The right usage of the verb "elaborate"

I'm writing a paper, please can you tell me which sentence is the right?

  1. The Pseudo-code is outlined in Fig 2 and we elaborate it in the following section.

  2. The Pseudo-code is outlined in Fig 2 and we elaborate on it in the following section.


As @Andrew Leach mentions in his comment, it depends on what you want to say. Merriam-Webster online has a definition that takes account of the distinction between the transitive and intransitive forms.


The Pseudo-code is outlined in Fig 2 and we elaborate it in the following section.

I should take this to mean that in the subsequent section the Pseudo-code itself appears, fleshed out, worked out, given in full detail.


The Pseudo-code is outlined in Fig 2 and we elaborate on it in the following section.

This I should understand as meaning that in the subsequent section the Pseudo-code is explained in much greater detail.