|Re: Excerpts from my book|
Message #5 Posted by Tom Barber on 11 Sept 2006, 12:36 a.m.,
in response to message #1 by Tom Barber
I think this will be the last one.
Here are a couple of excerpts from the chapter that deals with complex numbers and ordered pairs:
"When you input an ordered pair in polar coordinates, in certain circumstances it will be converted immediately to a symbolic representation that involves trig functions. Except for when that occurs, or for when you use a Unit object to override the currently selected angle measure, the polar angle is interpreted in accordance with the angle measure in effect at the time the ordered pair is entered. Subsequent changes to the selected angle measure will change the numerical value that you see for the polar angle in the display (if polar coordinates are selected), and this reflects the fact that changing the selected angle measure does not change the ordered pair itself. If you use the C->R command to return the real and imaginary parts of the ordered pair to the stack, you always get the same pair of real numbers for the ordered pair that you entered, no matter which coordinate system and angle measure are in effect when the command is performed. The V-> command, however, returns the coordinates of the vector per the coordinate system and angle measure in effect when the command is performed. It is appropriate to think of this as an actual coordinate system conversion, and if it is done with polar coordinates selected and using an angle measure different from the angle measure used when the ordered pair was entered (in polar coordinates), angle measure conversion will be performed as well. Keep in mind, however, that the interpretation of the value that you give for the polar angle is sometimes deferred, and this introduces the possibility for the value that you give to be interpreted using the wrong angle measure later on. I’ll say more about this in a bit, of course.
When entering ordered pairs, depending on the operating mode, the coordinate system, and whether you use quotes, the coordinates may be restricted to integers or real numbers. Except for the cases where conversion to symbolic form occurs, integers are converted to real. Note also that if Approx is set, integers are converted to real regardless, and when using quotes in RPN mode, this will influence whether the conversion to symbolic form will occur.
- When entering ordered pairs in Algebraic mode, if you use polar coordinates, the coordinates are restricted, and if you use rectangular coordinates, then unless both coordinates are real numbers, the ordered pair will be converted to the equivalent complex number in symbolic form.
- When entering ordered pairs in RPN mode, the coordinates are restricted unless you use quotes, and if you use quotes, then unless both coordinates are real numbers, the ordered pair will be converted to the alternate symbolic form. The alternate symbolic form for an ordered pair entered in polar coordinates is:
‘r*cos(pa) + r*sin(pa)*i’
and in this case, unless you use a Unit object for the polar angle, interpretation of the angle value is pending.
Note that pa in the symbolic expression above represents the polar angle, and I used that here because the characters for the Greek letters aren't supported, or if they are, I don't know how to access them. In any case, in the book, the customary Greek letter is used of course.