Algebraic and Analytic Methods - 1.11 Zeros of Polynomials
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 1.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{k} = \alpha b_{k+1}+a_{k}}
b_{k} = \alpha b_{k+1}+a_{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{k} = \alpha c_{k+1}+b_{k}}
c_{k} = \alpha c_{k+1}+b_{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D = b^{2}-4ac}
D = b^{2}-4ac |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (- 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3}}
\rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho^{2} = e^{-2\pi i/3}}
\rho^{2} = e^{-2\pi i/3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = (-3a^{2}+8b)/8}
p = (-3a^{2}+8b)/8 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = (a^{3}-4ab+8c)/8}
q = (a^{3}-4ab+8c)/8 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = (-3a^{4}+16a^{2}b-64ac+256d)/256}
r = (-3a^{4}+16a^{2}b-64ac+256d)/256 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0}
z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q}
\sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{n} = a+ib}
z^{n} = a+ib |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (z)^(n) = a + I*b |
(z)^(n) == a + I*b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.11#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{1} = a_{1}}
D_{1} = a_{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | D[1] = a[1] |
Subscript[D, 1] == Subscript[a, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |