WeylCharacterRing improvement

[bump]

The multiplication algorithm for WeylCharacterRings is changed by this patch to an algorithm based on the Brauer-Klimyk formula. This algorithm is asymmetric, so that a*b and b*a are equal but computed differently. They are sometimes interchanged in an attempt to give the most efficient evaluation. This patch gives a modest speedup for sage -t --long weyl_characters.py but in certain cases it is a dramatic improvement. As an example, create the spin character of Spin(9):

sage: B4=WeylCharacterRing("B4",style="coroots")
sage: spin=B4(0,0,0,1)

Now try raising this to different powers before and after the patch.

Apply: trac_13391-weyl_characters.patch

[nthiery]

Hi Dan!

For future record, can you add your timing, before and after the patch, to the ticket description?

Thanks!

[aschilling]

My timings before the patch::

   sage: %timeit spin^3
   5 loops, best of 3: 539 ms per loop
   sage: %timeit spin^4
   5 loops, best of 3: 6.31 s per loop

and with this patch::

   sage: %timeit spin^3
   5 loops, best of 3: 25.3 ms per loop
   sage: %timeit spin^4
   5 loops, best of 3: 126 ms per loop
   sage: %timeit spin^5
   5 loops, best of 3: 842 ms per loop
   sage: %timeit spin^6
   5 loops, best of 3: 520 ms per loop

This is definitely a huge improvement!

[aschilling]

Hi Dan,

This looks good and I am happy to give it a positive review. Here are just some minor comments about the documentation (I think after the INPUT variables there is supposed to be a double dash. Also for the html output it is nicer to use \rho than rho for example)::

    Auxiliary function for product_on_basis. 
	         
    INPUT: 
      
    - ``a'' -- a weight.

    Returns a pair `[\epsilon,b]` where `b` is a dominant weight and
    `\epsilon` = 0,1 or -1. To describe `b`, let `w` be an element of 
    the Weyl group such that `w(a+\rho)` is dominant. If 
    `w(a+\rho)-\rho` is dominant, then `\epsilon` is the sign of
    `w` and `b` is `w(a+\rho)-\rho`. Otherwise, `\epsilon` is zero. 

[bump]

The improvement in timing is minor for many tasks, and sage -t --long weyl_characters.py only comes in a few seconds faster. But for tensor product decompositions where the first factor is smaller than the other, the improvement is big, as Anne's posted timings show. One can get up to the 12th or 13th tensor power of the spin representation of spin=B4(0,0,0,1), which was previously hopeless.

I took Anne's doc comment into account and reposted the patch.

[aschilling]

Looks good!

Anne

[nthiery]

Replying to bump:

But for tensor product decompositions where the first factor is smaller than the other,

Would it make sense, in a later ticket, to commute the two factors if the second is smaller than the first? (I haven't looked at the code, maybe that's already done).

In any cases, nice improvement, thanks!

Cheers,

[nthiery]

Replying to nthiery:

Would it make sense, in a later ticket, to commute the two factors if the second is smaller than the first? (I haven't looked at the code, maybe that's already done).

Also: did you try computing the powers naively (that is as a*(a*(a*(a))) rather than using the default binary powering(a²2) as implemented by power? If it's better to have one small factor, it might be one of those monoids where binary powering is not the right thing to do.

Cheers,

Nicolas

[bump]

I was wondering about these exact points. There would be some minor overhead involved in deciding whether to switch a and b before computing a*b. I think in many cases it would be worthwhile.

I was also wondering about the power, and there ... watch this!

