reduce-historical/r36/xlog/ASSIST.LOG

REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...


% Tests of Assist Package version 2.1.
% DATE : 25 December 1993
% Author: H. Caprasse <caprasse@vm1.ulg.ac.be>
%load_package assist$

Comment 2. HELP for ASSIST:;

;


helpassist(assist);


 Arguments must be integers from 3 to 15 

 They correspond to the section numbers in the documentation:

 3 for switches    4 for lists        5 for bags      6 for sets 

 7 for utilities   8 for properties   9 for control functions 

 10 for polynomes 

 11 for trigonometric  or
                                                 hyperbolic functions

 12 for arrays     13 for  vectors 

 14 for grassmann variables           15 for matrices

;


helpassist(6);


{union,setp,mkset,setdiff,symdiff}

;


Comment 3. CONTROL OF SWITCHES:;

;


switches;


      **** exp:=t .................... allfac:= t ****

      **** ezgcd:=nil ................. gcd:= nil ****

      **** mcd:=t ....................... lcm:= t ****

      **** div:=nil ................... rat:= nil ****

      **** intstr:=nil ........... rational:= nil ****

      **** precise:=t ........... reduced:= nil ****

      **** complex:=nil ....... rationalize:= nil ****

      **** factor:= nil ....... combineexpt:= nil ****

      **** complex:= nil ....... distribute:= nil ****
off exp;

 on gcd;


switches;


      **** exp:=nil .................... allfac:= t ****

      **** ezgcd:=nil ................. gcd:= t ****

      **** mcd:=t ....................... lcm:= t ****

      **** div:=nil ................... rat:= nil ****

      **** intstr:=nil ........... rational:= nil ****

      **** precise:=t ........... reduced:= nil ****

      **** complex:=nil ....... rationalize:= nil ****

      **** factor:= nil ....... combineexpt:= nil ****

      **** complex:= nil ....... distribute:= nil ****
switchorg;


switches;


      **** exp:=t .................... allfac:= t ****

      **** ezgcd:=nil ................. gcd:= nil ****

      **** mcd:=t ....................... lcm:= t ****

      **** div:=nil ................... rat:= nil ****

      **** intstr:=nil ........... rational:= nil ****

      **** precise:=nil ........... reduced:= nil ****

      **** complex:=nil ....... rationalize:= nil ****

      **** factor:= nil ....... combineexpt:= nil ****

      **** complex:= nil ....... distribute:= nil ****
;


if !*mcd then "the switch mcd is on";


the switch mcd is on

if !*gcd then "the switch gcd is on";


;


Comment 4. MANIPULATION OF THE LIST STRUCTURE:;

;


t1:=mklist(4);


t1 := {0,0,0,0}


Comment   MKLIST does NEVER destroy anything ;


mklist(t1,3);


{0,0,0,0}

mklist(t1,10);


{0,0,0,0,0,0,0,0,0,0}

;


% Generation of n duplicates of list :
algnlist({a,x^2,1},3);


     2
{{a,x ,1},

     2
 {a,x ,1},

     2
 {a,x ,1}}

;


sequences 3;


{{0,0,0},

 {1,0,0},

 {0,1,0},

 {1,1,0},

 {0,0,1},

 {1,0,1},

 {0,1,1},

 {1,1,1}}

lisp;


nil

sequences 3;


((0 0 0) (1 0 0) (0 1 0) (1 1 0) (0 0 1) (1 0 1) (0 1 1) (1 1 1))

algebraic;


;


frequency append(t1,t1);


{{0,8}}

elmult(a1,t1);


0

insert(a1,t1,2);


{0,a1,0,0,0}

li:=list(1,2,5);


li := {1,2,5}

insert_keep_order(4,li,lessp);


{1,2,4,5}

merge_list(li,li,lessp);


{1,1,2,2,5,5}

for i:=1:4 do t1:= (t1.i:=mkid(a,i));


