partition -- partition a set or list by values of a function

i1 : L = {1,3,6,5,3,1,2,8,8,8}

o1 = {1, 3, 6, 5, 3, 1, 2, 8, 8, 8}

o1 : List

i2 : partition(odd, L)

o2 = HashTable{false => {6, 2, 8, 8, 8}}
               true => {1, 3, 5, 3, 1}

o2 : HashTable

i3 : partition(odd, set L)

o3 = HashTable{false => set {8, 6, 2}}
               true => set {5, 1, 3}

o3 : HashTable

i4 : partition(odd, tally L)

o4 = HashTable{false => Tally{2 => 1}}
                              6 => 1
                              8 => 3
               true => Tally{1 => 2}
                             3 => 2
                             5 => 1

o4 : HashTable

i5 : partition (even, {3,3,5},{true,false})

o5 = HashTable{false => {3, 3, 5}}
               true => {}

o5 : HashTable

i6 : R = QQ[a..f]

o6 = R

o6 : PolynomialRing

i7 : I = ideal"ab,ade,ac3,d4,b3,adf,f4,e10"

                           3   4   3          4   10
o7 = ideal (a*b, a*d*e, a*c , d , b , a*d*f, f , e  )

o7 : Ideal of R

i8 : partition(f -> first degree f, flatten entries gens I)

o8 = HashTable{2 => {a*b}             }
                             3
               3 => {a*d*e, b , a*d*f}
                        3   4   4
               4 => {a*c , d , f }
                       10
               10 => {e  }

o8 : HashTable