Follow the blog Ompy.
Operations and relations for angles and their different measures. (for now, to be developed).
are_bools(tuple_arg)
It checks if items in tuple are booleans data type.
Parameters: tuple_arg: tuple; required.
Returns: bool. True if all items are bools. False otherwise.
Examples:
>>> import ompy.ompy as op
>>> op.are_bools(True, 2, "Hello")
False
>>> op.are_bools(True, False, True)
True
to_dec_degrees(theta, from_sexagesimal=False, from_gradians=False, from_turns=False, from_radians=True)
It converts the provided angle to decimal degrees.
Parameters: theta: int, float or str; required.
Angle to convert. If provided as str, current unit has to be sexagesimal system as respective input is to be "DdMM'SS''" or
"DdMM'SS''" pattern; where D could be any digits number (under supported range), MM (whole num) and SS (could be decimal) are a 1 or 2 digit number lower than 60.
from_sexagesimal:
bool; default False.
Pass True if current unit to convert from is degrees, minutes and seconds (sexagesimal measurement system).
from_gradians:
bool; default False.
Pass True if current unit to convert from is gradians.
from_turns:
bool; default False.
Pass True if current unit to convert from is number of turns/revolutions.
from_radians:
bool; default True.
Pass True if current unit to convert from is radians.\
Returns: float; original angle now in decimal degrees.
Examples:
>>> import ompy.ompy as op
>>> op.to_dec_degrees(1.23456)
70.735077555671
>>> op.to_dec_degrees("12d34'56''", from_sexagesimal=True)
12.582222222222
>>> op.to_dec_degrees(12.3456, from_gradians=True)
11.11104
>>> op.to_dec_degrees(0.123456, from_turns=True)
44.44416
to_radians(theta, from_sexagesimal=False, from_gradians=False, from_turns=False, from_dec_degrees=True)
It converts the provided angle to radians.
Parameters: theta: int, float or str; required.
Angle to convert. If provided as str, current unit has to be sexagesimal system as
respective input is to be "DdMM'SS''" or "DdMM'SS''" pattern; where D could be any-digits number
(under supported range), MM (whole num) and SS (could be decimal) are a 1 or 2 digit number lower than 60.
from_sexagesimal:
bool; default False.
Pass True if current unit to convert from is degrees, minutes and seconds (sexagesimal measurement system).
from_gradians:
bool; default False.
Pass True if current unit to convert from is gradians.
from_turns:
bool; default False.
Pass True if current unit to convert from is number of turns/revolutions.
from_dec_degrees:
bool; default True.
Pass True if current unit to convert from is decimal degrees.
Returns: float; original angle now in radians.
Examples:
>>> import ompy.ompy as op
>>> op.to_radians(12.3456)
0.215471368134
>>> op.to_radians("12d34'56''", from_sexagesimal=True)
0.219601204995
>>> op.to_radians(12.3456, from_gradians=True)
0.193924231321
>>> op.to_radians(0.123456, from_turns=True)
0.775696925283
to_gradians(theta, from_dec_degrees=False, from_sexagesimal=False, from_turns=False, from_radians=True)
It converts the provided angle to gradians.
Parameters: theta: int, float or str; required.
Angle to convert. If provided as str, current unit has to be sexagesimal system as
respective input is to be "DdMM'SS''" or "DdMM'SS''" pattern; where D could be any-digits number
(under supported range), MM (whole num) and SS (could be decimal) are a 1 or 2 digit number lower than 60.
from_dec_degrees:
bool; default False.
Pass True if current unit to convert from is decimal degrees.
from_sexagesimal:
bool; default False.
Pass True if current unit to convert from is degrees, minutes and seconds (sexagesimal measurement system).
from_turns:
bool; default False.
Pass True if current unit to convert from is number of turns/revolutions.
from_radians:
bool; default True.
Pass True if current unit to convert from is radians.
Returns: float; original angle now in gradians.
Examples:
>>> import ompy.ompy as op
>>> op.to_gradians(1.23456)
78.594530617412
>>> op.to_gradians(12.3456, from_dec_degrees=True)
13.7173333333
>>> op.to_gradians("12d34'56''", from_sexagesimal=True)
13.98024691358
>>> op.to_gradians(0.123456, from_turns=True)
49.3824
to_turns(theta, from_dec_degrees=False, from_sexagesimal=False, from_gradians=False, from_radians=True)
It converts the provided angle to number of equivalent turns or revolutions.
