How to solve systems of polynomial inequalities?
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I am currently working on a project that deals with systems of inequalities and so far I have found algorithms for the basic case of a system of inequalities as well as the non-strict linear inequalities (using Linear Programming). I was wondering if there is an algorithm that will help solve a system of polynomial inequalities besides Cylindrical Decomposition. If there isn't one for both the strict/non-strict versions, an algorithm for just one will suffice.
inequality polynomials
asked Feb 25 '13 at 21:40
user1883573user1883573
161
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add a comment |
$begingroup$
I am currently working on a project that deals with systems of inequalities and so far I have found algorithms for the basic case of a system of inequalities as well as the non-strict linear inequalities (using Linear Programming). I was wondering if there is an algorithm that will help solve a system of polynomial inequalities besides Cylindrical Decomposition. If there isn't one for both the strict/non-strict versions, an algorithm for just one will suffice.
inequality polynomials
asked Feb 25 '13 at 21:40
user1883573user1883573
161
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1
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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.
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– Alex Becker
Feb 25 '13 at 21:49
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Thanks, I'm just trying to find other algorithms to compare them to cylindrical decomposition. More than efficiency I'm looking at implementability (it's a computer science problem). Thanks for your input though!
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– user1883573
Feb 25 '13 at 21:53
add a comment |
$begingroup$
I am currently working on a project that deals with systems of inequalities and so far I have found algorithms for the basic case of a system of inequalities as well as the non-strict linear inequalities (using Linear Programming). I was wondering if there is an algorithm that will help solve a system of polynomial inequalities besides Cylindrical Decomposition. If there isn't one for both the strict/non-strict versions, an algorithm for just one will suffice.
inequality polynomials
asked Feb 25 '13 at 21:40
user1883573user1883573
161
$endgroup$
I am currently working on a project that deals with systems of inequalities and so far I have found algorithms for the basic case of a system of inequalities as well as the non-strict linear inequalities (using Linear Programming). I was wondering if there is an algorithm that will help solve a system of polynomial inequalities besides Cylindrical Decomposition. If there isn't one for both the strict/non-strict versions, an algorithm for just one will suffice.
inequality polynomials
inequality polynomials
asked Feb 25 '13 at 21:40
user1883573user1883573
161
asked Feb 25 '13 at 21:40
user1883573user1883573
161
asked Feb 25 '13 at 21:40
user1883573user1883573
161
asked Feb 25 '13 at 21:40
user1883573user1883573
161
asked Feb 25 '13 at 21:40
user1883573user1883573
161
161
1
$begingroup$
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.
$endgroup$
– Alex Becker
Feb 25 '13 at 21:49
$begingroup$
Thanks, I'm just trying to find other algorithms to compare them to cylindrical decomposition. More than efficiency I'm looking at implementability (it's a computer science problem). Thanks for your input though!
$endgroup$
– user1883573
Feb 25 '13 at 21:53
add a comment |
1
$begingroup$
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.
$endgroup$
– Alex Becker
Feb 25 '13 at 21:49
$begingroup$
Thanks, I'm just trying to find other algorithms to compare them to cylindrical decomposition. More than efficiency I'm looking at implementability (it's a computer science problem). Thanks for your input though!
$endgroup$
– user1883573
Feb 25 '13 at 21:53
1
1
$begingroup$
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.
$endgroup$
– Alex Becker
Feb 25 '13 at 21:49
$begingroup$
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.
$endgroup$
– Alex Becker
Feb 25 '13 at 21:49
$begingroup$
Thanks, I'm just trying to find other algorithms to compare them to cylindrical decomposition. More than efficiency I'm looking at implementability (it's a computer science problem). Thanks for your input though!
$endgroup$
– user1883573
Feb 25 '13 at 21:53
$begingroup$
Thanks, I'm just trying to find other algorithms to compare them to cylindrical decomposition. More than efficiency I'm looking at implementability (it's a computer science problem). Thanks for your input though!
$endgroup$
– user1883573
Feb 25 '13 at 21:53
add a comment |
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$begingroup$
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.
$endgroup$
– Alex Becker
Feb 25 '13 at 21:49
$begingroup$
Thanks, I'm just trying to find other algorithms to compare them to cylindrical decomposition. More than efficiency I'm looking at implementability (it's a computer science problem). Thanks for your input though!
$endgroup$
– user1883573
Feb 25 '13 at 21:53