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D.6.15.8 is_regs
Procedure from library sing.lib (see sing_lib).
- Usage:
- is_regs(i[,id]); i poly, id ideal or module (default: id=0)
- Return:
- 1 if generators of i are a regular sequence modulo id, 0 otherwise
- Note:
- Let R be the basering and id a submodule of R^n. The procedure checks
injectivity of multiplication with i[k] on R^n/id+i[1..k-1].
The basering may be a quotient ring.
printlevel >=0: display comments (default)
printlevel >=1: display comments during computation
Example:
| | LIB "sing.lib";
int p = printlevel;
printlevel = 1;
ring r1 = 32003,(x,y,z),ds;
ideal i = x8,y8,(x+y)^4;
is_regs(i);
==> // checking whether element 1 is regular mod 1 .. 0
==> // checking whether element 2 is regular mod 1 .. 1
==> // checking whether element 3 is regular mod 1 .. 2
==> // elements 1..2 are regular, 3 is not regular mod 1..2
==> 0
module m = [x,0,y];
i = x8,(x+z)^4;;
is_regs(i,m);
==> // checking whether element 1 is regular mod 1 .. 0
==> // checking whether element 2 is regular mod 1 .. 1
==> // elements are a regular sequence of length 2
==> 1
printlevel = p;
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