|
 |
 |
 |
 |
 |
 |
 |
 |
 |
D.5.8.7 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; |