Changeset 56b0c8 in git


Ignore:
Timestamp:
Mar 8, 2010, 10:39:30 AM (14 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'b4f17ed1d25f93d46dbe29e4b499baecc2fd51bb')
Children:
ab76b4b0df4a9c7834ee87f4b78d6bb55b53c887
Parents:
12603fcdf508bfbd1d4ad1125836e1a42d5c77b0
Message:
new surfsig.lib

git-svn-id: file:///usr/local/Singular/svn/trunk@12619 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/surfsig.lib

    r12603f r56b0c8  
    22category="Singularities";
    33info="
    4 LIBRARY:  signature.lib        signature of surface singularity
    5 AUTHORS:  Gerhard Pfister,     pfister@mathematik.uni-kl.de
    6           Muhammad Ahsan,      ahsanbanyamin@gmail.com
     4LIBRARY:  surfsig.lib                 signature of surface singularity
     5AUTHORS:  Gerhard Pfister,            pfister@mathematik.uni-kl.de
     6          Muhammad Ahsan Banyamin,    ahsanbanyamin@gmail.com
    77
    88OVERVIEW:
    99 A library for computing the signature of irreducible surface singularity.
    10  The library contains also procedure for computing the newton pairs of surface singularity.
    11 
    12  PROCEDURES:
     10 It contains also a procedure for computing the newton pairs of a surface
     11 singularity.
     12
     13THEORY: The signature of a surface singularity is defined in
     14        [Durfee,A.:The Signature of Smoothings of Complex Surface
     15        Singularities, Math. Ann.,232,85-98 (1978)].
     16        The algorithm we use has been proposed in
     17        [Nemethi,A.:The signature of f(x,y)+z^n, Proceedings of Singularity
     18        Conference (C.T.C Wall's 60th birthday meeting),Liverpool 1996,
     19        London Math.Soc. LN 263(1999),131-149].
     20
     21PROCEDURES:
    1322 brieskornSign(a,b,c);   signature of Brieskorn singularity x^a+y^b+z^c=0
    1423 newtonpairs(f);         newton pairs of surface singularity
    1524 signature(N,f);         signature of singularity z^+f(x,y)=0,f irreducible
    16 
    1725";
    1826
    … …  
    2028///////////////////////////////////////////////////////////////////////////////
    2129proc signature(int N,poly f)
    22 "USAGE:signature(N,f);N=integer,f=irreducible poly in x,y
    23  RETURN:signature of surface singularity defined by z^N+f=0
    24  EXAMPLE:example signature; shows an example
     30"
     31USAGE:   signature(N,f); N=integer, f=irreducible poly in 2 variables
     32RETURN:  signature of surface singularity defined by z^N+f=0
     33EXAMPLE: example signature; shows an example
    2534"
    2635{
    2736   def R=basering;
    2837   ring S=0,(x,y),dp;
    29    map phi =R,x,y;
    30    poly f=phi(f);
     38   poly f = fetch(R,f);
    3139   list L=newtonpairs(f);
    3240   setring R;
    … …  
    4351 example
    4452{ "EXAMPLE:"; echo = 2;
    45    ring r=0,(x,y),dp;
    46    int N=2;
    47    poly f=y8+2x6y3+x10+x9y;
     53   ring r = 0,(x,y),dp;
     54   int N  = 3;
     55   poly f= x15-21x14+8x13y-6x13-16x12y+20x11y2-x12+8x11y-36x10y2
     56      +24x9y3+4x9y2-16x8y3+26x7y4-6x6y4+8x5y5+4x3y6-y8;
    4857   signature(N,f);
    49    f=y4+2x3y2+x6+x5y;
    50    signature(N,f);
    51    N=3;
    52    f=x15-21x14+8x13y-6x13-16x12y+20x11y2-x12+8x11y-36x10y2+24x9y3+4x9y2-16x8y3+26x7y4-6x6y4+8x5y5+4x3y6-y8;
    53    signature(N,f);
    54 }
    55 
     58}
     59
     60///////////////////////////////////////////////////////////////////////////
    5661proc newtonpairs(poly f)
    57 "USAGE:newtonpairs(f);f= irreducible bivariate poly
    58  RETURN:newton pairs of curve singularity f(x,y)=0
    59  EXAMPLE:example newtonpairs; shows an example
     62"USAGE:   newtonpairs(f); f= irreducible bivariate poly
