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

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PDEtools[diff_table] - set up a convenient representation for a function or expression and its derivatives

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.

U:=diff_tableux,y,t:

V:=diff_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.

e1:=Uy,t+Vx,x+UxUy+U[]Ux,y

e1:=ux,y,t2yxux,y,t+xux,y,tyux,y,t+2ytux,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]ux,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

e2:=Vt+Ux+Ux,x,y+UxV[]+U[]Vx

e2:=uvx+vux+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+yxxux,y,t+tvx,y,t

(4)

See Also

DEtools, lprint, PDEtools, PDEtools[declare], Physics, Setup


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