degStats(...,Verbose=>...) -- optional input to request verbose feedback

Description

Some of the functions that use this option by default exclude zero ideals when computing statistics on a set of ideals, while others do not. If Verbose => true, then the functions will display this type of additional informational. The default value is false.

i1 : n=3;D=3;p=0.0;N=3;

i5 : ideals = randomMonomialIdeals(n,D,p,N)

o5 = {monomialIdeal (), monomialIdeal (), monomialIdeal ()}

o5 : List

i6 : regStats(ideals)

o6 = (-infinity, 0)

o6 : Sequence

i7 : CMStats(ideals)

o7 = 1

o7 : QQ

In the examples above, one may wonder, for example, why 3 out of 3 ideals in the list are Cohen-Macaulay. In order to view the additional information, set Verbose => true:

i8 : regStats(ideals, Verbose => true)
All ideals in this list are the zero ideal.

o8 = (-infinity, 0)

o8 : Sequence

i9 : CMStats(ideals, Verbose => true)
There are 3 ideals in this sample. Of those, 3 are the zero ideal.
The zero ideals are included in the reported count of Cohen-Macaulay quotient rings.
3 out of 3 ideals in the given sample are Cohen-Macaulay.

o9 = 1

o9 : QQ

Other functions that have this option are as follows. Let us look at a list of nontrivial ideals to see more interesting statistics.

i10 : n=3;D=3;p=0.1;N=3;

i14 : ideals = randomMonomialIdeals(n,D,p,N)

                           3                                             
o14 = {monomialIdeal (x , x , x ), monomialIdeal (), monomialIdeal (x x ,
                       1   2   3                                     2 3 
      -----------------------------------------------------------------------
       2
      x )}
       3

o14 : List

i15 : regStats(ideals, Verbose => true)
There are 3 ideals in this sample. Of those, 1 are the zero ideal.
The zero ideals were extracted from the sample before reporting the regularity statistics.

o15 = (2.5, .5)

o15 : Sequence

i16 : CMStats(ideals, Verbose => true)
There are 3 ideals in this sample. Of those, 1 are the zero ideal.
The zero ideals are included in the reported count of Cohen-Macaulay quotient rings.
2 out of 3 ideals in the given sample are Cohen-Macaulay.

      2
o16 = -
      3

o16 : QQ

i17 : degStats(ideals, Verbose => true)
There are 3 ideals in this sample. Of those, 1 are the zero ideal.
The degree statistics do include those for the zero ideals.

o17 = (1.66667, .942809)

o17 : Sequence

i18 : dimStats(ideals, Verbose=>true)
There are 3 ideals in this sample. Of those, 1 are the zero ideal.
The Krull dimension statistics do include those for the zero ideals.

o18 = (1.66667, 1.24722)

o18 : Sequence

i19 : borelFixedStats(ideals, Verbose => true)
There are 3 ideals in this sample. Of those, 1 are the zero ideal.
The zero ideals are included in the reported count of Borel-fixed monomial ideals.
1 out of 3 monomial ideals in the given sample are Borel-fixed.

      1
o19 = -
      3

o19 : QQ

i20 : mingenStats(ideals, Verbose=>true)
There are 3 ideals in this sample. Of those, 1 are the zero ideal.
The statistics returned (mean and standard deviation of # of min gens and mean and standard deviation of degree complexity) do NOT include those for the zero ideals.

o20 = (2.5, .5, 2.5, .5)

o20 : Sequence

i21 : bettiStats(ideals, Verbose => true)
There are 3 ideals in this sample. Of those, 1 are the zero ideal.
The Betti statistics do include those for the zero ideals.

              0       1       2       3         0       1       2       3 
o21 = (total: 1       1       1 .333333, total: 1 1.66667 1.33333 .333333,
           0: 1 .333333 .333333       .      0: 1 .666667 .333333       . 
           1: . .333333 .333333       .      1: . .666667 .333333       . 
           2: . .333333 .333333 .333333      2: . .333333 .666667 .333333 
      -----------------------------------------------------------------------
                   1       2       3
      total: 2.35702 1.88562 .471405)
          0: .942809 .471405       .
          1: .942809 .471405       .
          2: .471405 .942809 .471405

o21 : Sequence

i22 : M = randomMonomialSets(n,D,p,N);

i23 : idealsFromGeneratingSets(M, Verbose => true)
There are 3 ideals in this sample. Of those, 1 are the zero ideal.

                             2
o23 = {monomialIdeal (x x , x ), monomialIdeal (), monomialIdeal(x x )}
                       1 2   3                                    2 3

o23 : List

Further information

Default value: false
Function: degStats -- statistics on the degrees of a list of objects
Option key: Verbose -- request verbose feedback

Functions with optional argument named Verbose:

check(...,Verbose=>...) -- see check -- perform tests of a package
checkDegrees(...,Verbose=>...) -- see checkDegrees -- compares the degrees of generators of two modules
copyDirectory(...,Verbose=>...) -- see copyDirectory(String,String)
copyFile(...,Verbose=>...) -- see copyFile(String,String)
bettiStats(...,Verbose=>...)
borelFixedStats(...,Verbose=>...)
CMStats(...,Verbose=>...)
degStats(...,Verbose=>...) -- optional input to request verbose feedback
dimStats(...,Verbose=>...)
idealsFromGeneratingSets(...,Verbose=>...)
mingenStats(...,Verbose=>...)
pdimStats(...,Verbose=>...)
regStats(...,Verbose=>...)
findProgram(...,Verbose=>...) -- see findProgram -- load external program
installPackage(...,Verbose=>...) -- see installPackage -- load and install a package and its documentation
isIsomorphic(...,Verbose=>...) -- see isIsomorphic -- Probabilistic test for isomorphism of modules
moveFile(...,Verbose=>...) -- see moveFile(String,String)
runProgram(...,Verbose=>...) -- see runProgram -- run an external program
symlinkDirectory(...,Verbose=>...) -- see symlinkDirectory(String,String) -- make symbolic links for all files in a directory tree

degStats(...,Verbose=>...) -- optional input to request verbose feedback

Description

Further information

See also

Functions with optional argument named Verbose: