Dear Dr. Arcos,

the system is not 0-dimensional, the singular locus has

complex dimension 1, hence Singular cannot find the (real)

solutions.

See the session below (I assume this is what you mean).

Moreover, if your input is

triangMH(jacob(w),2);

you should get a warning, as the a lex standard basis is required.

A lex std in char 0 is really hard, as you can see when

you compute it in char 322003 and use option(prot);,

it goes up to degree 160 (!) and goes probably

forever in char 0.

Best regards,

Gert-Martin Greuel

------------------------------------------------------------

LIB"all.lib";

option(prot); timer =1;

ring r0 = 0,(x,y,z,x(1..4),y(1..4),z(1..4)),lp;

ideal w =

((x-x(1))^2+(y-y(1))^2+(z-z(1))^2)*((x-x(2))^2+(y-y(2))^2+(z-z(2))^2)*((x-x(3))^2+(y-y(3))^2+(z-z(3))^2)*((x-x(4))^2+(y-y(4))^2+(z-z(4))^2);

ideal v = x(1),x(2),x(3),x(4),y(1),y(2),y(3),y(4),z(1),z(2),z(3),z(4);

ideal f = 0,39/100,0,0,0,0,12/25,0,0,0,0,29/100;

poly w1=substitute(w,v,f)[1];

ring r1 = 0,(x,y,z),dp;

poly w = imap(r0,w1);

ideal j = jacob(w);

ideal js = std(j);

dim(js);

// -> 1

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email:

greuel@mathematik.uni-kl.dePosted in old Singular Forum on: 2004-04-02 19:35:26+02