Artifact 45cf035038e9de39c114420f8f5a7fe2bfadf3f9377c0e1d6728132f386d9e15:
- Executable file
r37/packages/misc/liendmc1.red
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[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 7426) [annotate] [blame] [check-ins using] [more...]
- Executable file
r38/packages/misc/liendmc1.red
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 7426) [annotate] [blame] [check-ins using]
module liendmc1; % N-dimensional Lie algebras with 1-dimensional derived % algebra. % Author: Carsten Schoebel. % e-mail: cschoeb@aix550.informatik.uni-leipzig.de . % Copyright (c) 1993 The Leipzig University, Computer Science Dept. % All Rights Reserved. algebraic; operator heisenberg,commutative,lie_algebra; algebraic procedure liendimcom1(n); begin if (not(symbolic fixp(n)) or n<2) then symbolic rederr "dimension out of range"; symbolic (if gettype 'lienstrucin neq 'ARRAY then rederr "lienstrucin not ARRAY"); if length lienstrucin neq {n+1,n+1,n+1} then symbolic rederr "dimension of lienstrucin out of range"; matrix lientrans(n,n); array lie_cc(n,n,n); lieninstruc(n); lienjactest(n);if lie_jtest neq 0 then <<clear lie_cc,lie_jtest;symbolic rederr "not a Lie algebra">>; <<liendimcom(n); if lie_dim=0 then <<if symbolic !*tr_lie then write "The given Lie algebra is commutative"; lientrans:=lientrans**0;lie_list:={commutative(n)}>> else if lie_dim=1 then <<if lie_help=0 then liencentincom(n,lie_tt,lie_p,lie_q) else liencentoutcom(n,lie_tt,lie_s); if symbolic !*tr_lie then lienoutform(lientrans,n,lie_help,2*lie_kk!*+1); if lie_help=1 then lie_list:={lie_algebra(2),commutative(n-2)} else lie_list:={heisenberg(2*lie_kk!*+1),commutative(n-2*lie_kk!*-1)} >>else <<clear lie_dim,lie_help,lie_p,lie_q,lie_tt,lie_s,lie_kk!*, lie_jtest,lie_cc; symbolic rederr "dimension of derived algebra out of range">>; clear lie_dim,lie_help,lie_p,lie_q,lie_tt,lie_s,lie_kk!*,lie_control>>; clear lie_jtest,lie_cc;return lie_list end; algebraic procedure lieninstruc(n); begin for i:=1:n-1 do for j:=i+1:n do for k:=1:n do <<lie_cc(i,j,k):=lienstrucin(i,j,k); lie_cc(j,i,k):=-lienstrucin(i,j,k)>> end; algebraic procedure lienjactest(n); begin lie_jtest:=0; for i:=1:n-2 do for j:=i+1:n-1 do for k:=j+1:n do for l:=1:n do if (for r:=1:n sum lie_cc(j,k,r)*lie_cc(i,r,l)+lie_cc(i,j,r)*lie_cc(k,r,l)+ lie_cc(k,i,r)*lie_cc(j,r,l)) neq 0 then <<lie_jtest:=1; i:=n-1;j:=n;k:=n+1;l:=n+1>> end; algebraic procedure liendimcom(n); begin integer r; scalar he; lie_dim:=0; for i:=1:n-1 do for j:=i:n do for k:=1:n do if lie_cc(i,j,k) neq 0 then <<lie_dim:=1;lie_p:=i;lie_q:=j;r:=k;i:=n;j:=k:=n+1>>; if lie_dim neq 0 then <<for i:=1:n-1 do for j:=1:n do <<he:=lie_cc(i,j,r)/lie_cc(lie_p,lie_q,r); for k:=1:n do if lie_cc(i,j,k) neq (he*lie_cc(lie_p,lie_q,k)) then <<lie_dim:=2;i:=n;j:=n+1;k:=n+1>>>>; if lie_dim=1 then <<lie_help:=0; for i:=1:n do for j:=1:n do if (for k:=1:n sum (lie_cc(lie_p,lie_q,k)*lie_cc(k,i,j))) neq 0 then <<lie_help:=1;lie_s:=i;r:=j;i:=j:=n+1>>; for i:=1:n do lientrans(1,i):=lie_cc(lie_p,lie_q,i); if lie_help=0 then <<lientrans(2,lie_p):=lientrans(3,lie_q):=1;lie_kk!