The Homology of a Junction.
More...
#include <Homology.hpp>
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| typedef diff_t_C | Gens_t |
| | The type of our matrix of generators. More...
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| typedef col_vector_t< diff_t_C > | gen_t |
| | The dense type of our generators (a column in the generator matrix, always dense for convenience) More...
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| AbelianGroup< rank_t > | Groups |
| | Encodes the homology groups as follows: Groups=[1,2,3] means homology Z+Z/2+Z/3. This works even for Z/n coefficients: the free module (Z/n)^, is encoded as [n,n,...,n]. More...
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| Gens_t | Generators |
| | Encodes the generators homology groups as follows: The i-th column corresponds to the generator for Groups[i]. More...
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| bool | isZero |
| | 1 if the homology is trivial More...
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| template<typename Archive , typename srank_t , typename sdiff_t > |
| void | serialize (Archive &, Homology< srank_t, sdiff_t > &) |
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template<typename rank_t, typename diff_t>
class Mackey::Homology< rank_t, diff_t >
The Homology of a Junction.
- Template Parameters
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| rank_t | The rank type is a dense Eigen row vector of signed integer scalar eg Eigen::Matrix<int,1,-1>. It stores the ranks of the modules of the differentials Eg in the G equivariant case \([1,2,4]\) means \(Z[G/G}\oplus Z[G/G']\oplus Z[G/G'']\) where \(|G:G'|=2, |G/G''|=4\) (current implementation only for prime power cyclic groups) |
| diff_t | The different |
◆ Gens_t
The type of our matrix of generators.
◆ gen_t
The dense type of our generators (a column in the generator matrix, always dense for convenience)
◆ Homology() [1/2]
◆ Homology() [2/2]
Compute the homology of Junction from the given Junction
- Parameters
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| J | The given Junction |
| getQ | Whether we want to store the Q matrix; this is used by the boundary function |
◆ basis()
| rank_t basis |
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const gen_t & |
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const |
Given an element in homology, write it as a linear combination of the generators of the homology.
The answer is encoded as follows: basis=[-1,0,3] means element=-gen[0]+3*gen[2]
◆ boundary()
Given an x that is a boundary returns a y s.t. dy=x.
◆ serialize
| void serialize |
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Archive & |
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Homology< srank_t, sdiff_t > & |
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friend |
◆ Groups
Encodes the homology groups as follows: Groups=[1,2,3] means homology Z+Z/2+Z/3. This works even for Z/n coefficients: the free module (Z/n)^, is encoded as [n,n,...,n].
◆ Generators
Encodes the generators homology groups as follows: The i-th column corresponds to the generator for Groups[i].
◆ isZero
1 if the homology is trivial
The documentation for this class was generated from the following file:
