Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: polynomial solving with Singular or Maple
PostPosted: Thu Aug 11, 2005 5:31 pm 
I have a system of polynomial equations, when I let Singular
solve it it produces the message "Ideal i has to be 0-dimentional".
Somehow, Singular does not allow to solve it, while Maple does allow.
Do you know why?

email: singular@mathematik.uni-kl.de
Posted in old Singular Forum on: 2002-02-03 10:01:23+01


Report this post
Top
  
Reply with quote  
 Post subject:
PostPosted: Thu Sep 08, 2005 11:41 am 

Joined: Mon Aug 29, 2005 9:22 am
Posts: 41
Location: Kaiserslautern, Germany
Singular can solve numerically only 0-dim systems by using the library solve.lib. This is just redisigned and will work much better in near future.
Symbolically, Singular can treat systems of any dimension. For that you should consult the library primdec.lib.
So, for the first system you can use primdecGTZ, it gives all irreducible components ([2]:) together with the primary components ([1]:). Setting the polynomials to 0 gives the solutions (as you see, the solution set is 1-dimensional):
Code:
> LIB "primdec.lib";
> ring r=0,(s1,s12,s13,s123,lambda),lp;
> ideal i = 1402*s13*s1+9*s1^2-20*s12*s1*s13+66*s12*s1*s13^2+66*s12*s1^2*s13
.         -2822*s1^3+5608*s1^4-8430*s1^2*s13-5608*s13^2*s1+16824*s1^3*s13
.         +16824*s13^2*s1^2+5608*s1*s13^3-9*s12*s1^2-11*s12*s13^2+22*s12*s1^3
.         +22*s12*s13^3,
.         1691*s12*s1+1691*s12*s13-300*s1+600*s1^2+600*s13*s1,
.         -1091*s13*s1+302*s1^2-602*s12*s1*s13+1812*s12*s1*s13^2+1812*s12*s1^2*s13
.         -1208*s1^3+1208*s1^4+370*s1^2*s13+1578*s13^2*s1+3624*s1^3*s13
.         +3624*s13^2*s1^2+1208*s1*s13^3-302*s12*s1^2-300*s12*s13^2+604*s12*s1^3
.         +604*s12*s13^3;
> primdecGTZ(i);
[1]:
   [1]:
      _[1]=s13^2
      _[2]=s1*s13
      _[3]=1691*s1*s12-300*s1+1691*s12*s13
      _[4]=s1^2
  [2]:
      _[1]=s13
      _[2]=s1
[2]:
  [1]:
      _[1]=s12
      _[2]=2*s1+2*s13-1
  [2]:
      _[1]=s12
      _[2]=2*s1+2*s13-1
[3]:
  [1]:
      _[1]=s12
      _[2]=s1
  [2]:
      _[1]=s12
      _[2]=s1
[4]:
  [1]:
      _[1]=4016016*s13-46961
      _[2]=282961794*s12-36018575
      _[3]=4016016*s1-264661
  [2]:
      _[1]=4016016*s13-46961
      _[2]=282961794*s12-36018575
      _[3]=4016016*s1-264661


email: greuel@mathematik.uni-kl.de
Posted in old Singular Forum on: 2002-02-03 10:03:27+01


Report this post
Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

You can post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

It is currently Tue Dec 12, 2017 8:06 pm
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group