% for i:=1:2 do t1:=(t1.i:=mkid(a,i));
t1.1;


a1

t1:=(t1.1) . t1;


t1 := {a1,a1,a2,a3,a4}

position(a2,t1);


3

pair(t1,t1);


{{a1,a1},{a1,a1},{a2,a2},{a3,a3},{a4,a4}}

depth list t1;


2

depth a1;


0

appendn(li,li,li);


{1,2,5,1,2,5,1,2,5}

;


comment 5. THE BAG STRUCTURE AND ITS ASSOCIATED FUNCTIONS
 ;

aa:=bag(x,1,"A");


aa := bag(x,1,A)

putbag bg1,bg2;


t

on errcont;


putbag list;


***** list invalid as BAG

off errcont;


aa:=bg1(x,y**2);


             2
aa := bg1(x,y )

;


if bagp aa then "this is a bag";


this is a bag

;


clearbag bg2;


;


depth bg2(x);


0

;


if baglistp aa then "this is a bag or list";


this is a bag or list

if baglistp list(x) then "this is a bag or list";


this is a bag or list

;


ab:=bag(x1,x2,x3);


ab := bag(x1,x2,x3)

al:=list(y1,y2,y3);


al := {y1,y2,y3}

first ab;


bag(x1)
  third ab;


bag(x3)
  first al;


y1

last ab;


bag(x3)
 last al;


y3

belast ab;


bag(x1,x2)
 belast al;


{y1,y2}

rest ab;


bag(x2,x3)
 rest al;


{y2,y3}

depth al;


1
 depth bg1(ab);


2

;


ab.1;


x1
 al.3;


y3

on errcont;


ab.4;


***** Expression bag(x1,x2,x3) does not have part 4

off errcont;


kernlist(aa);


    2
{x,y }

listbag(list x,bg1);


bg1(x)

size ab;


3
 length al;


3

remove(ab,3);


bag(x1,x2)

delete(y2,al);


{y1,y3}

reverse al;


{y3,y2,y1}

member(x3,ab);


bag(x3)

al:=list(x**2,x**2,y1,y2,y3);


        2
al := {x ,

        2
       x ,

       y1,

       y2,

       y3}

;


elmult(x**2,al);


2

position(y3,al);


5

;


repfirst(xx,al);


     2
{xx,x ,y1,y2,y3}

represt(xx,ab);


bag(x1,xx)

insert(x,al,3);


  2  2
{x ,x ,x,y1,y2,y3}

insert( b,ab,2);


bag(x1,b,xx)

insert(ab,ab,1);


bag(bag(x1,xx),x1,xx)

substitute (new,y1,al);


  2  2
{x ,x ,new,y2,y3}

;


appendn(ab,ab,ab);


{x1,xx,x1,xx,x1,xx}

append(ab,al);


           2  2
bag(x1,xx,x ,x ,y1,y2,y3)

append(al,ab);


  2  2
{x ,x ,y1,y2,y3,x1,xx}

;


comment Association list or bag may be constructed and thoroughly used;

;


l:=list(a1,a2,a3,a4);


l := {a1,a2,a3,a4}

b:=bg1(x1,x2,x3);


b := bg1(x1,x2,x3)

al:=pair(list(1,2,3,4),l);


al := {{1,a1},{2,a2},{3,a3},{4,a4}}

ab:=pair(bg1(1,2,3),b);


ab := bg1(bg1(1,x1),bg1(2,x2),bg1(3,x3))

;


comment : A BOOLEAN function abaglistp to test if it is an association;

;


if abaglistp bag(bag(1,2)) then "it is an associated bag";


it is an associated bag

;


% Values associated to the keys can be extracted
% first occurence ONLY.
;


asfirst(1,al);


{1,a1}

asfirst(3,ab);


bg1(3,x3)

;


assecond(a1,al);


{1,a1}

assecond(x3,ab);


bg1(3,x3)

;


aslast(z,list(list(x1,x2,x3),list(y1,y2,z)));


{y1,y2,z}

asrest(list(x2,x3),list(list(x1,x2,x3),list(y1,y2,z)));


