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SYMBMATH.H17
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13. Keywords
SymbMath has three versions: Shareware Version A, Student
Version B and Advanced Version C. The shareware version lacks the
solve(), dsolve(), trig (except sin(x)), and hyerbolic functions on
input, and the student version lacks the hyerbolic and dsolve()
functions on input. You cannot input these lacked functions, but all
versions can output all functions.
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
is set to on.
The following special symbols (about 130 words) only include
the keywords in the SymbMath system and the initialization package
init.sm.
13.1 Keywords in Functional Order
---------------------------------------------------------------------
1. Built-in constants: i, e, pi, inf, zero, constant, discont,
undefined, complex_inf.
2. Built-in variables: last.
3. Negative and positive: -, +.
4. Algebraic operators: +, -, *, /, ^, **, ().
5. Relational operators: ==, >, >=, <, <=, <>.
6. Logic operators: and, or.
6. Algebraic functions: -x, sqrt(x), n!, fac(n), mod(x,y), div(x,y).
7. Complex functions: re(x), im(x), abs(x), arg(x), sgn(x).
8. Exponential functions: exp(x), ln(x), ei(n,x), gamma(n,x).
9. 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).
10. 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).
11. Assignments: =, :=.
12. Equation: ===.
13. User-defined functions: f(x_):=x^2, f(x_):=if(isnumber(x),x^2).
14. User-defined rules: d(si(x_),x_):=sin(x)/x.
15. Calculus functions:
d(y,x), d(y,x,order), d(y, x=x0), d(y, x=x0, order),
inte(f,x), inte(f,x,xmin,xmax),
dsolve(d(y)/d(x)===f(x,y), y),
subs(y, x=x0), lim(y, x=x0),
sum(f, x,xmin,xmax,dx), prod(f, x,xmin,xmax,dx),
16. Transformation functions: expand(expr), factor(expr), sum([a,b]),
solve(x^2===a,x), coef(expr,x), left(x===a), right(x===a),
float(x), ratio(x), round(x), trunc(x),
list(a+b), table(p[x], x,xmin,xmax,dx).
17. Numeric computation: num(expr).
18. Test function: isodd(x), iseven(x), isinteger(x), isreal(x),
isnumber(x), isfree(y,x).
19. Table: table(f, x,xmin,xmax,dx).
20. List: [a,b], list(f, x,xmin,xmax,dx).
21. Element of list: f[1], last[1].
22. Switches: numerical, output, expand, expexpand, lnexpand, lowercase,
=, on, off, basic, fortran, prolog, twodim.
23. Commands: system(dos), clear(x), block(), null.
24. Separators: "," , from, to, step.
25. Assume: assume(a>0), isreal(x)=1.
26. Rule: if(test, then), if(test, then, else).
27. Loop: do(expr, x,xmin,xmax,dx), repeat(expr, test).
28. Input: include('filename').
29. Output: openfile('filename'), closefile('filename').
30. Plot: plot(x^2,x).
31. Comment: #.
32. Action: done, cleared, assumed.
--------------------------------------------------------------------
13.2 Keywords in Alphabetical Order
----------------------------------------------------------------------
abs(x) acos(x) acosh(x) acot(x) acoth(x)
acsc(x) acsch(x) arg(x) asec(x) asech(x)
asin(x) asinh(x) assume(x>0) assumed atan(x)
atan2(x,y) atanh(x)
basic block()
clear(x) cleared closefile() coef(f,x) complex_inf
constant cos(x) cosh(x) cot(x) coth(x)
csc(x) csch(x)
d() div(x,y) discont do() done
dsolve(eq,y)
E e ei(n,x) end exp(x)
expand(f) expand expexpand
fac(x) factor(expr) float(x) fortran from
gamma(n,x)
i if() im(x) include() inf
inte() iseven(x) isfree(y,x) isinteger(x) isodd(x)
isreal(x) isnumber(x)
last left(x===a) lim() list()
ln(x) lnexpand lowercase
mod(x,y)
null num(expr) numerical
off on openfile() output
pi plot() prod() prolog
ratio(x) re(x) repeat() right(x===a) round(x)
sec(x) sech(x) sgn(x) sin(x) sinh(x)
solve(eq,x) sqrt(x) subs(f,x=x0) sum() step
system(dos)
table() tan(x) tanh(x) to trunc(x)
twodim
undefined
zero
+ - * / ^
** () [] = :=
== === > >= <
<= <> ! # ,
-----------------------------------------------------------------------