How to solve systems of polynomial inequalities?

Finley Mckinney
2022-06-14
Answered

How to solve systems of polynomial inequalities?

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Josie123

Answered 2022-06-15
Author has **16** answers

The study of these systems is called "Real Semialgebraic Geometry". Unfortunately, cylindrical decomposition is the best algorithm I'm aware of for solving them. But googling "Real Semialgebraic Geometry" may turn something up.

asked 2022-06-24

How to solve this system of ODE's?

$\left[\begin{array}{c}{\dot{x}}_{1}\\ {\dot{x}}_{2}\end{array}\right]=\left[\begin{array}{cc}\mathrm{cos}t& -\mathrm{sin}t\\ \mathrm{sin}t& \mathrm{cos}t\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]$

$\left[\begin{array}{c}{\dot{x}}_{1}\\ {\dot{x}}_{2}\end{array}\right]=\left[\begin{array}{cc}\mathrm{cos}t& -\mathrm{sin}t\\ \mathrm{sin}t& \mathrm{cos}t\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]$

asked 2021-08-11

Find the linear approximation of the function $f\left(x\right)=\sqrt{1-x}$ at a=0 and use it to approximate the numbers $\sqrt{0.9}$ and $\sqrt{0.99}$ .

asked 2022-04-14

Find the inverse of the function on the given domain

$f\left(x\right)={(x-10)}^{2},[10,\mathrm{\infty})$

${f}^{-1}\left(x\right)=$ .....

Note: There is a sample student explantion given in the feedback to this question.

Note: There is a sample student explantion given in the feedback to this question.

asked 2021-08-04

Plot a complex number graph. Specify the absolute value of the number.

4i

4i

asked 2022-04-30

How to solve this bi-quadratic example?

$5{\left(\frac{x+1}{x}\right)}^{2}-16\left(\frac{x-1}{x}\right)-52=0$

asked 2022-07-26

Find the number(s) c referred to in the mean value theorem for integrals for each function, over the interval indicated.

$f(x)=6{x}^{2}$ over [-3,4]

$f(x)=6{x}^{2}$ over [-3,4]

asked 2022-04-22

We have the sequence $\{0,1,2,3,3,4,6,9,8,\dots \}$ for which we have to find the summation of terms to the nth term, $C}_{n$

However, the number of terms in the sub sequence,$N\ne n$ , the number of terms in the larger sequence. What is a way to represent N in terms of n in order to arrive at a single formula for $C}_{n$ ? I've determined that it can be $N=\frac{n}{3}$ but this is only true for cases where n is a multiple of 3. How do I find those two cases where n isn't a multiple of 3?

However, the number of terms in the sub sequence,