CS99 Lecture5: Expressions and Statements
- week of 9/11

Advice about Studying & Labs

Lecture from lecture4 continued:

Worksheet Management
- need to know rules to handle assignments
- restart: clear all assignments
- kernel modes
  - shared (default) -- all worksheet know all values
  - parallel -- each worksheet runs independently 
- anames() -- show list of assigned names

Evaluating Expressions
- must understand how Maple's "brain" works
- automatic simplification and full evaluation

Automatic Simplification
- reduce "clearly" identical expressions
- > x-x; x+x; x/x;
- sometimes hard to predict

Full evaluation
- how Maple calculates (evaluates) results of an expression
- process:
  - convert expression into tree
  - replace all assigned names with expressions, which are also
    converted to trees
  - perform automatic simplification
  - perform mathematical operations and functions for subexpressions 
    until reaching the final answer
- works from bottom to top

Assignments Revisted
- how does Maple treat assignments during full evaluation?
  > expr;         fully evaluate expr
  > name:=expr    fully evaluate expr and store result in name
- what if expr contains a name n?
  if n is assigned, the assigned expression replaces n
  if n unassigned, n remains symbolic
  But Maple does not change any assignment INSIDE expr!
  example)
  > restart: x:=y+z: y:=1: x;
    output: 1+z
    explanation)
    clear assignments
    x gets y + z
    y gets 1   (the expression for x is still y+z: the assignment y:=1 only 
               changed y)
    evaluate x (Maple replaces y with 1 inside the expression for x 
               DURING full evaluation. So, x fully evaluates to 1+z,
               but x is NOT assigned to 1+z)
- Example 1: see figure 3-6
- Example 2: see figure 3-7

Unevaluation
- single quotes '' delay evaluation
- 'expr' tells Maple to first strip 'expr' of the quotes
- reason why unassignment works
  > a := 'a': 
  Maple strips left side of quotes, then Maple sees a:=a internally.
  So, the name a gets assigned to name a.

Chapter 4
- Types
  definition: classification of expression
  checking: use type function
  expression tree: surface, structured, nested
  finding types: whattype
- Real Numbers
  integers = whole numbers
  fractions = ratio of two integers
  rationals numbers = integers + fractions
  floats, decimals
  arithmetic: 
  + rational until forced into a float
  + evalf
  rounding:
  + Digits
  + Rounding
    evalf(0.05+0.4,1) -> 0.4
    evalf(0.05+0.5,1) -> 0.6
  irrational numbers
  + sqrt(2)
  + Pi
- Complex Numbers
  sqrt(-1) -> i
- Extended Numerics
  infinity: n + inf
  undefined: 0/0
- Boolean Expressions
  Logic:
  + operators: and, or, not
  + values: true, false
  ex) T and F -> F, T or F -> T
  Relations:
  + for comparisons
  + <,>,<>,=
  + expr rel expr
  ex) solve(x^2+4=0,x)
  Boolean
  + logical or relational expr
  + evalb(expr) -> evaluate truth of expr
- Multiple expressions
  + ranges
  ex) 1..2
  + sequences 
  ex) 1,2,3
  + lists
  ex) [1,2,3]
  + sets
  ex) {1,2,3}
  + selection
  ex) L:=[a,b,c]; L[1]; L[2..3];
- Names
  Indexing: resembles selection, no assignment in name
  Symbolic Constants: constants yields false, true, infinity,...
  Protected Names: predefined names
  Greek Letters: not really a type, but something built-in
- Miscellaneous
  Strings
  Functions