# DMelt:JMathlab/6 Functions

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## 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