Run Sage/Python in the long-lived kernel: stdout, then the repr of the last expression (or '(no output)'). Code runs on the kernel's main thread, one job at a time, so cysignals Sage code works; state persists per session. timeout_s is NOT a computation limit: on expiry you get the partial output and a job id, and the job keeps running (collect it with poll). timeout_s=0 returns at once. A submitted job waits behind the running one ("[queued: another job is running]"); if that one holds the GIL the submit itself is refused after ~10 s ("[kernel busy ...]", the job was not submitted) -- check status or interrupt, then retry.

Collect a job started by exec. since = the offset the previous call printed (0 to start), so you get only new output. wait_s blocks until the job finishes or that many seconds pass (0 = return immediately, the default).

Empty a session's namespace but keep the session (see drop).

Free idle sessions; refuses one with a queued/running job (kept, and the job id is reported). all=true drops every idle session.

Kernel state (running / busy / not running) with pid and uptime, one line per session with its name count, active jobs, the last error, the log path.

SIGINT the running computation: the job fails with KeyboardInterrupt and the session KEEPS its state -- the first thing to try for a runaway job. Refused when the running job belongs to another MCP client; a no-op when idle: SIGINT can never kill the kernel. force=true is the last resort instead: stop the whole kernel (graceful shutdown, then SIGTERM, then SIGKILL), losing every session's variables -- for a computation that ignores SIGINT, e.g. a wedged C-level loop. The next exec starts a fresh kernel and says so; if the signal fails the state files are kept and the pid reported, so a live kernel is never orphaned.

Run a file that already exists and return its output inline: exit code, duration, stdout and stderr. Nothing is copied or stored -- the file you name is the file that runs, with cwd = its own directory. lang=auto guesses from the extension and honours a #! for executables; lang=python uses Sage's own interpreter (so from sage.all import * works) and lang=sage shells out to sage. A non-zero exit or a timeout is an error, with the output attached; the timeout kills the whole process group.