# Singular

#### D.15.14.17 KeneshlouMatrixPresentation

Procedure from library `gradedModules.lib` (see gradedModules_lib).

Usage:
KeneshlouMatrixPresentation(intvec a), intvec a.

Return:

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 ```