How to extend "List-of-numbers-with-number" arithmetic to "List-of-X-with-X" arithmetic? [duplicate]

Question

I'll start with a couple of examples (since this is all one can get from the documentation anyway).

First, adding lists of numbers equal length is done term-by-term. E.g. {8, 2, 5} + {3, 0, 3} evaluates to {11, 2, 8}.

Second, adding a list of numbers to a single number is done by, effectively, "broadcasting" the single number into a list of the same size as that of the other addend, and then the same term-by-term addition as before is applied. For example {1, 2, 3} + 5 evaluates to {6, 7, 8}.

Conceptually, one could imagine extending this scheme to the case of adding a list L to a list-of-lists L^2. First "broadcast" L into a list of the appropriate number of copies of L, and then add the two lists-of-lists "term-by-term". For example, following this scheme, {1, 2} + {{5, 9}, {9, 7}, {1, 7}} would evaluate to {{6, 11}, {10, 9}, {2, 9}}.

To my surprise, however, Mathematica won't play along: The last sum would fail with an error beginning with Thread::tdlen: Objects of unequal length ... (The same goes for the remaining "basic operations", -, *, and /.)

What's the simplest way to carry out this proposed extension of arithmetic between a single object of type X and a List of objects of type X (assuming that arithmetic between single objects of type X is defined)?

Answer 1

Here's an alternative to Map:

{1, 2} + Transpose@{{5, 9}, {9, 7}, {1, 7}} // Transpose
(* {{6, 11}, {10, 9}, {2, 9}} *)

It can be faster than Map, too:

m = RandomInteger[{1, 9}, {10^6, 2}];

{1, 2} + Transpose@m // Transpose // AbsoluteTiming // First
(* 0.025621 *)

{1, 2} + # & /@ m // AbsoluteTiming // First
(* 0.148701 *)

Answer 2

 i@l_ := l + {1, 2}
 i /@ {{5, 9}, {9, 7}, {1, 7}}