The Definition of Arithmetic Expressions

The definition of a name for an arithmetic expression is performed by the command: 3 VAR(six-letter_name) = $\ldots$ arithmetic expression $\ldots$ ; [example: XVAL=[X,X]$\ast$0.1 + [A,A]$\ast$0.01 ;] [example: A=2 $\ast$0.5 -SIN(B) ;]

The $\ldots$ arithmetic expression $\ldots$ may contain the following items:

• constants [numbers like 4, 0.5 or 1.E-6]
• elements of the transfer matrix at z_i, for instance, [X,A], [Y,B], [X,AA], [X,AAD], $\ldots$
• operators [ like (+), ($^\wedge$), (#EQ#), (#MAX#), $\ldots$ ]
• functions [ like SIN,COS,LOG,EXP,TAN, $\ldots$ ]
• names of earlier defined variables
• system parameters like PI$, XM$ or TXA$

Variables, constants, operators and functions are used like in an ordinary programming language like FORTRAN. System parameters are like variables, but with an $ at the end. Unlike variables, their values cannot be changed by the user directly. System parameters are calculated by GICO during runtime. They have a threefold purpose:

1.

to spare the user the work to enter basic constants like $\pi$ or the speed of light directly

2.

to supply the user with values defined by commands like P X or R P

3.

to supply the user with certain numbers other than the matrix elements of the transfer matrix, which are calculated internally by GICO and are tedious or impossible to get by the use of arithmetic expressions alone

For a complete list of the available operators, functions and system parameters, see at the end of this manual.