Singular

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
[/code]

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

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