calc: Simplifying Formulas
11.3 Simplifying Formulas
=========================
The sections below describe all the various kinds of simplifications
Calc provides in full detail. None of Calc’s simplification commands
are designed to pull rabbits out of hats; they simply apply certain
specific rules to put formulas into less redundant or more pleasing
forms. Serious algebra in Calc must be done manually, usually with a
combination of selections and rewrite rules. 
Rearranging with
Selections. Rewrite Rules.
Simplification Modes, for commands to control what level of
simplification occurs automatically. Normally the algebraic
simplifications described below occur. If you have turned on a
simplification mode which does not do these algebraic simplifications,
you can still apply them to a formula with the ‘a s’ (‘calc-simplify’)
[‘simplify’] command.
There are some simplifications that, while sometimes useful, are
never done automatically. For example, the ‘I’ prefix can be given to
‘a s’; the ‘I a s’ command will change any trigonometric function to the
appropriate combination of ‘sin’s and ‘cos’s before simplifying. This
can be useful in simplifying even mildly complicated trigonometric
expressions. For example, while the algebraic simplifications can
reduce ‘sin(x) csc(x)’ to ‘1’, they will not simplify ‘sin(x)^2 csc(x)’.
The command ‘I a s’ can be used to simplify this latter expression; it
will transform ‘sin(x)^2 csc(x)’ into ‘sin(x)’. However, ‘I a s’ will
also perform some “simplifications” which may not be desired; for
example, it will transform ‘tan(x)^2’ into ‘sin(x)^2 / cos(x)^2’. The
Hyperbolic prefix ‘H’ can be used similarly; the ‘H a s’ will replace
any hyperbolic functions in the formula with the appropriate
combinations of ‘sinh’s and ‘cosh’s before simplifying.
Menu
Info Catalog
calc: Algebraic Manipulation
calc: Algebra
calc: Polynomials