Reference Guide

Full Command and Function Reference 3-99
Input/Output: None
See also: DEG, RAD
GRAMSCHMIDT
Type: Command
Description: Finds an orthonormal base of a vector space with respect to a given scalar product.
Access: Matrices, !Ø L VECTOR
Input: Level 2/Argument 1: A vector representing a basis of a vector space.
Level 1/Argument 2: A function that defines a scalar product in that space. This can be given as a
program, or as the name of a variable containing the definition of the function.
Output: An orthonormal base of the vector space with respect to the given scalar product.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example: Find an orthonormal base for the vector space with base [1, 1+X] with respect to the scalar
product defined by :
P Q⋅ P x( ) Q x( )⋅ xd
1–
1
∫
=
Command: GRAMSCHMIDT([1,1+X], « → P Q « PREVAL(INTVX(P*Q),-1,1) » »)
Result:
1
2
-------
X
1
3
---
6⋅
--------------
GRAPH
Type: Command
Description: Picture Environment Command: Selects the Picture environment
GRAPH is provided for compatibility with the HP 28 series. GRAPH is the same as PICTURE;
see its listing for details.
GREDUCE
Type: Command
Description: Reduces a polynomial with respect to a Grœbner basis.
Access: Catalog, …µ
Input: Level 3/Argument 1: A vector of polynomials in several variables.
Level 2/Argument 2: A vector of polynomials that is a Grœbner basis in the same variables.
Level 1/Argument 3: A vector giving the names of the variables.
Output: Level 1/Item 1: A vector containing the input polynomial reduced with respect to the Grœbner
basis, up to a constant; as with GBASIS, fractions in the result are avoided.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Radians mode must be set (flag –17 set).
Example: Reduce the polynomial:
x
2
y – xy – 1
with respect to the Grœbner basis (obtained in the example for GBASIS):
x, 2y
3
– 1
Command: GREDUCE(X^2*Y–X*Y–1, [X,2*Y^3–1], [X,Y])