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D.15.10.8 grsum
Procedure from library gradedModules.lib (see gradedModules_lib).
- Usage:
- grsum(A, B), graded objects A and B
- Return:
- graded direct sum of input objects
- Purpose:
- compute the graded direct sum of A and B
Example:
| | LIB "gradedModules.lib";
// if( defined(assumeLevel) ){ int assumeLevel0 = assumeLevel; } else { int assumeLevel; export(assumeLevel); }; assumeLevel = 5;
ring r=32003,(x,y,z),dp;
module A = grobj( module([x+y, x, 0, 0], [0, x+y, y, 0]), intvec(0,0,0,1) );
grview(A);
==> 1 2
==> --------
==> 0 : 1 . | 1
==> 0 : 1 1 | 2
==> 0 : . 1 | 3
==> 1 : . . | 4
==> ========
==> 1 1
module B = grobj( module([0,x,y]), intvec(15,1,1) );
grview(B);
==> 1
==> ----
==> 15 : . | 1
==> 1 : 1 | 2
==> 1 : 1 | 3
==> ====
==> 2
module C = grsum(A,B);
print(C);
==> x+y,0, 0,
==> x, x+y,0,
==> 0, y, 0,
==> 0, 0, 0,
==> 0, 0, 0,
==> 0, 0, x,
==> 0, 0, y
homog(C);
==> 1
grview(C);
==> 1 2 3
==> ------------
==> 0 : 1 . . | 1
==> 0 : 1 1 . | 2
==> 0 : . 1 . | 3
==> 1 : . . . | 4
==> 15 : . . . | 5
==> 1 : . . 1 | 6
==> 1 : . . 1 | 7
==> ============
==> 1 1 2
module D = grsum(
grsum(grpower(A,2), grtwist(1,1)),
grsum(grtwist(1,2), grpower(B,2))
);
print(D);
==> x+y,0, 0, 0, 0,0,0,0,
==> x, x+y,0, 0, 0,0,0,0,
==> 0, y, 0, 0, 0,0,0,0,
==> 0, 0, 0, 0, 0,0,0,0,
==> 0, 0, x+y,0, 0,0,0,0,
==> 0, 0, x, x+y,0,0,0,0,
==> 0, 0, 0, y, 0,0,0,0,
==> 0, 0, 0, 0, 0,0,0,0,
==> 0, 0, 0, 0, 0,0,0,0,
==> 0, 0, 0, 0, 0,0,0,0,
==> 0, 0, 0, 0, 0,0,0,0,
==> 0, 0, 0, 0, 0,0,x,0,
==> 0, 0, 0, 0, 0,0,y,0,
==> 0, 0, 0, 0, 0,0,0,0,
==> 0, 0, 0, 0, 0,0,0,x,
==> 0, 0, 0, 0, 0,0,0,y
homog(D);
==> 1
grview(D);
==> 1 2 3 4 5 6 7 8
==> --------------------------------
==> 0 : 1 . . . . . . . | 1
==> 0 : 1 1 . . . . . . | 2
==> 0 : . 1 . . . . . . | 3
==> 1 : . . . . . . . . | 4
==> 0 : . . 1 . . . . . | 5
==> 0 : . . 1 1 . . . . | 6
==> 0 : . . . 1 . . . . | 7
==> 1 : . . . . . . . . | 8
==> -1 : . . . . . . . . | 9
==> -2 : . . . . . . . . | 10
==> 15 : . . . . . . . . | 11
==> 1 : . . . . . . 1 . | 12
==> 1 : . . . . . . 1 . | 13
==> 15 : . . . . . . . . | 14
==> 1 : . . . . . . . 1 | 15
==> 1 : . . . . . . . 1 | 16
==> ================================
==> 1 1 1 1 -1 -2 2 2
module F = grobj( module([x,y,0]), intvec(1,1,5) );
grview(F);
==> 1
==> ----
==> 1 : 1 | 1
==> 1 : 1 | 2
==> 5 : . | 3
==> ====
==> 2
module T = grsum( F, grsum( grtwist(1, 10), B ) );
grview(T);
==> 1 2 3
==> ---------------
==> 1 : 1 . . | 1
==> 1 : 1 . . | 2
==> 5 : . . . | 3
==> -10 : . . . | 4
==> 15 : . . . | 5
==> 1 : . . 1 | 6
==> 1 : . . 1 | 7
==> ===============
==> 2 -10 2
// if( defined(assumeLevel0) ){ assumeLevel = assumeLevel0; } else { kill assumeLevel; } // restore the state of aL
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