sage: B4=WeylCharacterRing("B4",style="coroots"); spin=B4(0,0,0,1)
sage: time spin^8
1001*B4(0,0,0,0) + 3003*B4(1,0,0,0) + 5460*B4(0,1,0,0) + 7644*B4(0,0,1,0) + 8918*B4(0,0,0,2) + 3388*B4(2,0,0,0) + 8085*B4(1,1,0,0) + 12474*B4(1,0,1,0) + 15092*B4(1,0,0,2) + 5775*B4(0,2,0,0) + 11550*B4(0,1,1,0) + 15092*B4(0,1,0,2) + 6300*B4(0,0,2,0) + 10290*B4(0,0,1,2) + 4116*B4(0,0,0,4) + 1716*B4(3,0,0,0) + 4550*B4(2,1,0,0) + 7371*B4(2,0,1,0) + 9100*B4(2,0,0,2) + 4290*B4(1,2,0,0) + 9009*B4(1,1,1,0) + 12012*B4(1,1,0,2) + 5460*B4(1,0,2,0) + 9100*B4(1,0,1,2) + 3822*B4(1,0,0,4) + 1540*B4(0,3,0,0) + 3564*B4(0,2,1,0) + 4928*B4(0,2,0,2) + 2835*B4(0,1,2,0) + 4900*B4(0,1,1,2) + 2268*B4(0,1,0,4) + 825*B4(0,0,3,0) + 1540*B4(0,0,2,2) + 924*B4(0,0,1,4) + 210*B4(0,0,0,6) + 330*B4(4,0,0,0) + 924*B4(3,1,0,0) + 1540*B4(3,0,1,0) + 1925*B4(3,0,0,2) + 972*B4(2,2,0,0) + 2100*B4(2,1,1,0) + 2835*B4(2,1,0,2) + 1344*B4(2,0,2,0) + 2268*B4(2,0,1,2) + 980*B4(2,0,0,4) + 462*B4(1,3,0,0) + 1100*B4(1,2,1,0) + 1540*B4(1,2,0,2) + 924*B4(1,1,2,0) + 1617*B4(1,1,1,2) + 770*B4(1,1,0,4) + 300*B4(1,0,3,0) + 567*B4(1,0,2,2) + 350*B4(1,0,1,4) + 84*B4(1,0,0,6) + 84*B4(0,4,0,0) + 210*B4(0,3,1,0) + 300*B4(0,3,0,2) + 196*B4(0,2,2,0) + 350*B4(0,2,1,2) + 175*B4(0,2,0,4) + 84*B4(0,1,3,0) + 162*B4(0,1,2,2) + 105*B4(0,1,1,4) + 28*B4(0,1,0,6) + 14*B4(0,0,4,0) + 28*B4(0,0,3,2) + 20*B4(0,0,2,4) + 7*B4(0,0,1,6) + B4(0,0,0,8)
Time: CPU 20.33 s, Wall: 20.34 s

[Exit and restart sage to avoid caching effects ...]

sage: B4=WeylCharacterRing("B4",style="coroots"); spin=B4(0,0,0,1)
sage: time spin*(spin*(spin*(spin*(spin*(spin*(spin*spin))))))
1001*B4(0,0,0,0) + 3003*B4(1,0,0,0) + 5460*B4(0,1,0,0) + 7644*B4(0,0,1,0) + 8918*B4(0,0,0,2) + 3388*B4(2,0,0,0) + 8085*B4(1,1,0,0) + 12474*B4(1,0,1,0) + 15092*B4(1,0,0,2) + 5775*B4(0,2,0,0) + 11550*B4(0,1,1,0) + 15092*B4(0,1,0,2) + 6300*B4(0,0,2,0) + 10290*B4(0,0,1,2) + 4116*B4(0,0,0,4) + 1716*B4(3,0,0,0) + 4550*B4(2,1,0,0) + 7371*B4(2,0,1,0) + 9100*B4(2,0,0,2) + 4290*B4(1,2,0,0) + 9009*B4(1,1,1,0) + 12012*B4(1,1,0,2) + 5460*B4(1,0,2,0) + 9100*B4(1,0,1,2) + 3822*B4(1,0,0,4) + 1540*B4(0,3,0,0) + 3564*B4(0,2,1,0) + 4928*B4(0,2,0,2) + 2835*B4(0,1,2,0) + 4900*B4(0,1,1,2) + 2268*B4(0,1,0,4) + 825*B4(0,0,3,0) + 1540*B4(0,0,2,2) + 924*B4(0,0,1,4) + 210*B4(0,0,0,6) + 330*B4(4,0,0,0) + 924*B4(3,1,0,0) + 1540*B4(3,0,1,0) + 1925*B4(3,0,0,2) + 972*B4(2,2,0,0) + 2100*B4(2,1,1,0) + 2835*B4(2,1,0,2) + 1344*B4(2,0,2,0) + 2268*B4(2,0,1,2) + 980*B4(2,0,0,4) + 462*B4(1,3,0,0) + 1100*B4(1,2,1,0) + 1540*B4(1,2,0,2) + 924*B4(1,1,2,0) + 1617*B4(1,1,1,2) + 770*B4(1,1,0,4) + 300*B4(1,0,3,0) + 567*B4(1,0,2,2) + 350*B4(1,0,1,4) + 84*B4(1,0,0,6) + 84*B4(0,4,0,0) + 210*B4(0,3,1,0) + 300*B4(0,3,0,2) + 196*B4(0,2,2,0) + 350*B4(0,2,1,2) + 175*B4(0,2,0,4) + 84*B4(0,1,3,0) + 162*B4(0,1,2,2) + 105*B4(0,1,1,4) + 28*B4(0,1,0,6) + 14*B4(0,0,4,0) + 28*B4(0,0,3,2) + 20*B4(0,0,2,4) + 7*B4(0,0,1,6) + B4(0,0,0,8)
Time: CPU 0.33 s, Wall: 0.34 s

