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%body SINGULAR - A Computer Algebra System for Polynomial Computations Overview Objects Functionality Libraries Examples Applications Availability History Contributors Future %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
SINGULAR Examples Build. Blocks Comb. Appl. HCA Proving
Arrangements Branches Classify Coding Deformations Equidim Part Existence Finite Groups Flatness Genus Hilbert Series Membership Nonnormal Locus Normalization Primdec Puiseux Plane Curves Saturation Solving Space Curves Spectrum %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
SINGULAR Applications Robotics Circuit Design Medicine Glass Melting %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
LIB "normal.lib";

ring r=0,(x,y,z),ds;
ideal i=x^4-y*z^2,x*y-z^3,y^2-x^3*z;
 We now pass to a global ordering, which is necessary for normalization.
(Normalization internally uses the calculation of a radical which in turn relies on a global lexicographical ordering.)
ring rr=0,(x,y,z),dp;
ideal i=imap(r,i);
normal(i); // 'normal' created a list of 1 ring(s). // nor[1+1] is the delta-invariant in case of choose=wd. // To see the rings, type (if the name of your list is nor): show( nor); // To access the 1-st ring and map (similar for the others), type: def R = nor[1]; setring R; norid; normap; // R/norid is the 1-st ring of the normalization and // normap the map from the original basering to R/norid [1]: // characteristic : 0 // number of vars : 2 // block 1 : ordering a // : names T(1) T(2) // : weights 1 0 // block 2 : ordering dp // : names T(1) T(2) // block 3 : ordering C def rno=_[1];
setring rno;
norid;
norid[1]=T(2)^5-1 The ideal norid is generated by a polynomial in one variable of degree 5, which completely factors over the complex numbers. Hence the singularity has 5 branches.
<-- Branches of an isolated space curve singularity
<-- computed via Primary Decomposition
--> computed via Factorizing Gröbner