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D.8.5.1 triangL
Procedure from library triang.lib (see triang_lib).
- Usage:
- triangL(G); G=ideal
- Assume:
- G is the reduced lexicographical Groebner basis of the
zero-dimensional ideal (G), sorted by increasing leading terms.
- Return:
- a list of finitely many triangular systems, such that
the union of their varieties equals the variety of (G).
- Note:
- Algorithm of Lazard (see: Lazard, D.: Solving zero-dimensional
algebraic systems, J. Symb. Comp. 13, 117 - 132, 1992).
Example:
| | LIB "triang.lib";
ring rC5 = 0,(e,d,c,b,a),lp;
triangL(stdfglm(cyclic(5)));
==> [1]:
==> _[1]=a5-1
==> _[2]=b-a
==> _[3]=c2+3ca+a2
==> _[4]=d+c+3a
==> _[5]=e-a
==> [2]:
==> _[1]=a5-1
==> _[2]=b-a
==> _[3]=c-a
==> _[4]=d2+3da+a2
==> _[5]=e+d+3a
==> [3]:
==> _[1]=a5-1
==> _[2]=b6+4b5a+5b4a2+5b3a3+5b2a4+4b+a
==> _[3]=5c+8b5a+30b4a2+30b3a3+25b2a4+30b+22a
==> _[4]=5d-2b5a-10b4a2-15b3a3-10b2a4-10b-8a
==> _[5]=5e-6b5a-20b4a2-15b3a3-15b2a4-15b-9a
==> [4]:
==> _[1]=a10+123a5+1
==> _[2]=55b2-2ba6-233ba-8a7-987a2
==> _[3]=55c+a6+144a
==> _[4]=55d+a6+144a
==> _[5]=55e+55b-2a6-233a
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