Learn French: Pensez-vous que l'algorithme puisse calculer ça ? - Do you think that the algorithm can calculate that?

In affirmative sentences, verbs of opinion like penser and croire take the indicative because they express a certainty or strong belief (like Je pense qu'il peut). However, when you use them in a question or a negative sentence, you are introducing doubt. This doubt triggers the subjunctive, which is why we use puisse here.

What verb is puisse from, and why does it look so different?

It comes from pouvoir (to be able to). Pouvoir is highly irregular in the subjunctive. Instead of using a normal present tense stem, it uses the special stem puiss- for all its subjunctive forms. Since l'algorithme is singular (it), we add the standard -e ending to get puisse.

Would we still use the subjunctive if we asked the question without inversion?

Yes, if you use Est-ce que vous pensez que, the subjunctive is still perfectly correct because it is still a question introducing doubt. However, in casual spoken French using just voice intonation (Vous pensez que l'algorithme peut... ?), French speakers often just use the indicative.

The sentence starts formally with Pensez-vous but ends with the short word ça. Is it normal to mix them?