Tue Apr 15 00:34:40 2008 run on win32
*** + redefined
*** - redefined
*** * redefined
*** / redefined
*** ^ redefined
%===========================================
%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(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: 64 ms plus GC time: 6 ms
;
end;
Time for test: 64 ms, plus GC time: 7 ms