HP 48gII Graphing, 50g Graphing GRAPH, GREDUCE, GRAMSCHMIDT

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 LVECTOR
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 = ∫1 P(x) ⋅ Q(x)dx
			–1
Command:	GRAMSCHMIDT([1,1+X], « → P Q « PREVAL(INTVX(P*Q),-1,1) » »)
		1	X
		------	--------------
		2	1
			-- ⋅ 6
Result:			3
GRAPH	Command
Type:
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:
	x2y – xy – 1
	with respect to the Grœbner basis (obtained in the example for GBASIS):
	x, 2y3 – 1
Command:	GREDUCE(X^2*Y–X*Y–1, [X,2*Y^3–1], [X,Y])

Full Command and Function Reference 3-99