option redSB greeds memory and does not terminate

[gorzel]

All works Ok here

> ring rds = (0,g),(x,y),ds;
> minpoly =  16g6+4g3-1;
> poly f = x4-2*x2y+y2+(-32g5-10g2)*x5+(64g5+20g2)*x3y+(-32g5-10g2)*xy2
   +(30g4+4g)*x6+ (-66g4-9g)*x4y+(42g4+6g)*x2y2+(-6g4-g)*y3+(8g3+1)*x5y
   +(-16g3)*x3y2+(8g3-1)*xy3+(-32g5-9g2)*x4y2+(-2g2)*x2y3+(32g5+11g2)*y4
   +(48g4+8g)*x3y3+(-48g4-8g)*xy4+(8g3+2)*x2y4+(-8g3-1)*y5+(-32g5-10g2)*xy5;
> option(prot);
> option(mem);
> vdim(std(jacob(f)));
[4294967295:2]5ss6.7.8.9.10.11.12sH(12)
product criterion:1 chain criterion:0
11

but if you enable option(redSB) then the computation does not finish and greeds the memory until CTRL-C is pressed.

>  option(redSB);
> vdim(std(jacob(f)));
[4294967295:2]5ss6.7.8.9.10.11.12sH(12)
(S:1)-[1004k][2007k][3027k][4063k][3051k][4087k][5099k][6135k][7195k][8230k][721
8k][6206k][5194k][6254k][7314k][8374k][9434k][10822k][11978k][13134k][14290k][15
446k][14444k][13384k][12324k][11264k][10204k][11361k][12517k][13673k][14829k][15
985k][17142k][18298k][19454k][20610k][19454k][20610k][19454k][18298k][17142k][15
985k][14829k][13673k][12517k][11361k][10204k][11361k][12517k][13673k][14829k][15

89k][38661k][37309k][36218k][39069k][36989k][38661k][37309k][39839k][37759k][394
31k][38079k][36988k][39839k][37759k][39431k][38079k][40610k][38530k][40202k][388
50k][37759k][40610k][38530k][40202k]

// ** Interrupt at cmd:`std` in line:'vdim(std(jacob(f)));'
abort command(a), continue(c) or quit Singular(q) ?q

halt 2

N.B.: This bug is not caused by the new alsfact* versions but it still exists with it.

[Oleksandr]

should be fixed via libpolys (Frank's rational function fields?) => postponed to Singular/libpolys

[gorzel]

As far as I see, it is fixed in

Singular for ix86-Linux version 3-1-3 (3133- 14465 )  Dec 15 2011 04:48:30
with
        factory(@(#) factoryVersion = 3.1.3),libfac(3.1.3,March 2011),
        GMP(4.3),NTL(5.5.2),MP(1.1.2.1),32bit,static readline,Plural,DBM,
        dynamic modules,OM_NDEBUG,random=1323963557

[gorzel]

My last comment seems to be wrong.

I had done the computation with option(redSB); and option(redTail); Then the bug did not occur.

[gorzel]

Note that the bug occurs with the ordering ds but not if a weighted ordering adapted to the local Netonwboundary id used,

i.e. ws(1,2) in this case.

Here is another example which shows the same behaviour. The following polynomial of degree 9 has by construction an A_40 singularity at the origin:

In ordering ws(1,3) it works fast and without difficulties in ds and redSB it does not terminate.

> ring rd9ws = (0,d),(x,y),ws(1,3);
> minpoly = 262144d3+22662253093d2+2536522496d+54071296;
> poly f9 = y2-2*x3y-(-142509342720d2-12306491624216454d-30438834692682765)/24658700198262517*x2y3
  +x6 -(-682021093376d2-59035741242572168d-6041759345452088)/24658700198262517*xy5
   -(142509342720d2+12306491624216454d+55097534890945282)/24658700198262517*x5y2
   -(-283866300416d2-24674584642624128d-898716357760400)/24658700198262517*y7
   -(665493438464d2+57765246207275360d+5706699088036840)/24658700198262517*x4y4
   + x8y - (242504171520d2+19167155822846656d+560814895347136)/24658700198262517 *x3y6;

> option(prot);
>  option(mem);
>  vdim(std(jacob(f9)));
[4294967295:2]18s20.25.30.35.40.45.50.55s57sH(43)
product criterion:1 chain criterion:0
40

