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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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