Best Objectech Shareware Selections/UNTITLED.iso/boss/educ/math/021/symbmath.h14

Text File | 1993-04-21 | 8.4 KB | 288 lines

            8. Packages
    A package is a SymbMath program file for special use.
    In order to expand the special ability of SymbMath, some
packages should be included in the user program by
        include('filename')
    The filename is any MS-DOS filename.
    It is recommended that the filename is the same as the function
name in the program file, and the extension of the filename is .sm in
order to remember easily the name of the package. e.g. inte.sm is the
filename of the integral package as the name of integral function is
inte().
    After including the package, users can call the functions in
the package from their program.
    The include command must be in a single line anywhere.
    Many packages can be included at a time, however, all names of
the variables are public and name conflicts must be avoided.
    Alternately, a part of the package file rather than the whole
package file can be copied into the Edit window by pressing <F7>
(external copy) in order to save memory space.
    There are many packages. The following are some of them.

        Table 8.1      Packages
------------------------------------------------------------------------
File Name               Package Function

init.sm                 initial package when running the program in
            the Edit window. It contains switches on the
            default status.
plot.sm            plotting functions.
listplot.sm        plotting a list of data.
d.sm                    derivatives.
inte.sm                 integrals.

--------------- shareware version only has above packages --------------

units.sm                an units conversion.
trig.sm                 reduction of trig functions.
hyperbol.sm             reduction of hyerbolic functions.
dt.sm                   total derivatives.
NInte.sm                numeric integration.
NSolve.sm               numeric solver of equation.
ODE.sm            ordinary differential equation.
gamma.sm                gamma function.
ei.sm            exponential integral function.
series.sm        Taylor series.
sum.sm            symbolic sum.
InfSum.sm        infinite sum.
chemical.sm             the atomic weight of chemical elements.
inorgani.sm             inorganic chemical reactions.
-----------------------------------------------------------------------


        8.1 Initial Package
---------------------------------------------------------------------
#    The initial package init.sm
output=off
numerical=off
expand=off
sum(y_,x_,a_,b_) := sum(y,x,a,b,1)
prod(y_,x_,a_,b_) := prod(y,x,a,b,1)
list(y_,x_,a_,b_) := list(y,x,a,b,1)
table(y_,x_,a_,b_) := table(y,x,a,b,1)
table(y_,x_) := table(y,x,-5,5,1)
degree=pi/180
0!=1
inf!=inf
sgn(0)=0
sgn(zero)=1
sgn(e)=1
sgn(pi)=1
sgn(inf)=1
abs(zero)=zero
abs(e)=e
abs(pi)=pi
abs(inf)=inf
ln(0)=-inf
ln(inf)=inf
 include('plot.sm')
# include('d.sm')
block(output=basic,null)
end
---------------------------------------------------------------------

    When running the program in the Edit window, SymbMath
automatically first includes (or runs) the initial package 'init.sm'.
The commands in the 'init.sm' package seems the SymbMath system
commands. You can include other packages (e.g. d.sm) in the initial
package 'init.sm' so the derivatives table in the package 'd.sm' seems
to be in SymbMath system. Doing this is by changing the comment
statement in the last third line
        # include('d.sm')
to include statement
        include('d.sm')


        8.2 Derivative Package
       The package 'd.sm' is extention of the d(f(x),x) function.

        8.3 Total Derivative Package
       The package 'dt.sm' is for the total derivative function
dt(f(x,y),x,y).
    Example:
    Input:
include('dt.sm')
dt(x*y, x, y)
end
    Output:
y*d(x) + x*d(y)

        8.4 Integral Package
       The package 'inte.sm' is the extention of the function inte(f(x),x).

        8.5 Numeric Integration Package
    The function
        ninte(y, x from x0 to x1)
in the package 'NInte.sm' can do numerical integration.
    Example 8.5.1. Compare numerical and symbolic integrations
for 4/(x^2+1) with respect to x taken from x=0 to x=1.
    Input:
include('NInte.sm')
ninte(4/(x^2+1), x from 0 to 1)
num(inte(4/(x^2+1), x from 0 to 1))
end
    Output:
done
3.1415
3.1416

        8.6 Numerical Solving
    The function
        nsolve( f(x) === x, x, x0)
in the package 'NSolve.sm' can numerically solve an algebraic equation
with an initial value x0.
    Example 8.6.1. solve the equation sin(x) === 1 with x0=1.
    Input:
include('NSolve.sm')
nsolve( sin(x) === 1, x, 1)
end
    Output:
done
1.5364150214

