# Singular

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 Post subject: I am trying to solve a concrete problemPosted: Thu Aug 11, 2005 5:32 pm
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 doesnÂ´t seem to end. We are using the triangMH(jacob(w),2) option of SINGULAR.
Is the problem too big for SINGULAR?

email: gabrielarcos@cantv.net
Posted in old Singular Forum on: 2004-03-26 21:18:26+01

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 Post subject: Posted: Thu Sep 08, 2005 11:40 am

Joined: Mon Aug 29, 2005 9:22 am
Posts: 41
Location: Kaiserslautern, Germany
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).

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

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