			   CHANGING THE GRAPH PAPER

To change the background graph paper, first select Paper from the View menu.
Then you need to respond to three prompts (more if you select Log paper):

+ Select type of graph paper:
  - Rectangular is the default paper
  - Trig is labeled in multiples of pi along the x axis for trig functions
  - Polar paper consists of concentric circles marking the distance r, and
    radiating lines marking the angle theta at intervals of pi/6 radians.
  - Logarithmic paper allows you to scale one or both axes logarithmically,
    so that, for instance, 0.1, 1, and 10 are equally spaced.

If you select Log paper, you will also be asked to specify a base and choose
between semi-log (y axis only) and log-log paper (both axes logarithmic). If
you choose base 10, you will see 9 lines per decade just like real graph paper
if there is enough space to display them (generally when less than four
decades are shown). Otherwise, the graph paper will still be rectangular, but
with gridlines at integer powers of the base. Note that when you switch from
or to log paper, the graphs that are on-screen will have to be recalculated,
since the shape of the curves is distorted when you take the logarithm.

				      Press PgDn for more help on Graph Paper.
		      CHANGING THE GRAPH PAPER, continued

+ Select grid detail level:
  - No grid hides the gridlines completely
  - Dots draws reference dots everywhere the gridlines would cross
  - Gridlines draws dotted lines at every one or two units across the grid

+ To customize the look of the axes, respond to "Select axis decorations:"
  - No axes turns off the axes (legends may still be displayed along the
    invisible axes unless you turn them off with the Legends command)
  - Plain shows the axes without any decorations
  - Arrows draws arrows on the positive end of the axes
  - Labels shows 'x' and 'y' labels at the positive ends of the axes
  - Both draws both arrows and labels on the axes

			      CLEARING THE SCREEN

Select Clear in the View menu to clear the screen. Everything will be erased
and the grid will then be redrawn. If an error has garbled the whole screen,
here's a hint to help regenerate it: first press ESC until the top menu bar is
refreshed, and then use Clear to redraw the rest of the screen.

						 Press PgDn for help on Scale.
			      CHANGING THE SCALE

The scale function allows you to change the scale of the graph you have on-
screen while keeping the center of the display the same (the origin may move
but if (2,2) is at the middle of the screen, it will stay there). The scale is
relative to the size of the grid that is presently on the screen, so you need
not make any comparison with the default grid. To rescale the grid, select
Scale from the View menu. Then you must provide a "scale factor" to tell the
program how much to change the size of the grid.

Enter a positive number to zoom in, or a negative number to pan out. (In the
Camcorder terminology, a positive number acts as a telephoto and a negative as
a wide-angle lens.) The number of units across the screen will be divided or
multiplied by that number accordingly. Numbers between -1 and 1, inclusive,
are not allowed because they produce meaningless values. Decimals greater than
1 or less than -1 are valid though.

If you enter an invalid number, you will be asked to enter the scale again. To
abort rescaling, leave the field blank and just press enter.

The program remembers the value you type in and presents it as a default the
next time you Scale the grid. The original default is "2".
						 Press PgDn for help on Range.
                              ADJUSTING THE RANGE
Graphmatica allows you to adjust the start and end of the x- and y-ranges
independently, so as to create a perfect fit for whatever function you are
graphing. Or, you can constrain one or more of the coordinates to produce a
graph with a square aspect ratio without actually figuring out all of the
values by hand.

Choose the Range item from the View menu to modify the grid. To create a
"custom" grid, estimate the top-, bottom-, left- and rightmost extremities of
the graph, and type them in at the 4 Range prompts. The new grid may be
somewhat expanded or compressed depending on the aspect ratio, but it will
show the part of the graph you're interested in the best possible detail.

To create a "square" grid where both x and y axis have the same scale, just
type "auto" for any of the four coordinates and it will automatically be
scaled properly to fit the other three. If you pick the least significant
coordinate to AutoScale, you can match the other three exactly, framing your
graph almost as well as a custom range, but with a more natural aspect ratio.
If you want to show the same amount above as below the axis, type "auto" at
both of the y-coordinate prompts and the top and bottom of the grid will be
set to properly scaled equal and opposite values. (AutoScaling of both x-
coordinates based on the height of the grid is not supported.)
                           Press PgDn for help on changing the range of theta.
                          CHANGING THE RANGE OF THETA

Because the independent variable (theta) in polar coordinates is fundamentally
different from the 'x' of Cartesian coordinates, the Cartesian x/y ranges can
only be used to determine the size of the screen and not the domain of the
equation graphed for polar graphs. Although the default 0 to 2pi range is the
typical range of theta used for most graphs that go on forever (like spirals)
and some closed graphs (like circles), other graphs cannot be completely drawn
in this range of theta. For instance, the figure-8-shaped "r^2=64cos(2t)",
because it is undefined where the right half is less than zero, is missing a
couple of spots unless theta's range is extended to -2pi to 2pi. To allow the
greatest flexibility, Graphmatica allows theta's range to be changed
independently of all other options.

To change the range, select "T range" from the View menu and enter the start
and end of the range you want (or press enter on the blank line to keep the
current range). You can type in any expression, even using fractions and
functions, as long as it evaluates to a constant. In particular, although
Graphmatica works exclusively with radians, you can enter the range in degrees
by typing in a number times the constant 'd', which converts degrees to
radians, as in "45d" for 45 degrees. You can also easily specify a radian
measure as a multiple of pi, as in "2p" for 2 pi.
────────────────End of View help. Press ESC to return to menu.────────────────
