Math in ONE incorporates numerous
independent variables defined for different applications.
In the program, application descriptions explain the usage of independent variables.
This program supports a real and
complex independent variables.
Independent variables x and y are used to represent real numbers. Using x and y in a function as real
numbers, will not necessarily generate real results (e.g. sqrt(x) for x=-1). A complex number ' z ' is
defined as z = x + i( y ). ' i ' is an imaginary number and i * i = -1.
(if x and y are not real, evaluation of the expression may produce unexpected results.
It is the user's responsibility to ensure that the imaginary part of the expression indicated by
' i ' is a real value.) Note: x + i( sqrt( cos( y )) for some values of ' y ' (e.g. y = pi) will produce unexpected results.

Generate Graphs:

(W) To generate a graph, follow the outline below :

In a complex numbers expression, z
can be used as an independent variable (e.g. sin(z))
or a complex form is allowed f( x ) + i g( y )(e.g. sin( x ) + i (cos( y ))).

Variables t and θ are intended for
Parametric Equations and
Polar Coordinates respectively,
but x is acceptable as well. This program does not recognize any difference between x, t, and θ variable names. In
Cartesian Coordinates,
multiple number of expressions can be graphed at the same time. For Parametric Equations, a pair of two expressions
must be defined in the designated memory. All expressions need to be added to
Text Storage in the Input field.

Configure memory for selected graph type:
Graph display operates in From-To mode.
Data Entry To Memory window will help to configure
memories for different graph types.

Y(x) window can be launched in
Cartesian coordinate and
Level Curves display.
When a graph is displayed, right mouse click any place on the graph and select
Open Y(x) window.
A new window will open displaying a value of an independent variable and values of displayed functions that correlates
to the position last clicked on the graph.

Zoom in and out: When graph is displayed, right mouse click on any place on the graph and select
Zoom in or Zoom out.
The graph size will be adjusted 50% based on zoom selection. In the Cartesian coordinate and
the Level Curve display, the point on the graph where the mouse was clicked will be moved to the center of the disply area.

In a calculus mode, the display can be configured to include in a graph, the original expression, its derivatives 1st, 2nd, . . . and the integral of the expression for different initial conditions.
For further details, refer to the object popup help (derivative check box) and application description
(1st order differential equations).

drawCar( XY, Fn0 , Fn1, Fn2, ...) Draws functions Fn0, Fn1, Fn2, ... in Cartesian coordinates

Xmin - calculation range from (e.g. -5 or m1)

Xmax - calculation range to (e.g. 5 or m2)

Ymin - display Y range from (e.g. -5 or m3)

Ymax - display Y range to (e.g. 5 or m4)

Fn0 - first function that is evaluated (e.g. ln(x) or F0)

Fn1 - second function that is evaluated (e.g. exp(x)) or F1)

Fn2 - third function that is evaluated (e.g. x) or F2)

drawCar(-5,5,-5,5,ln(x),exp(x),x)

In Cartesian coordinates, when one touches the screen at a point, it will turn on the display of the function x and y values at that point. A tap on the circle in bottom left corner will turn off the display.

drawPol( XY, Pix, Fn0 ) Draws function Fn0 in Polar coordinates.

Xmin - calculation range from (e.g. 0 or m1)

Xmax - calculation range to (e.g. 15 or m2)

Ymin - display X & Y range from (e.g. -1 or m3)

Ymax - display X & Y range to (e.g. 1 or m4)

Pix - number of iterations (e.g. 700 or m5)

Fn0 - function that is evaluated (e.g. cos(x) or F0)

drawPol(0,15,-1,1,700,cos(x))

drawPar( XY, Pix, Fn0, Fn1 ) Draws two functions as parametric equations.

Xmin - calculation range from (e.g. 0 or m1)

Xmax - calculation range to (e.g. 50 or m2)

Ymin - display X & Y range from (e.g. -2 or m3)

Ymax - display X & Y range to (e.g. 2 or m4)

Pix - number of iterations (e.g. 1700 or m5)

Fn0 - first function of the pair that is evaluated (e.g. sin(x) or F0)

Fn1 - second function of the pair that is evaluated (e.g. cos(2*x) or F0)