Background

I am currently working on the homology of some moduli space and there exists a much simpler chain complex with the same homology. It is a quotient of a bisimplicial complex by a subcomplex. One could say, that some faces are degenerated, thus are zero. Unfortunately, it's too hard to compute the homology groups by hand.

Given a free chain complex of finite type over the coefficient ring $\mathbb{Z}$ or $\mathbb{Z}/{p^k}$, with $p$ prime, I cannot compute the homology groups by hand. Some matrices have approximately $18.000.000 \times 15.000.000$ entries. Is there a C/C++ library or an external program that:

• computes the homology groups
• describes the image of one or multiple cycles as linear combination of homology classes
• is efficient (e.g. it is capable of using multiple CPUs)

(descending order of importance)

Background

I am currently working on the homology of some moduli space and there exists a much simpler chain complex with the same homology. It is a quotient of a bisimplicial complex by a subcomplex. One could say that some faces are degenerate, thus are zero. Unfortunately, it's too hard to compute the homology groups by hand.

Given a free chain complex of finite type over the coefficient ring $\mathbb{Z}$ or $\mathbb{Z}/{p^k}$, with $p$ prime, I cannot compute the homology groups by hand. Some matrices have approximately $18.000.000 \times 15.000.000$ entries.

Question: Is there a C/C++ library or an external program that does the following (in descending order of importance)?

1. computes the homology groups of the given chain complex
2. describes the image of one or multiple cycles as a linear combination of homology classes
3. is efficient (e.g. it is capable of using multiple CPUs)

Background

I am currently working on the homology of some modulispace and there exists a much simpler chaincomplex with the same homology. It is a quotient of a bisimplicial complex by a subcomplex. One could say, that some faces are degenrated, thus are zero. Unfortunatly its to hard to compute the homology groups by hand.

Given a free chaincomplex of finite type over the coefficientring $\mathbb{Z}$ or $\mathbb{Z}/{p^k}$, with $p$ prime. I cannot compute the homology groups by hand. Some matrices have approximately $18.000.000 \times 15.000.000$ entries. Is there a C/C++ library or an external programm that:

• computes the homology groups
• describes the image of one or multiple cycles as linear combination of homology classes
• is efficient ( e.g. it is caplable of using multiple CPUs  )

(descending order of importance)

Background

I am currently working on the homology of some moduli space and there exists a much simpler chain complex with the same homology. It is a quotient of a bisimplicial complex by a subcomplex. One could say, that some faces are degenerated, thus are zero. Unfortunately, it's too hard to compute the homology groups by hand.

Given a free chain complex of finite type over the coefficient ring $\mathbb{Z}$ or $\mathbb{Z}/{p^k}$, with $p$ prime, I cannot compute the homology groups by hand. Some matrices have approximately $18.000.000 \times 15.000.000$ entries. Is there a C/C++ library or an external program that:

• computes the homology groups
• describes the image of one or multiple cycles as linear combination of homology classes
• is efficient (e.g. it is capable of using multiple CPUs)

(descending order of importance)

Background

I am currently working on the homology of some modulispace and there exists a much simpler chaincomplex with the same homology. Unfortunatly its to hard to compute the homology groups by hand.

Given a free chaincomplex of finite type over the coefficientring $\mathbb{Z}$ or $\mathbb{Z}/{p^k}$, with $p$ prime. I cannot compute the homology groups by hand. Some matrices have approximately $18.000.000 \times 15.000.000$ entries. Is there a C/C++ library or an external programm that:

• computes the homology groups
• describes the image of one or multiple cycles as linear combination of homology classes
• is efficient ( e.g. it is caplable of using multiple CPUs )

(descending order of importance)

Background

I am currently working on the homology of some modulispace and there exists a much simpler chaincomplex with the same homology. It is a quotient of a bisimplicial complex by a subcomplex. One could say, that some faces are degenrated, thus are zero. Unfortunatly its to hard to compute the homology groups by hand.

Given a free chaincomplex of finite type over the coefficientring $\mathbb{Z}$ or $\mathbb{Z}/{p^k}$, with $p$ prime. I cannot compute the homology groups by hand. Some matrices have approximately $18.000.000 \times 15.000.000$ entries. Is there a C/C++ library or an external programm that:

• computes the homology groups
• describes the image of one or multiple cycles as linear combination of homology classes
• is efficient ( e.g. it is caplable of using multiple CPUs )

(descending order of importance)