PRIORITY RULES FOR READING EQUATIONS
----agreed to by humans and computer programming languages!----------

high priority
^
|     f(...)    (...)    parentheses and function-invocations (parentheses implied)
|                              trump everything else.  Do stuff inside them 
|                                BEFORE stuff outside them. 
|                           Helpful note: use both ( and [ parens to make
|                              it easier to match them up:  ([()]) 
|       3    n
|      x    x                  exponentiation
|
|     x y     x / y        multiplication & division
|
|    x+y   x-y              add & subtract
V
low priority


So.  If you see

   sin(q) + x + y / z - d + h / (p+f)

That MEANS:
1. perform the sin (highest priority, named function):
   sin(q) + x + y / z - d + h / (p+f)
and the parentheses, FIRST.
2. perform the / :
   sin(q) + x + (y / z) - d + (h/(p+f))
3. finally perform the + and -'s. Result is
                  y         h
    sin(q) + x + --- - d + ---
                  z        p+f

WRONG would be:
   sin(q+x) + y/z - d + h/(p+f)    <-- wrongly doing + before sin!

   sin(q) + x + y/(z-d) + h/(p+f)    <-- wrongly doing - before /!


BAD HABITS: Try to avoid writing forms in which there is ambiguous
or confusing priority. Nobody is quite sure what you meant in those
bad cases. Perhaps including you.
------------------------------------------------------------------------------------
    GOOD:                         BAD SINCE UNCLEAR WHICH
                                  GOOD FORM WAS MEANT:
                    ln2    2
  ln(2)/3, ln(2/3), ---, ln-              ln2/3  <-- I admit our rules would interpret
                     3     3                          this unambiguously as ln(2)/3
                                                  but... if 2/3 is a
                                  single character (is on some typewriters & fonts)
                                   then this would be confusing. Why risk it?
 a   a c                                             
---, ---,  a/(bc),  ac/b                   a/bc 
b c   b

    a + b        b                        a + b
    -----,  a + ---                          --
      c          c                           c

        2          2                         2
   sin(x ),  sin(x)                       sin (x)   <-- I admit some books use these,
     [these not the same thing]                         but I think they are a bad idea!
                                             -1         Why ask for pain?
   arcsin(x), 1/sin(x)                    sin  (x)   <--Ask for clarity instead!

    L                         L                   L
  -----                     -----               -----
   \                         \                  \
    )  [sin(k) + 76],  76 +   )   sin(k)         )   sin(k) + 76
   /                         /                  /
  -----                     -----               -----
  k = F                     k = F               k = F


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