expand, but with "frontend"

Carl Love — Sun, 27 Jan 2013 22:33:50 Z

You need to expand (i.e., distribute sin(z) over the rest) the first expression; otherwise, it won't contain the subexpression that you told applyrule to look for. But simply using the command expand will do too much: It will also apply a trig identity expand cos(2*z). So do this

frontend(expand, [exprsn1]);

Then use applyrule on the result of this.

expand with option

Alejandro Jakubi — Mon, 28 Jan 2013 11:56:50 Z

To prevent a single function from the effect of expand, here cos(2*z), it is simpler to use the function name as an option for expand:

exprsn1:=sin(z)*(A*cos(z) + B*cos(x)*cos(2*z) + C*cos(x)):
exprsn2:= applyrule(sin(z)*cos(2*z)=1/2*(sin(3*z)-sin(z)), expand(exprsn1,cos));
exprsn2:=
    sin(z) A cos(z) + (1/2 sin(3 z) - 1/2 sin(z)) B cos(x) + sin(z) C cos(x)

On the other hand, the frontend trick is more handy to prevent expansion of all the subexpressions, see ?expand.

Certainly, it would have been better that expand worked the other way round: just apply the distributive property unless told to expand something else, and an option all to apply all the expansion rules. Also, a mathematical pattern matcher is needed that does not require from the user to accomodate the expressions and rules to such syntactic peculiarities.

MaplePrimes - answers and comments on Question, trouble with "applyrule"

expand, but with "frontend"

expand with option