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

- 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 freeResolution 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|  |
         +--+---+---+--+

## Ways to use multTableOneOne:

- `multTableOneOne(Ring)`

## For the programmer

The object multTableOneOne is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ResLengthThree.m2:538:0.