reduce-historical/r36/xlog/ORTHOVEC.LOG

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



*** + redefined 

*** - redefined 

*** * redefined 

*** / redefined 

*** ^ redefined 
%===========================================
%test file for ORTHOVEC version 2, June 1990
%===========================================

showtime;


Time: 20 ms


%example 1: vector identity
a:=svec(a1,a2,a3);


a := [a1,a2,a3]

b:=svec(b1,b2,b3);


b := [b1,b2,b3]

c:=svec(c1,c2,c3);


c := [c1,c2,c3]

d:=svec(d1,d2,d3);


d := [d1,d2,d3]


a><b*c><d - (a*c)*(b*d) + (a*d)*(b*c);


0

%showtime;

%example 2: Equation of Motion in cylindricals
vstart$


Select Coordinate System by number

1] cartesian

2] cylindrical

3] spherical

4] general

5] others

2

coordinate type = 2

coordinates = r,th,z

scale factors = 1,r,1
v:=svec(vr,vt,vz)$

b:=svec(br,bt,bz)$


depend v,r,th,z$


depend b,r,th,z$


depend p,r,th,z$



eom:=vout( vdf(v,tt) + v dotgrad v + grad(p) - curl(b) >< b )$


[1] ( - df(br,th)*bt - df(br,z)*bz*r + df(bt,r)*bt*r + df(bz,r)*bz*r + df(p,r)*r

                                                         2     2
      + df(vr,r)*r*vr + df(vr,th)*vt + df(vr,z)*r*vz + bt  - vt )/r

[2] (df(br,th)*br - df(bt,r)*br*r - df(bt,z)*bz*r + df(bz,th)*bz + df(p,th)

      + df(vt,r)*r*vr + df(vt,th)*vt + df(vt,z)*r*vz - br*bt + vr*vt)/r

[3] (df(br,z)*br*r + df(bt,z)*bt*r - df(bz,r)*br*r - df(bz,th)*bt + df(p,z)*r

      + df(vz,r)*r*vr + df(vz,th)*vt + df(vz,z)*r*vz)/r

%showtime;

%example 3: Taylor expansions
on div;


on revpri;


vtaylor(sin(x)*cos(y)+e**z,svec(x,y,z),svec(0,0,0),svec(3,4,5));


         1   2    1   3    1    4     1    5        1     2    1      4    1   3
1 + z + ---*z  + ---*z  + ----*z  + -----*z  + x - ---*x*y  + ----*x*y  - ---*x
         2        6        24        120            2          24          6

    1    3  2     1    3  4
 + ----*x *y  - -----*x *y
    12           144

vtaylor(sin(x)/x,x,0,5);


     1   2     1    4
1 - ---*x  + -----*x
     6        120

te:=vtaylor(svec(x/sin(x),(e**y-1)/y,(1+z)**10),svec(x,y,z),
svec(0,0,0),5);


                  2      4                      2       3      4    5
        360 + 60*x  + 7*x    720 + 360*y + 120*y  + 30*y  + 6*y  + y
te := [--------------------,------------------------------------------,1 + 10*z
               360                             720

             2        3        4        5
       + 45*z  + 120*z  + 210*z  + 252*z ]

%showtime;

%example 4: extract components
eom _2;


 -1                -1                            -1
r  *vr*vt - br*bt*r   + df(vt,z)*vz + df(vt,th)*r  *vt + df(vt,r)*vr

             -1                 -1
 + df(p,th)*r   + df(bz,th)*bz*r   - df(bt,z)*bz - df(bt,r)*br

                 -1
 + df(br,th)*br*r

te _1;


     1   2     7    4
1 + ---*x  + -----*x
     6        360

off div;


off revpri;


%showtime;

%example 5: Line Integral
vstart$


Select Coordinate System by number

1] cartesian

2] cylindrical

3] spherical

4] general

5] others

1

coordinate type = 1

coordinates = x,y,z

scale factors = 1,1,1
dlineint(svec(3*x**2+5*y,-12*y*z,2*x*y*z**2),svec(s,s**2,s**3),s,1,2);


 68491
-------
  42

%showtime;

%example 6: Volume Integral
ub:=sqrt(r**2-x**2)$


8 * dvolint(1,svec(0,0,0),svec(r,ub,ub),6);


     3
 16*r
-------
   3


%===========================================
% end of test
%===========================================
showtime;


Time: 1290 ms  plus GC time: 60 ms

;

end;
(TIME:  orthovec 1330 1390)