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D.15.14.17 KeneshlouMatrixPresentation
Procedure from library gradedModules.lib (see gradedModules_lib).
- Usage:
- KeneshlouMatrixPresentation(intvec a), intvec a.
- Return:
- graded object
- Purpose:
- matrix presentation for direct sum of omega^a[i](i) in form of a graded object
Example:
| | LIB "gradedModules.lib";
ring r = 32003,(x(0..4)),dp;
def N1 = KeneshlouMatrixPresentation(intvec(2,0,0,0,0));
grview(N1);
==> Graded homomorphism: r^2 <- 0, given by zero (2 x 0) matrix.
def N2 = KeneshlouMatrixPresentation(intvec(0,0,0,0,3));
grview(N2);
==> Graded homomorphism: r(-1)^3 <- 0, given by zero (3 x 0) matrix.
def N = KeneshlouMatrixPresentation(intvec(2,0,0,0,3));
grview(N);
==> Graded homomorphism: r^2 + r(-1)^3 <- 0, given by zero (5 x 0) matrix.
def M1 = KeneshlouMatrixPresentation(intvec(0,1,0,0,0));
grview(M1);
==> Graded homomorphism: r(-1)^10 <- r(-2)^10, given by a square matrix, with\
degrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 ....
==> --- --- --- --- --- --- --- --- --- --- +...
==> 1 : 1 1 - - 1 - - - - - |..1
==> 1 : 1 - 1 - - 1 - - - - |..2
==> 1 : 1 - - 1 - - 1 - - - |..3
==> 1 : - 1 1 - - - - 1 - - |..4
==> 1 : - 1 - 1 - - - - 1 - |..5
==> 1 : - - 1 1 - - - - - 1 |..6
==> 1 : - - - - 1 1 - 1 - - |..7
==> 1 : - - - - 1 - 1 - 1 - |..8
==> 1 : - - - - - 1 1 - - 1 |..9
==> 1 : - - - - - - - 1 1 1 |.10
==> === === === === === === === === === ===
==> 2 2 2 2 2 2 2 2 2 2
def M2 = KeneshlouMatrixPresentation(intvec(0,1,1,0,0));
grview(M2);
==> Graded homomorphism: r(-1)^20 <- r(-2)^15, given by a matrix, with degree\
s:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 .11 .12 .13 .14 .15 ....
==> --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- +...
==> 1 : 1 1 - - 1 - - - - - - - - - - |..1
==> 1 : 1 - 1 - - 1 - - - - - - - - - |..2
==> 1 : 1 - - 1 - - 1 - - - - - - - - |..3
==> 1 : - 1 1 - - - - 1 - - - - - - - |..4
==> 1 : - 1 - 1 - - - - 1 - - - - - - |..5
==> 1 : - - 1 1 - - - - - 1 - - - - - |..6
==> 1 : - - - - 1 1 - 1 - - - - - - - |..7
==> 1 : - - - - 1 - 1 - 1 - - - - - - |..8
==> 1 : - - - - - 1 1 - - 1 - - - - - |..9
==> 1 : - - - - - - - 1 1 1 - - - - - |.10
==> 1 : - - - - - - - - - - 1 1 - - - |.11
==> 1 : - - - - - - - - - - 1 - 1 - - |.12
==> 1 : - - - - - - - - - - 1 - - 1 - |.13
==> 1 : - - - - - - - - - - 1 - - - 1 |.14
==> 1 : - - - - - - - - - - - 1 1 - - |.15
==> 1 : - - - - - - - - - - - 1 - 1 - |.16
==> 1 : - - - - - - - - - - - 1 - - 1 |.17
==> 1 : - - - - - - - - - - - - 1 1 - |.18
==> 1 : - - - - - - - - - - - - 1 - 1 |.19
==> 1 : - - - - - - - - - - - - - 1 1 |.20
==> === === === === === === === === === === === === === === ===
==> 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
def M3 = KeneshlouMatrixPresentation(intvec(0,0,0,1,0));
grview(M3);
==> Graded homomorphism: r(-1)^5 <- r(-2), given by a matrix, with degrees:
==> .1 ...
==> -- +..
==> 1 : 1 |.1
==> 1 : 1 |.2
==> 1 : 1 |.3
==> 1 : 1 |.4
==> 1 : 1 |.5
==> ==
==> 2
def M = KeneshlouMatrixPresentation(intvec(1,1,1,0,0));
grview(M);
==> Graded homomorphism: r + r(-1)^20 <- r(-2)^15, given by a matrix, with de\
grees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 .11 .12 .13 .14 .15 ....
==> --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- +...
==> 0 : - - - - - - - - - - - - - - - |..1
==> 1 : 1 1 - - 1 - - - - - - - - - - |..2
==> 1 : 1 - 1 - - 1 - - - - - - - - - |..3
==> 1 : 1 - - 1 - - 1 - - - - - - - - |..4
==> 1 : - 1 1 - - - - 1 - - - - - - - |..5
==> 1 : - 1 - 1 - - - - 1 - - - - - - |..6
==> 1 : - - 1 1 - - - - - 1 - - - - - |..7
==> 1 : - - - - 1 1 - 1 - - - - - - - |..8
==> 1 : - - - - 1 - 1 - 1 - - - - - - |..9
==> 1 : - - - - - 1 1 - - 1 - - - - - |.10
==> 1 : - - - - - - - 1 1 1 - - - - - |.11
==> 1 : - - - - - - - - - - 1 1 - - - |.12
==> 1 : - - - - - - - - - - 1 - 1 - - |.13
==> 1 : - - - - - - - - - - 1 - - 1 - |.14
==> 1 : - - - - - - - - - - 1 - - - 1 |.15
==> 1 : - - - - - - - - - - - 1 1 - - |.16
==> 1 : - - - - - - - - - - - 1 - 1 - |.17
==> 1 : - - - - - - - - - - - 1 - - 1 |.18
==> 1 : - - - - - - - - - - - - 1 1 - |.19
==> 1 : - - - - - - - - - - - - 1 - 1 |.20
==> 1 : - - - - - - - - - - - - - 1 1 |.21
==> === === === === === === === === === === === === === === ===
==> 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
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