{x1,x2,x3}

;


clear a1;


;


% All occurences.
asflist(x,bg1(bg1(x,a1,a2),bg1(x,b1,b2)));


bg1(bg1(x,a1,a2),bg1(x,b1,b2))

asslist(a1,list(list(x,a1),list(y,a1),list(x,y)));


{{x,a1},{y,a1}}

restaslist(bag(a1,x),bg1(bag(x,a1,a2),bag(a1,x,b2),bag(x,y,z)));


bg1(bg1(x,b2),bg1(a1,a2))

restaslist(list(a1,x),bag(bag(x,a1,a2),bag(a1,x,b2),bag(x,y,z)));


bag(bag(x,b2),bag(a1,a2))

;


Comment 6. SETS AND THEIR MANIPULATION FUNCTIONS
;

ts:=mkset list(a1,a1,a,2,2);


ts := {a1,a,2}

if setp ts then "this is a SET";


this is a SET

;


union(ts,ts);


{a1,a,2}

diffset(ts,list(a1,a));


{2}

diffset(list(a1,a),ts);


{}

symdiff(ts,ts);


{}

intersect(listbag(ts,set1),listbag(ts,set2));


set1(a1,a,2)



Comment 7. GENERAL PURPOSE UTILITY FUNCTIONS :;

;


clear a1,a2,a3,a,x,y,z,x1,x2,op$


;


% DETECTION OF A GIVEN VARIABLE IN A GIVEN SET
;


mkidnew();


G0

mkidnew(a);


aG1

dellastdigit 23;


2

detidnum aa;


detidnum a10;


10

detidnum a1b2z34;


34

list_to_ids list(a,1,rr,22);


a1rr22

;


if oddp 3 then "this is an odd integer";


this is an odd integer

;


<<prin2 1; followline 7; prin2 8;>>;

1
       8
;


operator foo;


foo(x):=x;


foo(x) := x

foo(x)==value;


value

x:=x;


x := value

;


clear x;


;


randomlist(10,20);


{8,1,8,0,5,7,3,8,0,5,5,9,0,5,2,0,7,5,5,1}

% Generation of tables of random numbers:
% One dimensional:
mkrandtabl({4},10,ar);


{4}

;


% Two dimensional:
mkrandtabl({3,4},10,ar);


*** array ar redefined 

{3,4}

;


% With a base which is a decimal number:
on rounded;


mkrandtabl({5},3.5,ar);


*** array ar redefined 

{5}

off rounded;


;


combnum(8,3);


56

permutations(bag(a1,a2,a3));


bag(bag(a1,a2,a3),bag(a1,a3,a2),bag(a2,a1,a3),bag(a2,a3,a1),bag(a3,a1,a2),

    bag(a3,a2,a1))

permutations {1,2,3};


{{1,2,3},{1,3,2},{2,1,3},{2,3,1},{3,1,2},{3,2,1}}

cyclicpermlist{1,2,3};


{{1,2,3},{2,3,1},{3,1,2}}

combinations({1,2,3},2);


{{2,3},{1,3},{1,2}}

labc:={a,b,c};


labc := {a,bg1(x1,x2,x3),c}

symmetrize(labc,foo,cyclicpermlist);


foo(bg1(x1,x2,x3),c,a) + foo(a,bg1(x1,x2,x3),c) + foo(c,a,bg1(x1,x2,x3))

symmetrize(labc,list,permutations);


{bg1(x1,x2,x3),a,c} + {bg1(x1,x2,x3),c,a} + {a,bg1(x1,x2,x3),c}

 + {a,c,bg1(x1,x2,x3)} + {c,bg1(x1,x2,x3),a} + {c,a,bg1(x1,x2,x3)}

symmetrize({labc},foo,cyclicpermlist);


foo({bg1(x1,x2,x3),c,a}) + foo({a,bg1(x1,x2,x3),c}) + foo({c,a,bg1(x1,x2,x3)})

extremum({1,2,3},lessp);


1

extremum({1,2,3},geq);