Conclusion: don't binary!

[bump]

I revised __pow__ and reposted the patch so it needs review again.

The revision to __pow__ appears to be another very substantial speedup. Previously, it could not compute the 16th power of the spin representation of B4 in a reasonable amount of time, and now it can -- in 3.45 seconds.

I don't see how to change the status to needs_review. I'm only given options needs_info, needs_work ... none of which are correct.

[aschilling]

I can confirm that this is a huge speedup:

sage: B4=WeylCharacterRing("B4",style="coroots"); spin=B4(0,0,0,1)
sage: time spin^(16)
1844536720*B4(0,0,0,0) + 8300415240*B4(1,0,0,0) + 19920996576*B4(0,1,0,0) + 33201660960*B4(0,0,1,0) + 42140569680*B4(0,0,0,2) + 16709332640*B4(2,0,0,0) + 52634397816*B4(1,1,0,0) + 96675424560*B4(1,0,1,0) + 127247994720*B4(1,0,0,2) + 56393997660*B4(0,2,0,0) + 134271423000*B4(0,1,1,0) + 190871992080*B4(0,1,0,2) + 96675424560*B4(0,0,2,0) + 171784792872*B4(0,0,1,2) + 81802282320*B4(0,0,0,4) + 19747393120*B4(3,0,0,0) + 69115875920*B4(2,1,0,0) + 133294903560*B4(2,0,1,0) + 179028564000*B4(2,0,0,2) + 97749595944*B4(1,2,0,0) + 244373989860*B4(1,1,1,0) + 354476556720*B4(1,1,0,2) + 195499191888*B4(1,0,2,0) + 354476556720*B4(1,0,1,2) + 177238278360*B4(1,0,0,4) + 62610852304*B4(0,3,0,0) + 172499286960*B4(0,2,1,0) + 259486106880*B4(0,2,0,2) + 181124251308*B4(0,1,2,0) + 340575515280*B4(0,1,1,2) + 187664059440*B4(0,1,0,4) + 79062173190*B4(0,0,3,0) + 160557028632*B4(0,0,2,2) + 114683591880*B4(0,0,1,4) + 34405077564*B4(0,0,0,6) + 14990430000*B4(4,0,0,0) + 55404629280*B4(3,1,0,0) + 109929820000*B4(3,0,1,0) + 149492475000*B4(3,0,0,2) + 87424187760*B4(2,2,0,0) + 224856450000*B4(2,1,1,0) + 330242467500*B4(2,1,0,2) + 189958728960*B4(2,0,2,0) + 348736045680*B4(2,0,1,2) + 179390970000*B4(2,0,0,4) + 74144430360*B4(1,3,0,0) + 210159950000*B4(1,2,1,0) + 320089770000*B4(1,2,0,2) + 233025352560*B4(1,1,2,0) + 443644421220*B4(1,1,1,2) + 251499105000*B4(1,1,0,4) + 113486373000*B4(1,0,3,0) + 233345442330*B4(1,0,2,2) + 171476662500*B4(1,0,1,4) + 54323806680*B4(1,0,0,6) + 31455212880*B4(0,4,0,0) + 93616705000*B4(0,3,1,0) + 145495350000*B4(0,3,0,2) + 115335780560*B4(0,2,2,0) + 224062839000*B4(0,2,1,2) + 133370737500*B4(0,2,0,4) + 74144430360*B4(0,1,3,0) + 155563628220*B4(0,1,2,2) + 120033663750*B4(0,1,1,4) + 42251849640*B4(0,1,0,6) + 22049487460*B4(0,0,4,0) + 47975807880*B4(0,0,3,2) + 40795755000*B4(0,0,2,4) + 18847638810*B4(0,0,1,6) + 4038779745*B4(0,0,0,8) + 7475227760*B4(5,0,0,0) + 28541778720*B4(4,1,0,0) + 57666042720*B4(4,0,1,0) + 79064909000*B4(4,0,0,2) + 47705544432*B4(3,2,0,0) + 124943092560*B4(3,1,1,0) + 185011887060*B4(3,1,0,2) + 109041244416*B4(3,0,2,0) + 201831149520*B4(3,0,1,2) + 105721078320*B4(3,0,0,4) + 45247113912*B4(2,3,0,0) + 