22.18

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
22.18.E1	${\displaystyle{\displaystyle\left(x^{2}/a^{2}\right)+\left(y^{2}/b^{2}\right)=1}}$ \left(x^{2}/a^{2}\right)+\left(y^{2}/b^{2}\right) = 1		((x)^(2)/(a)^(2))+((y)^(2)/(b)^(2)) = 1	((x)^(2)/(a)^(2))+((y)^(2)/(b)^(2)) == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
22.18#Ex1	${\displaystyle{\displaystyle x=a\operatorname{sn}\left(u,k\right)}}$ x = a\Jacobiellsnk@{u}{k}		x = a*JacobiSN(u, k)	x == a*JacobiSN[u, (k)^2]	Failure	Failure	Failed [300 / 300] Result: 2.688604135+.3653402056*I Test Values: {a = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1} Result: 2.519684790-.2348240643e-1*I Test Values: {a = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[2.688604134627054, 0.3653402057357006] Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]} Result: Complex[2.5196847900911203, -0.02348240620400443] Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]} ... skip entries to safe data
22.18#Ex2	${\displaystyle{\displaystyle y=b\operatorname{cn}\left(u,k\right)}}$ y = b\Jacobiellcnk@{u}{k}		y = b*JacobiCN(u, k)	y == b*JacobiCN[u, (k)^2]	Failure	Failure	Failed [300 / 300] Result: -.433885744-.4073155167*I Test Values: {b = -3/2, u = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 1} Result: -.399423925+.2175647210e-1*I Test Values: {b = -3/2, u = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.43388574383527945, -0.40731551667372035] Test Values: {Rule[b, -1.5], Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]} Result: Complex[-0.39942392524307424, 0.021756471897004394] Test Values: {Rule[b, -1.5], Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]} ... skip entries to safe data
22.18.E4	${\displaystyle{\displaystyle l(r)=(1/\sqrt{2})\operatorname{arccn}\left(r,1/\sqrt{2}\right)}}$ l(r) = (1/\sqrt{2})\aJacobiellcnk@{r}{1/\sqrt{2}}		l(r) = (1/(sqrt(2)))*InverseJacobiCN(r, 1/(sqrt(2)))	l[r] == (1/(Sqrt[2]))*InverseJacobiCN[r, (1/(Sqrt[2]))^2]	Failure	Failure	Failed [18 / 18] Result: -4.122057553+.6299669258*I Test Values: {r = -3/2, l = 1} Result: -5.622057553+.6299669258*I Test Values: {r = -3/2, l = 2} ... skip entries to safe data	Failed [18 / 18] Result: Complex[-4.12205755429212, 0.629966925905157] Test Values: {Rule[l, 1], Rule[r, -1.5]} Result: Complex[-5.62205755429212, 0.629966925905157] Test Values: {Rule[l, 2], Rule[r, -1.5]} ... skip entries to safe data
22.18.E5	${\displaystyle{\displaystyle r=\operatorname{cn}\left(\sqrt{2}l,1/\sqrt{2}\right)}}$ r = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}		r = JacobiCN(sqrt(2)*l, 1/(sqrt(2)))	r == JacobiCN[Sqrt[2]*l, (1/(Sqrt[2]))^2]	Failure	Failure	Failed [18 / 18] Result: -1.810737930 Test Values: {r = -3/2, l = 1} Result: -.8262668012 Test Values: {r = -3/2, l = 2} ... skip entries to safe data	Failed [18 / 18] Result: -1.810737930333856 Test Values: {Rule[l, 1], Rule[r, -1.5]} Result: -0.8262668010254658 Test Values: {Rule[l, 2], Rule[r, -1.5]} ... skip entries to safe data
