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D.15.6.10 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
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