*Hi Tom,*
I noticed a small issue in your implementation. I’m not sure if this is a
standalone piece of code or part of a larger codebase, but I’d be happy to
help clarify.
The ring function returns a tuple containing the ring itself and all
variables defined within it. In your code:
``` R, m = ring('HillSeries2.m', domain=QQ) ```
You’re defining the variable 'HillSeries2.m' and storing it in m. However,
using dots in variable names can sometimes cause confusion. It’s generally
a good practice to use simple, consistent names for better readability.
In the series expansion:
``` α = rs_asin(α, HillSeries2.m, 3) # should be 11 ```
1. The first argument of rs_asin should be a function that is either a
*polynomial* or a *series*, and its variable must be part of the ring.
However, α is not defined before this line.
2. The second argument should be the ring variable, but HillSeries2.m is
not a separate variable. Instead, you should use m, since that’s where the
variable was stored when defining the ring.
Take a look at this code. I hope this helps,
```
from symp import QQ, ring
from sympy.polys.ring_series import rs_asin
R, α = ring('α', domain=QQ) # Define the ring with variable α
s = rs_asin(α, α, 8) # Compute the series expansion of asin(α) up to order
8
#output: 5/112*α**7 + 3/40*α**5 + 1/6*α**3 + α
```
Also, check out "rs_asin" document
https://docs.sympy.org/latest/modules/polys/ringseries.html#sympy.polys.ring_series.rs_asin
Jatin
On Wednesday, 26 February 2025 at 14:19:30 UTC+5:30 [email protected]
wrote:
> Hi Jatin,
>
>
>
> thanks, this looks very promising. I haven’t used polynomials much yet,
> since simple symbolic expressions do everything I need, and it looks like I
> have a deficit there. Here is my current code:
>
> from sympy.polys.domains import QQ
>
> from sympy.polys.rings import ring
>
> from sympy.polys.ring_series import rs_asin
>
> R, m = ring('HillSeries2.m', domain='QQ')
>
> α = rs_asin(α, HillSeries2.m, 3) # should be 11
>
>
>
> Exception in the last line:
>
> 'Add' object has no attribute 'ring'
>
> It looks like my expression needs to be a polynomial
>
> I added a line
>
> α = α.as_poly(domain='QQ')
>
> but that didn’t help.
>
>
>
> In the sample code
>
> R, m = ring('HillSeries2.m', domain='QQ')
>
> is not documented very well. It looks like it is defining a ring R, but
> not using it, but my IDE doesn’t give me a warning for that.
>
>
>
> I am using documentation
>
> https://docs.sympy.org/latest/modules/polys/ringseries.html#rs-series
>
>
>
> Tom
>
> (Dr. Thomas S. Ligon)
>
> [email protected]
>
> Frohnloher Str. 6a
> 81475 Muenchen
> Germany
> Tel. +49(89)74575075 <+49%2089%2074575075>
>
>
>
> *Von:* [email protected] <[email protected]> *Im Auftrag von *Jatin
> Bhardwaj
> *Gesendet:* Montag, 24. Februar 2025 22:08
> *An:* sympy <[email protected]>
> *Betreff:* [sympy] Re: sympy process out of memory calculating series of
> asin
>
>
>
> Hi Tom,
>
> Instead of series(asin(α)), you can use SymPy’s ring_series.rs_asin, which
> is optimized for power series manipulations and significantly reduces
> memory usage.
>
> ```
>
> from sympy.polys.rings import ring
> from sympy.polys.ring_series import rs_asin
>
> R, x = ring('x', domain='QQ')
>
> asin_series = rs_asin(x, 11)
> print(asin_series)
>
> ```
>
> This method is much more efficient and avoids the heavy symbolic
> differentiation that series() performs.
>
> You can also check out the documentation for the rs_series
> <https://docs.sympy.org/latest/modules/polys/ringseries.html#rs-series>
> in `ring series` module.
