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Online Algebra Calculator
Many of users do not use powerful Maxima computer algebra system for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only. To do this job, it is not useful to download the whole application from a web site.
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factorout
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(%i1)a:matrix([0,-(wz+c),(wy+b)],[(wz+c),0,-(wx+a)],[-(wy+b),(wx+a),0]); [ 0 - wz - c wy + b ] [ ] (%o1) [ wz + c 0 - wx - a ] [ ] [ - wy - b wx + a 0 ] (%i2) b:matrix([p,q,r]); (%o2) [ p q r ] (%i3) E:a.b; [ q (- wz - c) + r (wy + b) ] [ ] (%o3) [ p (wz + c) + r (- wx - a) ] [ ] [ p (- wy - b) + q (wx + a) ] (%i4) F:expand(E); [ - q wz + r wy + b r - c q ] [ ] (%o4) [ p wz - r wx - a r + c p ] [ ] [ - p wy + q wx + a q - b p ] (%i5) factorout(F[1,1],b,c); (%o5) - q wz + r wy + b r - c q (%i6)
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vdWP:R*T/(V-b)-a/V^2; R T a (%o1) ----- - -- V - b 2 V (%i2) vdW:P=vdWP; R T a (%o2) P = ----- - -- V - b 2 V (%i3) vdWT:solve(vdW,T); 3 2 P V - b P V + a V - a b (%o3) [T = -------------------------] 2 R V (%i4) alpha:(V)*diff(vdWT,V); 2 3 2 3 P V - 2 b P V + a 2 (P V - b P V + a V - a b) (%o4) [0 = V (-------------------- - -----------------------------)] 2 3 R V R V (%i5) kappa:-(1/V)/diff(vdWP,V); 1 (%o5) - ------------------ 2 a R T V (--- - --------) 3 2 V (V - b) (%i6) delC:T*V*(alpha^2/kappa); 2 3 2 4 3 P V - 2 b P V + a 2 (P V - b P V + a V - a b) 2 (%o6) [0 = - T V (-------------------- - -----------------------------) 2 3 R V R V 2 a R T (--- - --------)] 3 2 V (V - b) (%i7) factorout(delC,R); 2 3 2 4 3 P V - 2 b P V + a 2 (P V - b P V + a V - a b) 2 (%o7) [0 = - T V (-------------------- - -----------------------------) 2 3 R V R V 2 a R T (--- - --------)] 3 2 V (V - b) (%i8)
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globalsolve: true; (%o1) true (%i2) realonly: true; (%o2) true (%i3) /* Standard (x,y)-> (r,theta) coordinate translation */x(t) := r(t) * cos(theta(t)); (%o3) x(t) := r(t) cos(theta(t)) (%i4) y(t) := r(t) * sin(theta(t)); (%o4) y(t) := r(t) sin(theta(t)) (%i5) /* Constant course assumption */declare (slope,constant); (%o5) done (%i6) declare (slope,real); (%o6) done (%i7) declare (yintercept,constant); (%o7) done (%i8) declare (yintercept, real); (%o8) done (%i9) y(t)=slope * x(t) + yintercept; (%o9) r(t) sin(theta(t)) = slope r(t) cos(theta(t)) + yintercept (%i10) eq1: y(t)=slope * x(t) + yintercept; (%o10) r(t) sin(theta(t)) = slope r(t) cos(theta(t)) + yintercept (%i11) /* Constant speed assumption */declare (speedx,constant); (%o11) done (%i12) declare (speedx,real); (%o12) done (%i13) declare (speedy,constant); (%o13) done (%i14) declare (speedy,real); (%o14) done (%i15) declare (c1, constant); (%o15) done (%i16) declare (c1, real); (%o16) done (%i17) eq2: x(t) = speedx * (t + c1); (%o17) r(t) cos(theta(t)) = speedx (t + c1) (%i18) declare (c2, constant); (%o18) done (%i19) declare (c2, real); (%o19) done (%i20) eq3: y(t) = speedy * (t + c1) + c2*speedx; (%o20) r(t) sin(theta(t)) = speedy (t + c1) + c2 speedx (%i21) eq4: (rhs(eq3/eq2)); speedy (t + c1) + c2 speedx (%o21) --------------------------- speedx (t + c1) (%i22) eq5: factorout(eq4, speedx*(t+c1)); speedy (t + c1) + c2 speedx (%o22) --------------------------- speedx (t + c1) (%i23)
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