Input/Output:

 

 

Level 2/Argument 1

Level 1/Argument 2

 

Level 1/Item 1

 

 

 

 

 

 

 

 

w

z

→

wz

 

 

z

'symb'

→

'z^(symb)'

 

 

'symb'

z

→

'(symb)^z'

 

 

'symb1'

'symb2'

→

'symb1^('symb2)'

 

 

x_unit

y

→

xy_unity

 

 

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: 'symbold (name1 = symb1, name2 = symb2 …)'

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

 

 

 

 

 

 

 

 

'symbold'

{ name1, 'symb1', name2, 'symb2' … }

→

'symbnew'

 

 

x

{ name1, 'symb1', name2, 'symb2' … }

→

x

 

 

(x,y)

{ name1, 'symb1', name2, 'symb2' … }

→

(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 (x1, y1), the square root is this complex number:

(x2, y2) =

θ

θ

rcos--,

rsin --

 

 

2

2

where r = ABS (x1, y1), and θ = ARG (x1, y1). If (x1, y1) = (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 √.

3-286 Full Command and Function Reference