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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:
 


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