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ResLengthThree :: multTableOneTwo

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

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 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|   |  |
     +--+--+---+--+

Ways to use multTableOneTwo :

For the programmer

The object multTableOneTwo is a method function with options.