Reference Guide

Full Command and Function Reference 3-137
Flags: Numerical Results (–3), Infinite Result Exception (–22)
Input/Output:
Level 1/Argument 1 Level 1/Item 1
x
→
ln (x + 1)
'symb'
→
'LNP1(symb)'
See also: EXPM, LN
LOCAL
Type: Command
Description: Creates one or more local variables. This command is intended mainly for use in Algebraic mode;
it can not be single stepped when a program containing it is being debugged in Algebraic mode.
Access: Catalog, …µ
Input: Level 1/Argument 1: A list of one or more local variable names (names beginning with the local
variable identifier ←), each one followed by an equals sign and the value to be stored in it. Any
variable not followed by an equal sign and a value is set equal to zero.
Output: Level 1/Item 1: The input list.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example: Create local variables ←A and ←B and store the values 0 in the first and 2 in the second.
Command: LOCAL({ ← A, ← B=2})
Result: { ← A, ← B=2}
See also: DEF, STORE, UNBIND
LOG
Type: Analytic function
Description: Common Logarithm Analytic Function: Returns the common logarithm (base 10) of the
argument.
For x=0 or (0, 0), an Infinite Result exception occurs, or, if flag –22 is set (no error), LOG
returns –MAXR.
The inverse of ALOG is a relation, not a function, since ALOG sends more than one argument to
the same result. The inverse relation for ALOG is the general solution:
LOG(Z)+2*π*i*n1/2.30258509299
The function LOG is the inverse of a part of ALOG, a part defined by restricting the domain of
ALOG such that 1) each argument is sent to a distinct result, and 2) each possible result is
achieved. The points in this restricted domain of ALOG are called the principal values of the
inverse relation. LOG in its entirety is called the principal branch of the inverse relation, and the
points sent by LOG to the boundary of the restricted domain of ALOG form the branch cuts of
LOG.
The principal branch used by the calculator for LOG(z) was chosen because it is analytic in the
regions where the arguments of the real-valued function are defined. The branch cut for the
complex-valued LOG function occurs where the corresponding real-valued function is undefined.
The principal branch also preserves most of the important symmetries.
You can determine the graph for LOG(z) from the graph for LN (see LN) and the relationship
log z = ln z / ln 10.
Access: …Ã ( Ã is the right-shift of the Vkey).
Flags: Principal Solution (–1), Numerical Results (–3), Infinite Result Exception (–22)