A equation of a quintic curve with 6 or at least 5 double points
I ask for the equation of a quintic curve with 6 or at least 5 double points!
I have founded the equation with only 4 double points... (Worried)
Help me, please!(Wait)
Scifo from Italy
double points of F(x,y)=0 if Fx=Fy=0
The double points of a curve F(x,y)=0 is the points where the prime
derivative respect to x e to y is zero (but not all the seconds derivative)
I think...it is correct?(Thinking)
A quintic five double points irreducible
I thank you very much for your intelligent solution
about the five double points.
At last I have a quintic five double points!(Clapping)
Perhaps you help me again for the following problems:
May you create a quintic five double points irreducible?
It is no hope for a quintic six double point?
Perhaps a method for to find the 6-double points quintic equation?
I thank you for your useful information…(Clapping)
I wanted a your opinion on a method, than it has sprung to mind,
in order to find the a 6-double points quintic equation...
Practically, fixed in the cartesian plan 8 points, 6 double and 2 simple.
if F(x,y) is quintic polynomial and Fx(x,y) and Fy(x,y) its derivatives,
then for every Xi,Yi of the 6 double points I have the three equations
F(Xi,Yi)=0, Fx(Xi,Yi)=0, Fy(Xi,Yi)=0
and for every Xj,Yj of the 2 simple points I have the equation
I have so a linear omogeneous system of 20 equations in the 20 unknown quantities
that are the essential coefficients of the quintic, resolved which I have the equation…
That you think some?(Wondering)