wolfram mathematica - What does the <> symbol mean in InterpolatingFunction? -

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what <> (less followed greater than) mean in mathematica? example:

interpolatingfunction[{-6,6},{0,6}],<>[x,y]

i confused in such kind of expressions. have received such kind of output in ndsolve.

mathematica expressions come head , several arguments. example, output of operation might give output list[1,2,3,4,5]. however, mathematica knows list , output formatted {1,2,3,4,5} instead.

a function interpolation give special type of object (an interpolating function) has many components. unlike list, of components irrelevant, can ignore them. mathematica hides them using <> don't have @ them.

f = interpolation[randominteger[10, 10]] output: interpolatingfunction[{{1, 10}}, "<>"]

all shows head, interpolatingfunction, , first argument domain(s) of function. there 1 variable, there 1 domain {1,10} list of domains {{1,10}}.

all other arguments there, can find them. can evaluate f by:

f[2.3] output: 0.7385

(your output vary!) can @ pieces of f:

f[[2]] output: {4, 3, 0, {10}, {4}, 0, 0, 0, 0, automatic}

the second piece, hidden, list of different properties of interpolating function don't care about.

you can change head on many things using @@ changes header of 1 thing another. example:

mylist = {2,3,4,5}; plus@@mylist output: 14

you can our function:

list@@f output: {{{1, 10}}, {4, 3, 0, {10}, {4}, 0, 0, 0, 0, automatic},          {{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}}, {{9}, {2}, {0}, {6},           {10}, {6}, {7}, {5}, {0}, {6}}, {automatic}}

all of "guts" of interpolating function. that's what's missing in <>, because might describe interpolating function don't need see it.

if looking explicit polynomial interpolation, should doing:

interpolatingpolynomial[randominteger[10, 10], x]

which gives function of x (in non-simplified form) want.


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