			8.      Keywords

	SymbMath has three versions: Shareware Version A, Student
Version B and Advanced Version C. The shareware version lacks the 
solve(), trig (except sin(x) and cos(x)), and hyerbolic functions, 
(lack 10% keywords) and the student version lacks the hyerbolic
functions (lack 5% keywords). You cannot input these lack functions
in shareware or student version.
	Upper- and lower-case letters are different until the switch
lowercase is set to on (i.e. lowercase := on).
	All keywords are lower-case letters until the switch
lowercase := on.
	There are two types of the keywords: internal and external.
The internal keywords have been compiled into the SymbMath system,
so you cannot change them. The external ones are in files, so you
can change their name or property. Usages of both types are the same.
	The following only includes the internal and some external 
keywords. You can define your own keyword and add your defined function. 
If some keywords do not work, you should check whether or not the
libraries *.(x) are in the default directory.


	     8.1        Keywords in Topic Order
---------------------------------------------------------------------
1. Algebraic operators: +, -, *, /, ^, **, ().
2. Relational operators: ==, >, >=, <, <=, <>.
3. Assignments: :=
4. Equation: solve(x^2=1,x), solve([x+y=b,x-y=c], [x,y]), psolve(f(x),x),
             nsolve(cos(x)=x,x), nsolve(f(x)=0,x,x0),
             dsolve(y'(x)=f(x,y), y(x),x), =.
5. Comment: #.
6. Built-in constants: i, e, pi, inf, zero, constant, discont, c_inf,
	undefined.
7. Built-in variables: last.
8. Logic operators: and, or, not(x).
9. Algebraic functions: -x, sqrt(x), n!, fac(n), mod(x,y), div(x,y),
	random(x), expand(x), factor(x), factor(y,x), root(x,n).
10. Complex to real: re(x), im(x), abs(x), |x|, arg(x), sign(x).
11. Exponential functions: exp(x), ln(x), log10(x).
12. Trig functions: sin(x), cos(x), tan(x), csc(x), sec(x), cot(x), 
	asin(x), acos(x), atan(x), acot(x), asec(x), acsc(x), atan2(x,y).
13. Hyperbolic functions: sinh(x), cosh(x), tanh(x), csch(x), sech(x),
	coth(x), asinh(x), acosh(x), atanh(x), acoth(x), acsch(x),
	asech(x).
14. Special math functions: ei(x), ei(n,x), gamma(x), gamma(n,x), erf(x),
	si(x), ci(x), li(x), li(n,x).
15. Defining functions: f(x_):=x^2, f(x_) := if(x>0 then x^2).
16. Defining procedures: f(x_):=block(p:=x^2,p,local(p))
17. Defining rules: log(x_ * y_) := log(x)+log(y), f'(x_):=sin(x).
18. Clear: clear(x), clear(f(x)), clear(a>0).
19. Calculus functions: 
    Differentiating: d(y,x), d(y,x,n),  diff(y,x=x0), diff(y,x=x0,n), f'(x)
    Integrating:     inte(y,x), inte(y,x,xmin,xmax), ninte(y,x,xmin,xmax),
    Substituting:    subs(y,x=x0)
    Limit:           lim(y,x=x0), lim(y,x=x0+zero), nlim(y, x=x0),
        laplace(y,x), sum(y, x,xmin,xmax,dx), partsum(y,x), infsum(y,x),
	prod(y, x,xmin,xmax,dx), series(y,x), series(y,x,order).
20. Conversion functions:
        ratio(x), round(x), trunc(x), nume(a/b), deno(a/b), table(y,x),
        number(x), string(x), term(a+b), mult(a*b), type(x).
21. Numeric computation: num(x), nsolve(cos(x)=x,x), nsolve(cos(x)=x,x,x0),
        ninte(y,x,xmin,xmax), nlim(y,x=x0), numeric:=on.
22. Test functions: isodd(x), iseven(x), isinteger(x), isratio(x),
        isreal(x), iscomplex(x), isnumber(x), islist(x), isfree(y,x),
        issame(x), islarger(a,b), isless(a,b), type(x)=="real".
23. Table: table(y,x), table(y, x,xmin,xmax,dx).
24. Arrays and array index: a[1]:=1, do(a[x]:=x, x,xmin,xmax,dx), a[1].
25. Lists and list index: [a,b], [list(y,x,xmin,xmax)], member([a],j),
          last[1], reverse([x]).
26. Statistics: average([a,b]), max([a,b]), min([a,b]), listsum([a,b]),
                length([a,b]).
27. Switches: numeric, output, expand, expandexp, lowercase,
	:=, on, off, basic, fortran, prolog, math.
28. DOS Commands: system("dir").
29. Comma: , , from, to, step, then, else, until.
30. Assume: assume(a>0), isreal(x):=1.
31. Conditional: if(x>0 then x), if(x>0 then x else -x).
32. Loop: repeat(expr until x>5), do(expr, x,xmin,xmax,dx),
          list(y,x,xmin,xmax).
33. Reading: readfile("file"), readchar, readline.
34. Writing: openfile("file"), closefile("file"), writes(x), null, newline.
35. Plot: plot(x^3,x), plot(y,x,min,xmax), plot(y,x,xmin,xmax,ymin,ymax),
    dotplot(x^3,x), dotplot(y,x,min,xmax), dotplot(y,x,xmin,xmax,ymin,ymax),
    paraplot(x(t),y(t),t), paraplot(x(t),y(t),t,t1,t2), polaplot(r(t),t),
    polaplot(r,t,tmin,tmax), dataplot([x1,x2],[y1,y2]), listplot([y1,y2]).
36. Graph: graph, text, line(x1,y1,x2,y2), lineto(x,y), linerel(dx,dy),
           ellipse(x,y,), putpixel(x,y,color), moveto(x,y), moverel(dx,dy),
           arc(x,y,r,t1,t2), getmaxx, getmaxy, setcolor(white),
           setbkcolor(red), setviewport(x1,y1,x2,y2,clip),
        setlinestyle(style,dir,thick), settextstyle(font,dir,size),
        circle(x,y,r), oval(x,y,xr,yr), settextjustify(hor,ver),
        getx, gety, getbkcolor, getcolor.
37. String: "123", concat("a","b"), break("ab",1), length("a"), string(1).
38. Getting parts: type(x), left(a=b), right(a=b), term(a+b), mult(a*b),
            coef(y,x), coef(y,x,n), coefall(y,x), power(x^n), base(x^n),
            argue(x), sequence(x), re(x), im(x), int(x), frac(x).
39. Database: phoneno(x), colorno(x), atom_wei(x)
--------------------------------------------------------------------------


