Maple Maple check of Mathematica code for Puiseux expansion

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 $e^{2k\pi i/4}$.

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

Related Math Software Workshop News on Phys.org

"Maple check of Mathematica code for Puiseux expansion"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving