/usr/share/pyshared/sympy/geometry/curve.py is in python-sympy 0.7.1.rc1-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 | """Curves in 2-dimensional Euclidean space.
Contains
--------
Curve
"""
from sympy.core import sympify, C, Symbol
from sympy.core.compatibility import is_sequence
from sympy.geometry.exceptions import GeometryError
from sympy.geometry.point import Point
from entity import GeometryEntity
from util import _symbol
class Curve(GeometryEntity):
"""A curve in space.
A curve is defined by parametric functions for the coordinates, a
parameter and the lower and upper bounds for the parameter value.
Parameters
----------
function : list of functions
limits : 3-tuple
Function parameter and lower and upper bounds.
Attributes
----------
functions
parameter
limits
Raises
------
ValueError
When `functions` are specified incorrectly.
When `limits` are specified incorrectly.
Examples
--------
>>> from sympy import sin, cos, Symbol
>>> from sympy.abc import t
>>> from sympy.geometry import Curve
>>> C = Curve((sin(t), cos(t)), (t, 0, 2))
>>> C.functions
(sin(t), cos(t))
>>> C.limits
(t, 0, 2)
>>> C.parameter
t
"""
def __new__(cls, function, limits):
fun = sympify(function)
if not is_sequence(fun) or len(fun) != 2:
raise ValueError("Function argument should be (x(t), y(t)) but got %s" % str(function))
if not is_sequence(limits) or len(limits) != 3:
raise ValueError("Limit argument should be (t, tmin, tmax) but got %s" % str(limits))
return GeometryEntity.__new__(cls, tuple(sympify(fun)), tuple(sympify(limits)))
@property
def free_symbols(self):
free = set()
for a in self.functions + self.limits[1:]:
free |= a.free_symbols
free = free.difference(set([self.parameter]))
return free
@property
def functions(self):
"""The functions specifying the curve.
Returns
-------
functions : list of parameterized coordinate functions.
Examples
--------
>>> from sympy.abc import t
>>> from sympy.geometry import Curve
>>> C = Curve((t, t**2), (t, 0, 2))
>>> C.functions
(t, t**2)
"""
return self.__getitem__(0)
@property
def parameter(self):
"""The curve function variable.
Returns
-------
parameter : sympy symbol
Examples
--------
>>> from sympy.abc import t
>>> from sympy.geometry import Curve
>>> C = Curve([t, t**2], (t, 0, 2))
>>> C.parameter
t
"""
return self.__getitem__(1)[0]
@property
def limits(self):
"""The limits for the curve.
Returns
-------
limits : tuple
Contains parameter and lower and upper limits.
Examples
--------
>>> from sympy.abc import t
>>> from sympy.geometry import Curve
>>> C = Curve([t, t**3], (t, -2, 2))
>>> C.limits
(t, -2, 2)
"""
return self.__getitem__(1)
def arbitrary_point(self, parameter='t'):
"""
A parameterized point on the curve.
Parameters
----------
parameter : str or Symbol, optional
Default value is 't';
the Curve's parameter is selected with None or self.parameter
otherwise the provided symbol is used.
Returns
-------
arbitrary_point : Point
Raises
------
ValueError
When `parameter` already appears in the functions.
See Also
--------
Point
Examples
--------
>>> from sympy import Symbol
>>> from sympy.abc import s
>>> from sympy.geometry import Curve
>>> C = Curve([2*s, s**2], (s, 0, 2))
>>> C.arbitrary_point()
Point(2*t, t**2)
>>> C.arbitrary_point(C.parameter)
Point(2*s, s**2)
>>> C.arbitrary_point(None)
Point(2*s, s**2)
>>> C.arbitrary_point(Symbol('a'))
Point(2*a, a**2)
"""
if parameter is None:
return Point(*self.functions)
tnew = _symbol(parameter, self.parameter)
t = self.parameter
if tnew.name != t.name and tnew.name in (f.name for f in self.free_symbols):
raise ValueError('Symbol %s already appears in object and cannot be used as a parameter.' % tnew.name)
return Point(*[w.subs(t, tnew) for w in self.functions])
def plot_interval(self, parameter='t'):
"""The plot interval for the default geometric plot of the curve.
Parameters
----------
parameter : str or Symbol, optional
Default value is 't';
otherwise the provided symbol is used.
Returns
-------
plot_interval : list (plot interval)
[parameter, lower_bound, upper_bound]
Examples
--------
>>> from sympy import Curve, sin
>>> from sympy.abc import x, t, s
>>> Curve((x, sin(x)), (x, 1, 2)).plot_interval()
[t, 1, 2]
>>> Curve((x, sin(x)), (x, 1, 2)).plot_interval(s)
[s, 1, 2]
"""
t = _symbol(parameter, self.parameter)
return [t] + list(self.limits[1:])
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