3

extremum({a,b,c},ordp);


bg1(x1,x2,x3)

;


funcvar(x+y);


{x,y}

funcvar(sin log(x+y));


{x,y}

funcvar(sin pi);


funcvar(x+e+i);


{x}

;


depatom a;


a

depend a,x,y;


depatom a;


{x,y}

depend op,x,y,z;


implicit op;


op

explicit op;


op(x,y,z)

depend y,zz;


explicit op;


op(x,y(zz),z)

aa:=implicit op;


aa := op

clear op;


;


korder x,z,y;


korderlist;


(x z y)

;


if checkproplist({1,2,3},fixp) then "it is a list of integers";


it is a list of integers

;


if checkproplist({a,b1,c},idp) then "it is a list of identifiers";


it is a list of identifiers

;


if checkproplist({1,b1,c},idp) then "it is a list of identifiers";


;


lmix:={1,1/2,a,"st"};


            1
lmix := {1,---,a,st}
            2

;


extractlist(lmix,fixp);


{1}

extractlist(lmix,numberp);


    1
{1,---}
    2

extractlist(lmix,idp);


{a}

extractlist(lmix,stringp);


{st}

;


comment 8. PROPERTIES AND FLAGS:;

;


putflag(list(a1,a2),fl1,t);


t

putflag(list(a1,a2),fl2,t);


t

displayflag a1;


{fl1,fl2}

;


clearflag a1,a2;


displayflag a2;


{}

putprop(x1,propname,value,t);


x1

displayprop(x1,prop);


{}

displayprop(x1,propname);


{propname,value}

;


putprop(x1,propname,value,0);


displayprop(x1,propname);


{}

;


Comment 9. CONTROL FUNCTIONS:;

;


alatomp z;


t

z:=s1;


z := s1

alatomp z;


t

;


alkernp z;


t

alkernp log sin r;


t

;


precp(difference,plus);


t

precp(plus,difference);


precp(times,.);


precp(.,times);


t

;


if stringp x then "this is a string";


if stringp "this is a string" then "this is a string";


this is a string

;


if nordp(b,a) then "a is ordered before b";


operator op;


for all x,y such that nordp(x,y) let op(x,y)=x+y;


op(a,a);


op(a,a)

op(b,a);


op(bg1(x1,x2,x3),a)

op(a,b);


bg1(x1,x2,x3) + a

clear op;


;


depvarp(log(sin(x+cos(1/acos rr))),rr);


t

;


operator op;


symmetric op;


op(x,y)-op(y,x);


0

remsym op;


op(x,y)-op(y,x);


op(x,y) - op(y,x)

;


clear y,x,u,v;


clear op;


;


% DISPLAY and CLEARING of user's objects of various types entered
% to the console. Only TOP LEVEL assignments are considered up to now.
% The following statements must be made INTERACTIVELY. We put them
% as COMMENTS for the user to experiment with them. We do this because
% in a fresh environment all outputs are nil.
;


% THIS PART OF THE TEST SHOULD BE REALIZED INTERACTIVELY.
% SEE THE ** ASSIST LOG **  FILE .
%v1:=v2:=1;
%show scalars;
%aa:=list(a);
%show lists;
%array ar(2);
%show arrays;
%load matr$
%matrix mm;
%show matrices;
%x**2;
%saveas res;
%show saveids;
%suppress scalars;
%show scalars;
%show lists;
%suppress all;
%show arrays;
%show matrices;
;


comment end of the interactive part;

;


clear op;


operator op;


op(x,y,z);


op(x,y,s1)

clearop op;


t

clearfunctions abs,tan;


     *** abs is unprotected : Cleared ***
     *** tan is a protected function: NOT cleared ***


"Clearing is complete"

;


comment  THIS FUNCTION MUST BE USED WITH CARE !!"!!!;

;


Comment 10. HANDLING OF POLYNOMIALS

clear x,y,z;

COMMENT  To see the internal representation :;

;


off pri;


;


pol:=(x-2*y+3*z**2-1)**3;


