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Basic calculations

Symja can be used to calculate basic stuff:

>> 1 + 2
3

To submit a command to Symja, press Shift+Return in the Web interface or Return in the console interface. The result will be printed in a new line below your query.

Symja understands all basic arithmetic operators and applies the usual operator precedence. Use parentheses when needed:

>> 1 - 2 * (3 + 5) / 4
-3

The multiplication can be omitted:

>> 1 - 2 (3 + 5) / 4
-3

But function f(x) notation isn’t interpreted as f*(x)

>> f(x)

Powers expressions like 34 can be entered using ^:

>> 3 ^ 4
81

Integer divisions yield rational numbers like 46​ :

>> 6 / 4
3/2

To convert the result to a floating point number, apply the function N:

>> N(6 / 4)
1.5

For integer number bases other than 10 the ^^ operator can be used. Here’s an example for a hexadecimal number:

>> 16^^abcdefff
2882400255

The number can be converted back to hexadecimal form with the BaseForm function:

>> BaseForm(2882400255, 16)
Subscript[abcdefff,16]

Symbols with upper and lower case characters

Functions are applied using an identifier and parentheses ( and ). In general an identifier is a user-defined or built-in name for a variable, function or constant.

Only the identifiers which consists of only one character are case sensitive. For all other identifiers the input parser doesn’t distinguish between lower and upper case characters.

For example: the upper-case identifiers D, E, I, N, are different from the identifiers d, e, i, n, whereas the functions like Factorial, Integrate can be entered as factorial(100) or integrate(sin(x),x). If you type SIN(x) or sin(x), Symja assumes you always mean the same built-in Sin function.

Symja provides many common mathematical functions and constants.

For example Log calculates the natural logarithm for base E. Log2 and Log10 are variants for logarithm to the bases 2 and 10.

>> Log(E)
1


>> Sin(Pi)
0


>> Cos(0.5)
0.877583

When entering floating point numbers in your query, Symja will perform a numerical evaluation and present a numerical result, pretty much like if you had applied N.

Complex numbers

Of course, Symja has complex numbers and uses the equation:


√−1​=I

In Symja the imaginary unit is represented by the uppercase letter I:

>> Sqrt(-4)
2*I


>> I ^ 2
-1


>> (3 + 2*I) ^ 4
-119+I*120


>> (3 + 2*I) ^ (2.5 - I)
43.663+I*8.28556


>> Tan(I + 0.5)
0.195577+I*0.842966

Abs calculates absolute values for complex numbers:

>> Abs(-3)
3


>> Abs(3 + 4*I)
5

Symja can operate with pretty huge numbers:

>> 100!
9332621544394415268169923885626670049071596826438162146859296389521759999322991\
5608941463976156518286253697920827223758251185210916864000000000000000000000000

(! denotes the factorial function.) The precision of numerical evaluation can be set:

>> N(Pi, 100)
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067

Division by zero is forbidden and prints the message Power: Infinite expression 1/0 encountered.

>> 1 / 0
ComplexInfinity

Other expressions involving Infinity are evaluated:

>> Infinity + 2*Infinity
Infinity

In contrast to combinatorial belief, {0}^{0} is undefined and prints the message Power: Indeterminate expression 0^0 encountered.:

>> 0 ^ 0
Indeterminate

The result of the previous query to Symja can be accessed by %:

>> 3 + 4
7


>> % ^ 2
49

In the console available functions can be determined with the ? operator

>> ?ArcC*
ArcCos, ArcCosh, ArcCot, ArcCoth, ArcCsc, ArcCsch

Documentation can be displayed by asking for information for the function name.

>> ?Integrate

Tutorial

The following sections are introductions to the basic principles of the Symja language. A few examples and functions are presented. Only their most common usages are listed; for a full description of their possible arguments, options, etc., see their entry in the “function reference” of built-in symbols.

Reference