Sparse polynomial

Imagine you have a toy box filled with lots of different toys. Some of the toys are big and take up a lot of space in the toy box, while others are small and don't take up much space at all.

Now imagine that instead of toys, you have math equations. Some of these equations have lots of terms and take up a lot of space, while others only have a few terms and don't take up much space at all.

When we talk about a "sparse polynomial", we're talking about one of those math equations that doesn't take up much space. It only has a few terms (like the small toys), so it doesn't have a big "footprint".

Imagine if you had to write out a really long math equation. If it's a sparse polynomial, you wouldn't have to write as much because it's not taking up a lot of space. It's like having a smaller toy box - you don't need as much room to store everything.

So, a sparse polynomial is just a math equation that doesn't have a lot of terms and doesn't take up a lot of space.