(Source: Introduction to the homalg package)
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Q: Does outsourcing the matrices mean that homalg is able to compute spectral sequences, for example, without ever seeing the matrices involved in the computation?
A: Yes.
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Q: Can homalg profit from the implementation of homological constructions like Hom, Ext, ... in Singular?
A: No. This is for a lot of reasons incompatible with the idea and design of homalg.
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Q: Are the external systems involved in the higher algorithms?
A: No. They host all the matrices and do all matrix operations delegated to them without knowing what for. The meaning of the matrices and their logical interrelation is only known to GAP4.
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Q: Do developers of packages building upon the homalg package need to know anything about the communication with the external systems?
A: No, unless they want to use more features of the external systems than those reflected by homalg. For this purpose, developers can use the unified communication interface provideb by HomalgToCAS. This is the interface used by homalg.
