22.19

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
22.19.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}\theta(t)}{{\mathrm{d}t}^{2}}=-\sin\theta(t)}}$ \deriv[2]{\theta(t)}{t} = -\sin@@{\theta(t)}		diff(theta(t), [t$(2)]) = - sin(theta(t))	D[\[Theta][t], {t, 2}] == - Sin[\[Theta][t]]	Failure	Failure	Failed [60 / 60] Result: -1.247168970-.2207308174*I Test Values: {t = -3/2, theta = 1/2*3^(1/2)+1/2*I} Result: 1.342338585-1.241300956*I Test Values: {t = -3/2, theta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [60 / 60] Result: Complex[-1.247168970138959, -0.22073081765616068] Test Values: {Rule[t, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.3423385844153726, -1.2413009551766627] Test Values: {Rule[t, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
22.19.E2	${\displaystyle{\displaystyle\sin\left(\tfrac{1}{2}\theta(t)\right)=\sin\left(\frac{1}{2}\alpha\right)\operatorname{sn}\left(t+K,\sin\left(\tfrac{1}{2}\alpha\right)\right)}}$ \sin@{\tfrac{1}{2}\theta(t)} = \sin@{\frac{1}{2}\alpha}\Jacobiellsnk@{t+K}{\sin@{\tfrac{1}{2}\alpha}}		sin((1)/(2)*theta(t)) = sin((1)/(2)*alpha)*JacobiSN(t + EllipticK(k), sin((1)/(2)*alpha))	Sin[Divide[1,2]*\[Theta][t]] == Sin[Divide[1,2]*\[Alpha]]*JacobiSN[t + EllipticK[(k)^2], (Sin[Divide[1,2]*\[Alpha]])^2]	Failure	Failure	Error	Failed [300 / 300] Result: Plus[Complex[-0.6478293894548304, -0.30568930559799934], Times[-0.6816387600233341, JacobiSN[DirectedInfinity[], 0.4646313991661485]]] Test Values: {Rule[k, 1], Rule[t, -1.5], Rule[α, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.12355997139036334, 0.2467451262932382] Test Values: {Rule[k, 2], Rule[t, -1.5], Rule[α, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.19.E3	${\displaystyle{\displaystyle\theta(t)=2\operatorname{am}\left(t\sqrt{E/2},\sqrt{2/E}\right)}}$ \theta(t) = 2\Jacobiamk@{t\sqrt{E/2}}{\sqrt{2/E}}		theta(t) = 2*JacobiAM(t*sqrt(E/2), sqrt(2/E))	\[Theta][t] == 2*JacobiAmplitude[t*Sqrt[E/2], Power[Sqrt[2/E], 2]]	Failure	Failure	Failed [300 / 300] Result: .133442481-.3164102922*I Test Values: {E = 1/2*3^(1/2)+1/2*I, t = -3/2, theta = 1/2*3^(1/2)+1/2*I} Result: 2.182480587-.8654483982*I Test Values: {E = 1/2*3^(1/2)+1/2*I, t = -3/2, theta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.13344248094652933, -0.31641029231150586] Test Values: {Rule[E, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[x, Rational[3, 2]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[2.182480586623187, -0.865448397988164] Test Values: {Rule[E, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[x, Rational[3, 2]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
22.19.E5	${\displaystyle{\displaystyle V(x)=+\tfrac{1}{2}x^{2}+\tfrac{1}{4}\beta x^{4}}}$ V(x) = +\tfrac{1}{2}x^{2}+\tfrac{1}{4}\beta x^{4}		V(x) = +(1)/(2)*(x)^(2)+(1)/(4)*beta*(x)^(4)	V[x] == +Divide[1,2]*(x)^(2)+Divide[1,4]*\[Beta]*(x)^(4)	Skipped - no semantic math	Skipped - no semantic math	-	-
22.19.E6	${\displaystyle{\displaystyle x(t)=a\operatorname{cn}\left(t\sqrt{1+2\eta},k\right)}}$ x(t) = a\Jacobiellcnk@{t\sqrt{1+2\eta}}{k}		x(t) = a*JacobiCN(t*sqrt(1 + 2*eta), k)	x[t] == a*JacobiCN[t*Sqrt[1 + 2*\[Eta]], (k)^2]	Failure	Failure	Failed [300 / 300] Result: -2.032489573-.1028075729*I Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1} Result: -1.103953626-.7415756720e-2*I Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-2.032489572589819, -0.10280757291863922] Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.103953626215099, -0.007415756590236153] Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.19.E7	${\displaystyle{\displaystyle x(t)=a\operatorname{sn}\left(t\sqrt{1-\eta},k\right)}}$ x(t) = a\Jacobiellsnk@{t\sqrt{1-\eta}}{k}		x(t) = a*JacobiSN(t*sqrt(1 - eta), k)	x[t] == a*JacobiSN[t*Sqrt[1 - \[Eta]], (k)^2]	Failure	Failure	Failed [300 / 300] Result: -3.540811611+.4656977091*I Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1} Result: -3.440732980-.1498418752e-1*I Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-3.5408116110434387, 0.46569770889881135] Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-3.4407329797279083, -0.014984187659583321] Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.19.E8	${\displaystyle{\displaystyle x(t)=a\operatorname{dn}\left(t\sqrt{\eta},k\right)}}$ x(t) = a\Jacobielldnk@{t\sqrt{\eta}}{k}		x(t) = a*JacobiDN(t*sqrt(eta), k)	x[t] == a*JacobiDN[t*Sqrt[\[Eta]], (k)^2]	Failure	Failure	Failed [300 / 300] Result: -1.613955183-.2329422536*I Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1} Result: -3.968457087-.6161541466*I Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-1.6139551823182394, -0.23294225362869586] Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-3.968457085129692, -0.6161541479869231] Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.19.E9	${\displaystyle{\displaystyle x(t)=a\operatorname{cn}\left(t\sqrt{2\eta-1},k\right)}}$ x(t) = a\Jacobiellcnk@{t\sqrt{2\eta-1}}{k}		x(t) = a*JacobiCN(t*sqrt(2*eta - 1), k)	x[t] == a*JacobiCN[t*Sqrt[2*\[Eta]- 1], (k)^2]	Failure	Failure	Failed [300 / 300] Result: -1.736815452-.4365167404*I Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1} Result: -.272323884+.8696505748*I Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-1.7368154521565795, -0.4365167405198458] Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.27232388329398516, 0.8696505752545954] Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data