DMelt:JMathlab/6 Functions
Functions
The basic arithmetic operations are marked with the usual symbols (+ - * / ) . Exponention is performed with the accent character (^). Multiplication and division precede addition and subtraction; any order of evaluation can be forced by parenthesis.
>> 3.23*(14-2^5)/(15-(3^3-2^3))
ans = 14.535
>> 4.5e-23/0.0000013
ans = 3.4615E-17
>> 17.4^((3-2.13^1.2)^0.16)
ans = 13.125
>> 17.23e4/(1.12-17.23e4/(1.12-17.23e4/1.12))
ans = 76919
In addition to these arithmetic operators Jasymca provides operators for comparing numbers
< > >= <= == ~=
and for boolean functions
& | ~
. Logical true is the number 1, false is 0.
>> 1+eps>1
ans = 1
>> 1+eps/2>1 % defines eps
ans = 0
>> A=1;B=1;C=1; % semicolon suppresses output.
>> !(A&B)|(B&C) == (C~=A)
ans = 1
The most common implemented functions are the squareroot (sqrt(x)), the trigonometric functions (sin(x), cos(x), tan(x)) and inverses (atan(x), atan2(y,x)), and the hyperbolic functions (exp(x), log(x)). A large number of additional functions are available, see the list in chapter 4. Some functions are specific to integers, and also work with arbitrary large numbers: primes(Z) expands Z into primefactors, factorial(Z) calculates the factorial function. Modular division is provided by divide and treated later in the context of polynomials.
>> log(sqrt(854)) % natural logarithm
ans = 3.375
>> 0.5*log(854)
ans = 3.375
>> float(sin(pi/2)) % argument in radian
ans = 1
>> gammaln(1234) % log( gamma( x ) )
ans = 7547
>> primes(1000000000000000001)
ans = [ 101 9901 999999000001 ]
>> factorial(35)
ans = 1.0333E40
>> factorial(rat(35)) % to make it exact.
ans = 10333147966386144929666651337523200000000
Scalar
| Name(Arguments) | Function | Mod | |
|---|---|---|---|
| float($var$) | $var$ as floating point number | M,O | |
| rat($var$) | $var$ as exact number | M,O | |
| realpart($var$) | realpart of $var$ | M,O | |
| imagpart($var$) | imaginary part of $var$ | M,O | |
| abs($var$) | absolute value of $var$ | M,O | |
| sign($var$) | sign of $var$ | M,O | |
| conj($var$) | $var$ conjugate complex | M,O | |
| angle($var$) | angle of $var$ | M,O | |
| cfs($var$) [$var_T$]) | continued fraction expansion of $var$ with accuracy $var_T$ | M,O | |
| primes(VAR) | VAR decomposed into primes | M,O |
Scalar functions
| Name(Arguments) | Function | Mod | |
|---|---|---|---|
| sqrt($var$) | squareroot | M,O | |
| exp($var$) | exponential | M,O | |
| log($var$) | natural logarithm | M,O | |
| sinh($var$) | hyperbolic sine | O | |
| cosh($var$) | hyperbolic cosine | O | |
| asinh($var$) | hyperbolic areasine | O | |
| acosh($var$) | hyperbolic areacosine | O | |
| sech($var$) | hyperbolic secans | O | |
| csch($var$) | hyperbolic cosecans | O | |
| asech($var$) | hyperbolic areasecans | O | |
| acsch($var$) | hyperbolic areacosecans | O | |
| sin($var$) | sine (radian) | M,O | |
| cos($var$) | cosine (radian) | M,O | |
| tan($var$) | tangens (radian) | M,O | |
| asin($var$) | arcsine (radian) | M,O | |
| acos($var$) | arccosine (radian) | M,O | |
| atan($var$) | arctangens (radian) | M,O | |
| atan2($var_1$, $var_2$) | arctangens (radian) | M,O | |
| sec($var$) | secans (radian) | O | |
| csc($var$) | cosecans (radian) | O | |
| asec($var$) | arcsecans (radian) | O | |
| acsc($var$) | arccosecans (radian) | O | |
| factorial(N) | factorial $N!$ | M,O | |
| nchoosek(N,K) | binomial coefficient $N \choose K$ | O | |
| gamma($var$) | gammafunction | M,O | |
| gammaln($var$) | logarithm of gammafunction | M,O |