>
> Jatin Bhardwaj
>
> On Monday, 24 February 2025 at 13:52:57 UTC+5:30 [email protected]
> wrote:
>
> I am using sympy to analyze and run some code involving power series. In
> general, the code is always running on a partial sum of a power series, and
> this is a normal sympy symbolic expression. After doing certain
> calculations, the data is no longer a series, and I need to run a Taylor
> expansion in order to get a series. For example, if I calculate the
> quotient of two partial sums, I need Taylor in order to get another partial
> sum. In sympy, it is very convenient to call series() to do this.
>
>
>
> Now it is clear that this can use a lot of memory, because every
> additional derivative makes the expression more complex and longer. It
> appears as though series() does not use parallel processing, so the result
> is 100% usage of one CPU and increasing use of memory. On my laptop
> (running Windows 11 and Visual Studio), I have 16GB RAM and have sometimes
> run into memory issues.
>
>
>
> To solve this problem, I have allocated an Ubuntu Linux virtual machine on
> the Internet (Microsoft Azure). The machine has 2 virtual CPUs and 218GB
> RAM. With this, I have successfully calculated partial sums up to order 24
> or 31. This sometimes runs at 100% CPU allocation for more than 24 hours
> and completes successfully.
>
>
>
> Up to now, I have used series() for algebraic expressions of partial sums
> (quotient, square root, etc.) but recently started applying this to a
> trigonometric expression. This is because I need to calculate the solution
> of a cubic equation and the Cardano formula has run into unpleasant
> situations involving complex numbers, and I have been given a
> recommendation to try the trigonometric formula instead. Up to now, it
> looks very good, since the primary solution is real and does not require
> complex components. By the way, solving a cubic equation worked will with
> both the standard formula and via solve(). For the cubic equation, I have
> started with the formula because I can see if each individual step success
> before proceeding to the next one.
>
>
>
> Specifically, my code is
>
> α = asin(α)
>
> α = series(α, m, n=maxK+1) # calculate series up to maxK
>
>
>
> On my laptop, the series statement runs for some time and hits the memory
> limit of my PC, so I tried running this on the VM, which has more memory
> and does not have the overhead of Windows or Visual Studio.
>
> This first attempt ran for somewhere between 24 and 30 hours and the VM
> was stopped. This is presumably because the VM is configured to use a “spot
> price”, meaning that the administrators can stop it at any time they need
> additional capacity for something else.
>
> The second attempt ran for somewhere between 30 and 48 hours and my output
> file ended in the statement killed. Running dmesg gave me this information:
>
>
>
> [144763.491084]
> oom-kill:constraint=CONSTRAINT_NONE,nodemask=(null),cpuset=/,mems_allowed=0,global_oom,task_memcg=/user.slice/user-1000.slice/session-1.scope,task=python3.9,pid=1699,uid=1000
>
> [144763.491101] Out of memory: Killed process 1699 (python3.9)
> total-vm:226036448kB, anon-rss:223754920kB, file-rss:2740kB, shmem-rss:0kB,
> UID:1000 pgtables:438192kB oom_score_adj:0
>
> [144772.062513] oom_reaper: reaped process 1699 (python3.9), now
> anon-rss:0kB, file-rss:0kB, shmem-rss:0kB
>
>
>
> In this case, my partial sum is of order 11, and it would be very valuable
> for me to achieve this solution, but I don’t need to go past 11.
>
>
>
> Is this to be expected? Since the derivative of arcsin is 1/sqrt(1-x**2),
> I expect the calculations to be no worse than what I have done in the past.
>
> Is there any reason why series(asin(α)) would be expected to fail?
>
> Should I try anything else?
>
>
>
> Tom
>
> (Dr. Thomas S. Ligon)
>
> [email protected]
>
> Frohnloher Str. 6a
> 81475 Muenchen
> Germany
> Tel. +49(89)74575075 <+49%2089%2074575075>
>
>
>
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