TMS Analytics & Physics library is a set of classes that provide functionality
for building powerful math applications with Delphi. In the new version 3.2 of
the library, we introduced special FNC math components. The components bring new
possibilities to develop and tune your math application in design-time with
standard IDE tools.

In this article, we’ll consider the base concepts of the FNC math
components and provide information on how to work with functions, derivatives,
and integrals.

All FNC math components are nonvisual. Each component implements some
math concept and provides properties to manipulate and tune it in design- and
run-time. Let’s consider the following components:

• TFNCProvider – creates math environment; allows introducing
  variables and parameters for function evaluations, symbolic derivatives, and integrals.
• TFNCFunction1D – introduces a symbolic function of one
  variable; allows evaluating the function for the specified variable value.
• TFNCDerivative1D – introduces a symbolic derivative of a
  math expression; allows evaluating the derivative for the specified variable
  value.
• TFNCIntegral1D – introduces a symbolic integral of a
  math expression; allows evaluating the integral for the specified variable
  value.

To begin any FNC math application we first need to put a TFNCProvider component on the form. The
component has two published properties:

• Variables (TVariableCollection) – a collection of variables that can be used as arguments of functions.
• Parameters (TParameterCollection) – a collection of parameters that can be used in the math environment to
  build functions, derivatives, integrals, and other math expressions.

When you put a TFNCProvider
on the form in design-time, it automatically creates a default variable ‘x’ for your math application. You can
change the name of the variable or add/delete variables at design- and
run-time.

For the simplest math application, the
default environment with one variable ‘x’
is enough. So, let’s go forward and consider the next FNC component TFNCFunction1D and its properties:

• Provider (TFNCProvider) – a math environment for the function.
• Variable (TVariableProperty) – a variable specifying the argument of the function.
• Formula (TFormulaProperty) – a formula specifying the math expression of the function.

Placing a TFNCFunction1D on
the form, it assigns the default value ‘x’
to the Variable property. We need to
set up the Provider property and the
expression for the Formula property,
say ‘5*sin(6*x)’ in the Object
Inspector. The resulting properties are shown in the picture below: 

The function is ready to use. What can we
do with it? The first idea is to draw the function and see what it looks like.
We have the TFNCFunction1DPlotter
component especially developed for this purpose:

• TFNCFunction1DPlotter – a binding for an
  FNC function component and an FNC Chart; allows drawing any FNC function on the
  chart.

The component has several published properties that we can use to tune it
and show a function on the FNC Chart:

• Provider (TFNCProvider) – a math environment for the component.
• Min (TValueProperty) – the minimal value of the variable range to plot the function.
• Max (TValueProperty) – the maximal value of the variable range to plot the function.
• PointCount (Integer) – number of points to plot the function.
• AFunction (TFNCBaseFunction1D) – a FNC function to plot.
• AssignLegend (Boolean) – if true, assigns the function’s expression to the serie’s legend.
• Chart (TTMSFNCChart) – an FNC chart to draw the function.

First, we need to assign the appropriate Provider property. The Min
and Max properties have default
values ‘0’ and ‘10’ accordingly, and the PointCount
is 50.

When you assign the Chart property
in design-time, the component automatically creates a new serie for the chart.
The function will be drawn with this serie and you can set the appropriate properties
of the serie to get the suitable representation of the function.

For now, we have a simple math application, designed with the four
components: a provider; an FNC function; an FNC plotter; and an FNC chart. The form
in design-time is shown in the picture below:

In run-time, the
application works like in design-time: it shows the only function ‘5*sin(6*x)’.
Let’s move on and get the application drawing any function, the user can input
as a math expression.

First, let’s look at the Parameters property on the FNC provider
component. This is a collection of parameters. A parameter is a named value
that can be used in math expressions together with variables. The TParameterProperty class has the
following published properties:

•  Name (String) – name of the parameter.
• Value (String) – constant math expression of the parameter’s value.
• RealValue (Real) – read-only float number for the math expression.

Via common IDE’s interface, we can add or remove items of the Parameters collection to get desired math
environment. For our application, we created three new parameters and assigned
them some values, as shown in the following picture:

Now we can create a
simple user interface to input a math expression in a text box and a button
with the following event handler:

procedure
TForm1.Button1Click(Sender: TObject);
var
  f: string;
begin
  f:= Edit1.Text;
 
  FNCFunction1D1.Formula.Formula:= f;
end;
 

Thus, in run-time, the user can draw on the
chart any function that depends on the variable ‘x’ and three parameters ‘A’,
‘B’, and ‘L’. Here is an example of one such function draw:

The values of the
parameters can be changed as in design-time as in run-time. If a function
depends on the parameter, changing the value immediately leads to the function
and the chart update.

The TFNCDerivative1D
component is intended to work with derivatives and has the following
properties:

•  Provider (TFNCProvider) – a math environment for the component.
• Variable (TVariableProperty) – a variable specifying the argument of the function.
•  D (TVariableProperty) – a variable specifying the differential.
• Functional – a differentiable math expression.
• Formula (TFormulaProperty) – read-only formula denoting the resulting math expression of the
  derivative.

In general, this component works like an FNC function, but it evaluates
the derivative of the functional expression. Putting the component on the form
we can create another button with a simple event handler to draw derivative of
any function:

procedure
TForm1.Button2Click(Sender: TObject);
var
  f: string;
begin
  f:= Edit1.Text;
 
  FNCDerivative1D1.Functional:= f;
  FNCFunction1DPlotter1.AFunction:=
FNCDerivative1D1;
end;

Here we showed the resulting application in
run-time for the derivative of a simple math expression:

The TFNCIntegral1D
component has the same properties as the described TFNCDerivative1D component, but it evaluates the indefinite
integral of a math expression. An example of an integral is shown in the picture
below:

The source code of the demo project for the article can be downloaded
from here. To start developing your
FNC math application you need the latest versions of TMS Analytics & Physics
and TMC FNC Chart
products.