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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

with(PDEtools, 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.

U := diff_table(u(x,y,t)):

V := diff_table(v(x,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.

e1 := U[y,t] + V[x,x] + U[x]*U[y] + U[]*U[x,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,

PDEtools[declare](u(x,y,t), v(x,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

e2 := V[t] + U[x] + U[x,x,y] + U[x]*V[] + U[]*V[x];

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

(3)

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

lprint( (3) );

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