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D.4.15.16 primdecMon
Procedure from library monomialideal.lib (see monomialideal_lib).
- Usage:
- primdecMon (I[,alg]); I ideal, alg string
- Return:
- list, the components in a minimal primary decomposition of I.
(returns -1 if I is not a monomial ideal).
- Assume:
- I is a monomial ideal of the basering k[x(1)..x(n)].
- Note:
- This procedure returns a minimal primary decomposition of I.
One may call the procedure with different algorithms using
the optional argument 'alg':
- the direct method for a primary decomposition following
Vasconcelos' book (alg=vp),
- from the irreducible decomposition obtained via the direct
method following Vasconcelos' book (alg=vi),
- from the irreducible decomposition obtained via the
Alexander dual and using doble dual (alg=add),
- from the irreducible decomposition obtained via the
Alexander dual and quotients following E. Miller (alg=ad),
- from the irreducible decomposition obtained
via ........ (alg=for),
- from the irreducible decomposition obtained via the Scarf
complex following Milowski (alg=mil),
- from the irreducible decomposition obtained using the label
algorithm of Roune (alg=lr),
- from the irreducible decomposition obtained using the
algorithm of Gao-Zhu (alg=gz),
- from the irreducible decomposition obtained using the slice
algorithm of Roune (alg=sr).
Example:
| | LIB "monomialideal.lib";
ring R = 0,(w,x,y,z),Dp;
ideal I = w^3*x*y,w*x*y*z,x^2*y^2*z^2,x^2*z^4,y^3*z;
// Vasconcelos para primaria
primdecMon(I,"vp");
==> [1]:
==> _[1]=x2
==> _[2]=y3
==> _[3]=wxy
==> _[4]=w3
==> [2]:
==> _[1]=xy
==> _[2]=x2
==> _[3]=y3
==> [3]:
==> _[1]=z
==> _[2]=x
==> [4]:
==> _[1]=y3
==> _[2]=wyz
==> _[3]=w3
==> _[4]=z4
==> _[5]=y2z2
==> [5]:
==> _[1]=y
==> _[2]=z4
==> [6]:
==> _[1]=z
==> _[2]=w3
// Alexander dual
primdecMon(I,"add");
==> [1]:
==> _[1]=y
==> _[2]=z4
==> [2]:
==> _[1]=xy
==> _[2]=x2
==> _[3]=y3
==> [3]:
==> _[1]=w3
==> _[2]=z
==> [4]:
==> _[1]=w
==> _[2]=x2
==> _[3]=y3
==> [5]:
==> _[1]=x
==> _[2]=z
==> [6]:
==> _[1]=w
==> _[2]=y3
==> _[3]=z4
==> _[4]=y2z2
// label algorithm
primdecMon(I,"lr");
==> [1]:
==> _[1]=w
==> _[2]=x2
==> _[3]=y3
==> [2]:
==> _[1]=w
==> _[2]=y3
==> _[3]=z4
==> _[4]=y2z2
==> [3]:
==> _[1]=w3
==> _[2]=z
==> [4]:
==> _[1]=x
==> _[2]=z
==> [5]:
==> _[1]=xy
==> _[2]=x2
==> _[3]=y3
==> [6]:
==> _[1]=y
==> _[2]=z4
//slice algorithm
primdecMon(I,"sr");
==> [1]:
==> _[1]=w
==> _[2]=x2
==> _[3]=y3
==> [2]:
==> _[1]=w
==> _[2]=y3
==> _[3]=z4
==> _[4]=y2z2
==> [3]:
==> _[1]=w3
==> _[2]=z
==> [4]:
==> _[1]=x
==> _[2]=z
==> [5]:
==> _[1]=xy
==> _[2]=x2
==> _[3]=y3
==> [6]:
==> _[1]=y
==> _[2]=z4
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