1.11

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
1.11.E3	${\displaystyle{\displaystyle b_{k}=\alpha b_{k+1}+a_{k}}}$ b_{k} = \alpha b_{k+1}+a_{k}	${\displaystyle{\displaystyle k=n-1}}$	b[k] = alpha*b[k + 1]+ a[k]	Subscript[b, k] == \[Alpha]*Subscript[b, k + 1]+ Subscript[a, k]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E5	${\displaystyle{\displaystyle c_{k}=\alpha c_{k+1}+b_{k}}}$ c_{k} = \alpha c_{k+1}+b_{k}	${\displaystyle{\displaystyle k=n-1}}$	c[k] = alpha*c[k + 1]+ b[k]	Subscript[c, k] == \[Alpha]*Subscript[c, k + 1]+ Subscript[b, k]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#E10Xa	${\displaystyle{\displaystyle\displaystyle\sum_{1\leq j<k\leq n}z_{j}z_{k}=a_{n-2}/a_{n}}}$ \displaystyle\sum_{1\leq j<k\leq n}z_{j}z_{k} = a_{n-2}/a_{n}		sum(sum(z[j]*z[k], k = j + 1..n), j = 1..k - 1) = a[n - 2]/a[n]	Sum[Sum[Subscript[z, j]*Subscript[z, k], {k, j + 1, n}, GenerateConditions->None], {j, 1, k - 1}, GenerateConditions->None] == Subscript[a, n - 2]/Subscript[a, n]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex4	${\displaystyle{\displaystyle D=b^{2}-4ac}}$ D = b^{2}-4ac		(- 4*(p)^(3)- 27*(q)^(2)) = (b)^(2)- 4*a*c	(- 4*(p)^(3)- 27*(q)^(2)) == (b)^(2)- 4*a*c	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex10	${\displaystyle{\displaystyle\rho=-\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3}}}$ \rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3}		rho = -(1)/(2)+(1)/(2)*sqrt(- 3)	\[Rho] == -Divide[1,2]+Divide[1,2]*Sqrt[- 3]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex11	${\displaystyle{\displaystyle\rho^{2}=e^{-2\pi i/3}}}$ \rho^{2} = e^{-2\pi i/3}		(rho)^(2) = exp(- 2*Pi*I/3)	\[Rho]^(2) == Exp[- 2*Pi*I/3]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex13	${\displaystyle{\displaystyle p=(-3a^{2}+8b)/8}}$ p = (-3a^{2}+8b)/8		p = (- 3*(a)^(2)+ 8*b)/8	p == (- 3*(a)^(2)+ 8*b)/8	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex14	${\displaystyle{\displaystyle q=(a^{3}-4ab+8c)/8}}$ q = (a^{3}-4ab+8c)/8		q = ((a)^(3)- 4*a*b + 8*c)/8	q == ((a)^(3)- 4*a*b + 8*c)/8	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex15	${\displaystyle{\displaystyle r=(-3a^{4}+16a^{2}b-64ac+256d)/256}}$ r = (-3a^{4}+16a^{2}b-64ac+256d)/256		r = (- 3*(a)^(4)+ 16*(a)^(2)* b - 64*a*c + 256*d)/256	r == (- 3*(a)^(4)+ 16*(a)^(2)* b - 64*a*c + 256*d)/256	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E18	${\displaystyle{\displaystyle z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2}=0}}$ z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0		(z)^(3)- 2*p*(z)^(2)+((p)^(2)- 4*r)*z + (q)^(2) = 0	(z)^(3)- 2*p*(z)^(2)+((p)^(2)- 4*r)*z + (q)^(2) == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E20	${\displaystyle{\displaystyle\sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}}=-q}}$ \sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q		sqrt(- theta[1])*sqrt(- theta[2])*sqrt(- theta[3]) = - q	Sqrt[- Subscript[\[Theta], 1]]*Sqrt[- Subscript[\[Theta], 2]]*Sqrt[- Subscript[\[Theta], 3]] == - q	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11.E22	${\displaystyle{\displaystyle z^{n}=a+ib}}$ z^{n} = a+ib		(z)^(n) = a + I*b	(z)^(n) == a + I*b	Skipped - no semantic math	Skipped - no semantic math	-	-
1.11#Ex20	${\displaystyle{\displaystyle D_{1}=a_{1}}}$ D_{1} = a_{1}		D[1] = a[1]	Subscript[D, 1] == Subscript[a, 1]	Skipped - no semantic math	Skipped - no semantic math	-	-