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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)