Weierstrass Elliptic and Modular Functions - 23.20 Mathematical Applications

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23.20#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{3} = m^{2}-x_{1}-x_{2}}
x_{3} = m^{2}-x_{1}-x_{2}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
x[3] = (m)^(2)- x[1]- x[2]
Subscript[x, 3] == (m)^(2)- Subscript[x, 1]- Subscript[x, 2]
Skipped - no semantic math Skipped - no semantic math - -
23.20#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y_{3} = -m(x_{3}-x_{1})-y_{1}}
y_{3} = -m(x_{3}-x_{1})-y_{1}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
y[3] = - m*(x[3]- x[1])- y[1]
Subscript[y, 3] == - m*(Subscript[x, 3]- Subscript[x, 1])- Subscript[y, 1]
Skipped - no semantic math Skipped - no semantic math - -
23.20.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v^{8}(1+u^{8}) = 4u^{4}}
v^{8}(1+u^{8}) = 4u^{4}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = 2}
(v)^(8)*(1 + (u)^(8)) = 4*(u)^(4)
(v)^(8)*(1 + (u)^(8)) == 4*(u)^(4)
Skipped - no semantic math Skipped - no semantic math - -
23.20.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u^{4}-v^{4}+2uv(1-u^{2}v^{2}) = 0}
u^{4}-v^{4}+2uv(1-u^{2}v^{2}) = 0
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = 3}
(u)^(4)- (v)^(4)+ 2*u*v*(1 - (u)^(2)* (v)^(2)) = 0
(u)^(4)- (v)^(4)+ 2*u*v*(1 - (u)^(2)* (v)^(2)) == 0
Skipped - no semantic math Skipped - no semantic math - -
23.20.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u^{6}-v^{6}+5u^{2}v^{2}(u^{2}-v^{2})+4uv(1-u^{4}v^{4}) = 0}
u^{6}-v^{6}+5u^{2}v^{2}(u^{2}-v^{2})+4uv(1-u^{4}v^{4}) = 0
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = 5}
(u)^(6)- (v)^(6)+ 5*(u)^(2)* (v)^(2)*((u)^(2)- (v)^(2))+ 4*u*v*(1 - (u)^(4)* (v)^(4)) = 0
(u)^(6)- (v)^(6)+ 5*(u)^(2)* (v)^(2)*((u)^(2)- (v)^(2))+ 4*u*v*(1 - (u)^(4)* (v)^(4)) == 0
Skipped - no semantic math Skipped - no semantic math - -
23.20.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-u^{8})(1-v^{8}) = (1-uv)^{8}}
(1-u^{8})(1-v^{8}) = (1-uv)^{8}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = 7}
(1 - (u)^(8))*(1 - (v)^(8)) = (1 - u*v)^(8)
(1 - (u)^(8))*(1 - (v)^(8)) == (1 - u*v)^(8)
Skipped - no semantic math Skipped - no semantic math - -