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 allows one to declare constants.

 

• In the atlas package constants are constant 0-forms.

 

• Some constants are predefined such as Catalan, Pi, I and _Z (for RootOf procedure)

 

• The constant identifier can be either symbolic or indexed.

 

Examples: 

>	restart: with(atlas):

 

Declare some constants:  

>	Constants(lambda,alpha[1],C,c[k]);

 

(2.1)

 

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

>

kind(C);

 

(2.2)

 

>	type(C,const);

 

(2.3)

 

>	kind(c[i]);

 

(2.4)

 

>	type(c[j],const);

 

(2.5)

 

>	type(c[3],const);

 

(2.6)

 

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

 

(2.7)

 

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

>	'd(lambda)'=d(lambda);

 

(2.8)

 

Some more verifications:  

>	'd(lambda*F+alpha[1]*G-Pi*S)'=d(lambda*F+alpha[1]*G-Pi*S);

 

(2.9)

 

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

>	'd(F*G)'=d(F*G);

 

(2.10)

 

For better understanding (see atlas[Functions]):  

>	Functions(S=S(x,y),y=y(z));

 

(2.11)

 

Now S and y are functions: 

>	'd(y)'=d(y);

 

(2.12)

 

Obviously that: 

>	'd(S)'=d(S);

 

(2.13)

 

And corresponding exterior product (see atlas[`&^`]) is: 

>	'd(S)&^d(y)'=d(S)&^d(y);

 

(2.14)

 

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

(2.15)

 

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

(2.16)

 

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();

 

(2.17)

 

>

 

See Also:  

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