> option(redSB);
>  vdim(std(jacob(f9)));
[4294967295:2]18s20.25.30.35.40.45.50.55s57sH(43)
(S:2)---
product criterion:1 chain criterion:0
40
>
> // Everything OK upto here:

> ring rd9ds = (0,d),(x,y),ds;
> minpoly = 262144d3+22662253093d2+2536522496d+54071296;
> poly f9 = imap(rd9ws,f9);
> option(prot);
> option(mem);
> option();
//options: prot redSB intStrategy mem redefine loadLib usage prompt
> option(noredSB);
> vdim(std(jacob(f9)));
[4294967295:2]8ss10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31[1314k].32.33.34[2317k].35.36[3319k].38[4333k].40[5340k][6374k][5349k][6349k][5336k][6341k].42[7536k][8606k][9817k][8808k][7772k][6765k][7865k][8897k][7825k][8825k][9845k][8760k][9786k][8746k][7703k][6659k][7734k][8734k][7706k][8744k][7740k][6708k][7739k][8810k][7808k][6773k][7818k]s[6800k][5800k]H(41)[4796k]
[3783k][2783k][1781k][772k]product criterion:1 chain criterion:0
40
> // Everything OK here in ds, but now
> option(redSB);
> vdim(std(jacob(f9)));
[4294967295:2]8ss10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33[1774k].34.35[2779k].36.38[3782k].40[4784k][5790k][6821k][5795k][4791k][5874k][4826k][5833k].42[6846k][7887k][8913k][10123k][9116k][8068k][7061k][8262k][7245k][8272k][7201k][8201k][9294k][8278k][9304k][8287k][9314k][8243k][9243k][8220k][7164k][8200k][7172k][8210k][9310k][8243k][9320k][8253k][9331k][8305k][9387k][8341k][7333k][8342k][7301k]s[6274k][5266k]H(41)
(S:1)-[6267k][7268k][8272k][7270k][8271k][7266k][8272k][9274k][10275k][9271k][10280k][11283k][12299k][13312k][14324k][15336k][14332k][13329k][12325k][13348k][14349k][15350k][16352k][17354k][18356k][19358k][18358k][17357k][16356k][15354k][14352k][13350k][12348k][13349k][14350k][15352k][16353k][17356k][18358k][19361k][18340k][17338k][16333k][15331k][14329k][13326k][12324k][13324k][14326k][15328k][16330k][17333k][18336k][19339k][20346k][21369k][22393k][23417k][24441k][25464k][26488k][25485k][24483k][23481k][22479k][21477k][20470k][19467k][20467k][21468k][22470k][23471k][24472k][25474k][26475k][27477k][28479k][29481k][30482k][31484k][32487k][33489k][34538k][35584k][36631k][37632k][38678k][39679k][40726k][41727k][42773k][43820k][44866k][45913k][46914k][47960k][49008k][48003k][49007k][47962k][46960k][45959k][44958k][43956k][42955k][41954k][40952k][39950k][38949k][37947k][36945k][35943k][34941k][33939k][34940k][35941k][36942k][37943k][38944k][39945k][40946k][41948k][42949k][43950k][44951k][45952k][46954k][47955k][48956k][49958k][50959k][51960k][52962k][53963k][54964k][55966k][56967k][57969k][58970k][59972k][60973k][61975k][63171k][64172k][65173k][66265k][67357k][68449k][69541k][70633k][71725k][72817k][73909k][75001k][76093k][77185k][78277k][79369k][80461k][81553k][82645k][83737k][84829k][85921k][87013k][88105k][89197k][90289k][91290k][92460k][91368k][92460k][91368k][92460k][91368k][92460k][91368k][92460k][91368k][92460k][91368k][92460k][91368k][92460k][91368k][92460k][91368k][92460k][91368k][90367k][91381k][90367k][89366k][88365k][87364k][86362k][85361k][84360k][83359k][82358k][81357k][80355k][79354k][78353k][77352k][76350k][75349k][74348k][73346k][72345k][71344k][70342k][69341k][68339k][67338k][66337k][65335k][64329k][63328k][62326k][63327k][64419k][65511k][66603k][67695k][68787k][69879k][70972k][72064k][73156k][74248k][75340k][76432k][77524k][78616k][79708k][80800k

[Oleksandr]

even the code without the redSB takes too long and too much memory on spielwiese...

[Oleksandr]

redSB involves computation with rational functions, which is slow by nature.

singular-team