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ResLengthThree :: multTableOneOne

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

Synopsis

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 :

For the programmer

The object multTableOneOne is a method function with options.