     63 RETURN:  newton pairs of curve singularity f(x,y)=0
     64 EXAMPLE: example newtonpairs; shows an example
    6065"
    6166{
    6267 def R=basering;
    6368 ring S=0,(x,y),dp;
    64  map phi =R,x,y;
    65  poly f=phi(f);
     69 poly f = fetch(R,f);
    6670 list M=invariants(f);
    6771 setring R;
    … …  
    9397}
    9498
     99///////////////////////////////////////////////////////////////////////////
    95100proc brieskornSign(a,b,c)
    96 "USAGE:brieskornSign(a,b,c);a,b,c=integers
    97  RETURN:signature of Brieskorn singularity x^a+y^b+z^c
    98  EXAMPLE:example brieskornSign; shows an example
     101"USAGE:   brieskornSign(a,b,c);a,b,c=integers
     102 RETURN:  signature of Brieskorn singularity x^a+y^b+z^c
     103 EXAMPLE: example brieskornSign; shows an example
    99104"
    100105{
    … …  
    117122   brieskornSign(11,3,5);
    118123}
    119 
     124///////////////////////////////////////////////////////////////////////////
    120125static proc signsin(number n)
    121 "USAGE:signsin(n);n=number
    122  RETURN:the signature of value of sine corresponding to n
    123  EXAMPLE:example signSin; shows an example
     126"USAGE:   signsin(n); n=number
     127 RETURN:  the sign of sin(n) (sin(n) = the value of the sine of n)
     128 EXAMPLE: example signSin; shows an example
    124129"
    125130{
    … …  
    143148   signsin(11/3);
    144149}
    145 
     150///////////////////////////////////////////////////////////////////////////
    146151static proc split1(number n)
    147 "USAGE:split1(n);n=number
    148  RETURN:integral and fractional parts of number n
    149  EXAMPLE:example split1; shows an example
     152"USAGE:   split1(n); n=number
     153 RETURN:  integral and fractional parts of number n
     154 EXAMPLE: example split1; shows an example
    150155 "
    151156{
    … …  
    168173     split1(11/3);
    169174}
    170 
     175///////////////////////////////////////////////////////////////////////////
    171176static proc sin( int n)
    172 "USAGE:sin(n);n=integer
    173  RETURN:approximate value of sine by using maclaurin series corresponding to n
    174  EXAMPLE:example sin; shows an example
     177"USAGE:   sin(n); n=integer
     178 RETURN:  approximate value of the sine of n by using maclaurin series
     179 EXAMPLE:  example sin; shows an example
    175180 "
    176181{
    … …  
    182187   for(i=1;i<=n;i=i+2)
    183188   {
    184      f=f+(-1)^z*x^i/factorial(i,0) ;
     189     f=f+(-1)^z*x^i/factorial(i) ;
    185190     z++;
    186191   }
    … …  
    195200   sin(10);
    196201}
    197 
     202///////////////////////////////////////////////////////////////////////////
    198203static proc cos(int n)
    199 "USAGE:cos(n);n=integer
    200  RETURN:approximate value of cosine by using maclaurin series corresponding to n
    201  EXAMPLE:example cos; shows an example
     204"USAGE:   cos(n); n=integer
     205 RETURN:  approximate value of the cosine of n by using maclaurin series
     206 EXAMPLE: example cos; shows an example
    202207 "
    203208{
    … …  
    209214   for(i=0;i<=n;i=i+2)
    210215   {
    211       f=f+(-1)^z*x^i/factorial(i,0);
    212       z++;
     216     // f=f+(-1)^z*x^i/factorial(i,0);
     217     f=f+(-1)^z*x^i/factorial(i) ;
     218     z++;
    213219   }
    214220   setring R;
    … …  
    222228   cos(10);
    223229}
    224 
     230///////////////////////////////////////////////////////////////////////////
    225231static proc signcos(number n)
    226 "USAGE:signcos(n);n=number
    227  RETURN:the signature of value of cosine corresponding to n
