172
Chapter 15: Expressions and The Expression Stack
TI
-
89 / TI
-
92 Plus Developer Guide
Not for Distribution
Beta Version January 26, 2001
•
XOR_TAG, which represents the exclusive-or operator xor, is replaced by an
equivalent expression using the and operator and the or operator. Thus, a xor
b is replaced by not a and b or a and not b.
•
The tags representing transformation functions, such as factor( )
(FACTOR_TAG), expand( ) (EXPAND_TAG), and so on, never appear in the
internal tokenized form.
Calculator users prefer to see results in a more standard form, for example, x
N
y
rather than x + (
L
1
†
y) and a / b rather than a * (b^(
L
1)). Therefore, the system
provides a routine called
replace_top_with_post_simplified
to transform
internal tokenized form to external tokenized form. CHS_TAG,
SUBTRACT_TAG, DIVIDE_TAG, E_TAG, SINH_TAG, COSH_TAG,
TANH_TAG, SIN_TAG, COS_TAG, TAN_TAG, and I_TAG are restored where
they make the result more readable.
System routines typically accept only one tokenized form as input and produce
only one tokenized form as output. Applications must not pass external tokenized
form to a routine that expects internal tokenized form and must not pass internal
tokenized form to a routine that expects external tokenized form. The external
only tags listed above may cause an internal only routine to throw errors or may
cause unexpected behavior. Similarly, internal only tags such as EXP_TAG,
SIN2_TAG, and IM_RE_TAG will cause an external only routine to throw errors
or behave unexpectedly. Appendix A: System Routines describes many entry
points that operate on tokenized expressions. Each of the entry point
descriptions specifies the acceptable input form and the output form that is
returned.
15.4. Most Main Ordering and Internal Representations of
Exponentiation, Multiplication, and Addition
Another important aspect of internal tokenized form is ordering. When the
elements of an expression can be reordered, the simplifier does so using most
main ordering. Some of the aspects of most main ordering are:
•
Single alphabetic variables are ordered r > s > t . . . > x > y > z > a > b . . . > p > q.
•
Single alphabetic variables are more main than other variables. Thus, x is
more main than y, but y is more main than xx.
•
Single nonalphabetic variables and multicharacter variables are ordered by
ASCII sequence. Thus, z is more main than a, but aa is more main than zz.
•
Variables are more main than symbolic constants such as
π
.
•
Symbolic constants are more main than numbers.
See the description of the system routine
compare_expressions
for more
information on most main ordering.
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