Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: parametrization with respect to given variables
PostPosted: Thu Aug 11, 2005 5:31 pm 
I have 3 polynomials with the variables {s13, h13, h123,
h23, s12, h12, c, h1, h2, h3, s1}. Please see if you can express from
this the variables {s1,s12, s13} in terms of the others.

email: singular@mathematik.uni-kl.de
Posted in old Singular Forum on: 2002-02-03 10:08:32+01


Report this post
Top
  
Reply with quote  
 Post subject: Re: parametrization with respect to given variables
PostPosted: Thu Aug 11, 2005 5:42 pm 
For this example primdecGTZ is too expensive, however, minAssGTZ works
(here also triangMH or triangM seem to work too). For your purpose one has
to declare h13,h123,h23,h12,c,h1,h2,h3 as parameters and s1,s12,s13 as
variables:

option(prot);
ring r = (0,h13,h123,h23,h12,c,h1,h2,h3),(s1,s12,s13),lp;
ideal i =
12*h23*s1^2*s13^2+12*h13*s1^3*s13+2*h23*s12*s1^3-10*h23*s1^2*s13
...
+h3*s12*s13+h123*s12*s1+h123*s12*s13;

list ma = minAssGTZ(i); //the minimal associated primes
ma;
[1]:
_[1]=s13
_[2]=s1
[2]:
_[1]=(-2*c^2)*s13+(h13^2+h13*h123+2*h13*h23+h13*h1+h13*h2+h13*h3+h123*h23+h123*h1+h123*h2+h23^2+h23*h1+h23*h2+h23*h3+h1*h3+h2*h3)
_[2]=(-h13*c^2-h123*c^2-h23*c^2+c^3-c^2*h1-c^2*h2-c^2*h3)*s12+(-h13^2*h12-h13*h123*h12-2*h13*h23*h12+2*h13*h12*c-h13*h12*h1-h13*h12*h2-h13*h12*h3-h123*h23*h12
+h123*h12*c-h123*h12*h1-h123*h12*h2-h23^2*h12+2*h23*h12*c-h23*h12*h1-h23*h12*h2-h23*h12*h3-h12*c^2+h12*c*h1+h12*c*h2+h12*c*h3-h12*h1*h3-h12*h2*h3)
_[3]=(-2*c^2)*s1+(-h13^2-h13*h123-2*h13*h23+h13*c-h13*h1-h13*h2-h13*h3-h123*h23-h123*h1-h123*h2-h23^2+h23*c-h23*h1-h23*h2-h23*h3+c*h1+c*h2-h1*h3-h2*h3)
[3]:
_[1]=s12
_[2]=2*s1+2*s13-1
[4]:
_[1]=s12
_[2]=s1

//Or, if you wish to normalize the second solution, then you get the expression for
//s13,s12 and s1 directly (of course, you get the solutions by setting the
//polynomials 0):

normalize(ma[2]);
_[1]=s13+(-h13^2-h13*h123-2*h13*h23-h13*h1-h13*h2-h13*h3-h123*h23-h123*h1-h123*h2-h23^2-h23*h1-h23*h2-h23*h3-h1*h3-h2*h3)/(2*c^2)
_[2]=s12+(h13^2*h12+h13*h123*h12+2*h13*h23*h12-2*h13*h12*c+h13*h12*h1+h13*h12*h2+h13*h12*h3+h123*h23*h12-h123*h12*c+h123*h12*h1+h123*h12*h2+h23^2*h12-2*h23*h12*c
+h23*h12*h1+h23*h12*h2+h23*h12*h3+h12*c^2-h12*c*h1-h12*c*h2-h12*c*h3+h12*h1*h3+h12*h2*h3)/(h13*c^2+h123*c^2+h23*c^2-c^3+c^2*h1+c^2*h2+c^2*h3)
_[3]=s1+(h13^2+h13*h123+2*h13*h23-h13*c+h13*h1+h13*h2+h13*h3+h123*h23+h123*h1+h123*h2+h23^2-h23*c+h23*h1+h23*h2+h23*h3-c*h1-c*h2+h1*h3+h2*h3)/(2*c^2)

email: greuel@mathematik.uni-kl.de
Posted in old Singular Forum on: 2002-02-03 10:10:53+01


Report this post
Top
  
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 Sun Dec 17, 2017 1:52 pm
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group