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DEplot_polygon

  

generate the plot of the Newton polygon of a linear differential operator at a point

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

DEplot_polygon(L, y, (x = x0))

Parameters

L

-

linear homogeneous differential equation

y

-

unknown function to search for

x0

-

(optional) irreducible polynomial or infinity

Description

• 

The DEplot_polygon function computes a plot of the Newton polygon of a linear differential operator at the point x0. The linear differential operator L corresponds to the differential equation Ly=0.

• 

The equation Ly=0 must be homogeneous and linear in y and its derivatives, and its coefficients must be rational functions in the dependent variable x.

• 

x0 must be a rational or an algebraic number or the symbol infinity. If x0 is not passed as an argument, x0 = 0 is assumed.

• 

This function is part of the DEtools package, and so it can be used in the form DEplot_polygon(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[DEplot_polygon](..).

Examples

withDEtools:

odeⅆ4ⅆx4yxx7ⅆⅆxyxx+x7yxx9

ode:=ⅆ4ⅆx4yxx7ⅆⅆxyxx7+xyxx9

(1)

DEplot_polygonode,yx

The command to create the plot from the Plotting Guide is

DEplot_polygonode,yx,x=∞

See Also

DEtools

DEtools/newton_polygon

 


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