phystricks.src.phyFunctionGraph.phyFunctionGraph Class Reference

Inheritance diagram for phystricks.src.phyFunctionGraph.phyFunctionGraph:

Collaboration diagram for phystricks.src.phyFunctionGraph.phyFunctionGraph:

Public Member Functions
def	__init__ (self, fun, mx, Mx)
def	I (self)
def	F (self)
def	parametric_curve (self)
def	visualParametricCurve (self, xunit, yunit)
def	inverse (self, y)
def	PointsNiveau (self, y)
def	roots (self)
def	derivative (self, n=1)
def	get_point (self, x, advised=True)
def	get_normal_vector (self, xx)
def	get_tangent_vector (self, x, advised=False, numerical=False)
def	get_tangent_segment (self, x)
def	tangent_phyFunction (self, x0)
def	get_normal_point (self, x, dy)
def	get_regular_points (self, mx, Mx, dx)
def	getRegularLengthPoints (self, mx, Mx, dx)
def	speed (self)
def	length (self)
def	curvature (self)
def	get_wavy_points (self, mx, Mx, dx, dy)
def	get_minmax_data (self, mx, Mx)
def	xmax (self, deb, fin)
def	xmin (self, deb, fin)
def	ymax (self, deb, fin)
def	ymin (self, deb, fin)
def	graph (self, mx, Mx)
def	fit_inside (self, xmin, xmax, ymin, ymax)
def	surface_under (self, mx=None, Mx=None)
def	cut_y (self, ymin, ymax, plotpoints=None)
def	mark_point (self, pspict=None)
def	angle (self)
def	representative_graph_object (self)
def	action_on_pspict (self, pspict)
def	latex_code (self, language=None, pspict=None)
def	__call__ (self, xe, numerical=False)
def	__pow__ (self, n)
def	__mul__ (self, other)
def	__rmul__ (self, other)
def	__add__ (self, other)
def	__sub__ (self, other)
def	__neg__ (self)
def	__str__ (self)

Public Attributes
	sage
	sageFast
	string
	fx
	tikz
	ListeSurface
	listeTests
	TesteDX
	listeExtrema
	listeExtrema_analytique
	equation
	f
	mx
	Mx
	do_cut_y
	cut_ymin
	cut_ymax
	pieces
	nul_function
	linear_plotpoints

Private Member Functions
def	_bounding_box (self, pspict=None)

Private Attributes
	_derivative
	_parametric_curve

Detailed Description

INPUT:

- ``fun`` - sage symbolic expression that is to be interpreted as
            a function of `x`.

- ``mx,Mx`` - the initial and end values of the variable.

NOTE :

The end-used has to use :func:`phyFunction` instead. The latter accepts more
types of arguments.

Constructor & Destructor Documentation

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__init__	(		self,
			fun,
			mx,
			Mx
	)

Member Function Documentation

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__add__	(		self,
			other
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__call__	(		self,
			xe,
			numerical = False
	)

return the value of the function at given point

INPUT:
- ``xe`` - a number. The point at which we want to evaluate the function
- ``numerical`` (boolean, default=False) If True, return a numerical_approximation

EXAMPLES::

    sage: from phystricks import *
    sage: x=var('x')
    sage: f=phyFunction(cos(x))
    sage: f(1)
    cos(1)
    sage: f(1,numerical=True)
    0.540302305868140

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__mul__	(		self,
			other
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__neg__

(

self

)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__pow__	(		self,
			n
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__rmul__	(		self,
			other
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__str__

(

self

)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.__sub__	(		self,
			other
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph._bounding_box (   self,   pspict = None  )

private

def phystricks.src.phyFunctionGraph.phyFunctionGraph.action_on_pspict	(		self,
			pspict
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.angle

(

self

)

For put_mark.  

def phystricks.src.phyFunctionGraph.phyFunctionGraph.curvature

(

self

)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.cut_y	(		self,
			ymin,
			ymax,
			plotpoints = None
	)

Will not draw the function bellow 'ymin' and over 'ymax'. Will neither join the pieces.

This is useful when drawing functions like 1/x.

