The a s
(calc-simplify) [simplify] command
applies various algebraic rules to simplify a formula. This
includes rules which are not part of the default simplifications
because they may be too slow to apply all the time, or may not be
desirable all of the time. For example, non-adjacent terms of
sums are combined, as in ‘a + b +
2 a’ to ‘b + 3
a’, and some formulas like
‘sin(arcsin(x))’ are simplified to
‘x’.
The sections below describe all the various kinds of algebraic 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. See Rearranging with Selections. See Rewrite Rules.
See Simplification Modes, for commands to control what level of simplification occurs automatically. Normally only the “default simplifications” occur.
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 a s can reduce ‘sin(x) csc(x)’ to ‘1’, it 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.