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SYMBMATH.HL4
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20.3 Keywords Dictionary
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abs(x)
The absolute value function of x. e.g. abs(-1) gives 1.
acos(x)
The arc cosine function of x, the inverse function of cos(x).
The result is in radians.
acosh(x)
The arc hyerbolic cosine function of x, the inverse function of
cosh(x).
acot(x)
The arc cot function of x, the inverse function of cot(x).
The result is in radians.
acoth(x)
The arc coth function of x, the inverse function of coth(x).
acsc(x)
The arc csc function of x, the inverse function of csc(x).
The result is in radians.
acsch(x)
The arc csch function of x, the inverse function of csch(x).
asec(x)
The arc sec function of x, the inverse function of sec(x).
The result is in radians.
asech(x)
The arc sech function of x, the inverse function of sech(x).
asin(x)
The arc sine function of x, the inverse function of sin(x).
The result is in radians.
asinh(x)
The arc sinh function of x, the inverse function of sinh(x).
assume()
Assume a variable x to be positive, negative or real. All variables
are assumed as complex by default.
e.g. assume(x>0), assume(x<0), or assume(x == real).
assumed
It points out that the variable has been assumed.
atan(x)
The arc tan function of x, the inverse function of tan(x).
The result is in radians.
atanh(x)
The arc tanh function of x, the inverse function of tanh(x).
BASIC
Output in BASIC format. e.g. Output=BASIC.
clear()
Clear a variable, function or expression from memory. e.g. clear(p),
clear(f(x)).
clear_all
Clear all from memory.
cleared
It says that the variable, function or expression has been cleared
from memory.
coef(poly, x^n)
The coefficient function of x^n. It gives the coefficient of x^n in
the polynomial. e.g. coef(2*x^6+x+4, x^6) gives 2.
constant
The indefinite integral constant.
cos(x)
The cosine function of x. The angle x is measured in radians.
cosh(x)
The hyerbolic cosine function of x.
cot(x)
The cotan function of x. The angle x is measured in radians.
coth(x)
The hyerbolic cosine function of x, i.e. (exp(x)+exp(-x))/2.
csc(x)
The angle x is measured in radians.
csch(x)
d()
The derivative function.
d(f(x), x=c) gives the derivative of f(x) with respect to an
undefined variable x at x=c.
d(f(x), x=c, n) gives the n-th order derivative of f(x) with respect
to an undefined variable x at x=c.
d(f(x)/d(x)) differentiate y with respect to x.
e.g. d(x^2/d(x)) gives 2*x.
d(f(x)/d(x), n) gives the n-th order derivative of f(x) with respect
to an undefined variable x.
d(y) implicit differentiation, used in differential
equations, e.g. x*d(x)+y*d(y) == 0.
define()
Define an user function. e.g. define(f(x)=x^2).
defined
It indicates that the user function has been defined.
deno()
It gives the denominator of expr. e.g. deno(a/b) gives b.
discont
The discontinuity. If the function value is discont, the function has
a discontinuity and only has the one-sided limit at x=c. Users should
evaluate its left-sided limit or right-sided limit by x=c-zero or
x=c+zero.
done
It indicates that the action has been done.
system(system command)
execute operating system (DOS) command. e.g. system(dir).
E
The exponential part of a floating point number. e.g. 1.1E2.
e
(1) 2.718..., the built-in constant, e is converted to 2.718... when the
switch Numerical=On.
(2) The exponential part of a floating point number, the same as E.
e.g. 1.1e2.
erf(x)
The error function of x, or the probability integral function.
exp(x)
The exponential function of x based of e. The same as e^x, e=2.718...
It is the inverse to ln(x).
ExpExpand
The switch of exponential expansion.
ExpExpand=On e.g. c^(a+b) to c^a*c^b.
ExpExpand=Off disable exponential expansion, this is default.
expand(expr)
The expansion function. The expand(expr) is to expand expr, e.g.
expand((a+b)^2) gives a^2 + 2*a*b + b^2.
fac(n)
The factorial of n. The same as n!. e.g. fac(3) gives 6.
factor(expr)
The factorisation function. The factor(expr) is to factorise from
expr, e.g. factor(a^2 + 2*a*b + b^2) gives (a+b)^2.
FORTRAN
Output in FORTRAN format. e.g. Output=FORTRAN.
from
The separator, the same as the comma (,).
i
The imaginative sign of the complex number. e.g. 1+2*i.
im(x)
The imaginative part of complex numbers. e.g. im(1+2*i) gives 2.
inf
The positive infinity, as the built-in constant.
inte()
The integral function.
inte(f(x),x,a,b) find the definite integral of f(x) with respect to
an undefined variable x taken from x=a to x=b.
inte(f(x), x from a to b) the same as inte(f(x),x,a,b).
inte(f(x)*d(x)) find the indefinite integral of f(x) with respect
to an undefined variable x.
inte(y) implicit integration, used to integrate the
differential equations.
last
The last output, as the built-in variable.
last[1] the first element of the last output list.
left(equation)
It gives the left hand side of an equation. e.g. left(x+y==2)
gives x+y.
lim()
The limit function.
lim(x=c, expr) gives the limit of expr when x approaches c.
lim(x=c to expr) the same as lim(x=c, expr).
e.g. lim(x=0, sin(x)/x) gives 1.
