include(`../prg/largenum.txt'):
include(`../prg/factorial.txt'):

func(tayeul,{sub({let(a,[x]):let(b,[y]):let(c,[z]):
  print_largetrim((for(<k,0,[b],1>,{
    (((largepow([a],[k]))(zeros([b])))
    [l/]
    (largefac([k]))) [l+]
  })0),[c])
})}):

func(taycos,{sub({let(a,[x]):let(b,[y]):let(c,[z]):
  print_largetrim((for(<k,0,[b],2>,{
    (((largepow([a],[k]))(zeros([b])))
    [l/]
    (largefac([k]))) (iff([k]%2,{[l+]},{[l-]}))
  })0),[c])
})}):

func(taysin,{sub({let(a,[x]):let(b,[y]):let(c,[z]):
  print_largetrim((for(<k,1,[b],2>,{
    (((largepow([a],[k]))(zeros([b])))
    [l/]
    (largefac([k]))) (iff([k]%2,{[l-]},{[l+]}))
  })0),[c])
})}):

func(taycosh,{sub({let(a,[x]):let(b,[y]):let(c,[z]):
  print_largetrim((for(<k,0,[b],2>,{
    (((largepow([a],[k]))(zeros([b])))
    [l/]
    (largefac([k]))) [l+]
  })0),[c])
})}):

func(taysinh,{sub({let(a,[x]):let(b,[y]):let(c,[z]):
  print_largetrim((for(<k,1,[b],2>,{
    (((largepow([a],[k]))(zeros([b])))
    [l/]
    (largefac([k]))) [l+]
  })0),[c])
})}):

func(tayatanh,{sub({let(a,[x]):let(b,[y]):let(c,[z]):
  print_largetrim((for(<k,1,[b],2>,{
    (((largepow([a],[k]))(zeros([b])))
    [l/]
    ([k])) [l+]
  })0),[c])
})}):

func(tayln,{sub({let(a,[x]):let(b,[y]):let(c,[z]):
  let(p,([a]-1)[l/]([a]+1)):
  print_largetrim(largemul(2,tayatanh([p],[b],[c])),[c])
})}):

print_`taylor.txt',: