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I have 13 equations, using variables named d1 .. d13. I give you 3 examples of them:

eq 1 :$$-1512306498003420269625002340551784=\mathrm{d13}^2-73976030 \mathrm{d12} $$ eq 2 :$$\text{{some 220 digit integer}} =\mathrm{d1}^2- \text{{some 120 digit integer }}\mathrm{d2}^2 $$ eq 3: $$53224924879680228591105839482631095894942304639505087943900593662151240330638513930240=-2 \mathrm{d11}\, \mathrm{d9}+2 \mathrm{d12}\, \mathrm{d8}-2 \mathrm{d13}\, \mathrm{d7}+73976030 \mathrm{d6}+\mathrm{d10}^2 $$

And so on. To be clear: {some xxx digit integer} ofcourse means an actual number, not a variable. The same kind of equations, but in a smaller ammount, were solvable.

I then call solve():

sol : solve([eq13, eq12, eq11, eq10, eq9, eq8, eq7, eq6, eq5, eq4, eq3, eq2, eq1]);

It takes about ten minutes to calculate, and then crashes because the heap is exhausted. Are there things I can improve?

Erik-Jan O
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community May 31 '23 at 11:24
  • I don't understand the context here. You are surprised that if you make the numbers big and ugly enough that a computer struggles to handle them? How is that a surprise? Why would you think that you can circumvent that and improve things beyond what the software is already doing? – JMoravitz May 31 '23 at 12:07
  • recommend you give it just one equation, your eq 2 which is of Pell type $x^2 - a y^2 = b$ with large $a,b$ Your computer might give you an answer. Then read https://en.wikipedia.org/wiki/Archimedes%27s_cattle_problem – Will Jagy May 31 '23 at 16:41
  • meanwhile, suggest you also solve the variant of your equation 2 given by $x^2 - a y^2 = 1.$ You call my $a$ " some 120 digit integer. " Assuming your $a > 0$ there are infinitely many solutions to eq 2, ... Meanwhile, do you mean your variables to be integers????? – Will Jagy May 31 '23 at 17:54
  • As a reaction to the comments: Thank you. I tried converting my big integers into floats, but had the same problem. Solving eq2 first expresses one variable as a function of the other (a square root plus a constant), I inserted this solution in the rest of my equations and again called solve(), but then it almost immediately came back with: "algsys: Couldn't reduce system to a polynomial in one variable.". – Erik-Jan O Jun 01 '23 at 12:36
  • To give you some background and conclusion: I am developing electronic filters of a quite High order. Not to actually build them but to investigate a new approach. The conclusion seems to be that a this High order is simply to much for Maxima. – Erik-Jan O Jun 01 '23 at 13:50
  • Maybe Mathematica or Pari GP online can handle it – Тyma Gaidash Jun 01 '23 at 14:00
  • @Erik-JanO if you wish to reply to a comment and have that person be notified about your reply, you need to type in an @ sign followed by the first few letters of that username; at that point you should be given the full username to click on. Meanwhile, complete solutions for Pell $x^2 - a y^2 = 1$ and variants $x^2 - a y^2 = b$ are available; I don't know any online resource that spits it out and handles all possible details. – Will Jagy Jun 01 '23 at 17:54

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