Strategies for free resolutions -- overview of the different algorithms for computing free resolutions

There are several distinct algorithms for computing free resolutions in Macaulay2. They make different assumptions about the module or underlying ring.

freeResolution(..., Strategy => OverField) -- algorithm for computing free resolutions over a field
freeResolution(..., Strategy => OverZZ) -- algorithm for computing free resolutions of ZZ-modules
freeResolution(..., Strategy => Engine) -- algorithm for computing a free resolution
freeResolution(..., Strategy => 1) -- algorithm for computing free resolutions exploiting the Schreyer frame
freeResolution(..., Strategy => 3) -- algorithm for computing free resolutions step by step aided by Hilbert functions
freeResolution(..., Strategy => 2) -- algorithm for computing free resolutions step by step
freeResolution(..., Strategy => 0) -- algorithm for computing free resolutions exploiting the Schreyer frame
freeResolution(..., Strategy => Homogenization) -- algorithm for computing free resolutions by first homogenizing
freeResolution(..., Strategy => Syzygies) -- algorithm for computing free resolutions step by step using syzygies
freeResolution(..., Strategy => Nonminimal) -- algorithm for computing nonminimal free resolutions

One can always access the full list of possible strategies in Macaulay2 as follows.

i1 : hooks freeResolution

o1 = {0 => (freeResolution, Module, Strategy => Nonminimal)    }
     {1 => (freeResolution, Module, Strategy => Syzygies)      }
     {2 => (freeResolution, Module, Strategy => Homogenization)}
     {3 => (freeResolution, Module, Strategy => 0)             }
     {4 => (freeResolution, Module, Strategy => 2)             }
     {5 => (freeResolution, Module, Strategy => 3)             }
     {6 => (freeResolution, Module, Strategy => 1)             }
     {7 => (freeResolution, Module, Strategy => Engine)        }
     {8 => (freeResolution, Module, Strategy => OverZZ)        }
     {9 => (freeResolution, Module, Strategy => OverField)     }

o1 : NumberedVerticalList

Strategies for free resolutions -- overview of the different algorithms for computing free resolutions

See also