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D.15.14.34 matrixpres

Procedure from library gradedModules.lib (see gradedModules_lib).

Usage:
matrixpres(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 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