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

## Synopsis

• Usage:
multTableOneOne A
• Inputs:
• 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| | +--+---+---+--+

## Ways to use multTableOneOne :

• "multTableOneOne(Ring)"

## For the programmer

The object multTableOneOne is .