Changeset a81e0b7 in git
 Timestamp:
 Mar 16, 2009, 12:32:31 PM (15 years ago)
 Branches:
 (u'fiekerDuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', '45e267b9942dec9429fe249ce3e5e44ab80a6a3a')
 Children:
 e84f07da8f2670e970ff0e6ab0976ebcb34fc091
 Parents:
 24ac6662afb3eee19ffb69cec527d7c648d2e413
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 1 edited
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Singular/LIB/tropical.lib
r24ac666 ra81e0b7 1 version="$Id: tropical.lib,v 1.1 0 20090114 16:07:05 SingularExp $";1 version="$Id: tropical.lib,v 1.11 20090316 11:32:31 keilen Exp $"; 2 2 category="Tropical Geometry"; 3 3 info=" … … 45 45 Moreover, in Singular no negative exponents of monomials are allowed, so that the integer vectors 46 46 vi will have to have nonnegative 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. 48 49 If, however, for some reason you prefer to work with general vi, then you have to pass right away to 49 50 the tropicalisation of the equations, whereever this is allowed  these are linear polynomials … … 1602 1603 1603 1604 proc weierstrassForm (poly f,list #) 1604 "USAGE: weierstrassForm OfACubic(wf[,#]); wf poly, # list1605 "USAGE: weierstrassForm(wf[,#]); wf poly, # list 1605 1606 ASSUME: wf is a a polynomial whose Newton polygon has precisely one interior lattice 1606 1607 point, so that it defines an elliptic curve on the toric surface corresponding 1607 1608 to the Newton polygon 1608 RETURN: poly, the Weierstrass normal form of the poly gon1609 NOTE:  the algorithm for the coefficients of the Weierstrass form is due to 1609 RETURN: poly, the Weierstrass normal form of the polynomial 1610 NOTE:  the algorithm for the coefficients of the Weierstrass form is due to 1610 1611 Fernando Rodriguez Villegas, villegas@math.utexas.edu 1611 1612 @*  the characteristic of the base field should not be 2 or 3 … … 1647 1648 "EXAMPLE:"; 1648 1649 echo=2; 1649 ring r=(0,t),( y,x),lp;1650 ring r=(0,t),(x,y),lp; 1650 1651 // f is already in Weierstrass form 1651 1652 poly f=y2+yx+3yx32x24x6; … … 1655 1656 poly wg=weierstrassForm(g); 1656 1657 wg; 1657 // but it is not yet asimple, since it still has an xyterm, unlike swg1658 // but it is not yet simple, since it still has an xyterm, unlike swg 1658 1659 poly swg=weierstrassForm(g,1); 1659 1660 swg; … … 3949 3950 } 3950 3951 // 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"); 3952 3953 // we return a list which contains the parametrisation ring (with the parametrisation ideal) 3953 3954 // and the string representing the maximal ideal describing the necessary field extension … … 4904 4905 } 4905 4906 // 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"); 4907 4908 // we return a list which contains lists of the parametrisation rings (with the parametrisation ideal) 4908 4909 // and an integer N such that t should be replaced by t^1/N
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