reduce-historical/r34/xlog/orthovec.log

Sat Jun 29 14:15:50 PDT 1991
REDUCE 3.4, 15-Jul-91 ...

1: 1: 
2: 2: 
*** + redefined 

*** - redefined 

*** * redefined 

*** / redefined 

*** ^ redefined 

3: 3: %===========================================
%test file for ORTHOVEC version 2, June 1990
%===========================================

showtime;


Time: 17 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(P,R)*R + DF(VR,R)*R*VR + DF(VR,Z)*R*VZ + DF(VR,TH)*VT

      - DF(BR,Z)*R*BZ - DF(BR,TH)*BT + DF(BT,R)*R*BT + DF(BZ,R)*R*BZ

          2     2
      - VT  + BT )/R

[2] (DF(P,TH) + DF(VT,R)*R*VR + DF(VT,Z)*R*VZ + DF(VT,TH)*VT

      + DF(BR,TH)*BR - DF(BT,R)*R*BR - DF(BT,Z)*R*BZ + DF(BZ,TH)*BZ

      + VR*VT - BR*BT)/R

[3] (DF(P,Z)*R + DF(VZ,R)*R*VR + DF(VZ,Z)*R*VZ + DF(VZ,TH)*VT

      + DF(BR,Z)*R*BR + DF(BT,Z)*R*BT - DF(BZ,R)*R*BR - DF(BZ,TH)*BT)

    /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 + Z + ---*Z  + ---*Z  + ----*Z  + -----*Z  + X - ---*X*Y
         2        6        24        120            2

    1      4    1   3    1    3  2     1    3  4
 + ----*X*Y  - ---*X  + ----*X *Y  - -----*X *Y
    24          6        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
        360 + 60*X  + 7*X
TE := [--------------------,
               360

                          2       3      4    5
       720 + 360*Y + 120*Y  + 30*Y  + 6*Y  + Y                  2
      ------------------------------------------,1 + 10*Z + 45*Z
                         720

              3        4        5
       + 120*Z  + 210*Z  + 252*Z ]

%showtime;

%example 4: extract components
eom _2;


    -1          -1                    -1
 - R  *BR*BT + R  *VR*VT + DF(BZ,TH)*R  *BZ - DF(BT,Z)*BZ

                            -1                 -1
 - DF(BT,R)*BR + DF(BR,TH)*R  *BR + DF(VT,TH)*R  *VT + DF(VT,Z)*VZ

                           -1
 + DF(VT,R)*VR + DF(P,TH)*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: 7684 ms


;

end;

4: 4: 
Quitting
Sat Jun 29 14:15:59 PDT 1991