Reference Guide

Full Command and Function Reference 3-95
GAMMA
Type: Function
Description: Evaluate the Γ function at the given point. For a positive integer x, Γ(x) is equal to (x +1)!
GAMMA differs from the FACT and ! functions because it allows complex arguments. The Γ
function is defined by
Γ x( ) e
t–
t
x 1–
⋅ td
0
+∞
∫
=
.
Access: !´L SPECIAL
Input: A real or complex number, x.
Output: Γ(x). If the input x is an integer greater than 100, returns the symbolic expression GAMMA(x).
Flags: If the Underflow Exception (–20) or Overflow Exception (–21) flags are set then underflow or
overflow conditions give errors, otherwise they give zero or the maximum real number the
calculator can express.
Complex mode must be set (flag –103 set) if x is complex.
See also: FACT, PSI, Psi, !
GAUSS
Type: Command
Description: Returns the diagonal representation of a quadratic form.
Access: Matrices, !Ø QUADRATIC FORM
Input: Level 2/Argument 1: The quadratic form.
Level 1/Argument 2: A vector containing the independent variables.
Output: Level 4/Item 1: An array of the coefficients of the diagonal.
Level 3/Item 2: A matrix, P, such that the quadratic form is represented as P
T
DP, where the
diagonal matrix D contains the coefficients of the diagonal representation.
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:
x
2
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]}
See also: 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.
Access: Catalog, …µ
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.