    228  EXAMPLE:example signcos; shows an example
     232"USAGE:   signcos(n); n=number
     233 RETURN:  the sign of cosin(n) (cosin(n) = the value of the cosine of n)
     234 EXAMPLE: example signcos; shows an example
    229235"
    230236{
    … …  
    248254   signcos(11/3);
    249255}
    250 
     256///////////////////////////////////////////////////////////////////////////
    251257static proc  signa( number u)
    252 "USAGE:signa(u);u=number
    253  RETURN:the signa of a number
    254  EXAMPLE:example signa; shows an example
     258"USAGE:   signa(u); u=number
     259 RETURN:  the signa of a number
     260 EXAMPLE: example signa; shows an example
    255261"
    256262{
    … …  
    268274   signa(11/3);
    269275}
    270 
     276///////////////////////////////////////////////////////////////////////////
    271277static proc prods(list L)
    272 "USAGE:product(L);L=list of intvec
    273  RETURN:product of first components of Newton pairs in L
    274  EXAMPLE:example product; shows an example
     278"USAGE:   product(L); L=list of intvec
     279 RETURN:  product of first components of Newton pairs in L
     280 EXAMPLE: example product; shows an example
    275281"
    276282{
    … …  
    288294   prods(L);
    289295}
    290 
     296///////////////////////////////////////////////////////////////////////////
    291297static proc Generalcase(int N, list L)
    292 "USAGE:Generalcase(N,f);N=integer,list L of intvec
    293  RETURN:signature of surface singularity with Newton pairs in L
    294  ASSUME:number of newton pairs greater than 2
    295  EXAMPLE:example Generalcase; shows an example
     298"USAGE:   Generalcase(N,f);N=integer,list L of intvec
     299 RETURN:  signature of surface singularity with Newton pairs in L
     300 ASSUME:  number of newton pairs greater than 2
     301 EXAMPLE: example Generalcase; shows an example
    296302"
    297303{
    … …  
    339345   list L=intvec(2,3),intvec(2,1),intvec(2,1);
    340346   Generalcase(N,L);
    341 
    342 }
    343 
     347}
     348///////////////////////////////////////////////////////////////////////////
    344349static proc signtwopairs(int N,list L)
    345 "USAGE:signtwopairs(N,f);N=integer,L=list of intvec
    346  RETURN:signature of surface singularity with Newton pairs in L
    347  ASSUME:number of newton pairs equal to 2
    348  EXAMPLE:example signtwopairs; shows an example
     350"USAGE:   signtwopairs(N,f);N=integer,L=list of intvec
     351 RETURN:  signature of surface singularity with Newton pairs in L
     352 ASSUME:  number of newton pairs equal to 2
     353 EXAMPLE: example signtwopairs; shows an example
    349354"
    350355{
    … …  
    364369   signtwopairs(N,L);
    365370}
    366 
     371///////////////////////////////////////////////////////////////////////////
    367372static proc DedekindSum(number b, number c, int a)
    368373{
    … …  
    380385   return(s);
    381386}
    382 
     387///////////////////////////////////////////////////////////////////////////
     388
     389/*
     390Further examples
     391
     392   ring r = 0,(x,y),dp;
     393   int N;
     394   poly f;
     395
     396   N  = 5;
     397   poly f= x15-21x14+8x13y-6x13-16x12y+20x11y2-x12+8x11y-36x10y2    //3 characteristic pairs
     398      +24x9y3+4x9y2-16x8y3+26x7y4-6x6y4+8x5y5+4x3y6-y8;
     399
     400   N=6;
     401   f= y4+2x3y2+x6+x5y;                                             //2 characteristic pairs
     402
     403   N=7;
     404   f=x5+y11;                                                       //1 characteristc pair
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