Parameters: theta: int, float or str; required.
Angle to convert. If provided as str, current unit has to be sexagesimal system as
respective input is to be "DdMM'SS''" or "DdMM'SS''" pattern; where D could be any-digits number
(under supported range), MM (whole num) and SS (could be decimal) are a 1 or 2 digit number lower than 60.
from_dec_degrees:
bool; default False.
Pass True if current unit to convert from is decimal degrees.
from_sexagesimal:
bool; default False.
Pass True if current unit to convert from is degrees, minutes and seconds (sexagesimal measurement system).
from_gradians:
bool; default False.
Pass True if current unit to convert from is gradians.
from_radians:
bool; default True.
Pass True if current unit to convert from is radians.
Returns: float; original angle now in number of turns/revolutions.
Examples:
>>> import ompy.ompy as op
>>> op.to_turns(1.23456)
0.196486326544
>>> op.to_turns(12.3456, from_dec_degrees=True)
0.034293333333
>>> op.to_turns("12d34'56''", from_sexagesimal=True)
0.034950617284
>>> op.to_turns(12.3456, from_gradians=True)
0.030864
to_sexagesimal(theta, from_dec_degrees=False, from_gradians=False, from_turns=False, from_radians=True)
It converts the provided angle into the sexagesimal system, where the angle is
composed by the degrees, minutes and seconds magnitudes; following the pattern
D°MM'SS'' (D, MM, SS are the magnitudes; MM and SS are 1 or 2 digit numbers lower than 60).
Parameters: theta: int or float; required.
Angle to convert.
from_dec_degrees:
bool; default False.
Pass True if current unit to convert from is decimal degrees.
from_gradians:
bool; default False.
Pass True if current unit to convert from is gradians.
from_turns:
bool; default False.
Pass True if current unit to convert from is number of turns/revolutions.
from_radians:
bool; default True.
Pass True if current unit to convert from is radians.
Returns: Sexagesimal angle features (angle as str and its parts according to the sexagesimal system format) from the original angle.
'sexagesimal angle features', tuple-like; consisting on the following fieldnames and values:
"str_" : str; converted angle following the pattern "D°MM'SS''".
"degrees" : int; degrees section from converted angle.
"minutes" : int; minutes section from converted angle.
"seconds" : float; seconds section from converted angle.
Examples:
>>> import ompy.ompy as op
>>> op.to_sexagesimal(1.23456)
SexagesimalAngle(str_="70°44'6.279200415296''", degrees=70, minutes=44, seconds=6.279200415296)
>>> op.to_sexagesimal(1.23456).str_
"70°44'6.279200415296''"
>>> op.to_sexagesimal(1.23456).degrees
70
>>> op.to_sexagesimal(1.23456).minutes
44
>>> op.to_sexagesimal(1.23456).seconds
6.279200415296
>>> op.to_sexagesimal(12.3456, from_dec_degrees=True)
SexagesimalAngle(str_="12°20'44.16''", degrees=12, minutes=20, seconds=44.16)
>>> op.to_sexagesimal(12.3456, from_gradians=True)
SexagesimalAngle(str_="11°6'39.744''", degrees=11, minutes=6, seconds=39.744)
>>> op.to_sexagesimal(0.123456, from_turns=True)
SexagesimalAngle(str_="44°26'38.976''", degrees=44, minutes=26, seconds=38.976)
Analysis for cubic equations (for now, to be developed).
cbrt(radicand)
Calculates the real cubic root -principal value- of rational representations of real numbers.
Parameters: radicand: int, float, fractions.Fraction; required.
Number to take the root of.
Returns: float; cubic root.
Examples:
>>> import ompy.cubic as cb
>>> cb.cbrt(216)
6.0
>>> cb.cbrt(-27.0)
-3.0
>>> cb.cbrt(10)
2.154434690032
to_depressed(coef_a, coef_b, coef_c, coef_d)
Transforms a general cubic equation to a depressed cubic equation.
It takes general equation coefficients 'a', 'b', 'c', 'd' and returns depressed equation coefficients 'p', 'q'.
Parameters: coef_a: int, float; required (it cannot be 0).
coef_b: int, float; required.
coef_c: int, float; required.
coef_d: int, float; required.
Returns: tuple. [0]: coefficient 'p', [1]: coefficient 'q'.