Note that the correct answers only for the indeterminate forms:
0/0, inf/inf, 0*inf, 0^0, inf^0.
list()
The list function.
list(f(x), x from a to b step c) lists of f(x),
e.g. list(x^2, x from 1 to 3 step 1)
gives [1,4,9].
list(a+b) transform sum to list, e.g. list(a+b) gives [a,b].
ln(x)
The natural logarithmic function of x. Its base is e. It is the
inverse to exp(x). Warming that if it has multi-values, the ln(x)
only gives a principle value (P.V.) and other values are
P.V.+2*k*pi*i (where k=0, 1, 2,..., -1, -2, ...).
LnExpand
The switch of the logarithmic expansion.
LnExpand=On log expansion, e.g. ln(a*b) is expanded into
ln(a)+ln(b).
LnExpand=Off disable log expansion, this is default.
n!
The factorial of n. The same as fac(n). e.g. 3! gives 6.
nume()
It gives the numerator of expr. e.g. nume(a/b) gives a.
Numerical
The switch of numerical calculation.
Numerical=On numerical computation.
Numerical=Off disable numerical computation, this is default.
NumIntegrate
The switch of numeric integration.
NumIntegrate=On numeric integration.
NumIntegrate=Off disable numeric integration, this is default.
Off
When the switch is set to Off, it is inactive. e.g. Numerical=Off,
Output=Off, NumIntegrate=Off, Expand=Off.
On
When the switch is set to On, it is active. e.g. Numerical=On,
NumIntegrate=On, Expand=On, ExpExpand=On, LnExpand=On.
Output
The switch of the output format, e.g. Output=BASIC, Output=FORTRAN,
Output=PASCAL, Output=TwoDim, or Output=Off.
to
The separator, the same as the comma (,).
pi
3.1416..., as the built-in constant, pi is converted to 3.1416... when
the switch Numerical=On.
prod()
The product function.
prod(f(x), x from a to b step c) product of f(x).
prod(f(x), x from a to b) product of f(x) as step=1.
re(x)
The real part of complex numbers. e.g. re(1+2*i) gives 1.
real
Assume a variable x to be real. e.g. assume(x == real).
right(equation)
It gives the right hand side of an equation. e.g. right(x+y==3)
gives 3.
sec(x)
The angle x is measured in radians.
sech(x)
show_all
Show all in memory.
sgn(x)
The sign function of x. It is 1 when Re(x) > 0, or Re(x) = 0 and
Im(x) > 0; 0 when x=0; -1 otherwise.
sin(x)
The sine function of x. The angle x is measured in radians.
sinh(x)
The hyerbolic sine function of x, i.e. (exp(x)-exp(-x))/2.
solve(equation, unknown)
Solve a polynomial, systems of linear equations, linear differential
equations. e.g. solve(x^2+5*x+6==0, x), solve([x+y==3,x-y==1], [x,y]),
solve(d(y)/d(x)+x*y==2, y).
sqrt(x)
The square root function of x. It is the same as x^0.5.
subs(x=c to expr)
Substitutes x by c in expr. subs(x=c, expr) is the same
as subs(x=c to expr). e.g. subs(x=a to x^2) gives a^2.
sum()
The sum function.
sum(f(x), x from a to b step c) sum of f(x), e.g.
sum(2^n, n from 1 to 10 step 1.2).
sum(f(x), x from a to b) sum of f(x) as step=1, e.g.
sum(2^n, n from 1 to 10).
sum([a,b]) transform list to sum, e.g. sum([a,b]) gives a+b.
step
The separator, the same as the comma (,).
table()
Produce a table of the function values.
table(f(x), x from a to b step c) data table.
e.g. table(x^2, x from 1 to 20 step 2).
tan(x)
The angle x is measured in radians.
tanh(x)
TwoDim
Output in two dimension format. e.g. Output=TwoDim.
undefined
The built-in constant. It indicates that the value of the expression
is undefined. e.g. the indeterminate forms: 0/0, inf/inf, 0*inf, 0^0.
Users should try again by lim(x=c, f(x)).
zero
The right-hand sided value at x=0, as the built-in constant. -zero
is the left-sided limit from the negative direction. e.g. 1+zero is
to approach to 1 from the positive (+infinity) direction (the right-
hand sided value), and 1-zero is to approach to 1 from the negative
(-infinity) direction (the left-hand sided value), i.e. limit as
zero -> 0. e.g. exp(1/(0+zero)) gives inf, exp(1/(0-zero)) gives 0.
+ add or positive sign.
- subtract or negative sign.
* multiply.
/ divide.
^ power in BASIC, the same as ** in FORTRAN, e.g. 2^3 gives 8.
** power in FORTRAN, the same as ^ in BASIC.
! factorial, the same as fac(x), e.g. 3! or fac(3) gives 6.
< less than.
<= less than.
> greater than.
>= greater than.
<> unequals.
== equals, or equation sign.
= assignment.
, separator.
# comment statement.
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