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7.3.1 betti (plural)
Syntax:
betti ( list_expression )
betti ( resolution_expression )
betti ( list_expression , int_expression )
betti ( resolution_expression , int_expression )
Type:
- intmat
Note:
- in the non-commutative case, computing Betti numbers makes sense only if the basering
has homogeneous relations.
The output of the command can be pretty-printed using
print( , "betti") , i.e., with "betti" as second argument; see below example.
Purpose:
- with 1 argument: computes the graded Betti numbers of a minimal resolution of
The argument is considered to be the result of a mres or nres
command. This implies that a zero is only allowed (and counted) as a
generator in the first module.
For the computation betti uses only the initial monomials. This could lead to confusing results for a non-homogeneous input.
If the optional second argument is non-zero, the Betti numbers will be minimized.
Example:
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