####################################################################
#
#   The copyright to this file, and the images it draws are owned by 
# Frank Sottile.  We allow the free use of this, but you must first
# ask permission of either Frank Sottile or Adriana Ortiz, and 
# acknowledge our creation of these images.
#
####################################################################
interface(quiet=true):
with(plots):
plotsetup(x11,plotoptions=`width=6in,height=6in`):
   
POLYS:=[102+91*y+19*y^2-108*y^3-17*y^4+98*y^5-63*x-30*x*y-30*x*y^2-4*x*y^3-68*x*y^4-30*x^2-5*x^2*y-99*x^2*y^2-19*x^2*y^3+63*x^3+81*x^3*y+34*x^3*y^2+108*x^4-21*x^4*y-20*x^5,
-28+37*y-54*y^2-88*y^3-12*y^4+22*y^5-94*x-103*x*y+45*x*y^2+43*x*y^3-20*x*y^4-26*x^2+91*x^2*y+6*x^2*y^2-38*x^2*y^3-96*x^3+11*x^3*y-14*x^3*y^2+49*x^4+45*x^4*y+76*x^5
]:

N:=2:
f:=POLYS[N]:

L[1]:=[-4.5,18,-4.5,9]:
L[2]:=[-6.5,4,-6.5,4]:


H:=linalg[det](linalg[hessian](f,[x,y])):

B:=implicitplot(H,x=L[N][1]..L[N][2],y=L[N][3]..L[N][4],grid=[300,300],axes=none,color=blue):
#display(B,scaling=CONSTRAINED);
#
plotsetup(ps,plotoutput="7o2u.eps",plotoptions=`color,portrait,noborder,width=2in,height=2in`):
#plotsetup(gif,plotoutput="7o2u.gif",plotoptions=`height=500,width=500`):
display(B);

time();