Category Archives: wxMaxima

Euler problem 25.3

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showtime : false$
t0 : elapsed_real_time()$

t: 10^999$

j : 1$
while fib(j) < t do (
    j: j + 1
)$

j;

t1: elapsed_real_time()$

time_taken: t1-t0$

print("Time taken:", float(time_taken), "seconds");

4782

"Time taken:"0.4299999999999997"seconds"

— Me@2025-01-13 08:11:23 AM

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2025.01.13 Monday (c) All rights reserved by ACHK

Problem 14.5d1.2.3

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A First Course in String Theory

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The generating function is an infinite product:

\displaystyle{ \begin{aligned} \alpha' M_L^2: \end{aligned}}

\displaystyle{\begin{aligned} &f_{L, NS+}(x) \\ &= a_{NS+} (r) x^r \\ &= \frac{1}{x} \prod_{r=1}^\infty \frac{(1 + x^{r-\frac{1}{2}})^{32}}{(1 - x^r)^8} \\ \end{aligned}}

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To evaluate the infinite product, you can use wxMaxima. However, it does not provide \LaTeX rendering of answers yet. Instead, you can call Maxima‘s code in SageMath, if you use Jupyter Notebook to access SageMath.

reset()

%display latex

maxima('taylor((1/x)*product((1 + x^(r - 1/2))^32 / (1 - x^r)^8, r, 1, oo), x, 0, 6)')

\displaystyle {{1}\over{x}}+{{32}\over{\sqrt{x}}}+504+5248\,\sqrt{x}+40996\,x+ 258624\,x^{{{3}\over{2}}}+1384320\,x^2+6512384\,x^{{{5}\over{2}}}+ 27623826\,x^3+107640288\,x^{{{7}\over{2}}}+390667136\,x^4+1334500992 \,x^{{{9}\over{2}}}+4325559288\,x^5+13390178752\,x^{{{11}\over{2}}}+ 39794729472\,x^6+\cdots

— Me@2024-12-02 06:33:46 AM

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2024.12.31 Tuesday (c) All rights reserved by ACHK

SageMath for Ubuntu 24.04

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0. In this tutorial, you will need to go to the official website of NixOS. Make sure that its website is the real, official one. Any instructions from an imposter website can get your machine infected with malware.

1. Assuming your computer’s OS is Ubuntu 24.04 or above, go to the NixOS official website. Follow the instructions to install the Nix package manager (not the NixOS operating system) onto your OS. Choose the “single-user installation” method.

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2. Run this command to install SageMath:

nix-env -iA nixpkgs.sage

3. Run this to open:

sage --notebook=jupyterlab

— Me@2024-11-27 12:28:48 AM

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2024.12.24 Tuesday (c) All rights reserved by ACHK

Euler problem 24.3

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showtime : true;

digits: makelist(i,i,0,9);

p : permutations(digits)$

listify(p)[1000000];


Evaluation took 0.8800 seconds (1.0300 elapsed)
Evaluation took 0.0100 seconds (0.0100 elapsed)

[2,7,8,3,9,1,5,4,6,0]

— Me@2024-12-03 04:11:50 PM

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2024.12.04 Wednesday (c) All rights reserved by ACHK