Post a reply
Username:
Note:If not registered, provide any username. For more comfort, register here.
Subject:
Message body:
Enter your message here, it may contain no more than 60000 characters. 

Smilies
:D :) :( :o :shock: :? 8) :lol: :x :P :oops: :cry: :evil: :twisted: :roll: :wink: :!: :?: :idea: :arrow: :| :mrgreen:
Font size:
Font colour
Options:
BBCode is ON
[img] is ON
[flash] is OFF
[url] is ON
Smilies are ON
Disable BBCode
Disable smilies
Do not automatically parse URLs
Confirmation of post
To prevent automated posts the board requires you to enter a confirmation code. The code is displayed in the image you should see below. If you are visually impaired or cannot otherwise read this code please contact the %sBoard Administrator%s.
Confirmation code:
Enter the code exactly as it appears. All letters are case insensitive, there is no zero.
   

Topic review - Semialgebraic systems?
Author Message
  Post subject:  Re: Semialgebraic systems?  Reply with quote
Singular offers no syntax to denote inequalities. So the answer is almost no,
with the the exception of linear equations.
This is, the simplex method is available: http://www.singular.uni-kl.de/Manual/la ... htm#SEC426

To answer the question in a wider range about real algebraic computations,
Singular offers some libraries:
realrad_lib for Computation of real radicals
http://www.singular.uni-kl.de/Manual/la ... tm#SEC1336

Two libraries for
Counting the number of real roots of uni- and multivariate polynomial systems

rootsur_lib http://www.singular.uni-kl.de/Manual/la ... tm#SEC1918
and rootsmr_lib http://www.singular.uni-kl.de/Manual/la ... tm#SEC1902 respectively.

These implement:
Descartes' rule of signs, the Budan-Fourier theorem, Sturm sequences and Sturm-Habicht sequences.

The computation of the Sturm-Habicht sequences (subresultants) are imititated by Groebner basis calculations.
Hence it does not perform as well as a proper implementation could do.
(Although subresultants are implemented in the kernel of the factorization engines,
these commands are not directly accessible to the user.)

For those interested in usage of Groebner basis as a preprocces in semialgebraic computations,
see for instance:

David J. Wilson, Russell J. Bradford, James H. Davenport
Speeding up Cylindrical Algebraic Decomposition by Gröbner Bases

http://arxiv.org/abs/1205.6285 (Though, this work reports on calculations with Maple.)
Post Posted: Fri Nov 08, 2013 2:42 pm
  Post subject:  Semialgebraic systems?  Reply with quote
Is there any library able to solve semialgebraic polynomial systems? Or, at least, dealing with regular chains?

Thanks.
Post Posted: Tue Sep 17, 2013 9:14 pm


It is currently Mon Dec 18, 2017 9:17 am
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group