Level

Level(expr, levelspec)

gives a list of all sub-expressions of expr at the level(s) specified by levelspec.

Level uses standard level specifications:

n

levels 1 through n

Infinity

all levels from level 1

{n}

level n only

{m, n}

levels m through n

Level 0 corresponds to the whole expression. A negative level -n consists of parts with depth n.

Examples

Level -1 is the set of atoms in an expression:

>> Level(a + b ^ 3 * f(2 x ^ 2), {-1})
{a,b,3,2,x,2}

>> Level({{{{a}}}}, 3)
{{a},{{a}},{{{a}}}}

>> Level({{{{a}}}}, -4)
{{{{a}}}}

>> Level({{{{a}}}}, -5)
{}

>> Level(h0(h1(h2(h3(a)))), {0, -1})
{a,h3(a),h2(h3(a)),h1(h2(h3(a))),h0(h1(h2(h3(a))))}

Use the option Heads -> True to include heads:

>> Level({{{{a}}}}, 3, Heads -> True)
{List,List,List,{a},{{a}},{{{a}}}}

>> Level(x^2 + y^3, 3, Heads -> True)
{Plus,Power,x,2,x^2,Power,y,3,y^3}

>> Level(a ^ 2 + 2 * b, {-1}, Heads -> True)
{Plus,Power,a,2,Times,2,b}

>> Level(f(g(h))[x], {-1}, Heads -> True)
{f,g,h,x}

>> Level(f(g(h))[x], {-2, -1}, Heads -> True)
{f,g,h,g(h),x,f(g(h))[x]}

Implementation status

• ✅ - full supported

Github

• Implementation of Level