# 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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• 4,521
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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]] ...
• 4,521
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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 ...
• 4,521
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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.
• 1,627
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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 ...
• 549
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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 ...
• 15
1 vote
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,...
• 471
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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 ...
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1 vote
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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 $1/2^{n+1}$ ...
• 81
1 vote
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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 ...
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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 ...
• 2,076
1 vote
61 views

### Get limits of values from inequalites

My code above as below; ...
• 648
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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 ...
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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 ...
• 347
1 vote
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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] ...
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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 ...
• 297
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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 <...
• 553
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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 ...
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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 <...
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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 ...
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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. ...
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### 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
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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
87 views

### 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 ...
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### 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]? ...
• 353
1 vote
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### 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 ...
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### 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 ...
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### 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?
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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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### 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 ...
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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 ...