Question: Who is the mother of the person under whom the government inspiring the Carolingian empire reached its greatest extent?

full_context: Document 1: Roman Republic: The extensive campaigning abroad by Roman generals, and the rewarding of soldiers with plunder on these campaigns, led to a general trend of soldiers becoming increasingly loyal to their generals rather than to the state. Rome was also plagued by several slave uprisings during this period, in part because vast tracts of land had been given over to slave farming in which the slaves greatly outnumbered their Roman masters. In the 1st century BC at least twelve civil wars and rebellions occurred. This pattern continued until 27 BC, when Octavian (later Augustus) successfully challenged the Senate's authority, and was made princeps (first citizen).
Document 2: Roman Empire: The Roman Empire (Latin: Imperium Rōmānum, Classical Latin: (ɪmˈpɛ. ri. ũː roːˈmaː. nũː); Koine and Medieval Greek: Βασιλεία τῶν Ῥωμαίων, tr. Basileia tōn Rhōmaiōn) was the post-Roman Republic period of the ancient Roman civilization, with a government headed by emperors and large territorial holdings around the Mediterranean Sea in Europe, Africa and Asia. The city of Rome was the largest city in the world c. 100 BC -- c. AD 400, with Constantinople (New Rome) becoming the largest around AD 500, and the Empire's population grew to an estimated 50 to 90 million inhabitants (roughly 20% of the world's population at the time). The 500 - year - old republic which preceded it had been severely destabilized in a series of civil wars and political conflict, during which Julius Caesar was appointed as perpetual dictator and then assassinated in 44 BC. Civil wars and executions continued, culminating in the victory of Octavian, Caesar's adopted son, over Mark Antony and Cleopatra at the Battle of Actium in 31 BC and the annexation of Egypt. Octavian's power was then unassailable and in 27 BC the Roman Senate formally granted him overarching power and the new title Augustus, effectively marking the end of the Roman Republic.
Document 3: Charlemagne: Charlemagne (/ ˈʃɑːrlɪmeɪn /) or Charles the Great (2 April 742 -- 28 January 814), numbered Charles I, was King of the Franks from 768, King of the Lombards from 774 and Emperor of the Romans from 800. He united much of Europe during the early Middle Ages. He was the first recognised emperor in western Europe since the fall of the Western Roman Empire three centuries earlier. The expanded Frankish state that Charlemagne founded is called the Carolingian Empire.
Document 4: Trajan: As a civilian administrator, Trajan is best known for his extensive public building program, which reshaped the city of Rome and left numerous enduring landmarks such as Trajan's Forum, Trajan's Market and Trajan's Column. Early in his reign, he annexed the Nabataean Kingdom, creating the province of Arabia Petraea. His conquest of Dacia enriched the empire greatly, as the new province possessed many valuable gold mines.
Document 5: Middle Ages: Charlemagne planned to continue the Frankish tradition of dividing his kingdom between all his heirs, but was unable to do so as only one son, Louis the Pious (r. 814–840), was still alive by 813. Just before Charlemagne died in 814, he crowned Louis as his successor. Louis's reign of 26 years was marked by numerous divisions of the empire among his sons and, after 829, civil wars between various alliances of father and sons over the control of various parts of the empire. Eventually, Louis recognised his eldest son Lothair I (d. 855) as emperor and gave him Italy. Louis divided the rest of the empire between Lothair and Charles the Bald (d. 877), his youngest son. Lothair took East Francia, comprising both banks of the Rhine and eastwards, leaving Charles West Francia with the empire to the west of the Rhineland and the Alps. Louis the German (d. 876), the middle child, who had been rebellious to the last, was allowed to keep Bavaria under the suzerainty of his elder brother. The division was disputed. Pepin II of Aquitaine (d. after 864), the emperor's grandson, rebelled in a contest for Aquitaine, while Louis the German tried to annex all of East Francia. Louis the Pious died in 840, with the empire still in chaos.
