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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