# Gcdmod; Gramschmidt; Greduce - HP 48gII Advanced User's Reference Manual

Graphing calculator.

## GCDMOD

Type:
Function
Description:
Finds the greatest common divisor of two polynomials modulo the current modulus.
Arithmetic, !Þ
Access:
Input:
Level 2/Argument 1: A polynomial expression.
Level 1/Argument 2: A polynomial expression.
Output:
The greatest common divisor of the two expressions modulo the current modulus.
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 the greatest common divisor of 2x^2+5 and 4x^2-5x, modulo 13.
Command:
GCDMOD(2X^2+5,4X^2-5X)
Result:
-(4X-5)
GCD

### GRAMSCHMIDT

Type:
Command
Description:
Finds an orthonormal base of a vector space with respect to a given scalar product.
Matrices, !Ø L
Access:
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
=
Command:
GRAMSCHMIDT([1,1+X], «
1
X
------ -
--------------
1
2
-- -
3
Result:

### GREDUCE

Type:
Command
Description:
Reduces a polynomial with respect to a Grœbner basis.
Catalog, ...µ
Access:
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.
MODULO
VECTOR
1
P x
Q x x d
1 –
6
P Q « PREVAL(INTVX(P*Q),-1,1) " ")
Computer Algebra Commands 4-35