Singular

We are trying to determine the real singularities of the following
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);
where x_1,x_2,x_3,x_4,y_1,y_2,y_3,y_4,z_1,z_2,z_3,z_4=0,39/100,0,0,0,0,12/25,0,0,0,0,29/100;

The program run doesn´t seem to end. We are using the triangMH(jacob(w),2) option of SINGULAR.
Is the problem too big for SINGULAR?



email: [email protected]
Posted in old Singular Forum on: 2004-03-26 21:18:26+01

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

email: [email protected]
Posted in old Singular Forum on: 2004-04-02 19:35:26+02