Changeset efdded in git
- Timestamp:
- Apr 8, 2009, 2:42:19 PM (14 years ago)
- Branches:
- (u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
- Children:
- 7e96fe079ce8711823d420d4b4ba8e959e156a77
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- a7fcfab933710ef29f9ec64b1ac3f03f602e0edc
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Singular/LIB/tropical.lib
ra7fcfab refdded 1 version="$Id: tropical.lib,v 1.1 3 2009-04-07 16:18:06seelisch Exp $";1 version="$Id: tropical.lib,v 1.14 2009-04-08 12:42:19 seelisch Exp $"; 2 2 category="Tropical Geometry"; 3 3 info=" … … 23 23 point x in (K*)^n to the point (x^v0,...,x^vm). 24 24 The generic hyperplane sections are just the images of the hypersurfaces 25 in (K*)^n defined by the polynomials f=a0*x^v0+...+am*x^vm=0. Some properties 25 in (K*)^n defined by the polynomials f=a0*x^v0+...+am*x^vm=0. Some properties 26 26 of these hypersurfaces can be studied via tropicalisation. 27 27 … … 32 32 trop(f)=min{val(a0)+<v0,x>,...,val(am)+<vm,x>}. 33 33 Here, <v,x> denotes the standard scalar product of the integer vector v in Z^n 34 with the vector x=(x1,...,xn) of variables, so that trop(f) is a piecewise 34 with the vector x=(x1,...,xn) of variables, so that trop(f) is a piecewise 35 35 linear function on R^n. The corner locus of this function (i.e. the points 36 36 at which the minimum is attained a least twice) is the tropical hypersurface … … 92 92 PROCEDURES FOR DRAWING TROPICAL CURVES: 93 93 tropicalCurve computes a tropical curve and its Newton subdivision 94 drawTropicalCurve produces a post script image of a tropical curve 94 drawTropicalCurve produces a post script image of a tropical curve 95 95 drawNewtonSubdivision produces a post script image of a Newton subdivision 96 96 … … 2131 2131 NOTE: if # is empty, then the valuation of t will be 1, 2132 2132 @* if # is the string 'max' it will be -1; 2133 @* the latter supposes that we consider the maximum of the the2133 @* the latter supposes that we consider the maximum of the 2134 2134 computed linear forms, the former that we consider their minimum 2135 2135 EXAMPLE: example tropicalise; shows an example" … … 3613 3613 else 3614 3614 { 3615 ergl[j1]=0; //if the variable belongs not thethe d biggest ones,3615 ergl[j1]=0; //if the variable is not among the d biggest ones, 3616 3616 //save 0 in the list 3617 3617 erglini[j1]=0;
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