•Many CAS commands will give numeric results instead of symbolic results if numeric mode is set instead of being cleared. Though these results may be correct, they will not be what the user wants if a symbolic result is needed. For this reason, the Flags section of most operation descriptions says that numeric mode should not be set.

•If approximate mode is set instead of exact mode, CAS commands will often give reasonable results, but unexpected results can be obtained, because, for example, powers are real numbers, not integers, for instance a cube will be treated as x3.0 instead of x3. For this reason, the Flags section of most operation descriptions says that exact mode should be set. Some commands, like the numeric solvers, will only find approximate solutions if approximate mode is set.

•CAS operations are designed to work with integers if possible, and some CAS operations round their inputs before using them. FIX 0 mode will round to whole numbers, losing accuracy. STD mode will retain full accuracy, so it is the best display mode to use with the CAS and is used in most of the examples in this chapter.

•For the same reasons, the general solutions, symbolic constants and symbolic arguments flags (flags –1, –2 and –3) should normally be clear when working with the CAS.

•Where possible, integer numbers should be used as input, not real numbers. The functions RND, CEIL and FLOOR can round a real number to a whole real number, and RI will convert a whole real number to an integer.

•If complex inputs are given, approximate mode may need to be set to find solutions, and complex mode must be set (flag –103 set).

•Not only the trigonometry rewriting operations, but some other CAS operations require the angle mode to be set to radians (flag –17 clear), even if it is not immediately obvious that this is so. For this reason, the Flags section of many operation descriptions says that radians mode should be set.

•Some CAS operations will work one step at a time if step-by-step mode is set (flag –100 set). If a result is wanted immediately, and the calculator instead displays one step of the operation, cancel the operation, clear flag –100, then repeat the operation.

•If a mode needs to be changed for an operation to work, the calculator will by default ask if the mode can be changed. If the Silent mode switch flag (flag –120) is set, the calculator changes the mode without asking. If the mode switch disallowed flag (flag –123) is set, the mode will not be changed and an error will occur.

•All the system flags from –99 to –128 are intended for use by the CAS. It is worth reading Appendix C in the User’s Guide to learn the detailed effects of these flags on CAS operations and displays.

•Remember that in RPN mode, symbolic expressions typed on the command line should be enclosed in single quote marks ′x + y′. For clarity, it can be helpful to type expressions in single quote marks in Algebraic mode too.

•It is important to write symbolic expressions using the current variable. Some CAS operations will work with this variable, but treat other variables simply as unknown numbers. If an expression has been entered using a variable other than the current variable, it may be simpler to change the current variable in the CAS MODES form, rather than rewrite the whole expression.

•In algebraic mode (flag –95 set), some CAS commands will replace variables with their numeric values before returning a result, even if “argument to symbolic” mode is set (flag –3 clear). In RPN mode, they will be returned as variables. Some other CAS commands will always replace variables with their numeric results.

•Because of the above, variables used in symbolic operations should not have the same names as variables stored in the current directory/folder (or in directories above this directory). If, for example, x is the current variable, and a variable called ′x′ exists in the current directory or in the HOME directory, then the value stored in ′x′ might be used instead of the symbolic variable x.

•The modulo value used in modulus calculations is 13 after the calculator is reset. If the CAS modes are reset

with CASCFG, the modulo is also 13, but if the modes are reset using !RESET as above, the modulo is 3, otherwise it is the value most recently set. It is important to change this to the required value before carrying out any modulus operations.

4-2 Computer Algebra System