multTableOneTwo -- the multiplication table for products of elements in degree one with elements in degree two

Synopsis

• Usage:

  multTableOneTwo A

• Inputs:
  • A, a ring, created with resLengthThreeAlg or resLengthThreeTorAlg
• Optional inputs:
  • Labels => ..., default value true, an optional argument for multTableOneTwo determining whether to label rows and columns
• Outputs:
  • a list, of the rows in the multiplication table; use netList to display it as a table

Description

For a free resolution of length three described as a graded-commutative ring A, the function returns a list of the rows of the multiplication table of elements in degree one with elements in degree two. It also computes the multiplication table for products of elements in degree one with elements in degree two in the graded-commutative homology algebra obtained from A.

i1 : Q = QQ[x,y,z];

i2 : A = resLengthThreeAlg res ideal (x^2,y^2,z^2)

o2 = A

o2 : QuotientRing

i3 : multTableOneTwo A

o3 = {{0, f , f , f }, {e , 0, 0, g }, {e , 0, -g , 0}, {e , g , 0, 0}}
           1   2   3     1         1     2       1        3   1

o3 : List

i4 : netList multTableOneTwo A

     +--+--+---+--+
o4 = |0 |f |f  |f |
     |  | 1| 2 | 3|
     +--+--+---+--+
     |e |0 |0  |g |
     | 1|  |   | 1|
     +--+--+---+--+
     |e |0 |-g |0 |
     | 2|  |  1|  |
     +--+--+---+--+
     |e |g |0  |0 |
     | 3| 1|   |  |
     +--+--+---+--+