	   8.2          Keywords in Alphabetical Order
---------------------------------------------------------------------------
abs(x)          acos(x)         acosh(x)              acot(x)
acoth(x)        acsc(x)         acsch(x)              and
arc(x,y,ang1,ang2,r)            arg(x)                argue(x)
asec(x)         asech(x)        asin(x)               asinh(x)
assume(x>0)     atan(x)         atan2(x,y)            atanh(x)
atom_wei(x)     average([a,b])

base(x^n)       basic           block(p:=x^2,p,local(p))
break("ab",2)

ci(x)           circle(x,y,r)   clear(x)               cleared
closefile("x")  coef(y,x)       coef(y,x,n)            coefall(y,x)
colorno(x)      concat("a","b") constant               cos(x)
cosh(x)         cot(x)          coth(x)                csc(x)
csch(x)         c_inf

d(y,x)          d(y,x,n)        degree                  deno(a/b)
diff(y,x=x0)    diff(y,x=x0,n)  div(x,y)                discont
do(expr,x,xmin,xmax,dx)         done                    dotplot(y,x)
dotplot(y,x,xmin,xmax)          dsolve(y'(x)=sin(x),y(x),x)

e               ei(x)           ei(n,x)
ellipse(x,y,ang1,ang2,xr,yr)    else                    eval(x)
erf(x)          exp(x)          expand(x)               expand
expandexp

f'(x)           fac(x)          factor(x)               factor(y,x)
fortran         frac(x)         from

gamma(x)        gamma(n,x)      gcd(a,b)                getbkcolor
getcolor        getmaxx         getmaxy                 getx
gety            graph

i               if(c,t)         if(c,t,f)               im(x)
inf             infsum(y,x)     int(x)                  inte(y,x)
inte(y,x,xmin,xmax)             inverse(x)              iscomplex(x)
iseven(x)       isfree(y,x)     isinteger(x)            islarger(a,b)
isless(a,b)     islist(x)       isodd(x)                isratio(x)
isreal(x)       issame(x,y)     isnumber(x)

laplace(y,x)    last            left(a=b)               length(x)
li(x)           li(n,x)         lim(y,x=x0)             line(x1,y1,x2,y2)
lineto(x,y)     linerel(dx,dy)  list(y,x,xmin,xmax)     listsum(x)
ln(x)           local(a)        local(a,b)              log10(x)
lowercase

math            max([a,b])      member(x,n)             min([a,b])
mod(x,y)        moveto(x,y)     moverel(dx,dy)          mult(x*y)

newline         ninte(y,x,xmin,xmax)                    nlim(y,x=x0)
not(x)          nsolve(y,x)     nsolve(y,x,x0)          null
num(x)          number(x)       nume(a/b)               numeric

off             on              openfile("x")           or
order(y,x)      output          oval(x,y,xr,yr)

paraplot(x(t),y(t),t)           paraplot(x(t),y(t),t,t1,t2)
partsum(y,x)    pi              plot(y,x)               plot(y,x,xmin,xmax)
plot(y,x,xmin,xmax,ymin,ymax)   phoneno(x)              polaplot(r,t)
polaplot(r,t,t1,t2)             power(x^n)              prod(y,x,xmin,xmax)
prolog          psolve(f(x),x)  putpixel(x,y,color)

random          random(x)       ratio(x)                re(x)
react(x)        readchar	readfile("x")           readline
repeat(a:=1+a until a>2)        reverse([a])            right(a=b)
root(x,n)       round(x)

sec(x)          sech(x)         series(y,x)             serie(y,x,n)
sequence([x])   setbkcolor(0)   setcolor(1)
setlinestyle(style,dir,thick)   settextjustify(hor,ver)
settextstyle(font,dir,size)     setviewport(x1,y1,x2,y2,clip)
si(x)           sign(x)         sin(x)                  sinh(x)
solve(eq,x)     sqrt(x)         subs(y,x=x0)            sum(y,x,xmin,xmax)
step            string(x)       system("dir")

table(y,x)      table(y,x,xmin,xmax)                    tan(x)
tanh(x)         term(a+b)       text                    then
to              trunc(x)        type(x)

undefined       until

writes(x)

zero

+               -               *               /               ^ 
**              ()              []              =               := 
==              >               >=              <               <=
<>              !               #               ,               |x|
"x"             '
-----------------------------------------------------------------------
