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D.4.14.1 modPrimdecGTZ
Procedure from library modprimdec.lib (see modprimdec_lib).
- Usage:
- modPrimdecGTZ(I, #); I ideal, # an optional list which is either empty (not entered) or consists of precisely one integer which is 0 or 1.
- Assume:
- The basering of I is defined over the rationals.
- Return:
- A primary decomposition of I.
- Note:
- - The final result will be checked for correctness if # is either empty (not entered) or if #[1] = 1. Without the check, the functions reurns a result which is correct with high probability.
- For local orderings, the result represents a primary decomposition in the localization
of the polynomial ring, not in the power series ring.
Example:
| | LIB "modprimdec.lib";
ring R = 0, (x,y), dp;
ideal I = x9y2+x10, x2y7-y8;
modPrimdecGTZ(I);
==> [1]:
==> [1]:
==> _[1]=y-1
==> _[2]=x+1
==> [2]:
==> _[1]=y-1
==> _[2]=x+1
==> [2]:
==> [1]:
==> _[1]=y2+y+1
==> _[2]=x-y-1
==> [2]:
==> _[1]=y2+y+1
==> _[2]=x-y-1
==> [3]:
==> [1]:
==> _[1]=y12
==> _[2]=x2y7-y8
==> _[3]=x9y2+x10
==> [2]:
==> _[1]=y
==> _[2]=y2+10x
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