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error in ValueMolienSeries #300
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Thanks - I can reproduce this both in the master branch and GAP 4.7.8. |
No, as far as I know it calculates exactly, but i the past the Molien series code was a good way to note the existence (not necessarily find where…) of bugs in a broad range of code. |
I've tried
in all 4 combinations of 32/64-bit builds with/without GMP, and 26/27 is returned in all 4 cases. |
I can reproduce this with:
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But contrast this:
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Asking Mathematica for a Taylor series expansion gives
So, that looks about right, except of course for the constant term, which the above call to In other words, this gives me some hope that the Molien series is computed correctly, and that the bug is instead in |
I just used Mathematica to cross check the results |
"they sum up to" - well, it's not converging series at 0, so I don't quite On 4 November 2015 at 09:09, Max Horn notifications@github.com wrote:
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First few coefficients of the series are certainly OK; it can be checked directly from the character table: here is how to check for degree up to 36, and it agrees with the Taylor series
And here is the expansion into the Taylor series at 0 up to degree 300, using Sage. Looks OK; e.g. terms of degrees not divisible by 3 are all 0, as predicted by the theory here. 37017617_z^300 + 402747472_z^297 + 372723885_z^294 + 342894227_z^291 + 316865230_z^288 + 290972607_z^285 + 268474186_z^282 + 246064266_z^279 + 226678408_z^276 + 207340813_z^273 + 190691644_z^270 + 174057606_z^267 + 159807508_z^264 + 145545869_z^261 + 133392728_z^258 + 121206905_z^255 + 110881127_z^252 + 100505949_z^249 + 91767098_z^246 + 82966767_z^243 + 75601497_z^240 + 68165881_z^237 + 61985315_z^234 + 55728595_z^231 + 50565794_z^228 + 45323689_z^225 + 41031791_z^222 + 36659580_z^219 + 33109962_z^216 + 29480472_z^213 + 26560457_z^210 + 23562749_z^207 + 21174366_z^204 + 18711343_z^201 + 16769706_z^198 + 14757312_z^195 + 13188959_z^192 + 11554406_z^189 + 10296251_z^186 + 8976871_z^183 + 7975064_z^180 + 6917011_z^177 + 6125505_z^174 + 5283100_z^171 + 4663042_z^168 + 3997230_z^165 + 3515934_z^162 + 2993905_z^159 + 2623960_z^156 + 2218148_z^153 + 1936809_z^150 + 1624206_z^147 + 1412787_z^144 + 1174275_z^141 + 1017371_z^138 + 837383_z^135 + 722562_z^132 + 588201_z^129 + 505499_z^126 + 406444_z^123 + 347888_z^120 + 275824_z^117 + 235143_z^114 + 183477_z^111 + 155869_z^108 + 119376_z^105 + 101075_z^102 + 75781_z^99 + 64007_z^96 + 46776_z^93 + 39474_z^90 + 27981_z^87 + 23632_z^84 + 16146_z^81 + 13683_z^78 + 8938_z^75 + 7651_z^72 + 4709_z^69 + 4091_z^66 + 2346_z^63 + 2099_z^60 + 1087_z^57 + 1022_z^54 + 461_z^51 + 472_z^48 + 178_z^45 + 203_z^42 + 58_z^39 + 87_z^36 + 15_z^33 + 33_z^30 + 3_z^27 + 13_z^24 + 5_z^18 + 2*z^12 + 1 |
"They" in my remark referred to the result of Finally, evaluating |
It seems that the summands of the form p(z) / (1-z^r)^k correspond to maximal cyclic subgroups, up to conjugation. I didn't know that their Molien series have such a nice form. One needs to write this down, or to find a printed source, before understanding this bug... 300 was picked by accident. And I missed the 1st character while cutting/pasting, so it should be 437017617*z^300. And thus the difference is in fact 1/27, as expected. In case you need more coefs: 1408938228_z^348 + 1313744182_z^345 + 1228179934_z^342 + 1143741754_z^339 + 1068049576_z^336 + 993307279_z^333 + 926495399_z^330 + 860477584_z^327 + 801638887_z^324 + 743456479_z^321 + 691761821_z^318 + 640603391_z^315 + 595296931_z^312 + 550421484_z^309 + 510815336_z^306 + 471548904_z^303 + 437017617*z^300 + ... |
Yes, that fits with all the data: both the results of There is also http://www.gap-system.org/ForumArchive/Breuer.1/Thomas.1/Re__Moli.1/1.html |
I did a sanity check of |
We have a copy of the Computational group theory (Durham, 1982) proceedings in St Andrews. |
@dimpase Exactly what I trying to say :). |
I think I found the bug, sort of. Note that the rational function is formed OK in the reduced form (
and it happens to be a constant, equal to Needless to say, if From reading the code, it appears that |
I was looking at the old history, and saw
that is to say, it was a sticking point before... |
The commit message from May 10th, 2005 says |
right - the dates in my diff are backwards... |
This example uses the 2-argument version of Just in case if this rings any bells, but I can not be sure. |
ValueMolienSeries(m,0) must be 1 for any m. However, the following shows a bug:
I didn't look at the code yet, but I guess it computes an approximate value and gets it wrong.
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