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D.15.5.10 grpower

Procedure from library gradedModules.lib (see gradedModules_lib).

Usage:
grpower(A, p), graded object A, int p > 0

Return:
graded direct power A^p

Purpose:
compute the graded direct power A^p

Note:
the power p must be positive

Example:
 
LIB "gradedModules.lib";
ring r=32003,(x,y,z),dp;
module A = grobj( module([x+y, x, 0], [0, x+y, y]), intvec(1,1,1) );
grview(A);
==> Graded homomorphism: r(-1)^3 <- r(-2)^2, given by a matrix, with degrees: 
==>      ..1 ..2 ....
==>      --- --- +...
==>   1 :  1   - |..1
==>   1 :  1   1 |..2
==>   1 :  -   1 |..3
==>      === ===     
==>        2   2     
module B = grobj( module([x,y]), intvec(2,2) );
grview(B);
==> Graded homomorphism: r(-2)^2 <- r(-3), given by a matrix, with degrees: 
==>     .1 ...
==>     -- +..
==>  2 : 1 |.1
==>  2 : 1 |.2
==>     ==    
==>      3    
module D = grsum( grpower(A,2), grpower(B,2) );
print(D);
==> x+y,0,  0,  0,  0,0,
==> x,  x+y,0,  0,  0,0,
==> 0,  y,  0,  0,  0,0,
==> 0,  0,  x+y,0,  0,0,
==> 0,  0,  x,  x+y,0,0,
==> 0,  0,  0,  y,  0,0,
==> 0,  0,  0,  0,  x,0,
==> 0,  0,  0,  0,  y,0,
==> 0,  0,  0,  0,  0,x,
==> 0,  0,  0,  0,  0,y 
homog(D);
==> 1
grview(D);
==> Graded homomorphism: r(-1)^6 + r(-2)^4 <- r(-2)^4 + r(-3)^2, given by a m\
   atrix, with degrees: 
==>      ..1 ..2 ..3 ..4 ..5 ..6 ....
==>      --- --- --- --- --- --- +...
==>   1 :  1   -   -   -   -   - |..1
==>   1 :  1   1   -   -   -   - |..2
==>   1 :  -   1   -   -   -   - |..3
==>   1 :  -   -   1   -   -   - |..4
==>   1 :  -   -   1   1   -   - |..5
==>   1 :  -   -   -   1   -   - |..6
==>   2 :  -   -   -   -   1   - |..7
==>   2 :  -   -   -   -   1   - |..8
==>   2 :  -   -   -   -   -   1 |..9
==>   2 :  -   -   -   -   -   1 |.10
==>      === === === === === ===     
==>        2   2   2   2   3   3