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D.4.27.29 zero_decomp
Procedure from libraryprimdec.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
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 |