# Singular

#### D.13.3.11 conicWithTangents

Procedure from library `tropical.lib` (see tropical_lib).

Usage:
conicWithTangents(points[,#]); points list, # optional list

Assume:
points is a list of five points in the plane over K(t)

Return:
list, l[1] = the list points of the five given points
l[2] = the conic f passing through the five points
l[3] = list of equations of tangents to f in the given points
l[4] = ideal, tropicalisation of f (i.e. list of linear forms)
l[5] = a list of the tropicalisation of the tangents
l[6] = a list containing the vertices of the tropical conic f
l[7] = a list containing lists with vertices of the tangents
l[8] = a string which contains the latex-code to draw the tropical conic and its tropicalised tangents
l[9] = if # is non-empty, this is the same data for the dual conic and the points dual to the computed tangents

Note:
the points must be generic, i.e. no three on a line

Example:
 ```LIB "tropical.lib"; ring r=(0,t),(x,y),dp; // the input consists of a list of five points in the plane over Q(t) list points=list(1/t2,t),list(1/t,t2),list(1,1),list(t,1/t2),list(t2,1/t); list conic=conicWithTangents(points); // conic[1] is the list of the given five points conic[1]; // conic[2] is the equation of the conic f passing through the five points conic[2]; // conic[3] is a list containing the equations of the tangents // through the five points conic[3]; // conic[4] is an ideal representing the tropicalisation of the conic f conic[4]; // conic[5] is a list containing the tropicalisation // of the five tangents in conic[3] conic[5]; // conic[6] is a list containing the vertices of the tropical conic conic[6]; // conic[7] is a list containing the vertices of the five tangents conic[7]; // conic[8] contains the latex code to draw the tropical conic and // its tropicalised tangents; it can written in a file, processed and // displayed via kghostview write(":w /tmp/conic.tex",conic[8]); system("sh","cd /tmp; latex /tmp/conic.tex; dvips /tmp/conic.dvi -o; kghostview conic.ps &"); // with an optional argument the same information for the dual conic is computed // and saved in conic[9] conic=conicWithTangents(points,1); conic[9][2]; // the equation of the dual conic ```