ApCoCoA-1:Weyl.WPower

Weyl.WPower

Computes the integer-power N of a Weyl polynomial.

Syntax

Weyl.WPower(F:POLY,N:INT):POLY

Description

Computes the integer-power N of a Weyl ploynomial F:

F: a Weyl polynomial in normal form,

N: a positive integer, power to be calculated.

The result is a Weyl polynomial $F^{N}$ in Normal form.

Example

A2::=QQ[x[1..2],y[1..2]];	--Define appropriate ring
Use A2;
F1:=x[1]^2x[2] - y[1]^3 + 3x[2]y[2] - 4;
Weyl.WPower(F1,0);
1
-------------------------------
Weyl.WPower(F1,1);
x[1]^2x[2] - y[1]^3 + 3x[2]y[2] - 4
-------------------------------
Weyl.WPower(F1,2);
x[1]^4x[2]^2 - 2x[1]^2x[2]y[1]^3 + y[1]^6 + 6x[1]^2x[2]^2y[2] - 6x[2]y[1]^3y[2] - 6x[1]x[2]y[1]^2 + 9x[2]^2y[2]^2 - 5x[1]^2x[2] + 
8y[1]^3 - 6x[2]y[1] - 15x[2]y[2] + 16
-------------------------------
Weyl.WPower(F1,3);
x[1]^6x[2]^3 - 3x[1]^4x[2]^2y[1]^3 + 3x[1]^2x[2]y[1]^6 - y[1]^9 + 9x[1]^4x[2]^3y[2] - 18x[1]^2x[2]^2y[1]^3y[2] + 9x[2]y[1]^6y[2] - 
18x[1]^3x[2]^2y[1]^2 + 18x[1]x[2]y[1]^5 + 27x[1]^2x[2]^3y[2]^2 - 27x[2]^2y[1]^3y[2]^2 - 3x[1]^4x[2]^2 + 15x[1]^2x[2]y[1]^3 - 
12y[1]^6 - 54x[1]x[2]^2y[1]^2y[2] + 27x[2]^3y[2]^3 - 42x[1]^2x[2]^2y[1] + 36x[2]y[1]^4 - 18x[1]^2x[2]^2y[2] + 45x[2]y[1]^3y[2] + 
36x[1]x[2]y[1]^2 - 54x[2]^2y[1]y[2] - 27x[2]^2y[2]^2 + 21x[1]^2x[2] - 24x[1]x[2]^2 - 48y[1]^3 + 36x[2]y[1] + 63x[2]y[2] - 64

-------------------------------
Weyl.WPower(F1,-3);
ERROR: 2nd Parameter should be a positive integer
CONTEXT: Error("2nd Parameter should be a positive integer")
-------------------------------