Reference Guide

3-286 Full Command and Function Reference
Input/Output:
Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1
w z
→
w
z
z 'symb'
→
'z^(symb)'
'symb' z
→
'(symb)^z'
'symb
1
' 'symb
2
'
→
'symb
1
^('symb
2
)'
x_unit y
→
x
y
_unit
y
x_unit 'symb'
→
'(x_unit)^(symb)'
See also: EXP, ISOL, LN, XROOT
| (Where)
Type: Function
Description: Where Function: Substitutes values for names in an expression.
| is used primarily in algebraic objects, where its syntax is:
'symb
old
| (name
1
= symb
1
, name
2
= symb
2
…)'
It enables algebraics to include variable-like substitution information about names. Symbolic
functions that delay name evaluation (such as ∫ and ∂) can then extract substitution information
from local variables and include that information in the expression, avoiding the problem that
would occur if the local variables no longer existed when the local names were finally evaluated.
Access: @¦ (¦is the right-shift of the Ikey).
Flags: Numerical Results (–3)
Input/Output:
Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1
'symb
old
' { name
1
, 'symb
1
', name
2
, 'symb
2
' … }
→
'symb
new
'
x { name
1
, 'symb
1
', name
2
, 'symb
2
' … }
→
x
(x,y) { name
1
, 'symb
1
', name
2
, 'symb
2
' … }
→
(x,y)
See also: APPLY, QUOTE
√ (Square Root)
Type: Function
Description: Square Root Analytic Function: Returns the (positive) square root of the argument.
For a complex number (x
1
, y
1
), the square root is this complex number:
x
2
y
2
,( ) r
θ
2
---
r,cos
θ
2
---sin
 
 
=
where r = ABS (x
1
, y
1
), and θ = ARG (x
1
, y
1
).
If (x
1
, y
1
) = (0,0), then the square root is (0, 0).
The inverse of SQ is a relation, not a function, since SQ sends more than one argument to the
same result. The inverse relation for SQ is expressed by ISOL as this general solution:
's1*√Z'
The function √ is the inverse of a part of SQ, a part defined by restricting the domain of SQ 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 SQ are called the
principal values of the inverse relation. The √ function in its entirety is called the principal branch of
the inverse relation, and the points sent by √ to the boundary of the restricted domain of SQ
form the branch cuts of √.