130596626160*B4(2,2,1,0) + 200545816240*B4(2,2,0,2) + 149592499056*B4(2,1,2,0) + 287145145980*B4(2,1,1,2) + 165757256280*B4(2,1,0,4) + 77170733640*B4(2,0,3,0) + 159980867046*B4(2,0,2,2) + 119713573980*B4(2,0,1,4) + 39178987848*B4(2,0,0,6) + 25463743760*B4(1,4,0,0) + 77170733640*B4(1,3,1,0) + 120922802000*B4(1,3,0,2) + 98217297360*B4(1,2,2,0) + 192377185000*B4(1,2,1,2) + 116604130500*B4(1,2,0,4) + 66881302488*B4(1,1,3,0) + 141479678340*B4(1,1,2,2) + 111162604410*B4(1,1,1,4) + 40422765240*B4(1,1,0,6) + 22243329108*B4(1,0,4,0) + 48795907160*B4(1,0,3,2) + 42251849640*B4(1,0,2,4) + 20165655510*B4(1,0,1,6) + 4577283711*B4(1,0,0,8) + 7422629760*B4(0,5,0,0) + 23143120000*B4(0,4,1,0) + 36717450000*B4(0,4,0,2) + 31104353280*B4(0,3,2,0) + 61685316000*B4(0,3,1,2) + 38465900000*B4(0,3,0,4) + 23631229440*B4(0,2,3,0) + 50614003440*B4(0,2,2,2) + 40913730000*B4(0,2,1,4) + 15710872320*B4(0,2,0,6) + 10406235840*B4(0,1,4,0) + 23113850760*B4(0,1,3,2) + 20590570000*B4(0,1,2,4) + 10377647280*B4(0,1,1,6) + 2628105480*B4(0,1,0,8) + 2207383360*B4(0,0,5,0) + 5002998000*B4(0,0,4,2) + 4679675000*B4(0,0,3,4) + 2620618000*B4(0,0,2,6) + 876035160*B4(0,0,1,8) + 140280140*B4(0,0,0,10) + 2387047520*B4(6,0,0,0) + 9309485328*B4(5,1,0,0) + 19042129080*B4(5,0,1,0) + 26257522720*B4(5,0,0,2) + 16112570760*B4(4,2,0,0) + 42722725500*B4(4,1,1,0) + 63623997360*B4(4,1,0,2) + 38084258160*B4(4,0,2,0) + 70895311344*B4(4,0,1,2) + 37595998440*B4(4,0,0,4) + 16217881680*B4(3,3,0,0) + 47389914000*B4(3,2,1,0) + 73188389120*B4(3,2,0,2) + 55446199380*B4(3,1,2,0) + 107038019088*B4(3,1,1,2) + 62554686480*B4(3,1,0,4) + 29618696250*B4(3,0,3,0) + 61752703320*B4(3,0,2,2) + 4678235100*B4(1,0,5,0) + 3414290880*B4(1,0,4,2) + 3233230000*B4(1,0,3,4) + 1849407560*B4(1,0,2,6) + 640179540*B4(1,0,1,8) + 108788680*B4(1,0,0,10) + 791494704*B4(0,6,0,0) + 2544090120*B4(0,5,1,0) + 4092771760*B4(0,5,0,2) + 3607982352*B4(0,4,2,0) + 7255368120*B4(0,4,1,2) + 4664165220*B4(0,4,0,4) + 3006651960*B4(0,3,3,0) + 6529831308*B4(0,3,2,2) + 5441526090*B4(0,3,1,4) + 2204878104*B4(0,3,0,6) + 1571349780*B4(0,2,4,0) + 3539043816*B4(0,2,3,2) + 3250142280*B4(0,2,2,4) + 1728484758*B4(0,2,1,6) + 480134655*B4(0,2,0,8) + 495213264*B4(0,1,5,0) + 1138096960*B4(0,1,4,2) + 1097450640*B4(0,1,3,4) + 648493560*B4(0,1,2,6) + 237780972*B4(0,1,1,8) + 45189144*B4(0,1,0,10) + 75741120*B4(0,0,6,0) + 176243760*B4(0,0,5,2) + 174845000*B4(0,0,4,4) + 109103280*B4(0,0,3,6) + 44633160*B4(0,0,2,8) + 11231220*B4(0,0,1,10) + 1361360*B4(0,0,0,12) + 445429920*B4(7,0,0,0) + 1762874568*B4(6,1,0,0) + 3637677680*B4(6,0,1,0) + 5036784480*B4(6,0,0,2) + 3122292420*B4(5,2,0,0) + 8351811000*B4(5,1,1,0) + 12489169680*B4(5,1,0,2) + 7555176720*B4(5,0,2,0) + 14122368792*B4(5,0,1,2) + 7555176720*B4(5,0,0,4) + 3259095840*B4(4,3,0,0) + 9607312000*B4(4,2,1,0) + 14898723840*B4(4,2,0,2) + 11406835440*B4(4,1,2,0) + 22111711776*B4(4,1,1,2) + 13036383360*B4(4,1,0,4) + 6235515000*B4(4,0,3,0) + 13054290480*B4(4,0,2,2) + 9976824000*B4(4,0,1,4) + 3384445680*B4(4,0,0,6) + 2182606608*B4(3,4,0,0) + 6755687120*B4(3,3,1,0) + 10690318080*B4(3,3,0,2) + 8912310316*B4(3,2,2,0) + 17628745680*B4(3,2,1,2) + 10913033040*B4(3,2,0,4) + 6430894470*B4(3,1,3,0) + 13738086648*B4(3,1,2,2) + 11024390520*B4(3,1,1,4) + 4155347196*B4(3,1,0,6) + 2353791440*B4(3,0,4,0) + 5214553344*B4(3,0,3,2) + 4611509760*B4(3,0,2,4) + 2281367088*B4(3,0,1,6) + 548725320*B4(3,0,0,8) + 947320920*B4(2,5,0,0) + 3016650000*B4(2,4,1,0) + 4833270000*B4(2,4,0,2) + 4202518320*B4(2,3,2,0) + 8416582020*B4(2,3,1,2) + 5360355000*B4(2,3,0,4) + 3383289000*B4(2,2,3,0) + 7317942570*B4(2,2,2,2) + 6041587500*B4(2,2,1,4) + 2404737720*B4(2,2,0,6) + 1639638000*B4(2,1,4,0) + 3677834160*B4(2,1,3,2) + 3346200000*B4(2,1,2,4) + 1748106360*B4(2,1,1,6) + 469111500*B4(2,1,0,8) + 413884380*B4(2,0,5,0) + 947320920*B4(2,0,4,2) + 904995000*B4(2,0,3,4) 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81510000*B4(0,3,4,0) + 185391360*B4(0,3,3,2) + 173888000*B4(0,3,2,4) + 95855760*B4(0,3,1,6) + 28215000*B4(0,3,0,8) + 30568720*B4(0,2,5,0) + 70946304*B4(0,2,4,2) + 69871360*B4(0,2,3,4) + 42796208*B4(0,2,2,6) + 16628040*B4(0,2,1,8) + 3477760*B4(0,2,0,10) + 6961500*B4(0,1,6,0) + 16358760*B4(0,1,5,2) + 16575000*B4(0,1,4,4) + 10720710*B4(0,1,3,6) + 4647375*B4(0,1,2,8) + 1287000*B4(0,1,1,10) + 185640*B4(0,1,0,12) + 755820*B4(0,0,7,0) + 1790712*B4(0,0,6,2) + 1847560*B4(0,0,5,4) + 1234506*B4(0,0,4,6) + 566865*B4(0,0,3,8) + 175560*B4(0,0,2,10) + 33592*B4(0,0,1,12) + 3060*B4(0,0,0,14) + 37119160*B4(8,0,0,0) + 148476640*B4(7,1,0,0) + 308374560*B4(7,0,1,0) + 428298000*B4(7,0,0,2) + 267257952*B4(6,2,0,0) + 719540640*B4(6,1,1,0) + 1079310960*B4(6,1,0,2) + 657865728*B4(6,0,2,0) + 1233498240*B4(6,0,1,2) + 664191360*B4(6,0,0,4) + 285817532*B4(5,3,0,0) + 848030040*B4(5,2,1,0) + 1319157840*B4(5,2,0,2) + 1017636048*B4(5,1,2,0) + 1978736760*B4(5,1,1,2) + 1174195440*B4(5,1,0,4) + 565353360*B4(5,0,3,0) + 1187242056*B4(5,0,2,2) + 913263120*B4(5,0,1,4) + 313118784*B4(5,0,0,6) + 198696680*B4(4,4,0,0) + 619016580*B4(4,3,1,0) + 982566000*B4(4,3,0,2) + 825355440*B4(4,2,2,0) + 1637610000*B4(4,2,1,2) + 1020357000*B4(4,2,0,4) + 605260656*B4(4,1,3,0) + 1296987120*B4(4,1,2,2) + 1047566520*B4(4,1,1,4) + 399072960*B4(4,1,0,6) + 226972746*B4(4,0,4,0) + 504383880*B4(4,0,3,2) + 448957080*B4(4,0,2,4) + 224478540*B4(4,0,1,6) + 54872532*B4(4,0,0,8) + 91706160*B4(3,5,0,0) + 293930000*B4(3,4,1,0) + 472387500*B4(3,4,0,2) + 413853440*B4(3,3,2,0) + 831402000*B4(3,3,1,2) + 532950000*B4(3,3,0,4) + 338607360*B4(3,2,3,0) + 734657040*B4(3,2,2,2) + 610470000*B4(3,2,1,4) + 