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D.6.13.8 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;