from typing import Any, Callable, Literal
from sympy import SYMPY_DEBUG
from sympy.series.order import Order

def TR0(rv):
    ...

def TR1(rv):
    ...

def TR2(rv):
    ...

def TR2i(rv, half=...):
    ...

def TR3(rv):
    ...

def TR4(rv):
    ...

def TR5(rv, max=..., pow=...):
    ...

def TR6(rv, max=..., pow=...):
    ...

def TR7(rv):
    ...

def TR8(rv, first=...):
    ...

def TR9(rv):
    ...

def TR10(rv, first=...):
    ...

def TR10i(rv):
    ...

def TR11(rv, base=...):
    ...

def TR12(rv, first=...):
    ...

def TR12i(rv):
    ...

def TR13(rv):
    ...

def TRmorrie(rv):
    ...

def TR14(rv, first=...):
    ...

def TR15(rv, max=..., pow=...):
    ...

def TR16(rv, max=..., pow=...):
    ...

def TR111(rv):
    ...

def TR22(rv, max=..., pow=...):
    ...

def TRpower(rv):
    ...

def L(rv):
    ...

if SYMPY_DEBUG:
    ...
CTR1 = ...
CTR2 = ...
CTR3 = ...
CTR4 = ...
RL1 = ...
RL2 = ...
def fu(rv, measure=...):
    ...

def process_common_addends(rv, do, key2=..., key1=...) -> Order:
    ...

fufuncs = ...
FU = ...
_ROOT2 = ...
def trig_split(a, b, two=...):
    ...

def as_f_sign_1(e) -> tuple[Any, Any, Any] | tuple[Any | Order, Any | Order, Literal[1, -1]] | None:
    ...

def hyper_as_trig(rv) -> tuple[Any, Callable[..., Any]]:
    ...

def sincos_to_sum(expr):
    ...