245583360*B4(3,2,0,6) + 168127960*B4(3,1,4,0) + 378287910*B4(3,1,3,2) + 346417500*B4(3,1,2,4) + 182908440*B4(3,1,1,6) + 49884120*B4(3,1,0,8) + 44054920*B4(3,0,5,0) + 101146500*B4(3,0,4,2) + 97256250*B4(3,0,3,4) + 57057000*B4(3,0,2,6) + 20540520*B4(3,0,1,8) + 3708705*B4(3,0,0,10) + 27350960*B4(2,6,0,0) + 89266320*B4(2,5,1,0) + 144644500*B4(2,5,0,2) + 129841920*B4(2,4,2,0) + 262990000*B4(2,4,1,2) + 171666000*B4(2,4,0,4) + 112529664*B4(2,3,3,0) + 246158640*B4(2,3,2,2) + 208288080*B4(2,3,1,4) + 86561280*B4(2,3,0,6) + 62486424*B4(2,2,4,0) + 141751610*B4(2,2,3,2) + 132182820*B4(2,2,2,4) + 72099720*B4(2,2,1,6) + 20828808*B4(2,2,0,8) + 21719880*B4(2,1,5,0) + 50277500*B4(2,1,4,2) + 49227750*B4(2,1,3,4) + 29835000*B4(2,1,2,6) + 11377080*B4(2,1,1,8) + 2297295*B4(2,1,0,10) + 3960320*B4(2,0,6,0) + 9282000*B4(2,0,5,2) + 9350000*B4(2,0,4,4) + 5984000*B4(2,0,3,6) + 2545920*B4(2,0,2,8) + 680680*B4(2,0,1,10) + 91000*B4(2,0,0,12) + 4803656*B4(1,7,0,0) + 15872220*B4(1,6,1,0) + 25865840*B4(1,6,0,2) + 23581584*B4(1,5,2,0) + 48036560*B4(1,5,1,2) + 31744440*B4(1,5,0,4) + 21162960*B4(1,4,3,0) + 46558512*B4(1,4,2,2) + 39884040*B4(1,4,1,4) + 16930368*B4(1,4,0,6) + 12471030*B4(1,3,4,0) + 28452424*B4(1,3,3,2) + 26860680*B4(1,3,2,4) + 14965236*B4(1,3,1,6) + 4476780*B4(1,3,0,8) + 4855032*B4(1,2,5,0) + 11302720*B4(1,2,4,2) + 11203920*B4(1,2,3,4) + 6935760*B4(1,2,2,6) + 2738736*B4(1,2,1,8) + 586872*B4(1,2,0,10) + 1175720*B4(1,1,6,0) + 2771340*B4(1,1,5,2) + 2826250*B4(1,1,4,4) + 1847560*B4(1,1,3,6) + 813960*B4(1,1,2,8) + 230945*B4(1,1,1,10) + 34580*B4(1,1,0,12) + 143208*B4(1,0,7,0) + 340340*B4(1,0,6,2) + 353430*B4(1,0,5,4) + 238680*B4(1,0,4,6) + 111384*B4(1,0,3,8) + 35343*B4(1,0,2,10) + 7020*B4(1,0,1,12) + 680*B4(1,0,0,14) + 379236*B4(0,8,0,0) + 1264120*B4(0,7,1,0) + 2068560*B4(0,7,0,2) + 1905904*B4(0,6,2,0) + 3898440*B4(0,6,1,2) + 2598960*B4(0,6,0,4) + 1750320*B4(0,5,3,0) + 3866616*B4(0,5,2,2) + 3341520*B4(0,5,1,4) + 1439424*B4(0,5,0,6) + 1069640*B4(0,4,4,0) + 2450448*B4(0,4,3,2) + 2333760*B4(0,4,2,4) + 1319472*B4(0,4,1,6) + 403920*B4(0,4,0,8) + 442442*B4(0,3,5,0) + 1034280*B4(0,3,4,2) + 1034280*B4(0,3,3,4) + 649740*B4(0,3,2,6) + 262548*B4(0,3,1,8) + 58344*B4(0,3,0,10) + 120120*B4(0,2,6,0) + 284310*B4(0,2,5,2) + 292500*B4(0,2,4,4) + 194040*B4(0,2,3,6) + 87480*B4(0,2,2,8) + 25740*B4(0,2,1,10) + 4095*B4(0,2,0,12) + 19448*B4(0,1,7,0) + 46410*B4(0,1,6,2) + 48620*B4(0,1,5,4) + 33320*B4(0,1,4,6) + 15912*B4(0,1,3,8) + 5236*B4(0,1,2,10) + 1105*B4(0,1,1,12) + 120*B4(0,1,0,14) + 1430*B4(0,0,8,0) + 3432*B4(0,0,7,2) + 3640*B4(0,0,6,4) + 2548*B4(0,0,5,6) + 1260*B4(0,0,4,8) + 440*B4(0,0,3,10) + 104*B4(0,0,2,12) + 15*B4(0,0,1,14) + B4(0,0,0,16)
Time: CPU 3.77 s, Wall: 3.77 s
sage: %timeit spin^(16)
5 loops, best of 3: 3.63 s per loop

I give this revised patch a positive review!

Anne

[jdemeyer]

1) There are issues with the documentation:

dochtml.log:/release/merger/sage-5.4.beta0/local/lib/python2.7/site-packages/sage/combinat/root_system/weyl_characters.py:docstring of sage.combinat.root_system.weyl_characters.WeylCharacterRing.dot_reduce:7: WARNING: Inline interpreted text or phrase reference start-string without end-string.
dochtml.log:/release/merger/sage-5.4.beta0/local/lib/python2.7/site-packages/sage/combinat/root_system/weyl_characters.py:docstring of sage.combinat.root_system.weyl_characters.WeightRing:0: WARNING: Block quote ends without a blank line; unexpected unindent.
dochtml.log:/release/merger/sage-5.4.beta0/local/lib/python2.7/site-packages/sage/combinat/root_system/weyl_characters.py:docstring of sage.combinat.root_system.weyl_characters.WeylCharacterRing.dot_reduce:11: WARNING: Inline interpreted text or phrase reference start-string without end-string.
dochtml.log:/release/merger/sage-5.4.beta0/local/lib/python2.7/site-packages/sage/combinat/root_system/weyl_characters.py:docstring of sage.combinat.root_system.weyl_characters.WeightRing:2: WARNING: Definition list ends without a blank line; unexpected unindent.
dochtml.log:/release/merger/sage-5.4.beta0/local/lib/python2.7/site-packages/sage/combinat/root_system/weyl_characters.py:docstring of sage.combinat.root_system.weyl_characters.WeylCharacterRing.dot_reduce:14: WARNING: Inline interpreted text or phrase reference start-string without end-string.
dochtml.log:/release/merger/sage-5.4.beta0/local/lib/python2.7/site-packages/sage/combinat/root_system/weyl_characters.py:docstring of sage.combinat.root_system.weyl_characters.WeightRing:5: WARNING: Block quote ends without a blank line; unexpected unindent.
dochtml.log:/release/merger/sage-5.4.beta0/local/lib/python2.7/site-packages/sage/combinat/root_system/weyl_characters.py:docstring of sage.combinat.root_system.weyl_characters.WeightRing:4: ERROR: Unexpected indentation.

2) The patch needs a proper commit message.

[bump]

I fixed the doc problem, and a bit of testing showed that it is probably a good idea to switch the two factors in a product if the second is bigger ... I'm not sure I found the best way to do it, but there's a new version of the patch, which now needs review again.

[aschilling]

Hi Dan,

I think in your commit message, you can delete the two lines

imported patch weyl_characters.patch
* * *

I ran

sage -coverage weyl_characters.py 
----------------------------------------------------------------------
weyl_characters.py
SCORE weyl_characters.py: 94% (63 of 67)

Missing doctests:
	 * __pow__(self, n):
	 * irreducible_character_freudenthal(hwv, L, debug=False):
	 * get_branching_rule(Rtype, Stype, rule):
	 * __classcall__(cls, parent, prefix=None):


Possibly wrong (function name doesn't occur in doctests):
	 * _repr_(self):
	 * product_on_basis(self, a, b):
	 * simple_coroots(self):
	 * _repr_(self):
	 * product_on_basis(self, a, b):
	 * _repr_term(self, t):

Since the method __pow__(self, n) is new, I suppose at least this method should have a doctest. You can add #indirect doctest behind tests that indirectly test the function. Then sage -coverage probably won't complain about the possibly wrong functions any longer.

In the docstring for the method dot_reduce, I think you want the line

"Auxiliary function for product_on_basis."

as the first line. Then INPUT: and the - a ... with the same indent at INPUT.

Anne

[bump]

I made the changes Anne found, and doctest coverage is now 100 percent.

[aschilling]

Replying to bump:

I made the changes Anne found, and doctest coverage is now 100 percent.

Thank you, Dan! I wrote a review patch with mostly trivial doctest changes. If you are happy with it, please fold it into yours and post a positive review on my behalf!

Anne

[bump]

I folded trac_13391-review-as.patch into trac_13391-weyl_characters.patch and uploaded. Per message 21 the patch is now positive review.

[bump]

I'm changing the status from positive_review to needs_work because I'm planning on adding two methods for the symmetric and exterior powers of representations. These can go in this patch.

[bump]

I've posted a revised patch which includes reasonably fast methods for symmetric and exterior powers, and adams operations. It seems possible that the new methods can be made faster and am looking for speedups.

[aschilling]

Hi Dan,

I posted a new review patch (with changes to the documentation) that you can fold into your patch if you agree with the changes. The doctests pass! I am happy to set a positive review.

Anne

[bump]

The latest posted version contains the comments in trac_13391-review-as.patch as well as revision to the Lie thematic tutorial and some changes suggested by Nicolas.

[chapoton]

Why does nobody care about the red light given by the bot ?

[bump]

Apply trac_13391-weyl_characters.patch

[bump]

Why does nobody care about the red light given by the bot ?

The buildbot tried to apply the review patch, which was folded. According to the wiki, comment:32 might fix this?

[nthiery]

Replying to bump:

Why does nobody care about the red light given by the bot ?

The buildbot tried to apply the review patch, which was folded. According to the wiki, comment:32 might fix this?

Should I delete the reviewer's patch?

[bump]

Should I delete the reviewer's patch?

adding comment:32 convinced the buildbot not to try the reviewer's patch, but after uploading the main patch again, it forgot, so deleting the reviewer's patch might be helpful if it's easy to do.

[bump]

Apply trac_13391-weyl_characters.patch

[aschilling]

Hi Dan,

Looks good! I have another small review patch, which I will e-mail in order not to confuse the buildbot. If you agree with it and fold it, you can set a positive review on my behalf. With it, all doctests pass and the documentation looks good.

Thanks,

Anne

[bump]

Weyl Character Ring speedup of product_on_basis

[bump]

I've applied the changes mentioned in comment:38, and the buildbot gives green. Therefore I'm setting positive review.