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D.15.10.1 grobj
Procedure from library gradedModules.lib (see gradedModules_lib).
- Usage:
- grobj(M, w[, d]), matrix/ideal/module M, intvec w, d
- Return:
- graded object with matrix presentation M, row weighting w [and total graded degrees d of columns]
- Purpose:
- create a valid graded object with a given matrix presentation, weighting [and total graded degrees (in case of zero columns)]
Example:
| | LIB "gradedModules.lib";
ring r=32003,(x,y,z),dp;
def A = grobj( module([x+y, x, 0, 0], [0, x+y, y, 0]), intvec(0,0,0,1) );
grview(A);
==> Graded homomorphism: r^3 + r(-1) <- r(-1)^2, given by a matrix, with degr\
ees:
==> ..1 ..2 ....
==> --- --- +...
==> 0 : 1 - |..1
==> 0 : 1 1 |..2
==> 0 : - 1 |..3
==> 1 : - - |..4
==> === ===
==> 1 1
def F = grobj( module([x,y,0]), intvec(1,1,5) );
grview(F);
==> Graded homomorphism: r(-1)^2 + r(-5) <- r(-2), given by a matrix, with de\
grees:
==> ..1 ....
==> --- +...
==> 1 : 1 |..1
==> 1 : 1 |..2
==> 5 : - |..3
==> ===
==> 2
int d = 666; // zero can have any degree...
def Z = grobj( module([x,0], [0,0,0], [0, y]), intvec(1,2,3), intvec(2, d, 3) );
grview(Z);
==> Graded homomorphism: r(-1) + r(-2) + r(-3) <- r(-2) + r(-666) + r(-3), gi\
ven by a square matrix, with degrees:
==> ...1 ...2 ...3 .....
==> ---- ---- ---- +....
==> 1 : 1 - - |...1
==> 2 : - - 1 |...2
==> 3 : - - - |...3
==> ==== ==== ====
==> 2 666 3
print(Z);
==> x,0,0,
==> 0,0,y,
==> 0,0,0
attrib(Z);
==> attr:degHomog, type intvec
==> attr:isHomog, type intvec
grrange(Z); // module weights
==> 1,2,3
attrib(Z, "degHomog"); // total degrees
==> 2,666,3
// Zero object:
matrix z[3][0]; grview( grobj( z, intvec(1,2,3) ) );
==> Graded homomorphism: r(-1) + r(-2) + r(-3) <- 0, given by zero (3 x 0) ma\
trix.
grview( grobj( freemodule(0), intvec(1,2,3) ) );
==> Graded homomorphism: r(-1) + r(-2) + r(-3) <- 0, given by zero (3 x 0) ma\
trix.
matrix z1[0][3]; grview( grobj( z1, 0:0, intvec(1,2,3) ) );
==> Graded homomorphism: 0 <- r(-1) + r(-2) + r(-3), given by zero (0 x 3) ma\
trix.
grview( grobj( freemodule(0), 0:0, intvec(1,2,3) ) );
==> Graded homomorphism: 0 <- r(-1) + r(-2) + r(-3), given by zero (0 x 3) ma\
trix.
matrix z0[0][0]; grview( grobj( z0, 0:0 ) );
==> Graded homomorphism: 0 <- 0, given by zero (0^2) matrix.
grview( grobj( freemodule(0), 0:0 ) );
==> Graded homomorphism: 0 <- 0, given by zero (0^2) matrix.
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