RingElement * Character -- scalar multiple of a character

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = (ideal vars R)^3

             3   2    2      2            2   3   2      2   3
o2 = ideal (x , x y, x z, x*y , x*y*z, x*z , y , y z, y*z , z )

o2 : Ideal of R

i3 : Q = R/I

o3 = Q

o3 : QuotientRing

i4 : S3 = symmetricGroupActors R

o4 = {| y z x |, | y x z |, | x y z |}

o4 : List

i5 : A = action(Q,S3)

o5 = QuotientRing with 3 actors

o5 : ActionOnGradedModule

i6 : c = character(A,0,10)

o6 = Character over QQ
      
     (0, {0})  |  1  1  1
     (0, {1})  |  0  1  3
     (0, {2})  |  0  2  6

o6 : Character

i7 : 2*c

o7 = Character over QQ
      
     (0, {0})  |  2  2   2
     (0, {1})  |  0  2   6
     (0, {2})  |  0  4  12

o7 : Character

i8 : c*(1/3)

o8 = Character over QQ
      
               |  1  1  1
     (0, {0})  |  -  -  -
               |  3  3  3
               |     1  
     (0, {1})  |  0  -  1
               |     3  
               |     2  
     (0, {2})  |  0  -  2
               |     3  

o8 : Character

i9 : DR = c.degreesRing

o9 = DR

o9 : PolynomialRing

i10 : T = DR_0

o10 = T

o10 : DR

i11 : c * T^10

o11 = Character over QQ
       
      (0, {10})  |  1  1  1
      (0, {11})  |  0  1  3
      (0, {12})  |  0  2  6

o11 : Character