prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  SlashCommand Groups Issues
  This issue is to keep track of the issues since we reworked groups.
  
  </issue>
  <code>
  [start of examples/app_commands/slash_groups.py]
  1 import discord
  2 
  3 bot = discord.Bot()
  4 
  5 # If you use commands.Bot, @bot.slash_command should be used for
  6 # slash commands. You can use @bot.slash_command with discord.Bot as well
  7 
  8 math = bot.command_group(
  9     "math", "Commands related to mathematics."
  10 )  # create a slash command group
  11 
  12 
  13 @math.command(guild_ids=[...])  # create a slash command
  14 async def add(ctx, num1: int, num2: int):
  15     """Get the sum of 2 integers."""
  16     await ctx.respond(f"The sum of these numbers is **{num1+num2}**")
  17 
  18 
  19 # another way, creating the class manually
  20 
  21 from discord.commands import SlashCommandGroup
  22 
  23 math = SlashCommandGroup("math", "Commands related to mathematics.")
  24 
  25 
  26 @math.command(guild_ids=[...])
  27 async def add(ctx, num1: int, num2: int):
  28     ...
  29 
  30 
  31 bot.add_application_command(math)
  32 
  33 bot.run("TOKEN")
  34
  [end of examples/app_commands/slash_groups.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/examples/app_commands/slash_groups.py b/examples/app_commands/slash_groups.py
  --- a/examples/app_commands/slash_groups.py
  +++ b/examples/app_commands/slash_groups.py
  @@ -5,7 +5,7 @@
   # If you use commands.Bot, @bot.slash_command should be used for
   # slash commands. You can use @bot.slash_command with discord.Bot as well
   
  -math = bot.command_group(
  +math = bot.create_group(
       "math", "Commands related to mathematics."
   )  # create a slash command group
  
verification_info: {"golden_diff": "diff --git a/examples/app_commands/slash_groups.py b/examples/app_commands/slash_groups.py\n--- a/examples/app_commands/slash_groups.py\n+++ b/examples/app_commands/slash_groups.py\n@@ -5,7 +5,7 @@\n # If you use commands.Bot, @bot.slash_command should be used for\r\n # slash commands. You can use @bot.slash_command with discord.Bot as well\r\n \r\n-math = bot.command_group(\r\n+math = bot.create_group(\r\n     \"math\", \"Commands related to mathematics.\"\r\n )  # create a slash command group\n", "issue": "SlashCommand Groups Issues\nThis issue is to keep track of the issues since we reworked groups.\n", "before_files": [{"content": "import discord\r\n\r\nbot = discord.Bot()\r\n\r\n# If you use commands.Bot, @bot.slash_command should be used for\r\n# slash commands. You can use @bot.slash_command with discord.Bot as well\r\n\r\nmath = bot.command_group(\r\n    \"math\", \"Commands related to mathematics.\"\r\n)  # create a slash command group\r\n\r\n\r\n@math.command(guild_ids=[...])  # create a slash command\r\nasync def add(ctx, num1: int, num2: int):\r\n    \"\"\"Get the sum of 2 integers.\"\"\"\r\n    await ctx.respond(f\"The sum of these numbers is **{num1+num2}**\")\r\n\r\n\r\n# another way, creating the class manually\r\n\r\nfrom discord.commands import SlashCommandGroup\r\n\r\nmath = SlashCommandGroup(\"math\", \"Commands related to mathematics.\")\r\n\r\n\r\n@math.command(guild_ids=[...])\r\nasync def add(ctx, num1: int, num2: int):\r\n    ...\r\n\r\n\r\nbot.add_application_command(math)\r\n\r\nbot.run(\"TOKEN\")\r\n", "path": "examples/app_commands/slash_groups.py"}]}