# Gbasis; Gcd - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Level 2/Item 3: The diagonal representation of the quadratic form.
Level 1/Item 4: The vector of the variables.
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 Gaussian symbolic quadratic form of the following:
2
x
+
2axy
Command:
GAUSS(X^2+2*A*X*Y,[X,Y])
Result:
{[1,-A^2], [[1,A][0,1]], -(A^2*Y^2)+(A*Y+X)^2,[X,Y]}
AXQ, QXA

## GBASIS

Type:
Command
Description:
Returns a set of polynomials that are a Grœbner basis G of the ideal I generated from an
input set of polynomials F.
Catalog, ...µ
Access:
Input:
Level 2/Argument 1: A vector F of polynomials in several variables.
Level 1/Argument 2: A vector giving the names of the variables.
Output:
Level 1/Item 1: A vector containing the resulting set G of polynomials. The command
attempts to order the polynomials as given in the vector of variable names.
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 a Grœbner basis of the ideal polynomial generated by the polynomials:
x
+ 2xy
2
Command:
GBASIS([X^2 + 2*X*Y^2, X*Y + 2*Y^3 – 1], [X,Y])
Result:
[X, 2*Y^3-1]
Note this is not the minimal Grœbner basis, as the leading coefficient of the second term is not
1; the algorithm used avoids giving results with fractions.
GREDUCE

### GCD

Type:
Function
Description:
Returns the greatest common divisor of two objects.
Arithmetic, !Þ
Access:
Input:
Level 2/Argument 1: An expression, or an object that evaluates to a number.
Level 1/Argument 2: An expression, or an object that evaluates to a number.
Output:
The greatest common divisor of the two objects.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Find the greatest common divisor of 2805 and 99.
Command:
GCD(2805,99)
Result:
33
GCDMOD, EGCD, IEGCD, LCM
4-34 Computer Algebra Commands
, xy + 2y
– 1
2
3
L
POLY