        3                 2       2        2            2                4
pol := x  + ( - 6*y + 9*s1  - 3)*x  + (12*y  + ( - 36*s1  + 12)*y + 27*s1  - 18*

         2             3         2        2            4        2
       s1  + 3)*x - 8*y  + (36*s1  - 12)*y  + ( - 54*s1  + 36*s1  - 6)*y + 27*s1

       6        4       2
         - 27*s1  + 9*s1  - 1

;


pold:=distribute pol;


             6        4       2    3        2       2  2      2       2
pold := 27*s1  - 27*s1  + 9*s1  + x  - 6*y*x  + 9*s1 *x  - 3*x  + 12*y *x + 27*

          4          2          2                         3        2  2       2
        s1 *x - 18*s1 *x - 36*s1 *y*x + 12*y*x + 3*x - 8*y  + 36*s1 *y  - 12*y  

               4          2
        - 54*s1 *y + 36*s1 *y - 6*y - 1

;


on distribute;


leadterm (pold);


     6
27*s1

pold:=redexpr pold;


                4       2    3        2       2  2      2       2          4
pold :=  - 27*s1  + 9*s1  + x  - 6*y*x  + 9*s1 *x  - 3*x  + 12*y *x + 27*s1 *x -

              2          2                         3        2  2       2
         18*s1 *x - 36*s1 *y*x + 12*y*x + 3*x - 8*y  + 36*s1 *y  - 12*y  - 54*s1

        4          2
         *y + 36*s1 *y - 6*y - 1

leadterm pold;


        4
 - 27*s1

;


off distribute;


polp:=pol$


leadterm polp;


 3
x

polp:=redexpr polp;


                      2       2        2            2                4        2
polp := ( - 6*y + 9*s1  - 3)*x  + (12*y  + ( - 36*s1  + 12)*y + 27*s1  - 18*s1  

                    3         2        2            4        2               6
        + 3)*x - 8*y  + (36*s1  - 12)*y  + ( - 54*s1  + 36*s1  - 6)*y + 27*s1  -

              4       2
         27*s1  + 9*s1  - 1

leadterm polp;


              2       2
( - 6*y + 9*s1  - 3)*x

;


monom polp;


      6
{27*s1 ,

         4
  - 27*s1 ,

     2
 9*s1 ,

         2
  - 6*y*x ,

     2  2
 9*s1 *x ,

       2
  - 3*x ,

     2
 12*y *x,

      4
 27*s1 *x,

         2
  - 18*s1 *x,

         2
  - 36*s1 *y*x,

 12*y*x,

 3*x,

       3
  - 8*y ,

      2  2
 36*s1 *y ,

        2
  - 12*y ,

         4
  - 54*s1 *y,

      2
 36*s1 *y,

  - 6*y,

 -1}

;


on pri;


;


splitterms polp;


      2  2
{{9*s1 *x ,

        2
  12*x*y ,

  12*x*y,

       4
  27*s1 *x,

  3*x,

       2  2
  36*s1 *y ,

       2
  36*s1 *y,

       6
  27*s1 ,

      2
  9*s1 },

     2
 {6*x *y,

     2
  3*x ,

       2
  36*s1 *x*y,

       2
  18*s1 *x,

     3
  8*y ,

      2
  12*y ,

       4
  54*s1 *y,

  6*y,

       4
  27*s1 ,

  1}}

;


splitplusminus polp;


        6       4         2  2        2  2        2         2        2
{3*(9*s1  + 9*s1 *x + 3*s1 *x  + 12*s1 *y  + 12*s1 *y + 3*s1  + 4*x*y  + 4*x*y

     + x),

         4          4        2            2        2        2      3       2
  - 54*s1 *y - 27*s1  - 36*s1 *x*y - 18*s1 *x - 6*x *y - 3*x  - 8*y  - 12*y

  - 6*y - 1}

;


divpol(pol,x+2*y+3*z**2);


