isQuasiRegular -- tests a matrix or sequence or list for quasi-regularity on a module

Synopsis

Usage:

t = isQuasiRegular(ff,M)
Inputs:
- ff, a matrix,
- ff, a list,
- ff, a sequence,
- M, a module,
Outputs:
- t, a Boolean value,

Description

ff is quasi-regular if the length of ff is <= dim M and the annihilator of ff_i on M/(ff_0..ff_{(i-1))}M has finite length for all i=0..(length ff)-1.

i1 : kk=ZZ/101;

i2 : S = kk[a,b,c];

i3 : E = S^1/ideal"ab"++S^1/ideal vars S;

i4 : f1 =matrix"a";

             1      1
o4 : Matrix S  <-- S

i5 : f2 =matrix"a+b,c";

             1      2
o5 : Matrix S  <-- S

i6 : f3 = matrix"a+b";

             1      1
o6 : Matrix S  <-- S

i7 : f4 = matrix"a+b, a2+b";

             1      2
o7 : Matrix S  <-- S

i8 : isQuasiRegular(f1,E)

o8 = false

i9 : isQuasiRegular(f2,E)

o9 = true

i10 : isQuasiRegular(f3,E)

o10 = true

i11 : isQuasiRegular(f4,E)

o11 = false

Ways to use isQuasiRegular :

isQuasiRegular(List,Module)
isQuasiRegular(Matrix,Module)
isQuasiRegular(Sequence,Module)

For the programmer

The object isQuasiRegular is a method function.