Sat May 30 16:26:35 PDT 1992
REDUCE 3.4.1, 15-Jul-92 ...
1: 1:
2: 2:
*** + redefined
*** - redefined
*** * redefined
*** / redefined
*** ^ redefined
(ORTHOVEC)
3: 3:
Time: 51 ms
4: 4: %===========================================
%test file for ORTHOVEC version 2, June 1990
%===========================================
showtime;
Time: 0 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: 3043 ms plus GC time: 85 ms
;
end;
5: 5:
Time: 0 ms
6: 6:
Quitting
Sat May 30 16:26:40 PDT 1992