Digi Area Group - Math Tools for Professionals
   Maple and Mathematica packages - math tools for professionals

atlas™ - modern differential geometry for Maple™

> Features List & Examples
> Template Worksheets
> Screenshots
> Documentation & Downloads
> License & Pricing
> Buy Online

 
 
 
 
Google

Features List & Examples  |  Introduction  |  Dimension  |  Indexing  |  Forms  |  Metric  |  atlasWizard - Maplet™

atlas[kind] -  kind of a tensor

Calling Sequence:

     kind(T)

Parameters:

       T -any expression containing tensors, vectors, p-forms etc.

Description:

  • In the atlas  package one can declare: constants, functions, vectors, p-forms, tensors etc. Any undeclared  identifier is treated as 0-form  i.e. as non-constan scalar   (see atlas[types] ). User can construct any reasonable  expressions from declared or undeclared objects.
  • The kind  procedure finds out what kind of tensor is an expression.

Examples:
restart:
with(atlas):

Declare constants:
Constants(alpha,beta,C,lambda);

{Catalan, _Z, Pi, I, C, -I, alpha, beta, lambda}

Declare functions:
Functions(f=f(x,y),y=y(z));

{y, f}

Declare vectors:
Vectors(E[j],X,Y,Z,U[i]);

{E[j], U[i], X, Y, Z}

Declare forms:
Forms(e[j]=1,omega=2,theta=p);

{theta, e[j], omega}

Declare Tensors:
Tensors(T=[n,k]);

{T}

Let's find out the kind of some objects and expressions
kind(z);

[0, 0]

kind(omega);

[0, 2]

E[j]-f*Y;
kind(%);

E[j]-f*Y

[1, 0]

T&.d(theta);
kind(%);

`&.`(T,d(theta))

[n, 1+p+k]

d(z)&^d(x);
kind(%);

`&^`(d(z),d(x))

[0, 2]

d(z)&^d(f)+omega;
kind(%);

Diff(f,x)*`&^`(d(z),d(x))+omega

[0, 2]

Let's see "who is who"
Who();

PIECEWISE([{}, Domains],[{}, Mappings],[{T, theta, e[j], omega, E[j], U[i], X, Y, Z}, Tensors],[{theta, e[j], omega}, Forms],[{Catalan, _Z, Pi, I, C, -I, alpha, beta, lambda}, Constants],[{y, f}, Funct...

See Also:

atlas , atlas[Constants] , atlas[Functions] , atlas[Forms] , atlas[Tensors] , atlas[Who]