New Manhattan District Attorney Alvin Bragg has ordered prosecutors to stop pursuing prison sentences for many criminal cases, in a shake up of how his office will address some crimes, with just days on the job. Bragg’s office will “not seek a carceral sentence” except in cases of homicide, domestic violence felonies, public corruption, and some sex crimes, according to memo titled “Achieving Fairness and Safety” that Bragg sent to staff on Monday. “This rule may be excepted only in extraordinary circumstances based on a holistic analysis of the facts, criminal history, victim’s input (particularly in cases of violence or trauma), and any other information available,” the memo from Bragg, a Democrat, read. Prosecutors must also now consider the “impacts of incarceration,” Bragg ordered, noting that it must be taken into account whether prison terms do increase public safety, if convicts will face future barriers in housing and employment, cost …