atlas[Constants] - declaration of constants

Calling Sequence:

     Constants(C1, C2, ..., Ci, ... , Cn)

Parameters:

      C1, C2, ..., Ci, ... , Cn  - constants identifiers

Description:

• In the atlas  package any identifier is treated as 0-form  i.e. as non-constant scalar  (if it not declared as constant, p-form, tensor etc. (see atlas[types] )).
• The Constants  procedure declares constants.
• In the atlas  package constants are constant 0-forms.
• Some constants are predefined such as Catalan, Pi, I  and _Z  (for RootOf  procedure)
• Constant identifier can be symbol or indexed either.

Examples:
restart:
with(atlas):

Declare some constants:
Constants(lambda,alpha[1],C,c[k]);

Verify that C and c[k]  are constants using kind (see atlas[kind] ) and type procedures:
kind(C);

type(C,const);

kind(c[i]);

type(c[j],const);

type(c[3],const);

'd(Sum(c[i]*x[i],i=1..n))'=d(Sum(c[i]*x[i],i=1..n));

Verify that lambda is a constant using exterior derivative operator (see atlas[d] ):
'd(lambda)'=d(lambda);

Some more verifications:
'd(lambda*F+alpha[1]*G-Pi*S)'=d(lambda*F+alpha[1]*G-Pi*S);

As F, G, S was not declared as something thus they are nonconstant scalars (0-forms) by defaults:
'd(F*G)'=d(F*G);

For better understanding (see atlas[Functions] ):
Functions(S=S(x,y),y=y(z));

Now S and y are functions:
'd(y)'=d(y);

Obviously that:
'd(S)'=d(S);

And corresponding exterior product (see atlas[`&^`] ) is:
'd(S)&^d(y)'=d(S)&^d(y);

As n is 0-form   (just as x) then:  
'd(x^n)'=d(x^n);

 declared as a constant thus:
'd(x^lambda)'=d(x^lambda);

Let's see "who is who"
Who([S,F,lambda,x,y]);

S: function



F: 0 - form



lambda: constant



x: 0 - form

y: function


Who();

See Also:

atlas , atlas[Functions] , atlas[Forms] , atlas[Vectors] , atlas[Tensors] , atlas[d] , atlas[`&^`] , atlas[Who] .