        8.7 Series Package
    The series package 'Series.sm' has a function series() for the
Taylor series at x=0:
    You can call the function
        series(f(x), x, order)
        series(f(x), x)
to find the Taylor series. The arguement (order) is optional and
defaults to 6.
    Example 8.7.1. Find the power series expansion for cos(x)
about the point x=0 to order x^4.
    Input:
include('series.sm')
series(cos(x), x, 4)
end
    Output:
1 - 1/2*x^2 + 1/24*x^4

        8.8 Infinite Sum Package
    The infinite sum package 'InfSum.sm' has a function
        infsum(f(x),x)
to find the infinite sum, sum(f(x), x from 0 to inf).
    Example:
    Input:
include('infsum.sm')
infsum(1/n!, n)
end
    Output:
e

        8.9 Chemical Calculation Package
    SymbMath recognizes 100 symbols of chemical elements and
converts them into their atomic weights after the chemical package of
'Chemical.sm' is included.

    Example 8.9.1. Calculate the weight percentage of the
element C in the molecule CH4.
    Input:
include('chemical.sm')
numerical=on
C/(C+H*4)*100*%
end
    Output:
done
numerical = on
74.868 %

    Example 8.9.2. Calculate the molar concentration of CuO when
3 gram of CuO is in 0.5 litre of a solution.
    Input:
include('chemical.sm')
numerical=on
g=1/(Cu+O)*mol
3*g/(0.5*l)
end
    Output:
0.07543*mol/l

        8.10 Chemical Reactions Package
    SymbMath can provide the answers for inorganic chemical
reactions after the inorganic reaction package "Inorgani.sm" is included.

    Example 8.10.1.  What are the products when the reactors are
HCl + NaOH ?
    Input:
include('inorgani.sm')
HCl+NaOH
end
    Output:
H2O + NaCl


        8.11 Plot Function Package
---------------------------------------------------------------------
# The plot function package plot.sm
# to plot a function.
# plot(x^2, x)        # plot the function of x^2
# plot(x^2, x,-6,6)    # plot the function of x^2 from x=-6 to x=6
# end

output=off
plot(y_,x_,x1_,x2_,dx_) := block(openfile('symbmath.out'),
    table(y,x,x1,x2,dx),
    closefile('symbmath.out'),
    system(plotdata))
plot(y_,x_,x1_,x2_) := plot(y,x,x1,x2,(x2-x1)*0.5)
plot(y_,x_) := plot(y,x,-5,5,0.5)
output=on
end
----------------------------------------------------------------------

    If SymbMath is interfaced with the software PlotData, SymbMath
produces the data table of functions, and PlotData plots from the
table. So SymbMath seems to plot the function. This interface can be
used to solve equations graphically.
    In the plot package 'plot.sm' the funcion
        plot(y, x, x1, x2, dx)
first open a file 'SymbMath.Out' for writing, then write the data table
of the function y into the file 'SymbMath.out', then close the file,
and finally automatically call the software PlotData to plot. After it
exits from PlotData, it automatically return to SymbMath.
    The functions
        plot(y, x)
        plot(y, x from xmin to xmax)
call the function plot(y,x,x1,x2,dx)
    e.g. plot x^2.
    Input:
plot(x^2, x)
end

in the software PlotData, just select the option to read the file
'SymbMath.out' and to plot. PlotData read the data in the SymbMath
format without any modification (and in many data format).
    In PlotData,
in the main menu:
1 <Enter>
in the read menu:
1 <Enter>
<Enter>
in the main menu:
2 <Enter>
in the graph menu:
1 <Enter>

where <Enter> is the <Enter> key.
Refer to PlotData for detail.
    Note that if your monitor is Hercules, you must load the
MSHERC.COM program as a TRS program before you run PlotData.
Otherwise you will get Error when you plot.

        8.12 List Plot Package
----------------------------------------------------------------------
# the list plot package 'listplot.sm'
# to plot a list of data.
# listplot([1,2,3,4,5,4,3,2,1])
# end

output=off
listplot(y_) := if(islist(y), block(yy=y, length=length(yy),
    openfile('symbmath.out'),
    table(yy[xx],xx,1,length),
    closefile('symbmath.out'),
    system(plotdata) ))
output=on
end
---------------------------------------------------------------------