> 
#  Plotting with 2 and 3-dimensional functions
#                                       
# 
# 
# We need to use   with(plots)
# 
> with(plots):
> 
# The first function we look at is  sin(x)cos(y).
# We plot the curve and look at its contours.
# We then repeat this process with several other functions.
# 
> f:=sin(x)*cos(y);

                          f := sin(x) cos(y)

> plot3d(f,x=0..2*Pi,y=0..2*Pi);

> contourplot(f,x=0..2*Pi,y=0..2*Pi);

> 
# Second function:
# 
> g:=(x^2+3*y^2)*exp(-x^2-y^2);

                           2      2        2    2
                    g := (x  + 3 y ) exp(-x  - y )

> plot3d(g,x=-3..3,y=-3..3);

> contourplot(g,x=-3..3,y=-3..3);

> 
# Third function:
# 
> h:=x*y;

                               h := x y

> plot3d(h,x=-2..2,y=-2..2);

> contourplot(h,x=-2..2,y=-2..2);

> 
# Fourth function:
# 
> l:=x/(x^2+y^2+1);

                                     x
                           l := -----------
                                 2    2
                                x  + y  + 1

> plot3d(l,x=-4..4,y=-4..4);

> contourplot(l,x=-4..4,y=-4..4);

> 
# We now look at a function of three variables,
# and we plot two of its contours.
# The contours are ellipsoids.
# 
> q:=x^2+4*y^2+z^2;

                               2      2    2
                         q := x  + 4 y  + z

> 
# The function implicitplot3d will plot the points that
# give the function q a specified value;
# ie, implicitplot can be used to plot a contour of q.
# 
> implicitplot3d(q=1,x=-1..1,y=-1..1,z=-1..1,color=red);

> implicitplot3d(q=4,x=-2..2,y=-2..2,z=-2..2,color=yellow);

> 
# We are going to plot the two contours on the same graph.
# The second contour totally surrounds the first one,
# so we plot just half of the second contour.
# 
> one:=implicitplot3d(q=1,x=-1..1,y=-1..1,z=-1..1,color=red):
> two:=implicitplot3d(q=4,x=-2..2,y=0..2,z=-2..2,color=yellow):
> display3d({one,two});

>