HERMITE

Type:

Function

Description:

Returns the nth Hermite polynomial.

Access:

Arithmetic, !ÞPOLY L

Input:

A non-negative integer.

Output:

The corresponding polynomial expression.

Flags:

Exact mode must be set (flag –105 clear).

 

Numeric mode must not be set (flag –3 clear).

Example:

Find the Hermite polynomial with degree 4.

Command:

HERMITE(4)

Result:

16*X^4-48*X^2+12

See also:

LEGENDRE, TCHEBYCHEFF

HESS

Type:

Command

 

Description:

Returns the Hessian matrix and the gradient of an expression with respect to the specified

 

variables.

 

Access:

Calculus !ÖDERIV & INTEG

 

Input:

Level 2/Argument 1: An expression.

 

Level 1/Argument 2: A vector of the variables.

Output:

Level 3/Item 1: The Hessian matrix with respect to the specified variables.

 

Level 2/Item 2: The gradient with respect to the variables.

 

Level 1/Item 3: The vector of the variables.

Flags:

Exact mode must be set (flag –105 clear).

 

Numeric mode must not be set (flag –3 clear).

Example:

Find the Hessian matrix, and the gradient with respect to each variable, of the expression:

 

 

t2 + 2tu2.

Command:

HESS(T^2+2*T*U^2, [T, U])

 

Result:

{[[2, 2*(2*U)], [2*(2*U), 2*(2*T)]], [2*T+2*U^2, 2*T*(2*U)], [T, U]}

See also:

CURL, DIV

 

HEX

Command

 

Type:

 

Description:

Hexadecimal Mode Command: Selects hexadecimal base for binary integer operations. (The

 

default base is decimal.)

 

 

Binary integers require the prefix #. Binary integers entered and returned in hexadecimal base

 

automatically show the suffix h. If the current base is not hexadecimal, then you can enter a

 

hexadecimal number by ending it with h. It will be displayed in the current base when it is

 

entered.

 

 

The current base does not affect the internal representation of binary integers as unsigned binary

 

numbers.

 

Access:

!´BASE HEX

( ´is the left-shift of the Pkey).

 

!Ú BASE HEX

( Ú is the left-shift of the 6key).

Flags:

Binary Integer Wordsize (–5 through –10), Binary Integer Base (–11, –12)

3-104 Full Command and Function Reference