| 1 | /////////////////////////////////////////////////////////////////////////////// |
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| 2 | version="$Id: spectrum.lib,v 1.15 2001-05-03 07:56:41 mschulze Exp $"; |
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| 3 | category="Singularities"; |
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| 4 | info=" |
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| 5 | LIBRARY: spectrum.lib Singularity Spectrum for Nondegenerate Singularities |
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| 6 | AUTHOR: S. Endrass |
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| 7 | |
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| 8 | PROCEDURES: |
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| 9 | spectrumnd(poly f[,1]); spectrum of nondegenerate isolated singularity f |
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| 10 | "; |
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| 11 | |
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| 12 | /////////////////////////////////////////////////////////////////////////////// |
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| 13 | |
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| 14 | proc spectrumnd (poly f,list #) |
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| 15 | "USAGE: spectrumnd(f[,1]); poly f |
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| 16 | ASSUME: basering has characteristic 0 and local ordering, |
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| 17 | f has isolated singularity at 0 and nondegenerate principal part |
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| 18 | RETURN: |
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| 19 | @format |
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| 20 | list S: |
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| 21 | ideal S[1]: spectral numbers in increasing order |
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| 22 | intvec S[2]: |
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| 23 | int S[2][i]: multiplicity of spectral number S[1][i] |
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| 24 | @end format |
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| 25 | NOTE: if a second argument 1 is given, |
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| 26 | no test for a degenerate principal part will be done |
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| 27 | SEE_ALSO: gaussman_lib |
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| 28 | KEYWORDS: singularities; Gauss-Manin connection; spectrum |
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| 29 | EXAMPLE: example spectrumnd; shows an example |
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| 30 | " |
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| 31 | { |
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| 32 | if(charstr(basering)!="0") |
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| 33 | { |
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| 34 | ERROR("characteristic 0 expected"); |
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| 35 | } |
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| 36 | if(size(#)==0) |
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| 37 | { |
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| 38 | list S=system("spectrum",f); |
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| 39 | } |
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| 40 | else |
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| 41 | { |
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| 42 | list S=system("spectrum",f,#[1]); |
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| 43 | } |
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| 44 | ideal a=number(S[4][1])/S[5][1]-1; |
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| 45 | int i; |
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| 46 | for(i=S[3];i>1;i--) |
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| 47 | { |
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| 48 | a[i]=number(S[4][i])/S[5][i]-1; |
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| 49 | } |
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| 50 | return(list(a,S[6])); |
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| 51 | } |
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| 52 | example |
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| 53 | { "EXAMPLE:"; echo = 2; |
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| 54 | ring R=0,(x,y),ds; |
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| 55 | poly f=x^31+x^6*y^7+x^2*y^12+x^13*y^2+y^29; |
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| 56 | spectrumnd(f); |
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| 57 | } |
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| 58 | /////////////////////////////////////////////////////////////////////////////// |
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| 59 | |
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| 60 | proc semicont(list #) |
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| 61 | { |
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| 62 | ERROR("semicont was replaced by spsemicont in gaussman.lib"); |
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| 63 | } |
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| 64 | /////////////////////////////////////////////////////////////////////////////// |
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| 65 | |
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| 66 | proc semicontqh(list #) |
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| 67 | { |
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| 68 | ERROR("semicontqh was replaced by spsemicont in gaussman.lib"); |
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| 69 | } |
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| 70 | /////////////////////////////////////////////////////////////////////////////// |
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