22.18#Ex3	${\displaystyle{\displaystyle x=\operatorname{cn}\left(\sqrt{2}l,1/\sqrt{2}\right)\operatorname{dn}\left(\sqrt{2}l,1/\sqrt{2}\right)}}$ x = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}\Jacobielldnk@{\sqrt{2}l}{1/\sqrt{2}}		x = JacobiCN(sqrt(2)*l, 1/(sqrt(2)))*JacobiDN(sqrt(2)*l, 1/(sqrt(2)))	x == JacobiCN[Sqrt[2]*l, (1/(Sqrt[2]))^2]*JacobiDN[Sqrt[2]*l, (1/(Sqrt[2]))^2]	Failure	Failure	Failed [9 / 9] Result: 1.269911408 Test Values: {x = 3/2, l = 1} Result: 2.074437352 Test Values: {x = 3/2, l = 2} ... skip entries to safe data	Failed [9 / 9] Result: 1.2699114077583538 Test Values: {Rule[l, 1], Rule[x, 1.5]} Result: 2.0744373520381156 Test Values: {Rule[l, 2], Rule[x, 1.5]} ... skip entries to safe data
22.18.E7	${\displaystyle{\displaystyle ax^{2}y^{2}+b(x^{2}y+xy^{2})+c(x^{2}+y^{2})+2dxy+e(x+y)+f=0}}$ ax^{2}y^{2}+b(x^{2}y+xy^{2})+c(x^{2}+y^{2})+2dxy+e(x+y)+f = 0		a*(x)^(2)* (y)^(2)+ b*((x)^(2)* y + x*(y)^(2))+ c*((x)^(2)+ (y)^(2))+ 2*d*x*y + exp(1)*(x + y)+ f = 0	a*(x)^(2)* (y)^(2)+ b*((x)^(2)* y + x*(y)^(2))+ c*((x)^(2)+ (y)^(2))+ 2*d*x*y + E*(x + y)+ f == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
22.18#Ex5	${\displaystyle{\displaystyle x_{3}=\frac{x_{1}y_{2}+x_{2}y_{1}}{1-k^{2}x_{1}^{2}x_{2}^{2}}}}$ x_{3} = \frac{x_{1}y_{2}+x_{2}y_{1}}{1-k^{2}x_{1}^{2}x_{2}^{2}}		x[3] = (x[1]*y[2]+ x[2]*y[1])/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))	Subscript[x, 3] == Divide[Subscript[x, 1]*Subscript[y, 2]+ Subscript[x, 2]*Subscript[y, 1],1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
22.18#Ex6	${\displaystyle{\displaystyle y_{3}=\frac{y_{1}y_{2}+x_{2}(-(1+k^{2})x_{1}+2k^{2}x_{1}^{3})}{1-k^{2}x_{1}^{2}x_{2}^{2}}+x_{3}\frac{2k^{2}x_{1}y_{1}x_{2}^{2}}{1-k^{2}x_{1}^{2}x_{2}^{2}}}}$ y_{3} = \frac{y_{1}y_{2}+x_{2}(-(1+k^{2})x_{1}+2k^{2}x_{1}^{3})}{1-k^{2}x_{1}^{2}x_{2}^{2}}+x_{3}\frac{2k^{2}x_{1}y_{1}x_{2}^{2}}{1-k^{2}x_{1}^{2}x_{2}^{2}}		y[3] = (y[1]*y[2]+ x[2]*(-(1 + (k)^(2))*x[1]+ 2*(k)^(2)* (x[1])^(3)))/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))+ x[3]*(2*(k)^(2)* x[1]*y[1]*(x[2])^(2))/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))	Subscript[y, 3] == Divide[Subscript[y, 1]*Subscript[y, 2]+ Subscript[x, 2]*(-(1 + (k)^(2))*Subscript[x, 1]+ 2*(k)^(2)* (Subscript[x, 1])^(3)),1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]+ Subscript[x, 3]*Divide[2*(k)^(2)* Subscript[x, 1]*Subscript[y, 1]*(Subscript[x, 2])^(2),1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-