[rychlik@ruby Maxima]$ maxima GCL (GNU Common Lisp) Version(2.4.0) Sun Sep 22 00:12:12 MST 2002 Licensed under GNU Library General Public License Contains Enhancements by W. Schelter Maxima 5.6 Tue May 21 11:08:32 MST 2002 (with enhancements by W. Schelter). Licensed under the GNU Public License (see file COPYING) (C1) s^2-2*r*s*cos(theta)+r^2=d^2; 2 2 2 (D1) - 2 s COS(theta) + s + r = d (C2) solve(d1,s); 2 2 2 (D2) [s = COS(theta) - SQRT(COS (theta) - r + d ), 2 2 2 s = SQRT(COS (theta) - r + d ) + COS(theta)] (C3) s1 : rhs(d2[1]); 2 2 2 (D3) COS(theta) - SQRT(COS (theta) - r + d ) (C4) s1; 2 2 2 (D4) COS(theta) - SQRT(COS (theta) - r + d ) (C5) s2 : rhs(d2[2]); 2 2 2 (D5) SQRT(COS (theta) - r + d ) + COS(theta) (C6) s^2-2*r*s*cos(theta)+r^2=d^2; 2 2 2 (D6) - 2 r s COS(theta) + s + r = d (C7) solve(d1,s); 2 2 2 (D7) [s = COS(theta) - SQRT(COS (theta) - r + d ), 2 2 2 s = SQRT(COS (theta) - r + d ) + COS(theta)] (C8) s1 : rhs(d2[1]); 2 2 2 (D8) COS(theta) - SQRT(COS (theta) - r + d ) (C9) s2 : rhs(d2[2]); 2 2 2 (D9) SQRT(COS (theta) - r + d ) + COS(theta) (C10) batch("script.maxima"); batching #p/home/rychlik/481/InClassFiles2005/Maxima/script.maxima 2 2 2 (C11) eqn : r - 2 r s COS(theta) + s = d 2 2 2 (D11) - 2 r s COS(theta) + s + r = d (C12) SOLVE(eqn, s) 2 2 2 (D12) [s = r COS(theta) - SQRT(r (COS (theta) - 1) + d ), 2 2 2 s = SQRT(r (COS (theta) - 1) + d ) + r COS(theta)] (C13) s1 : RHS(D2 ) 1 2 2 2 (D13) COS(theta) - SQRT(COS (theta) - r + d ) (C14) s2 : RHS(D2 ) 2 2 2 2 (D14) SQRT(COS (theta) - r + d ) + COS(theta) (C15) batch("script.maxima"); batching #p/home/rychlik/481/InClassFiles2005/Maxima/script.maxima 2 2 2 (C16) eqn : r - 2 r s COS(theta) + s = d 2 2 2 (D16) - 2 r s COS(theta) + s + r = d (C17) solution : SOLVE(eqn, s) 2 2 2 (D17) [s = r COS(theta) - SQRT(r (COS (theta) - 1) + d ), 2 2 2 s = SQRT(r (COS (theta) - 1) + d ) + r COS(theta)] (C18) s1 : RHS(solution ) 1 2 2 2 (D18) r COS(theta) - SQRT(r (COS (theta) - 1) + d ) (C19) s2 : RHS(solution ) 2 2 2 2 (D19) SQRT(r (COS (theta) - 1) + d ) + r COS(theta) (C20) quit(); [rychlik@ruby Maxima]$ maxima GCL (GNU Common Lisp) Version(2.4.0) Sun Sep 22 00:12:12 MST 2002 Licensed under GNU Library General Public License Contains Enhancements by W. Schelter Maxima 5.6 Tue May 21 11:08:32 MST 2002 (with enhancements by W. Schelter). Licensed under the GNU Public License (see file COPYING) (C1) batch("script.maxima"); batching #p/home/rychlik/481/InClassFiles2005/Maxima/script.maxima 2 2 2 (C2) eqn : r - 2 r s COS(theta) + s = d 2 2 2 (D2) - 2 r s COS(theta) + s + r = d (C3) solution : SOLVE(eqn, s) 2 2 2 (D3) [s = r