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5.1.58 hres
Syntax:
hres ( ideal_expression, int_expression )
Type:
- resolution
Purpose:
- computes a free resolution of an ideal using the Hilbert-driven
algorithm.
More precisely, let R be the basering and I be the given ideal.
Then hres computes a minimal free resolution of R/I
If the int_expression k is not zero then the computation stops after
k steps and returns a list of modules
, i=1..k.
list L=hres(I,0); returns a list L of n modules (where n is the
number of variables of the basering) such that
in the above notation.
Note:
- The ideal_expression has to be homogeneous.
Accessing single elements of a resolution may require some partial
computations to be finished. Therefore, it may take some time.
Example:
| ring r=0,(x,y,z),dp;
ideal I=xz,yz,x3-y3;
def L=hres(I,0);
print(betti(L),"betti");
==> 0 1 2
==> ------------------------
==> 0: 1 - -
==> 1: - 2 1
==> 2: - 1 1
==> ------------------------
==> total: 1 3 2
==>
L[2]; // the first syzygy module of r/I
==> _[1]=-x*gen(1)+y*gen(2)
==> _[2]=-x2*gen(2)+y2*gen(1)+z*gen(3)
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See
betti;
fres;
ideal;
int;
lres;
minres;
module;
mres;
res;
sres.
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