** suivant:** Graph of a quadric
** monter:** Quadratic forms
** précédent:** Graph of a conic
** Table des matières**
** Index**

##

Conic reduction : `conique_reduite`

`conique_reduite` takes two arguments : the equation of a conic
and a vector of variable names.

`conique_reduite` returns a list whose elements are:
- the origin of the conic,
- the matrix of a basis in which the conic is reduced,
- 0 or 1 (0 if the conic is degenerated),
- the reduced equation of the conic
- a vector of it's parametric equations.

Input :
`conique_reduite(2*x``^`

2+2*x*y+2*y`^`

2+5*x+3,[x,y])

Output :
`[[-5/3,5/6],[[-1/(sqrt(2)),1/(sqrt(2))],[-1/(sqrt(2)), -1/(sqrt(2))]],1,3*x``^`

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

3*x*^{2} + *y*^{2} - 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 2 with `tstep`= 2/60.
**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 :

`conique_reduite(x``^`

2-y`^`

2+3*x+y+2)

Output :
`[[(-3)/2,1/2],[[1,0],[0,1]],0,x``^;`

2-y`^`

2, [[(-1+2*i)/(1-i),(1+2*i)/(1-i)], [(-1+2*i)/(1-i),(-1)/(1-i)]]]

** suivant:** Graph of a quadric
** monter:** Quadratic forms
** précédent:** Graph of a conic
** Table des matières**
** Index**
giac documentation written by Renée De Graeve and Bernard Parisse