It is wise to use a value of plotpoints that is not a multiple of the difference Mx-mx. The default behaviour is most of time like that.

If an other cut_y is already imposed, the most restrictive is used.

def phystricks.src.phyFunctionGraph.phyFunctionGraph.derivative	(		self,
			n = 1
	)

return the derivative of the function. 

INPUT:

- ``n`` - an interger (default = 1) the order of derivative. If n=0, return self.

EXAMPLES::

    sage: from phystricks import *
    sage: f=phyFunction(x**2)
    sage: print f.derivative()
    x |--> 2*x
    sage: print f.derivative()(3)
    6
    sage: g(x)=cos(x)
    sage: print [g.derivative(i) for i in range(0,5)]
    [x |--> cos(x), x |--> -sin(x), x |--> -cos(x), x |--> sin(x), x |--> cos(x)]

def phystricks.src.phyFunctionGraph.phyFunctionGraph.F

(

self

)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.fit_inside	(		self,
			xmin,
			xmax,
			ymin,
			ymax
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.get_minmax_data	(		self,
			mx,
			Mx
	)

return numerical approximations of min and max of the function on the interval

INPUT:
- ``mx,Mx`` - the interval on which we look at the extrema

OUTPUT:

dictionary conaining `xmax`, `ymax`, `xmin` and `ymin`

Notice that we are only interested in ymax and ymin.

EXAMPLES::

    sage: from phystricks import *
    sage: f=phyFunction(x)
    sage: f.get_minmax_data(-3,pi)      # random


In the case of the sine function, the min and max are almost -1 and 1::

    sage: from phystricks import *
    sage: f=phyFunction(sin(x))
    sage: f.get_minmax_data(0,2*pi)     # random

NOTE:

This function is victim of the `Trac 10246 <http://trac.sagemath.org/sage_trac/ticket/10246>` The try/except block is a workaround.

def phystricks.src.phyFunctionGraph.phyFunctionGraph.get_normal_point	(		self,
			x,
			dy
	)

return a point at distance `dy` in the normal direction of the point `(x,f(x))` 

def phystricks.src.phyFunctionGraph.phyFunctionGraph.get_normal_vector	(		self,
			xx
	)

return a normalized normal vector to the graph of the function at xx

The direction of the vector is outside

INPUT:
- ``x`` - a number, the position at which we want the normal vector

OUTPUT:
a vector

EXAMPLES:
sage: from phystricks import *
sage: x=var('x')
sage: f=phyFunction(x**2)
sage: print f.get_normal_vector(0)
<vector I=<Point(0,0)> F=<Point(0,-1)>>

def phystricks.src.phyFunctionGraph.phyFunctionGraph.get_point	(		self,
			x,
			advised = True
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.get_regular_points	(		self,
			mx,
			Mx,
			dx
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.get_tangent_segment	(		self,
			x
	)

Return a tangent segment at point (x,f(x)).

The difference with self.get_tangent_vector is that self.get_tangent_segment returns a segment that will
be symmetric. The point (x,f(x)) is the center of self.get_tangent_segment.

def phystricks.src.phyFunctionGraph.phyFunctionGraph.get_tangent_vector	(		self,
			x,
			advised = False,
			numerical = False
	)

return a tangent vector at the point (x,f(x))

def phystricks.src.phyFunctionGraph.phyFunctionGraph.get_wavy_points	(		self,
			mx,
			Mx,
			dx,
			dy
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.getRegularLengthPoints	(		self,
			mx,
			Mx,
			dx
	)

return a list of points regularly spaced (with respect to the arc length) on the graph of `self`.

