The function dimStats computes the average and standard deviation of the Krull dimension for a list of monomial ideals.
i1 : R=ZZ/101[a,b,c]; |
i2 : ideals = {monomialIdeal"a3,b,c2", monomialIdeal"a3,b,ac"} 3 2 3 o2 = {monomialIdeal (a , b, c ), monomialIdeal (a , b, a*c)} o2 : List |
i3 : dimStats(ideals) o3 = (.5, .5) o3 : Sequence |
The following examples use the existing functions randomMonomialSets and idealsFromGeneratingSets or randomMonomialIdeals to automatically generate a list of ideals, rather than creating the list manually:
i4 : ideals = idealsFromGeneratingSets(randomMonomialSets(4,3,1.0,3)) o4 = {monomialIdeal (x , x , x , x ), monomialIdeal (x , x , x , x ), monomialIdeal (x , x , x , x )} 1 2 3 4 1 2 3 4 1 2 3 4 o4 : List |
i5 : dimStats(ideals) o5 = (0, 0) o5 : Sequence |
i6 : ideals = randomMonomialIdeals(4,3,1.0,3) o6 = {monomialIdeal (x , x , x , x ), monomialIdeal (x , x , x , x ), monomialIdeal (x , x , x , x )} 1 2 3 4 1 2 3 4 1 2 3 4 o6 : List |
i7 : dimStats(ideals) o7 = (0, 0) o7 : Sequence |
i8 : ideals = idealsFromGeneratingSets(randomMonomialSets(3,7,0.01,10)) 4 2 4 5 5 3 2 2 5 3 2 o8 = {monomialIdeal (x , x x x , x x ), monomialIdeal(x x ), monomialIdeal (x x , x x x ), monomialIdeal (x , x x x ), 1 1 2 3 2 3 1 2 1 2 1 2 3 1 1 2 3 ---------------------------------------------------------------------------------------------------------------------------- 2 2 4 5 4 2 monomialIdeal x , monomialIdeal(x x ), monomialIdeal (), monomialIdeal(x x ), monomialIdeal (), monomialIdeal(x x x )} 2 2 3 1 2 1 2 3 o8 : List |
i9 : dimStats(ideals) o9 = (2.1, .538516) o9 : Sequence |
i10 : ideals = randomMonomialIdeals(5,7,0.05,8) 6 3 4 2 5 2 6 4 2 6 7 3 2 4 5 4 2 o10 = {monomialIdeal (x x , x x , x x , x x , x , x x , x x x , x x , x , x x , x x x , x x x , x x x , x x x , x x x , x x x , 1 2 1 2 1 2 2 3 3 1 4 1 2 4 2 4 4 1 5 1 2 5 1 2 5 1 3 5 2 4 5 3 4 5 1 4 5 --------------------------------------------------------------------------------------------------------------------------- 4 3 3 3 4 6 4 2 2 2 2 2 2 3 3 2 4 6 2 4 x x , x x , x x ), monomialIdeal (x , x , x x x , x x , x , x x , x x x , x x x , x x , x x , x x ), monomialIdeal (x x , 2 5 4 5 2 5 1 2 1 2 3 1 3 4 1 5 1 2 5 2 3 5 2 5 3 5 2 5 1 2 --------------------------------------------------------------------------------------------------------------------------- 5 2 6 5 3 4 2 4 5 6 3 2 2 2 4 3 x x x , x x , x x , x x , x x x , x x , x x x , x x , x x x , x x , x x , x x x , x x x , x x x ), monomialIdeal (x , 1 2 3 2 3 1 3 1 4 2 3 4 3 4 2 3 4 3 4 1 2 5 2 5 3 5 2 4 5 2 4 5 2 4 5 2 --------------------------------------------------------------------------------------------------------------------------- 2 2 2 2 6 3 4 5 6 2 2 4 4 x x x , x x , x x , x , x x x , x x , x x x x , x x x , x x , x ), monomialIdeal (x x , x x , x , x x x , x x , x x ), 1 2 3 2 3 1 3 4 1 2 5 3 5 2 3 4 5 3 4 5 3 5 5 1 3 2 3 4 1 2 5 2 5 3 5 --------------------------------------------------------------------------------------------------------------------------- 2 5 2 3 3 6 2 4 3 5 2 2 2 2 3 2 monomialIdeal (x x , x x , x x x , x x x , x , x x , x x x x , x x x x x , x x x , x x x , x x x , x x x x x , x x x x , 1 3 1 4 2 3 4 1 3 4 4 2 5 1 2 4 5 1 2 3 4 5 3 4 5 1 4 5 3 4 5 1 2 3 4 5 2 3 4 5 --------------------------------------------------------------------------------------------------------------------------- 3 2 3 4 3 5 6 2 2 5 5 2 4 3 2 3 3 2 4 2 2 2 4 2 3 x x , x x x , x x , x x x ), monomialIdeal (x , x x , x x , x x , x x , x x x , x x x x , x x x , x x , x x , x x , x x x , 3 5 1 4 5 4 5 2 4 5 1 1 2 1 2 1 3 1 3 1 2 3 1 2 3 4 1 3 4 1 4 2 4 3 4 1 3 4 --------------------------------------------------------------------------------------------------------------------------- 3 3 2 3 3 4 2 5 2 2 4 3 3 3 4 3 4 6 3 2 x x , x x x x , x x , x x x x , x x x x , x x , x x , x x , x x , x x x , x x ), monomialIdeal (x x , x , x x , x x , x x , 3 4 1 2 3 5 3 5 1 3 4 5 2 3 4 5 4 5 1 5 4 5 2 5 1 3 5 2 5 1 2 2 1 3 2 3 2 4 --------------------------------------------------------------------------------------------------------------------------- 2 3 2 3 2 4 6 3 3 2 x x x , x x x , x x , x x , x x , x x x , x )} 2 3 4 2 3 4 2 4 2 4 1 5 3 4 5 5 o10 : List |
i11 : dimStats(ideals) o11 = (1.625, .484123) o11 : Sequence |
i12 : ideals = idealsFromGeneratingSets(randomMonomialSets(5,7,1,10)) 3 2 2 2 2 3 3 3 o12 = {monomialIdeal(x x x x ), monomialIdeal(x x x ), monomialIdeal(x x x x ), monomialIdeal(x x x ), monomialIdeal x , 1 2 3 5 2 3 5 1 3 4 5 1 2 5 3 --------------------------------------------------------------------------------------------------------------------------- 3 2 3 2 3 3 2 2 3 4 monomialIdeal(x x x x ), monomialIdeal(x x x x ), monomialIdeal(x x ), monomialIdeal(x x x ), monomialIdeal(x x )} 2 3 4 5 1 2 3 5 1 3 2 3 4 1 4 o12 : List |
i13 : dimStats(ideals) o13 = (4, 0) o13 : Sequence |
The object dimStats is a method function with options.