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
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[email protected]Posted in old Singular Forum on: 2002-02-03 10:03:27+01
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