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D.15.6.11 grtranspose
Procedure from library gradedModules.lib (see gradedModules_lib).
- Usage:
- grtranspose(M), graded object M
- Return:
- graded object
- Purpose:
- graded transpose of M
- Note:
- no reordering is performend by this procedure
Example:
| LIB "gradedModules.lib";
ring r=32003,(x,y,z),dp;
module M = grtwists( intvec(-2, 0, 4, 4) ); grview(M);
==> Graded homomorphism: r(-2) + r + r(4)^2 <- 0, given by zero (4 x 0) matri\
x.
module N = grsyz( grtranspose( M ) ); grview(N);
==> Graded homomorphism: r(2) + r + r(-4)^2 <- r(2) + r + r(-4)^2, given by a\
diagonal matrix, with degrees:
==> ..1 ..2 ..3 ..4 ....
==> --- --- --- --- +...
==> -2 : 0 - - - |..1
==> 0 : - 0 - - |..2
==> 4 : - - 0 - |..3
==> 4 : - - - 0 |..4
==> === === === ===
==> -2 0 4 4
module L = grtranspose(N); grview( L );
==> Graded homomorphism: r(-2) + r + r(4)^2 <- r(-2) + r + r(4)^2, given by a\
diagonal matrix, with degrees:
==> ..1 ..2 ..3 ..4 ....
==> --- --- --- --- +...
==> 2 : 0 - - - |..1
==> 0 : - 0 - - |..2
==> -4 : - - 0 - |..3
==> -4 : - - - 0 |..4
==> === === === ===
==> 2 0 -4 -4
module K = grsyz( L ); grview(K);
==> Graded homomorphism: r(-2) + r + r(4)^2 <- 0, given by zero (4 x 0) matri\
x.
// Corner cases: 0 <- 0!
module Z = grzero(); grview(Z);
==> Graded homomorphism: 0 <- 0, given by zero (0^2) matrix.
grview( grtranspose( Z ) );
==> Graded homomorphism: 0 <- 0, given by zero (0^2) matrix.
// Corner cases: * <- 0
matrix M1[3][0];
module Z1 = grobj( M1, intvec(-1, 0, 1) ); grview(Z1);
==> Graded homomorphism: r(1) + r + r(-1) <- 0, given by zero (3 x 0) matrix.
grview( grtranspose( Z1 ) );
==> Graded homomorphism: 0 <- r(-1) + r + r(1), given by zero (0 x 3) matrix.
// Corner cases: 0 <- *
matrix M2[0][3];
module Z2 = grobj( M2, 0:0, intvec(-1, 0, 1) ); grview(Z2);
==> Graded homomorphism: 0 <- r(1) + r + r(-1), given by zero (0 x 3) matrix.
grview( grtranspose( Z2 ) );
==> Graded homomorphism: r(-1) + r + r(1) <- 0, given by zero (3 x 0) matrix.
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