Document 6: Middle Ages: The importance of infantry and light cavalry began to decline during the early Carolingian period, with a growing dominance of elite heavy cavalry. The use of militia-type levies of the free population declined over the Carolingian period. Although much of the Carolingian armies were mounted, a large proportion during the early period appear to have been mounted infantry, rather than true cavalry. One exception was Anglo-Saxon England, where the armies were still composed of regional levies, known as the fyrd, which were led by the local elites. In military technology, one of the main changes was the return of the crossbow, which had been known in Roman times and reappeared as a military weapon during the last part of the Early Middle Ages. Another change was the introduction of the stirrup, which increased the effectiveness of cavalry as shock troops. A technological advance that had implications beyond the military was the horseshoe, which allowed horses to be used in rocky terrain.
Document 7: Salonia Matidia: Salonia Matidia (4 July 68 CE – 23 December 119 CE) was the daughter and only child of Ulpia Marciana and wealthy praetor Gaius Salonius Matidius Patruinus. Her maternal uncle was the Roman emperor Trajan. Trajan had no children and treated her like his daughter. Her father died in 78 CE and Matidia went with her mother to live with Trajan and his wife, Pompeia Plotina.
Document 8: Roman Republic: The Roman Republic (Latin: Res publica Romana; Classical Latin: [ˈreːs ˈpuːb.lɪ.ka roːˈmaː.na]) was the period of ancient Roman civilization beginning with the overthrow of the Roman Kingdom, traditionally dated to 509 BC, and ending in 27 BC with the establishment of the Roman Empire. It was during this period that Rome's control expanded from the city's immediate surroundings to hegemony over the entire Mediterranean world. During the first two centuries of its existence, the Roman Republic expanded through a combination of conquest and alliance, from central Italy to the entire Italian peninsula. By the following century, it included North Africa, Spain, and what is now southern France. Two centuries after that, towards the end of the 1st century BC, it included the rest of modern France, Greece, and much of the eastern Mediterranean. By this time, internal tensions led to a series of civil wars, culminating with the assassination of Julius Caesar, which led to the transition from republic to empire. The exact date of transition can be a matter of interpretation. Historians have variously proposed Julius Caesar's crossing of the Rubicon River in 49 BC, Caesar's appointment as dictator for life in 44 BC, and the defeat of Mark Antony and Cleopatra at the Battle of Actium in 31 BC. However, most use the same date as did the ancient Romans themselves, the Roman Senate's grant of extraordinary powers to Octavian and his adopting the title Augustus in 27 BC, as the defining event ending the Republic.
Document 9: Roman Empire: The imperial period of Rome lasted approximately 1,500 years compared to the 500 years of the Republican era. The first two centuries of the empire's existence were a period of unprecedented political stability and prosperity known as the Pax Romana, or ``Roman Peace ''. Following Octavian's victory, the size of the empire was dramatically increased. After the assassination of Caligula in AD 41, the Senate briefly considered restoring the republic, but the Praetorian Guard proclaimed Claudius emperor instead. Under Claudius, the empire invaded Britannia, its first major expansion since Augustus. After Claudius' successor, Nero, committed suicide in AD 68, the empire suffered a series of brief civil wars, as well as a concurrent major rebellion in Judea, during which four different legionary generals were proclaimed emperor. Vespasian emerged triumphant in AD 69, establishing the Flavian dynasty, before being succeeded by his son Titus, who opened the Colosseum shortly after the eruption of Mount Vesuvius. His short reign was followed by the long reign of his brother Domitian, who was eventually assassinated. The Senate then appointed the first of the Five Good Emperors. The empire reached its greatest extent under Trajan, the second in this line.
Document 10: 1st century: During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio - Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman emperor, and founder of the Flavian dynasty. The Roman Empire generally experienced a period of prosperity and dominance in this period and the First Century is remembered as part of the Empire's golden age.