*:=1; for i:=1:n do <<if (lie_cc(lie_p,lie_q,i) neq 0 and i neq lie_p and i neq lie_q) then <<lie_tt:=i;i:=n+1>>>>>> else <<lientrans(2,lie_s):= lie_cc(lie_p,lie_q,r)/(for k:=1:n sum (lie_cc(lie_p,lie_q,k)*lie_cc(k,lie_s,r))); for i:=1:n do <<if (lie_cc(lie_p,lie_q,i) neq 0 and i neq lie_s) then <<lie_tt:=i;i:=n+1>>>>>>>>>>; end; algebraic procedure liencentincom(n,tt,p,q); begin integer con1,con2; matrix lie_lamb(n,n); lie_control:=0; con1:=con2:=0; for i:=4:n do if (i neq tt and i neq p and i neq q) then lientrans(i,i):=1 else if (tt neq 1 and p neq 1 and q neq 1 and con1 neq 1) then <<lientrans(i,1):=1;con1:=1>> else if (tt neq 2 and p neq 2 and q neq 2 and con2 neq 1) then <<lientrans(i,2):=1;con2:=1>> else lientrans(i,3):=1; if n>3 then <<liennewstruc(n,2,tt); if n>4 then for i:=4 step 2 until n do if (i+1)=n then <<lienfindpair(n,i); if lie_control=1 then lie_kk!*:=lie_kk!*+1>> else if i+1<n then <<lienfindpair(n,i);if lie_control=1 then <<liennewstruc(n,i,tt),lie_kk!*:=lie_kk!*+1>>else i:=n+1>>>> end; algebraic procedure lienfindpair(n,m); begin scalar he; matrix lie_a(n,n); lie_control:=0; for i:=m:n-1 do for j:=i+1:n do <<if lie_lamb(i,j) neq 0 then <<lie_control:=1; lie_a(i,m):=lie_a(m+1,j):=lie_a(j,m+1):=1; lie_a(m,i):=1/lie_lamb(i,j); for k:=1:n do if (k neq i and k neq j and k neq m and k neq (m+1)) then lie_a(k,k):=1; lientrans:=lie_a*lientrans;i:=n;j:=n+1>>>>;clear lie_a end; algebraic procedure liennewstruc(n,m,tt); begin matrix lie_a(n,n); lie_a:=lie_a**0; for i:=m:n-1 do for j:=i+1:n do lie_lamb(i,j):=(for k:=1:n sum for l:=1:n sum lientrans(i,k)*lientrans(j,l)*lie_cc(k,l,tt))/lientrans(1,tt); for i:=m+2:n do <<lie_a(i,m+1):=-lie_lamb(m,i);lie_a(i,m):=lie_lamb(m+1,i)>>; lientrans:=lie_a*lientrans; for i:=m+2:n-1 do for j:=i+1:n do lie_lamb(i,j):=(for k:=1:n sum for l:=1:n sum lientrans(i,k)*lientrans(j,l)*lie_cc(k,l,tt))/lientrans(1,tt); clear lie_a end; algebraic procedure liencentoutcom(n,tt,s); begin integer pp,qq; matrix lie_lamb(2,n),lie_a(n,n); for i:=3:n do <<lientrans(i,i):=1;lie_lamb(1,i):=(for j:=1:n sum lientrans(1,j)*lie_cc(j,i,tt))/lientrans(1,tt); lie_lamb(2,i):=lie_cc(s,i,tt)*lientrans(2,s)/lientrans(1,tt)>>; if (tt>2 and s>2) then <<lientrans(tt,tt):=lientrans(s,s):=0; lientrans(tt,1):=lientrans(s,2):=1; lie_lamb(1,tt):=(for j:=1:n sum lientrans(1,j)*lie_cc(j,1,tt)/lientrans(1,tt)); lie_lamb(1,s):=(for j:=1:n sum lientrans(1,j)*lie_cc(j,2,tt)/lientrans(1,tt)); lie_lamb(2,tt):=lie_cc(s,1,tt)*lientrans(2,s)/lientrans(1,tt); lie_lamb(2,s):=lie_cc(s,2,tt)*lientrans(2,s)/lientrans(1,tt) >> else if (tt>2 or s>2) then <<if tt>2 then <<pp:=3-s;qq:=tt>> else <<pp:=3-tt;qq:=s>>; lientrans(qq,qq):=0;lientrans(qq,pp):=1; lie_lamb(1,qq):=(for j:=1:n sum lientrans(1,j)*lie_cc(j,pp,tt))/lientrans(1,tt); lie_lamb(2,qq):=lie_cc(s,pp,tt)*lientrans(2,s)/lientrans(1,tt)>>; lie_a:=lie_a**0; for i:=3:n do <<lie_a(i,2):=-lie_lamb(1,i);lie_a(i,1):=lie_lamb(2,i)>>; lientrans:=lie_a*lientrans;clear lie_lamb,lie_a end; algebraic procedure lienoutform(at,n,lhelp,kk); begin operator y; lie_a:=at; if lhelp=1 then <<write "Your Lie algebra is the direct sum of the Lie algebra L(2) and"; write "the ",n-2,"-dimensional commutative Lie algebra, where L(2) is"; write "2-dimensional and there exists a basis {X(1),X(2)} in L(2) with"; write "[X(1),X(2)]=X(1).">>else <<write "Your Lie algebra is the direct sum of the Lie algebra H(",kk,")"; write "and the ",n-kk,"-dimensional commutative Lie algebra, where"; write "H(",kk,") is ",kk,"-dimensional and there exists a basis"; write "{X(1),...,X(",kk,")} in H(",kk,") with:"; write "[X(2),X(3)]=[X(2*i),X(2*i+1)]=...=[X(",kk-1,"),X(",kk,")]=X(1)" >>; write "The transformation into this form is:"; for i:=1:n do write "X(",i,"):=",for j:=1:n sum lie_a(i,j)*y(j);clear y,lie_a end; endmodule; end;