...
internet's user avatar
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3 votes
4 answers
194 views

How to to solve inequality $(a+b\cos x)^2+(c \sin x)^2\leq 1$ for any $x$?

Does Mathematica have the ability to solve this inequality: (a + b * Cos[x])^2 + (c * Sin[x])^2 <= 1 for any x ∈ [0, 2*Pi]? ...
Aerterliusi's user avatar
1 vote
0 answers
60 views

Decide whether a system of polynomial equalities and inequalities is feasible? [closed]

Consider a system of polynomial equations $f_1(x) = ... = f_n(x) = 0$ and polynomial inequalities $g_1(x), ... ,g_m(x) \ge 0$. All polynomials are in rational coefficients, $x = (x_1, ... , x_l)$ is ...
giulio bullsaver's user avatar
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1 answer
53 views

How to find a conditional solution of inequalities?

Im trying to find the conditions of: a>0,b>0,c>1,d>0 (a + (2 a - b/c) d + (a + b - b/c) d^2 + (-b + (2 b)/c) d^3 + (b d^4)/ c - (b d^5)/c) > 0 I ...
Adel 's user avatar
9 votes
5 answers
696 views

How can I test if two inequalities have a common part?

I want to check whether $1 \leq x\leq2$ and $1.5\leq x\leq2.5$ have common part, what function can do this?
HANG YU's user avatar
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3 votes
2 answers
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Find combinations of this set that verify condition

So I have the following expression: expr = 3 Sqrt[87.3047 (TolC2)^2 + 55.3027 (TolL1)^2 + 3.19092 (TolL3)^2 + 1.36097 (TolRin)^2 + 1.09369 (TolRout)^2] All the ...
Granger Obliviate's user avatar
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0 answers
33 views

Solve Inequalities with Functional Arguments

I would like to solve the following inequality: $\frac{(\rho +\tau -1) \left(n g'(n) \left((g(n)-c) F'(g(n))+F(g(n))-1\right)+(c-g(n)) (F(g(n))-1)\right)}{n^2}>0$ Under some assumptions (listed ...
MaB21's user avatar
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3 votes
3 answers
212 views

How do I adjust the form of the inequality?

I have some inequality ,like this $$ \left\{\begin{array}{l} x+y+z \geqslant 1 \\ 2 x+6 y+3 z \geqslant 6 \\ a x+b y+c z \geqslant d \end{array}\right. $$ I want to put all the y's in this inequality ...
我心永恒's user avatar
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5 votes
2 answers
166 views

Routine to find all sets that are solution of a equation

So I have been wodering if Mathematica has any in-built function that would easily solve me these problem without manual search using for cycles that slow down the computation. Let's imagine I have a ...
Granger Obliviate's user avatar
1 vote
1 answer
106 views

How to include a function plot in RegionPlot Mathematica

I have a RegionPlot graph in Mathematica, which shows the solution to complex inequalities. In the same 2-dimensional space, I would like to plot a function . Any Help? Thanks! Update 1 Here is my try ...
MaB21's user avatar
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1 vote
2 answers
246 views

The result is much greater than the error rate

I have the following script: ...
j.doe's user avatar
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4 votes
2 answers
212 views

Plotting an inequality over the range of a parameter

I have a simple inequality, $$x+\cos(\theta)\, y > 0$$ and I'd like to plot the region in $x,y$ space which satisfies this inequality for all values of the angle $\theta$. I'm trying to do this ...
su.jai's user avatar
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1 vote
3 answers
122 views

How to calculate the range of $a$ that satisfies $a^x>x$ for any real number $x$?

I'm trying to calculate the range of $a$ that satisfies $a^x>x$ for any real number $x$. Reduce[a^x > x, a] fails. If it's not possible to get a symbolic ...
xiver77's user avatar
  • 125
0 votes
1 answer
113 views

Scatter plot matrix in older version of Mathematica

I need to plot a similar graph of a function [Scatter plot matrices]: For: $f(x,y,z,t) \rightarrow x^2 + y^3 + z^2 + t^2 ≤ 1,x + y - z = t^2$ But, I work in older version of Mathematica - 12.0 My ...
dtn's user avatar
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2 votes
2 answers
114 views

Solving Inequality with more than one parameter

I want to solve this inequality for x1 when a,b,d, E, and alpha are positive parameters I tried this code and I did not get the required answer ...
Doaa mahmoud's user avatar
0 votes
1 answer
104 views

Finding positive integer triples $(m,n,r)$ with $\frac{mr}{m+n}$ being an integer and $r-n > \frac{mr}{m+n}-1$ and $r\le \max{(m,n)}$ [closed]

I would like to use Mathematica to find all positive integer triples $(m,n,r)$ satisfying (1) $\frac{mr}{m+n}$ is an integer; (2) $r-n > \frac{mr}{m+n}-1$; (3) $r\le \max{(m,n)}$; (4) $1\le m < ...
taylor's user avatar
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2 votes
1 answer
131 views

Permutations with inequalities constraint

In how many ways can I arrange the first $6$ positive integers such that this inequalities chain will hold? $a < b > c < d < e > f$ One of these arrangements is $\{5, 6, 1, 2, 4, 3\}$, ...
user967210's user avatar

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