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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 to determine the validity of inequalities under given premises? [closed]

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Why is there a difference in computational speed when judging the size of inequalities in these two forms? [closed]

Method One: Reduce[ForAll[{x, y, z}, {x > y > 1 > z > 0, a == (1 + x z)/z, b == (1 + x y)/x, c == (1 + y z)/y}, a > b && c < a]] ...
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How to perform linear programming in Mathematica based on the following conditions?

How to perform linear programming in Mathematica based on the following conditions, to draw the feasible region defined by -1 <= a + b <= 1 and 1 <= a - b <= 3, and find the range of t==3 ...
csn899's user avatar
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Why does FindInstance[x>0,x] give 27? [closed]

Why does FindInstance[x>0,x] give 27? I would think it would give 1… maybe 2 or some small positive decimal.
Just Some Old Man's user avatar
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Verifying set emptiness with FindInstance versus Reduce [closed]

I have a semialgebraic set in $\mathbb{R}^4$ that I believe to be empty. FindInstance claims that it is empty in less than ten seconds. But Reduce has run for a week without visible progress --- and ...
Lyle Ramshaw's user avatar
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Inequality too complex for Mathematica to solve? [closed]

I'm trying to solve some quite complicated inequalities (not a system), one of them for example being ...
oanesdof's user avatar
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1 answer
110 views

Unable to solve/reduce geometric Brownian motion inequality

I am trying to solve a few inequalities like the one below for Z: S * Exp[(mu - sigma^2/2)*T + Sqrt[T]*sigma*Z] > k Manually,...
Phil-ZXX's user avatar
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1 answer
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How can I solve this inequation over positive integers?

$$2023^i + 2023^{101-i}(-1)^i < 0, \quad i\in \mathbb N^+$$ My code: Reduce[2023^x+2023^(101-x)*(-1)^x<0 && x ∈ PositiveIntegers, x] gives an error ...
neo742's user avatar
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Most efficient way of defining the following sets for every step $n$

For each $n\in\mathbb{N}$, how do we compute sets $A_n$ and $B_n$ below: Let $A_1=[0,2/3)$. Let $B_1=(2/3,1]$. If $A_n$ is a union of intervals, then for each interval cut out the middle $1/2^{n+1}$ ...
Arbuja's user avatar
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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
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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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1 answer
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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
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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
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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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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 ...
tyogi'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
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`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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1 answer
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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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0 answers
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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
93 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
259 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 votes
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
446 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 vote
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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
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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: ...
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0 answers
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How to merge the solution sets of inequality involving Trigonometric functions?

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csn899's user avatar
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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
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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, ...
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
54 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
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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\...
rrrrr's user avatar
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1 vote
1 answer
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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
195 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
68 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
0 votes
1 answer
56 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
705 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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5 votes
4 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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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
213 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 ...
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