# Maple check of Mathematica code for Puiseux expansion

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1. Nov 24, 2012

### jackmell

Hi,

I was wondering if anyone here with Maple could run the algcurve[puiseux] routine to compute the expansion of the algebraic function:

$$f[z,w]=2 w^9+5 w^{10}+20 w^7 z+3 w^8 z+8 w^5 z^{10}+9 w^6 z^{10}+z^{14}+3 z^{15}+4 w^3 z^{15}+w^4 \left(10 z^5-z^6+2 z^7\right)+w^2 \left(3 z^{15}-20 z^{16}\right)+w \left(2 z^{15}+2 z^{16}\right)=0$$

into it's Puiseux series and tabulate the first 50 coefficients of the 4-cycle branch:

$$w(z)=\sum_{n=0}^{\infty} a_n \left(\sqrt[4]{z}\right)^n$$

and tabulate the results? Kinda' a lot to be asking probably. I'm writing a routine in Mathematica to do this and would like to check it. Here's my results in case anyone is interested in helping me. Note my results is only one of four conjugate series so may differ from Maple by a factor of $e^{2k\pi i/4}$.

$$\begin{array}{ccc} \text{Term} & \text{Value} & \text{Power} \\ 1 & -0.397635-0.397635 i & \frac{9}{4} \\ 2 & -0.308167-0.308167 i & \frac{13}{4} \\ 3 & 0.34731\, +0.34731 i & \frac{17}{4} \\ 4 & 0.05 & 5 \\ 5 & -0.561862-0.561862 i & \frac{21}{4} \\ 6 & 0.\, +0.158114 i & \frac{11}{2} \\ 7 & 0.16 & 6 \\ 8 & 1.17965\, +1.17965 i & \frac{25}{4} \\ 9 & 0.\, -0.0711512 i & \frac{13}{2} \\ 10 & 0.0115 & 7 \\ 11 & -2.67318-2.67318 i & \frac{29}{4} \\ 12 & 0.\, +0.277292 i & \frac{15}{2} \\ 13 & 0.0770178\, -0.0770178 i & \frac{31}{4} \\ 14 & -0.0613 & 8 \\ 15 & 6.2881\, +6.2881 i & \frac{33}{4} \\ 16 & 0.\, -0.77876 i & \frac{17}{2} \\ 17 & -0.805347+0.805347 i & \frac{35}{4} \\ 18 & -0.012575 & 9 \\ 19 & -15.7664-15.7664 i & \frac{37}{4} \\ 20 & 0.\, +2.04684 i & \frac{19}{2} \\ 21 & 0.43977\, -0.43977 i & \frac{39}{4} \\ 22 & -0.078822 & 10 \\ 23 & 39.6881\, +39.6881 i & \frac{41}{4} \\ 24 & 0.\, -5.80905 i & \frac{21}{2} \\ 25 & -1.07709+1.07709 i & \frac{43}{4} \\ 26 & 0.0843794 & 11 \\ 27 & -102.536-102.536 i & \frac{45}{4} \\ 28 & 0.\, +15.6853 i & \frac{23}{2} \\ 29 & 2.92025\, -2.92025 i & \frac{47}{4} \\ 30 & 0.327377 & 12 \\ 31 & 269.397\, +269.397 i & \frac{49}{4} \\ 32 & 0.\, -46.3669 i & \frac{25}{2} \\ 33 & -7.31934+7.31934 i & \frac{51}{4} \\ 34 & 0.231618 & 13 \\ 35 & -716.358-716.358 i & \frac{53}{4} \\ 36 & 0.\, +128.117 i & \frac{27}{2} \\ 37 & 19.2855\, -19.2855 i & \frac{55}{4} \\ 38 & -0.164816 & 14 \\ 39 & 1925.9\, +1925.9 i & \frac{57}{4} \\ 40 & 0.\, -363.357 i & \frac{29}{2} \\ 41 & -53.0957+53.0957 i & \frac{59}{4} \\ 42 & -0.150301 & 15 \\ 43 & -5220.92-5220.92 i & \frac{61}{4} \\ 44 & 0.\, +1039.99 i & \frac{31}{2} \\ 45 & 143.775\, -143.775 i & \frac{63}{4} \\ 46 & -0.594137 & 16 \\ 47 & 14271.4\, +14271.4 i & \frac{65}{4} \\ 48 & 0.\, -2984.69 i & \frac{33}{2} \\ 49 & -404.81+404.81 i & \frac{67}{4} \\ 50 & 0.154331 & 17 \\ \end{array}$$