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) = ∫

+∞

–t

⋅ t

x – 1

 

 

e

 

 

dt

 

 

0

 

 

 

.

 

 

 

 

 

 

Access:

!´LSPECIAL

 

 

 

 

 

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 PTDP, 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:

 

x2 + 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.

Full Command and Function Reference 3-95