Changes between Version 1 and Version 2 of Ticket #9894, comment 64


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Timestamp:
03/29/12 20:37:20 (10 years ago)
Author:
SimonKing
Comment:

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  • Ticket #9894, comment 64

    v1 v2  
    1010> Maybe comparisons or `__eq__` need to be implemented, too.
    1111
    12 I think that the answers are consistent, for the following reason:
    13  * `H0.2*H0.3` is zero in the cohomology ''group'' H^2^(D8). As elements in that group, they are zero, hence "is_zero()" returns True.
    14  * However, even though they vanish and thus represent a relation of the cohomology ring, they are still cocycles of degree 2. Thus, they are not equal to `H0.zero_element()`, which is a cocycle of degree 2. Hence, the comparison with the zero of the cohomology ''ring'' returns False.
     12I think that the answers are consistent, for the following reasons:
     13 * `H0.2*H0.3` is zero in the cohomology ''group'' H^2^(D8). As elements of that group, the product is zero, hence "is_zero()" returns True.
     14 * However, even though the product vanishes and thus represents a relation of the cohomology ring, it still is a cocycle of degree 2. Thus, it is not equal to `H0.zero_element()`, which is a cocycle of degree 2. Hence, the comparison with the zero of the cohomology ''ring'' returns False.