multTableOneOne -- the multiplication table for products of elements in degree one

Synopsis

• Usage:

  multTableOneOne A

• Inputs:
  • A, a ring, created with resLengthThreeAlg or resLengthThreeTorAlg
• Optional inputs:
  • Compact => ..., default value false, an optional argument for multTableOneOne that prints dots below the diagonal
  • Labels => ..., default value true, an optional argument for multTableOneOne 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. It also computes the multiplication table for products of elements in degree one 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 : multTableOneOne A

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

o3 : List

i4 : netList multTableOneOne A

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