# directSum(Character) -- direct sum of characters

## Synopsis

• Function: directSum
• Usage:
character(c)
character(c1,c2,...)
• Inputs:
• c, an instance of the type Character, or sequence of characters
• Outputs:

## Description

Returns the direct sum of the input characters. The operator ++ may be used for the same purpose.

 i1 : R = QQ[x_1..x_3] o1 = R o1 : PolynomialRing i2 : I = ideal(x_1+x_2+x_3) o2 = ideal(x + x + x ) 1 2 3 o2 : Ideal of R i3 : J = ideal(x_1-x_2,x_1-x_3) o3 = ideal (x - x , x - x ) 1 2 1 3 o3 : Ideal of R i4 : S3 = {matrix{{x_2,x_3,x_1}}, matrix{{x_2,x_1,x_3}}, matrix{{x_1,x_2,x_3}} } o4 = {| x_2 x_3 x_1 |, | x_2 x_1 x_3 |, | x_1 x_2 x_3 |} o4 : List i5 : A = action(I,S3) o5 = Ideal with 3 actors o5 : ActionOnGradedModule i6 : B = action(J,S3) o6 = Ideal with 3 actors o6 : ActionOnGradedModule i7 : a = character(A,1) o7 = Character over R (0, {1}) => | 1 1 1 | o7 : Character i8 : b = character(B,1) o8 = Character over R (0, {1}) => | -1 0 2 | o8 : Character i9 : a ++ b o9 = Character over R (0, {1}) => | 0 1 3 | o9 : Character i10 : K = ideal(x_1,x_2,x_3) o10 = ideal (x , x , x ) 1 2 3 o10 : Ideal of R i11 : C = action(K,S3) o11 = Ideal with 3 actors o11 : ActionOnGradedModule i12 : c = character(C,1) o12 = Character over R (0, {1}) => | 0 1 3 | o12 : Character i13 : a ++ b === c o13 = true