To answer your question, let's forget about も for a while. も is a particle that can replace は, and this question is actually more about the usage of は.
Consider the following conversations:
A: わたしはロボットこうがくです。 As for me, (it's) robotics. (× I am robotics.)
A: Bさんのめんせつはいつですか。 When is your (job) interview?
B: きょうです。 Today.
A: わたしはあしたです。 As for me, (it's) tomorrow. (× I am tomorrow.)
How do you go to Osaka? As for me, (by) bus. (× I am a bus.)
To understand A's statements, you have to keep in mind that は is a topic/contrast marker, not a subject marker. In Japanese, there is nothing wrong if you say わたしはコンピューターかがくです (when talking about one's major), わたしはライオンです (when talking about your favorite animal), わたしはピザです (when talking about the food you ordered), and so on. See: What's the difference between wa (は) and ga (が)?
Now, let's go back to your original example. When A's major is robotics, there are two options to say that (in contrast to B's major) without any omission:
- (1): わたしのせんこうはロボットこうがくです。
(lit. As for my major, it is robotics.)
- (2): わたしはせんこうはロボットこうがくです。
(lit. As for me, the major is robotics.)
You may be surprised to see Sentence (2) has two は's, but that's okay because the first は after わたし is used as a contrast marker. No possessive marker の is used in Sentence (2).
What if A's major is also computer science and you want to use も? Replace は with も:
- (3): わたしのせんこうもコンピューターかがくです。
(As for my major, too, it's computer science.)
- (4): わたしもせんこうはコンピューターかがくです。§
(As for me, too, the major is computer science.)
But せんこうは is redundant in the Sentence (4) and can be dropped:
- (4-2): わたしもコンピュータかがくです。
(As for me, too, computer science.)
So, in your example, no possessive particle is omitted nor implied, because there was no の in the first place!
§ （わたしは）せんこうもコンピューターかがくです is grammatically valid but means something totally different: "(Not only my hobby but) also my major is computer science."