% Authors: R/"udiger Achilles and Davide Aliffi
% achilles@dm.unibo.it, aliffi@dm.unibo.it

COMMENT
 
This is an example session demonstrating and testing the facilities
offered by the module SEGRE, an extension of the REDUCE package CALI.
 
END COMMENT;
  
comment
 
        ##################################################
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        ###       Segre numbers and L\^e numbers       ###
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        ##################################################
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% The following examples are taken from
% [D.B. Massey: L\^e cycles and hypersurface singularities.
% Lecture Notes Math. 1615, Springer-Verlag, Berlin-Heidelberg, 1995].

% Example 1. This example shows that - unlike the Milnor number -
% the L\^e numbers in a family need not be upper-semicontinuous.
% The tuple of L\^e numbers ("reverse le(f)") is only lexigraphically 
% upper-semicontinous in the t-variable.

setring({x,y,z},{},lex);
f:=z^2-y^3-t*x*y^2;

% Case t not equal to 0.

le(f);

% Case t = 0.

le (sub({t=0},f));

% Example 2. Coordinate planes in C^3 
% D.B. Massey: "\lambda^1 is somewhat messier to calculate"

setring({x,y,z},{},lex);
le(x*y*z);

% Example 3. Whitney umbrella.

setring({x,y,z},{},lex);
le(y^2-z*x^2);

% Example 4. FM cone.

setring({u,v,w,x,y},{},lex);
h:= y^2-x^3-*(u^2+v^2+w^2)*x^2;
le h;
;end;