Apply

f @ expr

returns f(expr)

Apply(f, expr)

f @@ expr

replaces the head of expr with f.

Apply(f, expr, levelspec)

applies f on the parts specified by levelspec.

Examples

>> f @@ {1, 2, 3}
f(1, 2, 3)
>> Plus @@ {1, 2, 3}
6

The head of expr need not be List:

>> f @@ (a + b + c)
f(a, b, c)

Apply on level 1:

>> Apply(f, {a + b, g(c, d, e * f), 3}, {1})
{f(a, b), f(c, d, e*f), 3}

The default level is 0:

>> Apply(f, {a, b, c}, {0})
f(a, b, c)

Range of levels, including negative level (counting from bottom):

>> Apply(f, {{{{{a}}}}}, {2, -3})
{{f(f({a}))}}

Convert all operations to lists:

>> Apply(List, a + b * c ^ e * f(g), {0, Infinity})
{a,{b,{c,e},{g}}}

Level specification x + y is not of the form n, {n}, or {m, n}.

>> Apply(f, {a, b, c}, x+y)
Apply(f, {a, b, c}, x + y)

The A001597 Perfect powers: m^k where m > 0 and k >= 2

>> $min = 0; $max = 10^4; Union@ Flatten@ Table( n^expo, {expo, Prime@ Range@ PrimePi@ Log2@ $max}, {n, Floor(1 + $min^(1/expo)), $max^(1/expo)})
{1,4,8,9,16,25,27,32,36,49,64,81,100,121,125,128,144,169,196,216,225,243,256,289,"324,343,361,400,441,484,512,529,576,625,676,729,784,841,900,961,1000,1024,1089,1156,1225,1296,1331,1369,1444,1521,1600,1681,1728,1764,1849,1936,2025,2048,2116,2187,2197,2209,2304,2401,2500,2601,2704,2744,2809,2916,3025,3125,3136,3249,3364,3375,3481,3600,3721,3844,3969,4096,4225,4356,4489,4624,4761,4900,4913,5041,5184, "5329,5476,5625,5776,5832,5929,6084,6241,6400,6561,6724,6859,6889,7056,7225,7396,7569,7744,7776,7921,8000,8100,8192,8281,8464,8649,8836,9025,9216,9261,9409,9604,9801,10000}

Implementation status

• ✅ - full supported

Github

• Implementation of Apply