# Singular

#### D.15.20.34 matrixpres

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

Usage:
matrixpres(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 R=matrixpres(intvec(1,4,0,0,0)); ==> // ** redefining j ( int j=size(a)-i;) grview(R); ==> Graded homomorphism: r(-1)^21 <- r(-2)^4, given by a matrix, with degrees\ : ==> ..1 ..2 ..3 ..4 .... ==> --- --- --- --- +... ==> 1 : - - - - |..1 ==> 1 : 1 - - - |..2 ==> 1 : 1 - - - |..3 ==> 1 : 1 - - - |..4 ==> 1 : 1 - - - |..5 ==> 1 : 1 - - - |..6 ==> 1 : - 1 - - |..7 ==> 1 : - 1 - - |..8 ==> 1 : - 1 - - |..9 ==> 1 : - 1 - - |.10 ==> 1 : - 1 - - |.11 ==> 1 : - - 1 - |.12 ==> 1 : - - 1 - |.13 ==> 1 : - - 1 - |.14 ==> 1 : - - 1 - |.15 ==> 1 : - - 1 - |.16 ==> 1 : - - - 1 |.17 ==> 1 : - - - 1 |.18 ==> 1 : - - - 1 |.19 ==> 1 : - - - 1 |.20 ==> 1 : - - - 1 |.21 ==> === === === === ==> 2 2 2 2 def S=matrixpres(intvec(0,0,3,0,0)); ==> // ** redefining j ( int j=size(a)-i;) grview(S); ==> Graded homomorphism: r(-1)^30 <- 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 - - - - - - - - - - - - |..2 ==> 1 : 1 - - 1 - - - - - - - - - - - |..3 ==> 1 : 1 - - - 1 - - - - - - - - - - |..4 ==> 1 : - 1 1 - - - - - - - - - - - - |..5 ==> 1 : - 1 - 1 - - - - - - - - - - - |..6 ==> 1 : - 1 - - 1 - - - - - - - - - - |..7 ==> 1 : - - 1 1 - - - - - - - - - - - |..8 ==> 1 : - - 1 - 1 - - - - - - - - - - |..9 ==> 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 ==> 1 : - - - - - - - - - - 1 1 - - - |.21 ==> 1 : - - - - - - - - - - 1 - 1 - - |.22 ==> 1 : - - - - - - - - - - 1 - - 1 - |.23 ==> 1 : - - - - - - - - - - 1 - - - 1 |.24 ==> 1 : - - - - - - - - - - - 1 1 - - |.25 ==> 1 : - - - - - - - - - - - 1 - 1 - |.26 ==> 1 : - - - - - - - - - - - 1 - - 1 |.27 ==> 1 : - - - - - - - - - - - - 1 1 - |.28 ==> 1 : - - - - - - - - - - - - 1 - 1 |.29 ==> 1 : - - - - - - - - - - - - - 1 1 |.30 ==> === === === === === === === === === === === === === === === ==> 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 def N1 = matrixpres(intvec(2,0,0,0,0)); grview(N1); ==> Graded homomorphism: r(-1)^2 <- 0, given by zero (2 x 0) matrix. def N2 = matrixpres(intvec(0,0,0,0,3)); grview(N2); ==> Graded homomorphism: r^3 <- 0, given by zero (3 x 0) matrix. def N = matrixpres(intvec(2,0,0,0,3)); grview(N); ==> Graded homomorphism: r(-1)^2 + r^3 <- 0, given by zero (5 x 0) matrix. def M1 = matrixpres(intvec(0,1,0,0,0)); ==> // ** redefining j ( int j=size(a)-i;) grview(M1); ==> 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 M2 = matrixpres(intvec(0,1,1,0,0)); ==> // ** redefining j ( int j=size(a)-i;) ==> // ** redefining j ( int j=size(a)-i;) grview(M2); ==> Graded homomorphism: r(-1)^15 <- r(-2)^6, given by a matrix, with degrees\ : ==> ..1 ..2 ..3 ..4 ..5 ..6 .... ==> --- --- --- --- --- --- +... ==> 1 : 1 - - - - - |..1 ==> 1 : 1 - - - - - |..2 ==> 1 : 1 - - - - - |..3 ==> 1 : 1 - - - - - |..4 ==> 1 : 1 - - - - - |..5 ==> 1 : - 1 1 - - - |..6 ==> 1 : - 1 - 1 - - |..7 ==> 1 : - 1 - - 1 - |..8 ==> 1 : - 1 - - - 1 |..9 ==> 1 : - - 1 1 - - |.10 ==> 1 : - - 1 - 1 - |.11 ==> 1 : - - 1 - - 1 |.12 ==> 1 : - - - 1 1 - |.13 ==> 1 : - - - 1 - 1 |.14 ==> 1 : - - - - 1 1 |.15 ==> === === === === === === ==> 2 2 2 2 2 2 def M3 = matrixpres(intvec(0,0,0,1,0)); ==> // ** redefining j ( int j=size(a)-i;) grview(M3); ==> 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 M = matrixpres(intvec(1,1,1,0,0)); ==> // ** redefining j ( int j=size(a)-i;) ==> // ** redefining j ( int j=size(a)-i;) grview(M); ==> Graded homomorphism: r(-1)^16 <- r(-2)^6, given by a matrix, with degrees\ : ==> ..1 ..2 ..3 ..4 ..5 ..6 .... ==> --- --- --- --- --- --- +... ==> 1 : - - - - - - |..1 ==> 1 : 1 - - - - - |..2 ==> 1 : 1 - - - - - |..3 ==> 1 : 1 - - - - - |..4 ==> 1 : 1 - - - - - |..5 ==> 1 : 1 - - - - - |..6 ==> 1 : - 1 1 - - - |..7 ==> 1 : - 1 - 1 - - |..8 ==> 1 : - 1 - - 1 - |..9 ==> 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 ==> === === === === === === ==> 2 2 2 2 2 2 ```