7777}
7878
7979
80- def objects (object_list : tuple , jd : float , lat : float = None , lon : float = None , house_system : int = None , part_formula : int = None ) -> dict :
80+ def objects (object_list : tuple , jd : float , lat : float | None = None , lon : float | None = None , house_system : int | None = None , part_formula : int | None = None ) -> dict :
8181 """ Helper function returns a dict of all passed chart objects. """
8282 return _objects (
8383 object_list = object_list ,
@@ -91,7 +91,7 @@ def objects(object_list: tuple, jd: float, lat: float = None, lon: float = None,
9191 )
9292
9393
94- def armc_objects (object_list : tuple , jd : float , armc : float , lat : float = None , lon : float = None , obliquity : float = None , house_system : int = None , part_formula : int = None ) -> dict :
94+ def armc_objects (object_list : tuple , jd : float , armc : float , lat : float | None = None , lon : float | None = None , obliquity : float | None = None , house_system : int | None = None , part_formula : int | None = None ) -> dict :
9595 """ Helper function returns a dict of all passed chart objects
9696 with points & angles calculated from the passed ARMC. """
9797 return _objects (
@@ -106,7 +106,7 @@ def armc_objects(object_list: tuple, jd: float, armc: float, lat: float = None,
106106 )
107107
108108
109- def get (index : int | str , jd : float , lat : float = None , lon : float = None , house_system : int = None , part_formula : int = None ) -> dict :
109+ def get (index : int | str , jd : float , lat : float | None = None , lon : float | None = None , house_system : int | None = None , part_formula : int | None = None ) -> dict :
110110 """ Helper function to retrieve an angle, house, planet, point,
111111 asteroid, or fixed star. """
112112 return _get (
@@ -121,7 +121,7 @@ def get(index: int | str, jd: float, lat: float = None, lon: float = None, house
121121 )
122122
123123
124- def armc_get (index : int | str , jd : float , armc : float , lat : float = None , lon : float = None , obliquity : float = None , house_system : int = None , part_formula : int = None ) -> dict :
124+ def armc_get (index : int | str , jd : float , armc : float , lat : float | None = None , lon : float | None = None , obliquity : float | None = None , house_system : int | None = None , part_formula : int | None = None ) -> dict :
125125 """ Helper function to retrieve an angle, house, planet, point,
126126 asteroid, or fixed star with houses & angles calculated from the
127127 passed ARMC. """
@@ -245,7 +245,7 @@ def armc_house(index: int, armc: float, lat: float, obliquity: float, house_syst
245245 )
246246
247247
248- def point (index : int , jd : float , lat : float = None , lon : float = None , house_system : int = None , part_formula : int = None ) -> dict :
248+ def point (index : int , jd : float , lat : float | None = None , lon : float | None = None , house_system : int | None = None , part_formula : int | None = None ) -> dict :
249249 """ Returns a calculated point by Julian date, and additionally by lat / lon
250250 coordinates. """
251251 return _point (
@@ -260,7 +260,7 @@ def point(index: int, jd: float, lat: float = None, lon: float = None, house_sys
260260 )
261261
262262
263- def armc_point (index : int , jd : float , armc : float , lat : float , obliquity : float , house_system : int = None , part_formula : int = None ) -> dict :
263+ def armc_point (index : int , jd : float , armc : float , lat : float , obliquity : float , house_system : int | None = None , part_formula : int | None = None ) -> dict :
264264 """ Returns a calculated point by Julian date, and additionally by the
265265 passed ARMC. """
266266 return _point (
@@ -521,7 +521,7 @@ def _is_daytime(jd: float, lat: float, lon: float, armc: float, armc_obliquity:
521521
522522
523523@cache
524- def _angles_houses_vertex (jd : float , lat : float , lon : float , house_system : int , first_house_lon : float = None ) -> dict :
524+ def _angles_houses_vertex (jd : float , lat : float , lon : float , house_system : int , first_house_lon : float | None = None ) -> dict :
525525 """ Returns ecliptic longitudes for the houses, main angles, and the vertex,
526526 along with their speeds. Defaults to Placidus for main angles & vertex if
527527 an PLANET_ON_FIRST house system is chosen. Based on Julian date and
@@ -530,7 +530,7 @@ def _angles_houses_vertex(jd: float, lat: float, lon: float, house_system: int,
530530
531531
532532@cache
533- def _angles_houses_vertex_armc (armc : float , lat : float , obliquity : float , house_system : int , first_house_lon : float = None ) -> dict :
533+ def _angles_houses_vertex_armc (armc : float , lat : float , obliquity : float , house_system : int , first_house_lon : float | None = None ) -> dict :
534534 """ Returns ecliptic longitudes for the houses, main angles, and the vertex,
535535 along with their speeds. Defaults to Placidus for main angles & vertex if
536536 an PLANET_ON_FIRST house system is chosen. Based on ARMC, latitude and
@@ -637,7 +637,7 @@ def _syzygy(jd: float) -> dict:
637637
638638
639639@cache
640- def _part (index : int , jd : float , lat : float , lon : float , formula : int , armc : float = None , armc_obliquity : float = None ) -> dict :
640+ def _part (index : int , jd : float , lat : float , lon : float , formula : int , armc : float | None = None , armc_obliquity : float | None = None ) -> dict :
641641 """ Calculates Parts of Fortune, Spirit, and Eros. """
642642 sun = planet (chart .SUN , jd )
643643 moon = planet (chart .MOON , jd )
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