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.
376
questions
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0
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66
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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.
...
- 376
1
vote
0
answers
37
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Parametric Plotting 6D dimensions to 3D for Visualizing a Solution
I am trying to find out when: $$f(x,y,z,α,β,γ):= zcos(β)cos(γ)+y(cos(γ)sin(α)sin(β)+cos(α)sin(γ))+x(−cos(α)cos(γ)sin(β)+sin(α)sin(γ)),$$ where $α,β, \text{and } γ$ can be any value in $[-2\pi,2\pi]$ ...
- 455
3
votes
3
answers
195
views
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 ...
- 33
2
votes
2
answers
123
views
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:
...
- 150
-1
votes
1
answer
80
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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:
...
- 425
1
vote
0
answers
80
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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 ...
- 163
2
votes
1
answer
85
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 ...
- 2,695
1
vote
4
answers
239
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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:
...
- 2,695
-1
votes
1
answer
40
views
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:
...
- 2,695
2
votes
5
answers
422
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? ...
- 2,695
1
vote
1
answer
68
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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 ...
- 2,695
1
vote
1
answer
64
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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:
...
- 2,695
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votes
0
answers
44
views
0
votes
2
answers
50
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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
...
- 2,695
4
votes
1
answer
77
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Understanding the MeshShading options
The following code draws the intersection of a surface N: eqNcar=0 with three other surfaces defined by eq1=0, ...
- 592
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votes
1
answer
61
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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 ...
- 1,731
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56
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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:
$$
\left(\alpha\frac{B-K_R}{p_e}\...
- 1
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1
answer
47
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1
vote
2
answers
97
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Generate family of linear inequalities from vector variable for use in `FindInstance`
Suppose that I have a vector variable xvec = Array[x, 10].
How do I generate the family of linear inequalities
$$F = \{ {x\in\mathbb{R}^{10}:x_1\geq x_2,\ldots,x_9\...
- 125
1
vote
1
answer
118
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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+...
- 1,873
3
votes
2
answers
82
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 ...
- 85
1
vote
1
answer
34
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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.
...
- 11
1
vote
1
answer
57
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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 ...
- 431
3
votes
4
answers
188
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]?
...
- 343
1
vote
0
answers
54
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 ...
- 437
0
votes
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 ...
- 1
9
votes
5
answers
693
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?
- 91
3
votes
2
answers
114
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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 ...
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0
answers
39
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Simplified inequality from many inequalities
Any simplified inequality resulting from below?
...
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0
answers
33
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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 ...
- 70
3
votes
3
answers
209
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 ...
- 1,382
5
votes
2
answers
165
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 ...
1
vote
1
answer
83
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 ...
- 70
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vote
2
answers
242
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4
votes
2
answers
199
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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 ...
- 43
1
vote
3
answers
122
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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 ...
- 125
0
votes
1
answer
107
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 ...
- 2,344
2
votes
2
answers
113
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
...
- 93
0
votes
1
answer
102
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 < ...
- 101
2
votes
1
answer
115
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 $\{5, 6, 1, 2, 4, 3\}$, ...
- 245
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votes
1
answer
67
views
Reducing an inequality with a complicated Log term?
I am trying to symbolically Reduce the following (admittedly complicated) inequality:
...
- 547
1
vote
1
answer
87
views
Inconsistency in Plot3D and RegionPlot
New user of Mathematica here. I am trying to understand what is going on with the output of Plot3D and RegionPlot since the two seem inconsistent:
$\pi_u = \frac{(d_u-1) (d_u+1)^2}{16 \left(2 \alpha ...
- 35
2
votes
1
answer
61
views
Allowed range of parameters in an inequality
I have an inequality as following:
m2/r + m1/r^0.5 < 0
I need to understand the allowed range of m1 and m2 that satisfies the above inequality for different ...
- 31
1
vote
1
answer
35
views
Plotting inequalities yields undesired kink using RegionPlot [closed]
I would like to plot two inequalities being satisfied.
Plotting them both separately yields
...
- 201
0
votes
1
answer
108
views
Solve an Inequality using Mathematica [closed]
I would like to solve a simple inequality 0 < 2 A + B <= 1 with 0 < B < 1 and 0<A<1/2 , using Mathematica.
I tried using the command FindInstance ...
- 53
1
vote
2
answers
170
views
Extracting lower and upper bounds of an inequality solution from Reduce/Solve
I am solving a set of inequalities and 1 equation
...
- 451
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votes
0
answers
61
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Finding points satisfying inequalities
I want to find a bunch of points $(x,y,z,u,v)$ s.t
$x^2-4u>0$ and $y^2-4v>0$ and $z^2-4uv>0$.
Here is what I did:
...
- 647
1
vote
1
answer
92
views
Finding a (sufficient) condition for an inequality - Solve takes too long
I have the following inequality
$ 2 \sqrt{2} n^2 \sqrt{\frac{r}{r-1}} \exp \left(2^{-\frac{\sqrt[3]{\log (n)}}{10 \sqrt[3]{\log (r)}}} \left(\frac{1}{r+1}\right)^{-\frac{\sqrt[3]{\log
(n)}}{10 \...
- 251
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votes
1
answer
83
views
How to plot two regions such that both are visible and also highlight the overlap?
I try to plot the following inequalities f[x,y,z]<=1 and g[x,y,z]<=1 in a single plot such that both the regions are ...
- 539
2
votes
1
answer
84
views
Inequality cannot be solved using Reduce (no transcendental functions) [closed]
I have these assumptions:
...
- 199