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5.1.122 res

Procedure from library standard.lib (see standard_lib).

Syntax:
res ( ideal_expression, int_expression [, any_expression ])
res ( module_expression, int_expression [, any_expression ])
Type:
resolution
Purpose:
computes a (possibly minimal) free resolution of an ideal or module using a heuristically chosen method.
The second (int) argument (say k) specifies the length of the resolution. If it is not positive then k is assumed to be the number of variables of the basering.
If a third argument is given, the returned resolution is minimized.

Depending on the input, the returned resolution is computed using the following methods:

quotient rings:
nres (classical method using syzygies) , see nres.

homogeneous ideals and k=0:
lres (La'Scala's method), see lres.

not minimized resolution and (homogeneous input with k not 0, or local rings):
sres (Schreyer's method), see sres.

all other inputs:
mres (classical method), see mres.
Note:
Accessing single elements of a resolution may require some partial computations to be finished and may therefore take some time.
See also betti; hres; ideal; lres; minres; module; mres; nres; resolution; sres.

Example:
 


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