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PDEtools

  

diff_table

  

set up a convenient representation for a function or expression and its derivatives

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

diff_table(expr)

Parameters

expr

-

any valid Maple expression of type algebraic, typically an unknown function - say u(t)

Description

• 

The diff_table command is basically the inverse facility of PDEtools[declare]: it permits entering (input) expressions and their derivatives using compact mathematical notation without using macros or aliases. The notation implemented by diff_table is the jet notation also used by the DifferentialAlgebra package and represents a remarkable saving in redundant typing on input. diff_table also works with anticommutative variables set using the Physics package.

Examples

withPDEtools,diff_table:

Let U and V be the "differentiation tables" of ux,y,t and vx,y,t, that is, handy representations for these objects and their derivatives.

Udiff_tableux,y,t:

Vdiff_tablevx,y,t:

You can now input the functions ux,y,t or vx,y,t or any of its partial derivatives using mathematical notation directly, resulting in the expected expression on output.

e1Uy,t+Vx,x+UxUy+U[]Ux,y

e1ux,y,t2xyux,y,t+xux,y,tyux,y,t+2tyux,y,t+2x2vx,y,t

(1)

diff_table can be used simultaneously with PDEtools[declare] so that both input and output are simplified while the actual contents of the expressions generated is the standard expected one. For example, calling declare with ux,y,t,vx,y,t,

PDEtoolsdeclareux,y,t,vx,y,t

ux,y,twill now be displayed asu

vx,y,twill now be displayed asv

(2)

the output corresponding to input entered using V,U is displayed using the same mathematical notation

e2Vt+Ux+Ux,x,y+UxV[]+U[]Vx

e2uvx+uxv+ux+ux,x,y+vt

(3)

The actual contents of this expression is the expected one. (See lprint and show.)

lprint

u(x,y,t)*diff(v(x,y,t),x)+diff(u(x,y,t),x)*v(x,y,t)+diff(u(x,y,t),x)+diff(diff(diff(u(x,y,t),x),x),y)+diff(v(x,y,t),t)

show

ux,y,txvx,y,t+xux,y,tvx,y,t+xux,y,t+3yx2ux,y,t+tvx,y,t

(4)

See Also

DEtools

lprint

PDEtools

PDEtools[declare]

Physics

Setup