Top
Back: spectrum_lib
Forward: semicont
FastBack: spcurve_lib
FastForward: Invariant theory
Up: spectrum_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.5.10.1 spectrumnd

Procedure from library spectrum.lib (see spectrum_lib).

Usage:
spectrumnd(f[,1]); poly f

Assume:
f has nondegenerate principal part

Return:
a list containing the Newton spectrum of f
 
int l[1]: Milnor number
int l[2]: geometric genus
int l[3]: number of different spectral numbers
intvec l[4]: numerators of the spectral numbers of the Newton filtration
intvec l[5]: denominators of the spectral numbers of the Newton filtration
intvec l[6]: multiplicities of the spectral numbers
NOTE if a second argument 1 is given,
no test for a degenerate principal part will be done

Example:
 
LIB "spectrum.lib";
ring r=0,(x,y),ds;
poly f=x^31+x^6*y^7+x^2*y^12+x^13*y^2+y^29;
spectrumnd(f);
==> [1]:
==>    198
==> [2]:
==>    101
==> [3]:
==>    175
==> [4]:
==>    12,17,13,22,17,24,27,21,29,11,32,34,25,13,36,37,39,1,16,15,41,31,17,44\
   ,33,18,46,17,35,48,19,49,37,20,51,19,53,39,21,54,20,41,56,22,21,58,43,23,\
   59,22,60,61,24,45,23,63,25,64,47,65,24,66,26,49,68,25,27,69,51,70,26,71,2\
   8,72,53,73,27,29,74,55,75,76,28,30,77,57,78,1,80,59,81,32,30,82,83,61,84,\
   33,31,85,63,86,34,87,32,88,65,89,35,33,90,67,36,92,34,93,69,94,37,95,35,7\
   1,38,97,98,36,99,39,73,100,37,40,102,75,38,104,41,77,105,39,107,42,79,109\
   ,43,110,81,41,112,44,83,114,45,85,117,43,46,3,119,121,122,45,91,124,126,4\
   7,129,95,131,134,99,136,103,141,146
==> [5]:
==>    79,79,58,79,58,79,79,58,79,29,79,79,58,29,79,79,79,2,31,29,79,58,31,79\
   ,58,31,79,29,58,79,31,79,58,31,79,29,79,58,31,79,29,58,79,31,29,79,58,31,\
   79,29,79,79,31,58,29,79,31,79,58,79,29,79,31,58,79,29,31,79,58,79,29,79,3\
   1,79,58,79,29,31,79,58,79,79,29,31,79,58,79,1,79,58,79,31,29,79,79,58,79,\
   31,29,79,58,79,31,79,29,79,58,79,31,29,79,58,31,79,29,79,58,79,31,79,29,5\
   8,31,79,79,29,79,31,58,79,29,31,79,58,29,79,31,58,79,29,79,31,58,79,31,79\
   ,58,29,79,31,58,79,31,58,79,29,31,2,79,79,79,29,58,79,79,29,79,58,79,79,5\
   8,79,58,79,79
==> [6]:
==>    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,\
   1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1\
   ,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,4,1,2,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,\
   1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1\
   ,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1


Top Back: spectrum_lib Forward: semicont FastBack: spcurve_lib FastForward: Invariant theory Up: spectrum_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 2-0-0, February 2001, generated by texi2html.