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D.4.27.29 zero_decomp
Procedure from library primdec.lib (see primdec_lib).
- Usage:
- zero_decomp(j,ser,@wr); j,ser ideals, @wr=0 or 1
(@wr=0 for primary decomposition, @wr=1 for computation of associated
primes)
- Return:
- list = list of primary ideals and their radicals (at even positions
in the list) if the input is zero-dimensional and a standardbases
with respect to lex-ordering
If ser!=(0) and ser is contained in j or if j is not zero-dimen-
sional then ideal(1),ideal(1) is returned
- Note:
- Algorithm of Gianni/Trager/Zacharias
Example:
| | LIB "primdec.lib";
ring r = 0,(x,y,z),lp;
poly p = z2+1;
poly q = z4+2;
ideal i = p^2*q^3,(y-z3)^3,(x-yz+z4)^4;
i=std(i);
list pr= zero_decomp(i,ideal(0),0);
pr;
==> [1]:
==> _[1]=z4+2z2+1
==> _[2]=y3-3y2z3+3yz6-z9
==> _[3]=x4-4x3yz+4x3z4+6x2y2z2-12x2yz5+6x2z8
==> [2]:
==> _[1]=z2+1
==> _[2]=y-z3
==> _[3]=x-yz+z4
==> [3]:
==> _[1]=z12+6z8+12z4+8
==> _[2]=y3-3y2z3+3yz6-z9
==> _[3]=x4-4x3yz+4x3z4+6x2y2z2-12x2yz5+6x2z8
==> [4]:
==> _[1]=z4+2
==> _[2]=y-z3
==> _[3]=x-yz+z4
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