Document 11: Roman conquest of the Iberian Peninsula: The Roman conquest of Hispania was a process by which the Roman Republic seized the Carthaginian territories in the south and east in 206 BC (during the Second Punic War) and then gradually extended control over most of the Iberian Peninsula without annexations. It was completed after the fall of the Republic (27 BC), by Augustus, the first Roman emperor, who annexed the whole of Hispania to the Roman Empire in 19 BC. Hispania was the Roman name for the Iberian Peninsula. The peninsula had various ethnic groups and a large number of tribes.
Document 12: Trajan: Marcus Ulpius Traianus was born on 18 September 53AD in the Roman province of Hispania Baetica (in what is now Andalusia in modern Spain), in the city of Italica (now in the municipal area of Santiponce, in the outskirts of Seville). Although frequently designated the first provincial emperor, and dismissed by later writers such as Cassius Dio (himself of provincial origin) as "an Iberian, and neither an Italian nor even an Italiot", Trajan appears to have hailed on his father's side from the area of Tuder (modern Todi) in Umbria, at the border with Etruria, and on his mother's side from the Gens Marcia, of an Italic family of Sabine origin. Trajan's birthplace of Italica was founded as a Roman military colony of "Italian" settlers in 206BC, though it is unknown when the Ulpii arrived there. It is possible, but cannot be substantiated, that Trajan's ancestors married local women and lost their citizenship at some point, but they certainly recovered their status when the city became a municipium with Latin citizenship in the mid-1st century BC.
Document 13: Military history of France: Under Charlemagne the Franks reached the height of their power. After campaigns against Lombards, Avars, Saxons, and Basques, the resulting Carolingian Empire stretched from the Pyrenees to Central Germany, from the North Sea to the Adriatic. In 800 the Pope made Charlemagne Emperor of the West in return for protection of the Church. The Carolingian Empire was a conscious effort to recreate a central administration modeled on that of the Roman Empire,[13] but the motivations behind military expansion differed. Charlemagne hoped to provide his nobles an incentive to fight by encouraging looting on campaign. Plunder and spoils of war were stronger temptations than imperial expansion, and several regions were invaded over and over in order to bolster the coffers of Frankish nobility.[14] Cavalry dominated the battlefields, and while the high costs associated with equipping horses and horse-riders helped limit their numbers, Carolingian armies maintained an average size of 20,000 by recruiting infantry from imperial territories near theaters of operation.[15] The Empire lasted from 800 to 843, when, following Frankish tradition, it was split between the sons of Louis the Pious by the Treaty of Verdun.
Document 14: Middle Ages: The coronation of Charlemagne as emperor on Christmas Day 800 is regarded as a turning point in medieval history, marking a return of the Western Roman Empire, since the new emperor ruled over much of the area previously controlled by the western emperors. It also marks a change in Charlemagne's relationship with the Byzantine Empire, as the assumption of the imperial title by the Carolingians asserted their equivalence to the Byzantine state. There were several differences between the newly established Carolingian Empire and both the older Western Roman Empire and the concurrent Byzantine Empire. The Frankish lands were rural in character, with only a few small cities. Most of the people were peasants settled on small farms. Little trade existed and much of that was with the British Isles and Scandinavia, in contrast to the older Roman Empire with its trading networks centred on the Mediterranean. The empire was administered by an itinerant court that travelled with the emperor, as well as approximately 300 imperial officials called counts, who administered the counties the empire had been divided into. Clergy and local bishops served as officials, as well as the imperial officials called missi dominici, who served as roving inspectors and troubleshooters.
Document 15: Roman mythology: The Aeneid and Livy's early history are the best extant sources for Rome's founding myths. Material from Greek heroic legend was grafted onto this native stock at an early date. The Trojan prince Aeneas was cast as husband of Lavinia, daughter of King Latinus, patronymical ancestor of the Latini, and therefore through a convoluted revisionist genealogy as forebear of Romulus and Remus. By extension, the Trojans were adopted as the mythical ancestors of the Roman people.
ground_truth: Marcia
sub_queries: What government was the Carolingian Empire inspired by? Answer: the Roman Empire
when did the Roman Empire reach its greatest extent Answer: under Trajan
Who is under Trajan 's mother? Answer: Marcia