COS(theta) - SQRT(r (COS (theta) - 1) + d ), 2 2 2 s = SQRT(r (COS (theta) - 1) + d ) + r COS(theta)] (C4) s1 : RHS(solution ) 1 2 2 2 (D4) r COS(theta) - SQRT(r (COS (theta) - 1) + d ) (C5) s2 : RHS(solution ) 2 2 2 2 (D5) SQRT(r (COS (theta) - 1) + d ) + r COS(theta) (C6) solve([x^2+y^2-3=7, x*y=1],[x,y]); 1 (D6) [[x = - SQRT(2 SQRT(6) + 5), y = - ---------------------------], SQRT(2 SQRT(2) SQRT(3) + 5) 1 [x = SQRT(2 SQRT(6) + 5), y = ---------------------------], SQRT(2 SQRT(2) SQRT(3) + 5) 1 [x = - SQRT(5 - 2 SQRT(6)), y = - ---------------------------], SQRT(5 - 2 SQRT(2) SQRT(3)) 1 [x = SQRT(5 - 2 SQRT(6)), y = ---------------------------]] SQRT(5 - 2 SQRT(2) SQRT(3)) (C7) solve(x^3+5*x-1=7,x); SQRT(3) %I 1 5 (---------- - -) SQRT(557) 1/3 SQRT(3) %I 1 2 2 (D7) [x = (--------- + 4) (- ---------- - -) - --------------------, 3 SQRT(3) 2 2 SQRT(557) 1/3 3 (--------- + 4) 3 SQRT(3) SQRT(3) %I 1 5 (- ---------- - -) SQRT(557) 1/3 SQRT(3) %I 1 2 2 x = (--------- + 4) (---------- - -) - --------------------, 3 SQRT(3) 2 2 SQRT(557) 1/3 3 (--------- + 4) 3 SQRT(3) SQRT(557) 1/3 5 x = (--------- + 4) - --------------------] 3 SQRT(3) SQRT(557) 1/3 3 (--------- + 4) 3 SQRT(3) (C8) %,numer; (D8) [x = 2.044182212811586 (- 0.86602540378444 %I - 0.5) - 0.81532196896201 (0.86602540378444 %I - 0.5), x = 2.044182212811586 (0.86602540378444 %I - 0.5) - 0.81532196896201 (- 0.86602540378444 %I - 0.5), x = 1.228860243849574] (C9) expand(%); (D9) [x = - 2.476403263643772 %I - 0.61443012192479, x = 2.476403263643772 %I - 0.61443012192479, x = 1.228860243849574] (C10) %pi,numer; (D10) %PI (C11) %pi,numer; (D11) 3.141592653589793 (C12) s1; 2 2 2 (D12) r COS(theta) - SQRT(r (COS (theta) - 1) + d ) (C13) s2; 2 2 2 (D13) SQRT(r (COS (theta) - 1) + d ) + r COS(theta) (C14) s : s1, theta = omega * t; 2 2 2 (D14) r COS(omega t) - SQRT(r (COS (omega t) - 1) + d ) (C15) x^2+y^2, y=8; 2 (D15) x + 64 (C16) s ; 2 2 2 (D16) r COS(omega t) - SQRT(r (COS (omega t) - 1) + d ) (C17) diff(x^2+1, x) ; (D17) 2 x (C18) diff(x^2+1, x) ; (D18) 2 x (C19) diff(x^2+1, x, 2) ; (D19) 2 (C20) diff(exp(1/(x-1)),x,2); 1 1 ----- ----- x - 1 x - 1 2 %E %E (D20) --------- + -------- 3 4 (x - 1) (x - 1) (C21) expand(%); 1 1 ----- ----- x - 1 x - 1 %E 2 %E (D21) -------------------------- + ------------------- 4 3 2 3 2 x - 4 x + 6 x - 4 x + 1 x - 3 x + 3 x - 1 (C22) simplify(%); 1 1 ----- ----- x - 1 x - 1 %E 2 %E (D22) simplify(-------------------------- + -------------------) 4 3 2 3 2 x - 4 x + 6 x - 4 x + 1 x - 3 x + 3 x - 1 (C23) d21,simp; 1 1 ----- ----- x - 1 x - 1 %E 2 %E (D23) -------------------------- + ------------------- 