conique_reduite takes two arguments : the equation of a conic
and a vector of variable names.
conique_reduite returns a list whose elements are:
Input :
^2+2*x*y+2*y^2+5*x+3,[x,y])Output :
^2+y^2+-7/6,[[(-10+5*i)/6+ (1/(sqrt(2))+(i)/(sqrt(2)))*((sqrt(14)*cos(‘ t‘))/6+ ((i)*sqrt(42)*sin(‘ t‘))/6),‘ t‘,0,2*pi,(2*pi)/60]]]Which means that the conic is not degenerated, it’s reduced equation is
| 3x2+y2−7/6=0 |
origin is −5/3+5*i/6, axis are parallel to the vectors (−1,1) and (−1,−1). It’s parametric equation is
| + |
| * |
|
where the suggested parameters value for drawing are t from 0 to 2π with tstep= 2π/60.
Remark :
Note that if the conic is degenerated and is made of 1 or 2 line(s),
the lines are not given by
their parametric equation but by the list of two points of the line.
Input :
^2-y^2+3*x+y+2)Output :
^;2-y^2, [[(-1+2*i)/(1-i),(1+2*i)/(1-i)], [(-1+2*i)/(1-i),(-1)/(1-i)]]]