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DifferentialGeometry[Tools]

  

DGmap

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

DGmap(n, f, X, arg1, arg2, ..., argN)

Parameters

n

-

a positive integer

f

-

a Maple procedure

X

-

any DifferentialGeometry object

argN

-

(optional) arguments for the procedure f

Description

• 

The command DGmap is similar to the command map.  DGmap will apply the procedure f to the coefficients of the object X.  The integer n indicates the position of the coefficients of X in the argument list of  f.  Thus DGmap(1, f, X, arg1, arg2, ..., argN) will replace the coefficient C of X with  f(C, arg1, arg2, ..., argN); DGmap(2, f, X, arg1, arg2, ..., argN) will replace the coefficient C of X with f(arg1, C, arg2, ..., argN); and so on.

• 

This command is part of the DifferentialGeometry:-Tools package, and so can be used in the form DGmap(...) only after executing the commands with(DifferentialGeometry) and with(Tools) in that order.  It can always be used in the long form DifferentialGeometry:-Tools:-DGmap.

Examples

withDifferentialGeometry:withTools:

 

Define a manifold M with local coordinates [x, y].

DGsetupx,y,M

frame name: M

(1)

 

Example 1. 

Define a vector field X depending on parameters C1 and C2. Differentiate the coefficients of X with respect to C1 and C2.

XevalDGC1x+C2D_x+C1yD_y

XC1x+C2D_x+C1yD_y

(2)

DGmap1,diff,X,C1

xD_x+yD_y

(3)

DGmap1,diff,X,C2

D_x

(4)

 

Example 2. 

Define a differential 1-form omega depending on a parameter t.  Integrate the coefficients of omega with respect to t from t = 0 .. 1

ωevalDGt2x2dxt3xy2dy

ωx2t2dxy2xt3dy

(5)

DGmap1,int,ω,t=0..1

x2dx3y2xdy4

(6)

 

Example 3. 

Evaluate the tensor T at x = 0 by taking the limit of the coefficients as x -> 0.

TevalDGⅇx1dx &t dxx+sin2xdy &t dyx

Tⅇx1dxxdx+sin2xdyxdy

(7)

DGmap1,limit,T,x=0

dxdx+2dydy

(8)

 

Example 4. 

Substitute s = 1 into the transformation Phi:

ΦTransformationM,M,x=sx+s1y,y=sy

Φx=sx+s1y,y=sy

(9)

DGmap2,subs,Φ,s=1

x=x,y=y

(10)
M > 

See Also

DifferentialGeometry

Tools

Transformation

 


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