Examples:
>>> import ompy.cubic as cb
>>> cb.to_depressed(1, -3, -3, 1)
(-6.0, -4.0)
>>> cb.to_depressed(1, 1, 1, 1)
(0.6666666666666667, 0.7407407407407407)
>>> cb.to_depressed(1, 0, 2, 3)
(2.0, 3.0)
>>> cb.to_depressed(2, 0, 0, 0)
(0.0, 0.0)
cbdelta(coef_p, coef_q, as_frac=False)
Calculates the cubic discriminant (delta) for a depressed cubic equation
Parameters: coef_p: int, float, fractions.Fraction; required. Coefficient 'p' from depressed equation.
coef_q: int, float, fractions.Fraction; required. Coefficient 'q' from depressed equation.
as_frac: bool (True or False); optional. False by default. Object type to be returned.
Returns: Cubic delta number.
fractions.Fraction object if as_frac passed as True, float otherwise.
Examples:
>>> import ompy.cubic as cb
>>> cb.cbdelta(3, 4)
20.0
>>> cb.cbdelta(-3, -2)
0.0
>>> cb.delta(5.55555, -4.44444)
-5.6495085912265
>>> cb.cbdelta(-11, 8)
Fraction(-3596, 27)
depressed_roots(coef_p, coef_q, symbolic)
For depressed cubic equations returns a tuple with its roots.
Parameters: coef_p: int, float, fractions.Fraction; required.
Coefficient 'p' from depressed equation.
coef_q: int, float, fractions.Fraction; required.
Coefficient 'q' from depressed equation.
symbolic: bool (True or False) ; optional. False by default. For requesting symbolic math output.
Returns: Equation roots.
sympy objects display; if symbolic passed as True.
tuple otherwise:
[0] : str; first root, represents a real number.
[1] : str; second root, represents a real or complex number.
[2] : str; third root, represents a real or complex number.
Examples:
>>> import ompy.cubic as cb
>>> cb.depressed_roots(-3, -2)
('2.0', '-1.0', '-1.0')
>>> cb.depressed_roots(1, 0)
('0.0', '-0.0 + 1.0i', '-0.0 - 1.0i')
>>> cb.depressed_roots(0, 1)
('-1.0', '0.5 + 0.86602540378i', '0.5 - 0.86602540378i')
>>> cb.depressed_roots(1.11111, 2.22222)
('-1.02650941551',
'0.513254707755 + 1.37891304479i',
'0.513254707755 - 1.37891304479i')
roots(coef_a, coef_b, coef_c, coef_d)
Calculates cubic general equations roots.
Parameters: coef_a: int, float, fractions.Fraction; required (it cannot be 0).
Equation coefficient 'a'.
coef_b: int, float, fractions.Fraction; required.
Equation coefficient 'b'.
coef_c: int, float, fractions.Fraction; required.
Equation coefficient 'c'.
coef_d: int, float, fractions.Fraction; required.
Equation coefficient 'd'.
symbolic: bool (True or False) ; optional. False by default. For requesting symbolic math output.
Returns: Equation roots.
sympy objects display; if symbolic passed as True.
Tuple otherwise:
[0] : str; first root, represents a real number.
[1] : str; second root, represents a real or complex number.
[2] : str; third root, represents a real or complex number.
Examples:
>>> import ompy.cubic as cb
>>> cb.roots(1, -15, 75, -125)
('5.0', '5.0', '5.0')
>>> cb.roots(2, -3, -11, 6)
('3.0', '-2.0', '0.5')
>>> cb.roots(3, 0, 0, 0)
(0.0, 0.0, 0.0)
>>> cb.roots(1, 2, 3, 4)
('-1.6506291914',
'-0.1746854043 + 1.5468688872i',
'-0.1746854043 - 1.5468688872i')
[WORK IN PROGRESS]
To cite SymPy in publications use
Meurer A, Smith CP, Paprocki M, Čertík O, Kirpichev SB, Rocklin M, Kumar A, Ivanov S, Moore JK, Singh S, Rathnayake T, Vig S, Granger BE, Muller RP, Bonazzi F, Gupta H, Vats S, Johansson F, Pedregosa F, Curry MJ, Terrel AR, Roučka Š, Saboo A, Fernando I, Kulal S, Cimrman R, Scopatz A. (2017) SymPy: symbolic computing in Python. PeerJ Computer Science 3:e103 https://doi.org/10.7717/peerj-cs.103
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