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D.4.3.3 CompInt
Procedure from library cimonom.lib (see cimonom_lib).
- Usage:
- CompInt(d); d intvec.
- Return:
- 1 if the toric ideal I(d) is a complete intersection or 0 otherwise.
- Assume:
- d is a vector of positive integers.
- Note:
- If printlevel > 0, additional info is displayed in case
I(d) is a complete intersection:
if printlevel >= 1, it displays a minimal set of generators of the toric
ideal formed by quasihomogeneous binomials. Moreover, if printlevel >= 2
and gcd(d) = 1, it also shows the Frobenius number of the semigroup
generated by the elements in d.
Example:
| LIB "cimonom.lib";
"printlevel = 0;";
==> printlevel = 0;
printlevel = 0;
"intvec d = 14,15,10,21;";
==> intvec d = 14,15,10,21;
intvec d = 14,15,10,21;
"CompInt(d);";
==> CompInt(d);
CompInt(d);
==> 1
" ";
==>
"printlevel = 2;";
==> printlevel = 2;
printlevel = 3;
"d = 36,54,125,150,225;";
==> d = 36,54,125,150,225;
d = 36,54,125,150,225;
"CompInt(d);";
==> CompInt(d);
CompInt(d);
==> // Toric ideal:
==> id[1]=-x(1)^3+x(2)^2
==> id[2]=-x(4)^3+x(5)^2
==> id[3]=-x(3)^3+x(4)*x(5)
==> id[4]=-x(1)^11*x(2)+x(4)^3
==> // Frobenius number of the numerical semigroup:
==> 793
==> 1
" ";
==>
"d = 45,70,75,98,147;";
==> d = 45,70,75,98,147;
d = 45,70,75,98,147;
"CompInt(d);";
==> CompInt(d);
CompInt(d);
==> 0
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