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D.4.7.2 cup

Procedure from library homolog.lib (see homolog_lib).

Usage:
cup(M,[,any,any]); M=module

Compute:
cup-product Ext^1(M',M') x Ext^1(M',M') ---> Ext^2(M',M'), where M':=R^m/M, if M in R^m, R basering (i.e. M':=coker(matrix(M))).
If called with >= 2 arguments: compute symmetrized cup-product

Assume:
all Ext's are finite dimensional

Return:
- if called with 1 argument: matrix, the columns of the output present the coordinates of b_i&b_j with respect to a kbase of Ext^2, where b_1,b_2,... is a kbase of Ext^1 and & denotes cup product;
- if called with 2 arguments: matrix, the columns of the output present the coordinates of (1/2)(b_i&b_j + b_j&b_i) with respect to a kbase of Ext^2;
- if called with 3 arguments: list,
 
      L[1] = matrix see above (symmetric case, for >=2 arguments)
      L[2] = matrix of kbase of Ext^1
      L[3] = matrix of kbase of Ext^2

Note:
printlevel >=1; shows what is going on.
printlevel >=2; shows result in another representation.
For computing cupproduct of M itself, apply proc to syz(M)!

Example:
 


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