Add a way to get a simpler invocation of pip

This makes it possible to provide more terse suggestions that are still
correct, depending on the user's environment.

src/pip/_internal/utils/entrypoints.py

@@ -1,7 +1,23 @@
+import itertools
+import os
+import shutil
 import sys
 from typing import List, Optional
 
 from pip._internal.cli.main import main
+from pip._internal.utils.compat import WINDOWS
+
+_EXECUTABLE_NAMES = [
+    "pip",
+    f"pip{sys.version_info.major}",
+    f"pip{sys.version_info.major}.{sys.version_info.minor}",
+]
+if WINDOWS:
+    _allowed_extensions = {"", ".exe", ".EXE"}
+    _EXECUTABLE_NAMES = [
+        "".join(parts)
+        for parts in itertools.product(_EXECUTABLE_NAMES, _allowed_extensions)
+    ]
 
 
 def _wrapper(args: Optional[List[str]] = None) -> int:
@@ -25,3 +41,34 @@ def _wrapper(args: Optional[List[str]] = None) -> int:
         "running pip directly.\n"
     )
     return main(args)
+
+
+def get_best_invocation_for_this_pip() -> str:
+    """Try to figure out the best way to invoke pip in the current environment."""
+    binary_directory = "Scripts" if WINDOWS else "bin"
+    binary_prefix = os.path.join(sys.prefix, binary_directory)
+
+    # Try to use pip[X[.Y]] names, if those executables for this environment are
+    # the first on PATH with that name.
+    exe_are_in_PATH = binary_prefix in os.environ.get("PATH", "").split(os.pathsep)
+    if exe_are_in_PATH:
+        for exe_name in _EXECUTABLE_NAMES:
+            if shutil.which(exe_name) == os.path.join(binary_prefix, exe_name):
+                return exe_name
+
+    # Use the `-m` invocation, if there's no "nice" invocation.
+    return f"{get_best_invocation_for_this_python()} -m pip"
+
+
+def get_best_invocation_for_this_python() -> str:
+    """Try to figure out the best way to invoke the current Python."""
+    exe = sys.executable
+    exe_name = os.path.basename(exe)
+
+    # Try to use the basename, if it's the first executable.
+    found_executable = shutil.which(exe_name)
+    if found_executable and os.path.samefile(found_executable, exe):
+        return exe_name
+
+    # Use the full executable name, because we couldn't find something simpler.
+    return exe