     4       2          2         2    2                     2
{9*s1  + 6*s1 *x - 24*s1 *y - 9*s1  + x  - 8*x*y - 3*x + 28*y  + 18*y + 3,

        3       2
  - 64*y  - 48*y  - 12*y - 1}

;


lowestdeg(pol,y);


0

;


Comment 11.  HANDLING OF SOME TRANSCENDENTAL FUNCTIONS:;

;


trig:=((sin x)**2+(cos x)**2)**4;


trig := 

      8           6       2           4       4           2       6         8
cos(x)  + 4*cos(x) *sin(x)  + 6*cos(x) *sin(x)  + 4*cos(x) *sin(x)  + sin(x)

trigreduce trig;


1

trig:=sin (5x);


trig := sin(5*x)

trigexpand trig;


                4            2       2         4
sin(x)*(5*cos(x)  - 10*cos(x) *sin(x)  + sin(x) )

trigreduce ws;


sin(5*x)

trigexpand sin(x+y+z);


cos(s1)*cos(x)*sin(y) + cos(s1)*cos(y)*sin(x) + cos(x)*cos(y)*sin(s1)

 - sin(s1)*sin(x)*sin(y)

;


;


hypreduce (sinh x **2 -cosh x **2);


-1

;


;


clear a,b,c,d;


;



Comment 12. COERCION FROM ARRAY TO LIST AND VICE-VERSA:;

on rounded;


array_to_list ar;


{2.77546499305,1.79693268486,3.43100115041,2.11636272025,3.45447023392}

;


off rounded;


ll:={{a,b},{b,c},{c,d}}$


list_to_array(ll,1,ar);


*** array ar redefined 

ar(1);


{b,c}

list_to_array(ll,2,ar);


*** array ar redefined 

ar(1,1);


c

;


clear ar;


;


Comment 13. HANDLING OF N-DIMENSIONAL VECTORS:;

;


clear u1,u2,v1,v2,v3,v4,w3,w4;


u1:=list(v1,v2,v3,v4);


u1 := {v1,v2,v3,v4}

u2:=bag(w1,w2,w3,w4);


u2 := bag(w1,w2,w3,w4)

%
sumvect(u1,u2);


{v1 + w1,

 v2 + w2,

 v3 + w3,

 v4 + w4}

minvect(u2,u1);


bag( - v1 + w1, - v2 + w2, - v3 + w3, - v4 + w4)

scalvect(u1,u2);


v1*w1 + v2*w2 + v3*w3 + v4*w4

crossvect(rest u1,rest u2);


{v3*w4 - v4*w3,

  - v2*w4 + v4*w2,

 v2*w3 - v3*w2}

mpvect(rest u1,rest u2, minvect(rest u1,rest u2));


0

scalvect(crossvect(rest u1,rest u2),minvect(rest u1,rest u2));


0

;


Comment 14. HANDLING OF GRASSMANN OPERATORS:;

;


putgrass eta,eta1;


grasskernel:=
{eta(~x)*eta(~y) => -eta y * eta x when nordp(x,y),
(~x)*(~x) => 0 when grassp x};


grasskernel := {eta(~x)*eta(~y) =>  - eta(y)*eta(x) when nordp(x,y),

                ~x*~x => 0 when grassp(x)}

;


eta(y)*eta(x);


eta(y)*eta(x)

eta(y)*eta(x) where grasskernel;


 - eta(x)*eta(y)

let grasskernel;


eta(x)^2;


0

eta(y)*eta(x);


 - eta(x)*eta(y)

operator zz;


grassparity (eta(x)*zz(y));


1

grassparity (eta(x)*eta(y));


0

grassparity(eta(x)+zz(y));


parity undefined

clearrules grasskernel;


grasskernel:=
{eta(~x)*eta(~y) => -eta y * eta x when nordp(x,y),
eta1(~x)*eta(~y) => -eta x * eta1 y,
eta1(~x)*eta1(~y) => -eta1 y * eta1 x when nordp(x,y),
(~x)*(~x) => 0 when grassp x};


grasskernel := {eta(~x)*eta(~y) =>  - eta(y)*eta(x) when nordp(x,y),

                eta1(~x)*eta(~y) =>  - eta(x)*eta1(y),

                eta1(~x)*eta1(~y) =>  - eta1(y)*eta1(x) when nordp(x,y),

                ~x*~x => 0 when grassp(x)}

;


let grasskernel;


eta1(x)*eta(x)*eta1(z)*eta1(w);