4 3 2 3 2 x - 4 x + 6 x - 4 x + 1 x - 3 x + 3 x - 1 (C24) simp(d21); SIMP evaluates to TRUE Improper name or value in functional position. -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) (C25) (x+1)^2; 2 (D25) (x + 1) (C26) expand(%); 2 (D26) x + 2 x + 1 (C27) factor(%); 2 (D27) (x + 1) (C28) xthru((x+1)*(a+b)); (D28) (b + a) (x + 1) (C29) trigsimp(sin(x)^2+cos(x)^2); (D29) 1 (C30) diff(s, t, 2); t d 2 2 2 (D30) --- (r COS(omega t) - SQRT(r (COS (omega t) - 1) + d )) t dt (C31) diff(s, t, 2); 2 2 2 omega r SIN (omega t) (D31) - --------------------------------- 2 2 2 SQRT(r (COS (omega t) - 1) + d ) 2 4 2 2 2 2 2 omega r COS (omega t) SIN (omega t) omega r COS (omega t) + ------------------------------------- + --------------------------------- 2 2 2 3/2 2 2 2 (r (COS (omega t) - 1) + d ) SQRT(r (COS (omega t) - 1) + d ) 2 - omega r COS(omega t) (C32) ratsimp(%); 2 2 2 2 4 2 2 4 4 (D32) - ((d omega r - omega r ) SIN (omega t) - omega r COS (omega t) 2 2 2 2 2 3 3 + SQRT(r COS (omega t) - r + d ) (omega r COS (omega t) 2 2 2 3 + (d omega r - omega r ) COS(omega t)) 2 4 2 2 2 2 2 2 2 2 3/2 + (omega r - d omega r ) COS (omega t))/(r COS (omega t) - r + d ) (C33) trigsimp(%); 2 4 4 2 2 2 (D33) - (omega r SIN (omega t) + SQRT(d - r SIN (omega t)) 2 3 2 2 2 (omega r COS(omega t) SIN (omega t) - d omega r COS(omega t)) 2 2 2 2 2 2 2 - 2 d omega r SIN (omega t) + d omega r ) 2 2 2 2 2 2 /(SQRT(d - r SIN (omega t)) (r SIN (omega t) - d )) (C34) d33; 2 4 4 2 2 2 (D34) - (omega r SIN (omega t) + SQRT(d - r SIN (omega t)) 2 3 2 2 2 (omega r COS(omega t) SIN (omega t) - d omega r COS(omega t)) 2 2 2 2 2 2 2 - 2 d omega r SIN (omega t) + d omega r ) 2 2 2 2 2 2 /(SQRT(d - r SIN (omega t)) (r SIN (omega t) - d )) (C35) trigreduce(%); 2 4 2 (D35) omega r COS(4 omega t)/(2 SQRT(2) r COS(2 omega t) 2 2 2 2 SQRT(r COS(2 omega t) - r + 2 d ) - 2 SQRT(2) r 2 2 2 2 SQRT(r COS(2 omega t) - r + 2 d ) + 4 SQRT(2) d 2 3 2 2 2 omega r COS(3 omega t) SQRT(r COS(2 omega t) - r + 2 d )) - --------------------------------- 2 2 2 2 r COS(2 omega t) - 2 r + 4 d 2 4 2 2 2 2 + 3 omega r /(2 SQRT(2) r COS(2 omega t) SQRT(r COS(2 omega t) - r + 2 d ) 2 2 2 2 - 2 SQRT(2) r SQRT(r COS(2 omega t) - r + 2 d ) 2 2 2 2 + 4 SQRT(2) d SQRT(r COS(2 omega t) - r + 2 d )) 2 4 2 2 2 - 2 omega r COS(2 omega t)/(SQRT(r COS(2 omega t) - r + 2 d ) 2 2 2 (SQRT(2) r COS(2 omega t) - SQRT(2) r + 2 SQRT(2) d )) 2 2 2 2 2 2 + 4 d omega r COS(2 omega t)/(SQRT(r COS(2 omega t) - r + 2 d ) 2 2 2 (SQRT(2) r COS(2 omega t) - SQRT(2) r + 2 SQRT(2) d )) 2 3 2 2 omega r COS(omega t) 2 d omega r COS(omega