class_docstr: 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 Curve, sin, cos, interpolate
  >>> from sympy.abc import t, a
  >>> C = Curve((sin(t), cos(t)), (t, 0, 2))
  >>> C.functions
  (sin(t), cos(t))
  >>> C.limits
  (t, 0, 2)
  >>> C.parameter
  t
  >>> C = Curve((t, interpolate([1, 4, 9, 16], t)), (t, 0, 1)); C
  Curve((t, t**2), (t, 0, 1))
  >>> C.subs(t, 4)
  Point2D(4, 16)
  >>> C.arbitrary_point(a)
  Point2D(a, a**2)
  
  See Also
  ========
  
  sympy.core.function.Function
  sympy.polys.polyfuncs.interpolate
class_docstr_tok: ["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","Curve",",","sin",",","cos",",","interpolate",">",">",">","from","sympy.abc","import","t",",","a",">",">",">","C","=","Curve","(","(","sin","(","t",")",",","cos","(","t",")",")",",","(","t",",","0",",","2",")",")",">",">",">","C.functions","(","sin","(","t",")",",","cos","(","t",")",")",">",">",">","C.limits","(","t",",","0",",","2",")",">",">",">","C.parameter","t",">",">",">","C","=","Curve","(","(","t",",","interpolate","(","[","1",",","4",",","9",",","16","]",",","t",")",")",",","(","t",",","0",",","1",")",")",";","C","Curve","(","(","t",",","t","*","*","2",")",",","(","t",",","0",",","1",")",")",">",">",">","C.subs","(","t",",","4",")","Point2D","(","4",",","16",")",">",">",">","C.arbitrary_point","(","a",")","Point2D","(","a",",","a","*","*","2",")","See","Also","========","sympy.core.function.Function","sympy.polys.polyfuncs.interpolate"]
docstr: Override GeometryEntity.scale since Curve is not made up of Points.
  
  Returns
  =======
  
  Curve :
      returns scaled curve.
  
  Examples
  ========
  
  >>> from sympy import Curve
  >>> from sympy.abc import x
  >>> Curve((x, x), (x, 0, 1)).scale(2)
  Curve((2*x, x), (x, 0, 1))
docstr_tok: ["Override","GeometryEntity.scale","since","Curve","is","not","made","up","of","Points",".","Returns","=======","Curve",":","returns","scaled","curve",".","Examples","========",">",">",">","from","sympy","import","Curve",">",">",">","from","sympy.abc","import","x",">",">",">","Curve","(","(","x",",","x",")",",","(","x",",","0",",","1",")",")",".scale","(","2",")","Curve","(","(","2","*","x",",","x",")",",","(","x",",","0",",","1",")",")"]
code: def scale(self, x=1, y=1, pt=None):
      """Override GeometryEntity.scale since Curve is not made up of Points.
  
      Returns
      =======
  
      Curve :
          returns scaled curve.
  
      Examples
      ========
  
      >>> from sympy import Curve
      >>> from sympy.abc import x
      >>> Curve((x, x), (x, 0, 1)).scale(2)
      Curve((2*x, x), (x, 0, 1))
  
      """
      if pt:
          pt = Point(pt, dim=2)
          return (
              self.translate(*(-pt).args)
              .scale(x, y)
              .translate(*pt.args)
          )
      fx, fy = self.functions
      return self.func((fx * x, fy * y), self.limits)
  
imports: from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.core import diff
  from sympy.core.containers import Tuple
  from sympy.core.symbol import _symbol
  from sympy.geometry.entity import GeometryEntity, GeometrySet
  from sympy.geometry.point import Point
  from sympy.integrals import integrate
  from sympy.matrices import Matrix, rot_axis3
  from sympy.utilities.iterables import is_sequence
  from mpmath.libmp.libmpf import prec_to_dps
label_desc: Use image node_id 14 for calling the Curve obj's underlying member method code with example usage: obj.scale(x, y, pt) and returns: self, self