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 degenerate, its reduced equation is
3x^{2}+y^{2}−7/6=0 
its origin is −5/3+5*i/6, its axes are parallel to the vectors (−1,1) and (−1,−1). Its parametric equation is
 + 
 * 

where the suggested parameter values for drawing are t from 0 to 2π with tstep= 2π/60.
Remark :
Note that if the conic is degenerate 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 :
^
2y^
2+3*x+y+2)Output :
^;
2y^
2, [[(1+2*i)/(1i),(1+2*i)/(1i)], [(1+2*i)/(1i),(1)/(1i)]]]