|
D.4.7.3 cupproduct
Procedure from library homolog.lib (see homolog_lib).
- Usage:
- cupproduct(M,N,P,p,q[,any]); M,N,P modules, p,q integers
- Compute:
- cup-product Ext^p(M',N') x Ext^q(N',P') ---> Ext^(p+q)(M',P'),
where M':=R^m/M, if M in R^m, R basering (i.e. M':=coker(matrix(M)))
- Assume:
- all Ext's are of finite dimension
- Return:
- - if called with 5 arguments: matrix of the associated linear map
Ext^p (tensor) Ext^q --> Ext^(p+q), i.e. the columns of <matrix>
present the coordinates of the cup products (b_i & c_j) with respect
to a kbase of Ext^p+q (b_i resp. c_j are the chosen bases of Ext^p,
resp. Ext^q).
- if called with 6 arguments: list L,
| L[1] = matrix (see above)
L[2] = matrix of kbase of Ext^p(M',N')
L[3] = matrix of kbase of Ext^q(N',P')
L[4] = matrix of kbase of Ext^p+q(N',P')
|
- Note:
- printlevel >=1; shows what is going on.
printlevel >=2; shows the result in another representation.
For computing the cupproduct of M,N itself, apply proc to syz(M),
syz(N)!
Example:
|