t) + --------------------------------- - ----------------------------- 2 2 2 2 2 2 2 r COS(2 omega t) - 2 r + 4 d r COS(2 omega t) - r + 2 d (C36) d33; 2 4 4 2 2 2 (D36) - (omega r SIN (omega t) + SQRT(d - r SIN (omega t)) 2 3 2 2 2 (omega r COS(omega t) SIN (omega t) - d omega r COS(omega t)) 2 2 2 2 2 2 2 - 2 d omega r SIN (omega t) + d omega r ) 2 2 2 2 2 2 /(SQRT(d - r SIN (omega t)) (r SIN (omega t) - d )) (C37) batch("script.maxima"); batching #p/home/rychlik/481/InClassFiles2005/Maxima/script.maxima 2 2 2 (C38) eqn : r - 2 r s COS(theta) + s = d 2 2 2 (D38) - 2 r (r COS(omega t) - SQRT(r (COS (omega t) - 1) + d )) COS(theta) 2 2 2 2 2 2 + (r COS(omega t) - SQRT(r (COS (omega t) - 1) + d )) + r = d (C39) solution : SOLVE(eqn, s) (D39) [] (C40) s1 : RHS(solution ) 1 Improper index to list or matrix -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) (C41) batch("script.maxima"); batching #p/home/rychlik/481/InClassFiles2005/Maxima/script.maxima (C42) KILL(s, eqn, solution, s1, s2, s, theta, omega) (D42) DONE 2 2 2 (C43) eqn : r - 2 r s COS(theta) + s = d 2 2 2 (D43) - 2 r s COS(theta) + s + r = d (C44) solution : SOLVE(eqn, s) 2 2 2 (D44) [s = r COS(theta) - SQRT(r (COS (theta) - 1) + d ), 2 2 2 s = SQRT(r (COS (theta) - 1) + d ) + r COS(theta)] (C45) s1 : RHS(solution ) 1 2 2 2 (D45) r COS(theta) - SQRT(r (COS (theta) - 1) + d ) (C46) s2 : RHS(solution ) 2 2 2 2 (D46) SQRT(r (COS (theta) - 1) + d ) + r COS(theta) (C47) EV(s : s1, theta = omega t) 2 2 2 (D47) r COS(omega t) - SQRT(r (COS (omega t) - 1) + d ) (C48) s : TRIGSIMP(RATSIMP(s)) 2 2 2 (D48) r COS(omega t) - SQRT(d - r SIN (omega t)) (C49) batch("script.maxima"); batching #p/home/rychlik/481/InClassFiles2005/Maxima/script.maxima (C50) KILL(s, eqn, solution, s1, s2, s, theta, omega, ds2) (D50) DONE 2 2 2 (C51) eqn : r - 2 r s COS(theta) + s = d 2 2 2 (D51) - 2 r s COS(theta) + s + r = d (C52) solution : SOLVE(eqn, s) 2 2 2 (D52) [s = r COS(theta) - SQRT(r (COS (theta) - 1) + d ), 2 2 2 s = SQRT(r (COS (theta) - 1) + d ) + r COS(theta)] (C53) s1 : RHS(solution ) 1 2 2 2 (D53) r COS(theta) - SQRT(r (COS (theta) - 1) + d ) (C54) s2 : RHS(solution ) 2 2 2 2 (D54) SQRT(r (COS (theta) - 1) + d ) + r COS(theta) (C55) EV(s : s1, theta = omega t) 2 2 2 (D55) r COS(omega t) - SQRT(r (COS (omega t) - 1) + d ) (C56) ds2 : TRIGSIMP(RATSIMP(DIFF(s, t, 2))) 2 4 4 2 2 2 (D56) - (omega r SIN (omega t) + SQRT(d - r SIN (omega t)) 2 3 2 2 2 (omega r COS(omega t) SIN (omega t) - d omega r COS(omega t)) 2 2 2 2 2 2 2 - 2 d omega r SIN (omega t) + d omega r ) 2 2 2 2 2 2 /(SQRT(d - r SIN (omega t)) (r SIN (omega t) - d )) (C57) string(d56); (D57) (C58)