INPUT:

- ``mx,Mx`` - the minimal and maximal values of `x` between we will search for points. 
- ``dx`` - the arc length between two points

OUTPUT:
A list of points
    
EXAMPLES::

    sage: from phystricks import *
    sage: f=phyFunction(x+1)
    sage: print [P.coordinates() for P in f.get_regular_points(-2,2,sqrt(2))]  # random

These are almost the points (-1,0),(0,1), and (1,2).

def phystricks.src.phyFunctionGraph.phyFunctionGraph.graph	(		self,
			mx,
			Mx
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.I

(

self

)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.inverse	(		self,
			y
	)

returns a list of values x such that f(x)=y 

def phystricks.src.phyFunctionGraph.phyFunctionGraph.latex_code	(		self,
			language = None,
			pspict = None
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.length

(

self

)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.mark_point	(		self,
			pspict = None
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.parametric_curve

(

self

)

return a parametric curve with the same graph as `self`.

def phystricks.src.phyFunctionGraph.phyFunctionGraph.PointsNiveau	(		self,
			y
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.representative_graph_object

(

self

)

Return is the object that will be drawn. It serves to control the chain 
function --> parametric_curve --> interpolation curve

def phystricks.src.phyFunctionGraph.phyFunctionGraph.roots

(

self

)

return roots of the function as a list of Points. Some can miss ! 

def phystricks.src.phyFunctionGraph.phyFunctionGraph.speed

(

self

)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.surface_under	(		self,
			mx = None,
			Mx = None
	)

Return the graph of a surface under the function.

If mx and Mx are not given, try to use self.mx and self.Mx, assuming that the method is used on
an instance of phyFunctionGraph that inherits from here.

def phystricks.src.phyFunctionGraph.phyFunctionGraph.tangent_phyFunction	(		self,
			x0
	)

Return the tangent at the given point as a :class:`phyFunction`.

INPUT:

- ``x0`` - a number

OUTPUT:

A :class:`phyFunction` that represents the tangent. This is an affine function.

EXAMPLE::

    sage: from phystricks import *
    sage: g=phyFunction(cos(x))
    sage: print g.tangent_phyFunction(pi/2)
    x |--> 1/2*pi - x
    sage: g.tangent_phyFunction(pi/2)(1)
    1/2*pi - 1

def phystricks.src.phyFunctionGraph.phyFunctionGraph.visualParametricCurve	(		self,
			xunit,
			yunit
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.xmax	(		self,
			deb,
			fin
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.xmin	(		self,
			deb,
			fin
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.ymax	(		self,
			deb,
			fin
	)

def phystricks.src.phyFunctionGraph.phyFunctionGraph.ymin	(		self,
			deb,
			fin
	)

Member Data Documentation

phystricks.src.phyFunctionGraph.phyFunctionGraph._derivative

private

phystricks.src.phyFunctionGraph.phyFunctionGraph._parametric_curve

private

phystricks.src.phyFunctionGraph.phyFunctionGraph.cut_ymax

phystricks.src.phyFunctionGraph.phyFunctionGraph.cut_ymin

phystricks.src.phyFunctionGraph.phyFunctionGraph.do_cut_y

phystricks.src.phyFunctionGraph.phyFunctionGraph.equation

phystricks.src.phyFunctionGraph.phyFunctionGraph.f

phystricks.src.phyFunctionGraph.phyFunctionGraph.fx

phystricks.src.phyFunctionGraph.phyFunctionGraph.linear_plotpoints

phystricks.src.phyFunctionGraph.phyFunctionGraph.listeExtrema

phystricks.src.phyFunctionGraph.phyFunctionGraph.listeExtrema_analytique

phystricks.src.phyFunctionGraph.phyFunctionGraph.ListeSurface

phystricks.src.phyFunctionGraph.phyFunctionGraph.listeTests

phystricks.src.phyFunctionGraph.phyFunctionGraph.mx

phystricks.src.phyFunctionGraph.phyFunctionGraph.Mx

phystricks.src.phyFunctionGraph.phyFunctionGraph.nul_function

phystricks.src.phyFunctionGraph.phyFunctionGraph.pieces

phystricks.src.phyFunctionGraph.phyFunctionGraph.sage

phystricks.src.phyFunctionGraph.phyFunctionGraph.sageFast

phystricks.src.phyFunctionGraph.phyFunctionGraph.string

phystricks.src.phyFunctionGraph.phyFunctionGraph.TesteDX

phystricks.src.phyFunctionGraph.phyFunctionGraph.tikz

---

The documentation for this class was generated from the following file:

• src/phyFunctionGraph.py