smoothed out: while Caesar is ordering, if Ceasar is giving commands
hac pugna nuntiata
as written: this battle having been announced/reported
smoothed out: when this battle had been reported, because this battle had been announced
N.B. A 'smoothed-out' clause has to fit in the sentence. Thus the tense of the verb in the clause will follow/depend on the main verb, i.e. it will be contemporaneous with or antecedent of the main verb.
There is one Ablative Absolute without a participle, which is understood as "being" (ens)
eo magistro nihil discemus - He being the teacher, we will learn nothing.
This is sometime called the Nominative Absolute in English
Henrico rege, Thoma occisus est - Henry being the king / While Henry was king / Because Henry was King, Thomas was killed.
Augusto imperatore - Augustus being the emperor/commander
This is how the Romans often date things: While Augustus was emperor... Jesus was born.
Canon Law canon 868 §2: Infans in periculo mortis licite baptizatur, etiam invitis parentibus - An infant in danger of death is lawfully baptized, even parents being unwilling / even if the parents are unwilling.