Changeset a81e0b7 in git


Ignore:
Timestamp:
Mar 16, 2009, 12:32:31 PM (15 years ago)
Author:
Thomas Markwig <keilen@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '45e267b9942dec9429fe249ce3e5e44ab80a6a3a')
Children:
e84f07da8f2670e970ff0e6ab0976ebcb34fc091
Parents:
24ac6662afb3eee19ffb69cec527d7c648d2e413
Message:
Einige Hilfstexte verbessert.


git-svn-id: file:///usr/local/Singular/svn/trunk@11560 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/tropical.lib

    r24ac666 ra81e0b7  
    1 version="$Id: tropical.lib,v 1.10 2009-01-14 16:07:05 Singular Exp $";
     1version="$Id: tropical.lib,v 1.11 2009-03-16 11:32:31 keilen Exp $";
    22category="Tropical Geometry";
    33info="
     
    4545     Moreover, in Singular no negative exponents of monomials are allowed, so that the integer vectors
    4646     vi will have to have non-negative entries. Shifting all exponents by a fixed integer vector does not
    47      change the tropicalisation nor does it change the toric variety. Thus this does not cause any restriction.
     47     change the tropicalisation nor does it change the toric variety.
     48     Thus this does not cause any restriction.
    4849     If, however, for some reason you prefer to work with general vi, then you have to pass right away to
    4950     the tropicalisation of the equations, whereever this is allowed -- these are linear polynomials
     
    16021603
    16031604proc weierstrassForm (poly f,list #)
    1604 "USAGE:      weierstrassFormOfACubic(wf[,#]); wf poly, # list
     1605"USAGE:      weierstrassForm(wf[,#]); wf poly, # list
    16051606ASSUME:      wf is a a polynomial whose Newton polygon has precisely one interior lattice
    16061607             point, so that it defines an elliptic curve on the toric surface corresponding
    16071608             to the Newton polygon
    1608 RETURN:      poly, the Weierstrass normal form of the polygon
    1609 NOTE:        - the algorithm for the coefficients of the Weierstrass form is due to
     1609RETURN:      poly, the Weierstrass normal form of the polynomial
     1610NOTE:        - the algorithm for the coefficients of the Weierstrass form is due to 
    16101611               Fernando Rodriguez Villegas, villegas@math.utexas.edu
    16111612@*           - the characteristic of the base field should not be 2 or 3
     
    16471648   "EXAMPLE:";
    16481649   echo=2;
    1649    ring r=(0,t),(y,x),lp;
     1650   ring r=(0,t),(x,y),lp;
    16501651// f is already in Weierstrass form
    16511652   poly f=y2+yx+3y-x3-2x2-4x-6;
     
    16551656   poly wg=weierstrassForm(g);
    16561657   wg;
    1657 // but it is not yet a simple, since it still has an xy-term, unlike swg
     1658// but it is not yet simple, since it still has an xy-term, unlike swg
    16581659   poly swg=weierstrassForm(g,1);
    16591660   swg;
     
    39493950  }
    39503951  // kill the gfan files in /tmp
    3951   system("sh","cd /tmp; /bin/rm gfaninput; /bin/rm gfanoutput");
     3952  system("sh","cd /tmp; /usr/bin/touch gfaninput; /usr/bin/touch gfanoutput; /bin/rm gfaninput; /bin/rm gfanoutput"); 
    39523953  // we return a list which contains the parametrisation ring (with the parametrisation ideal)
    39533954  // and the string representing the maximal ideal describing the necessary field extension
     
    49044905  }
    49054906  // kill the gfan files in /tmp
    4906   system("sh","cd /tmp; /bin/rm gfaninput; /bin/rm gfanoutput");
     4907  system("sh","cd /tmp; /usr/bin/touch gfaninput; /usr/bin/touch gfanoutput; /bin/rm gfaninput; /bin/rm gfanoutput"); 
    49074908  // we return a list which contains lists of the parametrisation rings (with the parametrisation ideal)
    49084909  // and an integer N such that t should be replaced by t^1/N
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