 - eta(x)*eta1(s1)*eta1(w)*eta1(x)

clearrules grasskernel;


remgrass eta,eta1;


clearop zz;


t

;


Comment  15. HANDLING OF MATRICES:;

;


clear m,mm,b,b1,bb,cc,a,b,c,d,a1,a2;


load_package matrix;


baglmat(bag(bag(a1,a2)),m);


t

m;


[a1  a2]


on errcont;


;


baglmat(bag(bag(a1),bag(a2)),m);


***** (mat ((*sq ((((a1 . 1) . 1)) . 1) t) (*sq ((((a2 . 1) . 1)) . 1) t))) 
should be an identifier 

off errcont;


%    **** i.e. it cannot redefine the matrix! in order
%         to avoid accidental redefinition of an already given matrix;

clear m;

 baglmat(bag(bag(a1),bag(a2)),m);


t

m;


[a1]
[  ]
[a2]


on errcont;


baglmat(bag(bag(a1),bag(a2)),bag);


***** operator bag invalid as matrix

off errcont;


comment  Right since a bag-like object cannot become a matrix.;

;


coercemat(m,op);


op(op(a1),op(a2))

coercemat(m,list);


{{a1},{a2}}

;


on nero;


unitmat b1(2);


matrix b(2,2);


b:=mat((r1,r2),(s1,s2));


     [r1  r2]
b := [      ]
     [s1  s2]


b1;


[1  0]
[    ]
[0  1]

b;


[r1  r2]
[      ]
[s1  s2]


mkidm(b,1);


[1  0]
[    ]
[0  1]


;


seteltmat(b,newelt,2,2);


[r1    r2  ]
[          ]
[s1  newelt]


geteltmat(b,2,1);


s1

%
b:=matsubr(b,bag(1,2),2);


     [r1  r2]
b := [      ]
     [1   2 ]


;


submat(b,1,2);


[1]


;


bb:=mat((1+i,-i),(-1+i,-i));


      [i + 1   - i]
bb := [           ]
      [i - 1   - i]


cc:=matsubc(bb,bag(1,2),2);


      [i + 1  1]
cc := [        ]
      [i - 1  2]


;


cc:=tp matsubc(bb,bag(1,2),2);


      [i + 1  i - 1]
cc := [            ]
      [  1      2  ]


matextr(bb, bag,1);


bag(i + 1, - i)

;


matextc(bb,list,2);


{ - i, - i}

;


hconcmat(bb,cc);


[i + 1   - i  i + 1  i - 1]
[                         ]
[i - 1   - i    1      2  ]


vconcmat(bb,cc);


[i + 1   - i ]
[            ]
[i - 1   - i ]
[            ]
[i + 1  i - 1]
[            ]
[  1      2  ]


;


tpmat(bb,bb);


[ 2*i     - i + 1   - i + 1  -1]
[                              ]
[  -2     - i + 1   i + 1    -1]
[                              ]
[  -2     i + 1     - i + 1  -1]
[                              ]
[ - 2*i   i + 1     i + 1    -1]


bb tpmat bb;


[ 2*i     - i + 1   - i + 1  -1]
[                              ]
[  -2     - i + 1   i + 1    -1]
[                              ]
[  -2     i + 1     - i + 1  -1]
[                              ]
[ - 2*i   i + 1     i + 1    -1]


;


clear hbb;


hermat(bb,hbb);


[ - i + 1   - (i + 1)]
[                    ]
[   i          i     ]


% id hbb changed to a matrix id and assigned to the hermitian matrix
% of bb.
;


end;
(TIME:  assist 940 950)