Builtin types The calculator has the following built-in types. null value This is the undefined value type. The function 'null' returns this value. Functions which do not explicitly return a value return this type. If a function is called with fewer parameters than it is defined for, then the missing parameters have the null type. Defining a new variable initializes it to the null type. The null value is false if used in an IF test. rational numbers This is the basic data type of the calculator. These are fractions whose numerators and denominators can be arbitrarily large. The fractions are always in lowest terms. Integers have a denominator of 1. The numerator of the number contains the sign, so that the denominator is always positive. When a number is entered in floating point or exponential notation, it is immediately converted to the appropriate fractional value. Printing a value as a floating point or exponential value involves a conversion from the fractional representation. Numbers are stored in binary format, so that in general, bit tests and shifts are quicker than multiplies and divides. Similarly, entering or displaying of numbers in binary, octal, or hex formats is quicker than in decimal. The sign of a number does not affect the bit representation of a number. complex numbers Complex numbers are composed of real and imaginary parts, which are both fractions as defined above. An integer which is followed by an 'i' character is a pure imaginary number. Complex numbers such as "2+3i" when typed in, are processed as the sum of a real and pure imaginary number, resulting in the desired complex number. Therefore, parenthesis are sometimes necessary to avoid confusion, as in the two values: 1+2i ^2 (which is -3) (1+2i) ^2 (which is -3+4i) Similar care is required when entering fractional complex numbers. Note the differences below: 3/4i (which is -(3/4)i) 3i/4 (which is (3/4)i) The imaginary unit itself is input using "1i". strings Strings are a sequence of zero or more characters. They are input using either of the single or double quote characters. The quote mark which starts the string also ends it. Various special characters can also be inserted using back-slash. Example strings: "hello\n" "that's all" 'lots of """"' 'a' "" There is no distinction between single character and multi-character strings. The 'str' and 'ord' functions will convert between a single character string and its numeric value. The 'str' and 'eval' functions will convert between longer strings and the corresponding numeric value (if legal). The 'strcat', 'strlen', and 'substr' functions are also useful. matrices These are one to four dimensional matrices, whose minimum and maximum bounds can be specified at runtime. Unlike C, the minimum bounds of a matrix do not have to start at 0. The elements of a matrix can be of any type. There are several built-in functions for matrices. Matrices are created using the 'mat' statement. lists These are a sequence of values, which are linked together so that elements can be easily be inserted or removed anywhere in the list. The values can be of any type. Lists are created using the 'list' function. files These are text files opened using stdio. Files may be opened for sequential reading, writing, or appending. Opening a file using the 'fopen' function returns a value which can then be used to perform I/O to that file. File values can be copied by normal assignments between variables, or by using the result of the 'files' function. Such copies are indistinguishable from each other.