directSum(Character) -- direct sum of characters

Function: directSum
Usage:

character(c)

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

Description

Returns the direct sum of the input characters. The operators + and ++ and the function plus(Character,Character) 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 QQ
      
     (0, {1})  |  1  1  1

o7 : Character

i8 : b = character(B,1)

o8 = Character over QQ
      
     (0, {1})  |  -1  0  2

o8 : Character

i9 : a ++ b

o9 = Character over QQ
      
     (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 QQ
       
      (0, {1})  |  0  1  3

o12 : Character

i13 : a ++ b === c

o13 = true

Ways to use this method:

directSum(Character) -- direct sum of characters

The source of this document is in BettiCharacters.m2:3859:0.