Procedures

calculate the auxiliary parameter $\varepsilon$ for the given elliptic modulus $k$

calculate the auxiliary parameter $\varepsilon$ for the given elliptic modulus $k$

calculate the auxiliary parameter $\varepsilon$ for the given elliptic modulus $k$

calculate the auxiliary parameter $\varepsilon$ and ${ \varepsilon }^{ 4 }$ for the given elliptic modulus $k$

calculate the auxiliary parameter $\varepsilon$ and ${ \varepsilon }^{ 4 }$ for the given elliptic modulus $k$

calculate the auxiliary parameter $\varepsilon$ and ${ \varepsilon }^{ 4 }$ for the given elliptic modulus $k$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} \varepsilon &:= \frac{ 1 }{ 2 } \frac{ 1 - \sqrt{ { k }^{ \prime } } }{ 1 + \sqrt{ { k }^{ \prime } } } \\ q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$$

Calculate the elliptic nome $q$ for the given elliptic modulus $k$

Calculate the elliptic nome $q$ for the given elliptic modulus $k$

Calculate the elliptic nome $q$ for the given elliptic modulus $k$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \end{align*}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\varepsilon ( 1 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} )$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\varepsilon ( 1 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} )$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\varepsilon ( 1 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} )$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \end{align*}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ \end{aligned}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \end{align*}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \end{align*}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \end{align*}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \end{align*}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \end{align*}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \\ & ( 268616 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \\ & ( 268616 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \\ & ( 268616 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$$

Calculate the elliptic nome $q$ using the Horner's method and the following polynomial: $$\begin{align*} q(\varepsilon) &:= \varepsilon \\ & + 2 { \varepsilon }^{ 5 } \\ & + 15 { \varepsilon }^{ 9 } \\ & + 150 { \varepsilon }^{ 13 } \\ & + 1707 { \varepsilon }^{ 17 } \\ & + 20910 { \varepsilon }^{ 21 } \\ & + 268616 { \varepsilon }^{ 25 } \\ & + 3567400 { \varepsilon }^{ 29 } \\ & + 48555069 { \varepsilon }^{ 33 } \end{align*}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \\ & ( 268616 + { \varepsilon }^{ 4 } \cdot \\ & ( 3567400 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \\ & ( 268616 + { \varepsilon }^{ 4 } \cdot \\ & ( 3567400 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate the following for the given $\varepsilon$ and ${ \varepsilon }^{ 4 }$: $$\begin{aligned} \varepsilon \cdot {} & ( 1 + { \varepsilon }^{ 4 } \cdot \\ & ( 2 + { \varepsilon }^{ 4 } \cdot \\ & ( 15 + { \varepsilon }^{ 4 } \cdot \\ & ( 150 + { \varepsilon }^{ 4 } \cdot \\ & ( 1707 + { \varepsilon }^{ 4 } \cdot \\ & ( 20910 + { \varepsilon }^{ 4 } \cdot \\ & ( 268616 + { \varepsilon }^{ 4 } \cdot \\ & ( 3567400 + { \varepsilon }^{ 4 } \cdot \texttt{pre_step} ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ & ) \\ \end{aligned}$$

Calculate ${ k }^{ 2 }$ and ${ k }^{ \prime } := \sqrt{ 1 - { k }^{ 2 } }$ for the given elliptic modulus $k$

Calculate ${ k }^{ 2 }$ and ${ k }^{ \prime } := \sqrt{ 1 - { k }^{ 2 } }$ for the given elliptic modulus $k$

Calculate ${ k }^{ 2 }$ and ${ k }^{ \prime } := \sqrt{ 1 - { k }^{ 2 } }$ for the given elliptic modulus $k$