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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "These two functions allow \+
us to take a Vector and produce a Matrix with entries from the vector.
 " }}{PARA 0 "" 0 "" {TEXT -1 100 "The first v_dim entries of the vect
or become the first column of the matrix, the next v_dim entries " }}
{PARA 0 "" 0 "" {TEXT -1 179 "become the second column of the matrix a
nd so on.   First we make a copy  of the plaintext vector which has le
ngth a multiple of v_dim (just to simplify the coding of the Matrix).
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "The r
everse function is Decompose_mat().  It takes a matrix and produces a \+
Vector." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 326 "Parse_mat := pr
oc(p_vec, v_dim)\nlocal i, j, h_dim, p_vec_copy,p_mat;\n\nh_dim := cei
l(LinearAlgebra[Dimension](p_vec)/v_dim);\np_vec_copy := Vector(h_dim*
v_dim, p_vec);\n\np_mat :=Matrix(v_dim,h_dim);\nfor j from 1 to h_dim \+
do\n   for i from 1 to v_dim do\n     p_mat[i,j] := p_vec_copy[i+v_dim
*(j-1)];\n   od;\nod;\nRETURN(p_mat);\nend;\n" }{XPPMATH 20 "6#>%*Pars
e_matGR6$%&p_vecG%&v_dimG6'%\"iG%\"jG%&h_dimG%+p_vec_copyG%&p_matG6\"F
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{XPPMATH 20 "6#>%*Parse_matGR6$%&p_vecG%&v_dimG6'%\"iG%\"jG%&h_dimG%+p
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TURNG6#FHF/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "h := Vec
tor([1,2,3,4,5,6,7,8,9,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG-
%'RTABLEG6$\"(WR?%-%'MATRIXG6#7,7#\"\"\"7#\"\"#7#\"\"$7#\"\"%7#\"\"&7#
\"\"'7#\"\"(7#\"\")7#\"\"*7#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "type (h,Vector);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "H :=Parse_mat(h,3
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"HG-%'RTABLEG6$\"(#*ow&-%'MAT
RIXG6#7%7&\"\"\"\"\"%\"\"(\"\"!7&\"\"#\"\"&\"\")F17&\"\"$\"\"'\"\"*F1
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "type (H,Matrix);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 299 "Decompose_mat := proc(p_mat,v_dim)\nlocal i,j, h_dim
, count, p_vec;\n\nh_dim :=LinearAlgebra[ColumnDimension](p_mat); \np_
vec :=Vector((v_dim*h_dim));\ncount :=1;\nfor  j from 1 to h_dim do\n \+
  for i from 1 to v_dim do\n     p_vec[count] := p_mat[i,j];\n     cou
nt := count +1;\n   od;\nod;\nRETURN(p_vec);\nend;" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#>%.Decompose_matGR6$%&p_matG%&v_dimG6'%\"iG%\"jG%&h_d
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6#FC&F96$FHFE>FC,&FCF@F@F@-%'RETURNG6#F;F/F/F/" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 19 "Decompose_mat(H,2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'RTABLEG6$\"([8t&-%'MATRIXG6#7*7#\"\"\"7#\"\"#7#\"\"%
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