```# Graphs with grids that chose the user
#
BF=6; HF=3
f = function(x) sin(x)*sqrt(2)
x1=-pi*3; x2=pi*3; y1=-1.5; y2=1.5
# I specify the distances between the grid lines horizontally and vertically
#     (if I do not specify the distances only the axes are plotted)
TICKx=pi/4; TICKy=1/2; Plane2(x1,x2, y1,y2)
graph(f, x1,x2, "brown")

# I also added directions along the axes.
abovex("x"); abovey("sqrt(2)*x")
underX("-pi",-pi); underX("pi",pi)
underY(-1,-1); underY(1,1)
# This is an adequate way to easily get such charts.
# We see a more sophisticated way
#                            # # # # # # # # #
f = function(x) sin(x)*sqrt(2)
x1=-pi*3; x2=pi*3; y1=-1.5; y2=1.5
TICKx=pi/4; TICKy=1/2; Plane2(x1,x2, y1,y2)
# I trace thicker lines to draw the x-axis and y-axis.
segm(x1,0, x2,0, "blue"); segm(0,y1,0, y2, "blue")
# and an additional grid.
GridV( seq(-pi*3,pi*3,pi) )
graph(f, x1,x2, "brown")
# I put the numeric markings on the edge of the grid by writing the formulas
# using "bquote" (see)
for(y in seq(y1,y2,0.5)) underY(y,y)
for(i in 2:3) { x=i*pi; underX( bquote(.(i)*pi), x) }
for(i in -3:-2) { x=i*pi; underX( bquote(.(i)*pi), x) }
abovex("x"); abovey(bquote(sqrt(2)%.%sin(x)))
underX(0,0); underX( bquote(-pi),-pi); underX( bquote(pi),pi)
# I trace, subtle, also the line representing the maximum value of f
line(x1,sqrt(2), x2,sqrt(2), "brown")
AboveY(bquote(sqrt(2)),sqrt(2))

# With PLANE2 I behave similarly for a monometric system.
# Here I choose a grate less dense, then a thicker than the standard one.
BF=3; HF=3
TICKx=1/2; TICKy=1/2; PLANE2(-1,1, -1,1)
circle(0,0, 1/2, "brown"); polylineR(0,0, 1, 4,0, "red"); polylineR(0,0, 1, 8,0, "blue")
TICKx=0.1; TICKy=0.1; PLANE2(-1,1, -1,1)
circle(0,0, 1/2, "brown"); polylineR(0,0, 1, 4,0, "red"); polylineR(0,0, 1, 8,0, "blue")
# or choose no one:
PLANE2(-1,1, -1,1)
circle(0,0, 1/2, "brown"); polylineR(0,0, 1, 4,0, "red"); polylineR(0,0, 1, 8,0, "blue")

```