| 1 | | |
| 2 | | Now it behaves worse than before (and runs slower in determining the multiplicities.) |
| 3 | | My example from comment #2, checked with the recent nightly, built gives: |
| 4 | | {{{ |
| 5 | | > ring rw =(0,w),(x,y),dp;minpoly = w4-w3+2w2+w+1; |
| 6 | | > poly f = x15-y15-15*x13+15*y13+90*x11-90*y11-275*x9+275*y9+450*x7-450*y7-378*x5+378*y5+140*x3-140*y3-15*x+15*y; |
| 7 | | > factorize(f); |
| 8 | | [1]: |
| 9 | | _[1]=1 |
| 10 | | _[2]=x-y |
| 11 | | _[3]=x2+xy+y2-3 |
| 12 | | _[4]=x2+(1/2w3+3/2)*xy+y2+(1/2w3-3/2) |
| 13 | | _[5]=x10+(-1/2w3-3/2)*x9y+(1/2w3+3/2)*x8y2+(-1/2w3-3/2)*x6y4+(1/2w3+5/2)*x5y5+(-1/2w3-3/2)*x4y6+(1/2w3+3/2)*x2y8+(-1/2w3-3/2)*xy9+y10+(-1/2w3-21/2)*x8+(4w3+11)*x7y+(-2w3-6)*x6y2+(-2w3-10)*x5y3+(5w3+14)*x4y4+(-2w3-10)*x3y5+(-2w3-6)*x2y6+(4w3+11)*xy7+(-1/2w3-21/2)*y8+(7/2w3+77/2)*x6+(-9w3-18)*x5y+(-3w3-6)*x4y2+(17/2w3+83/2)*x3y3+(-3w3-6)*x2y4+(-9w3-18)*xy5+(7/2w3+77/2)*y6+(-7w3-57)*x4+(5/2w3-29/2)*x3y+(8w3+16)*x2y2+(5/2w3-29/2)*xy3+(-7w3-57)*y4+(4w3+29)*x2+(7/2w3+55/2)*xy+(4w3+29)*y2+(-1/2w3-7/2) |
| 14 | | [2]: |
| 15 | | 1,1,1,1,1 |
| 16 | | > factorize(_[1][5]); |
| 17 | | [1]: |
| 18 | | _[1]=1 |
| 19 | | _[2]=x2+(-1/2w3-1/2)*xy+y2+(-1/2w3-7/2) |
| 20 | | _[3]=x8-x7y+x5y3-x4y4+x3y5-xy7+y8-7*x6+4*x5y+3*x4y2-9*x3y3+3*x2y4+4*xy5-7*y6+14*x4+3*x3y-8*x2y2+3*xy3+14*y4-8*x2-8*xy-8*y2+1 |
| 21 | | [2]: |
| 22 | | 1,1,1 |
| 23 | | > factorize(_[1][3]); |
| 24 | | [1]: |
| 25 | | _[1]=1 |
| 26 | | _[2]=x4+(-1/2w3-3/2)*x3y+(1/2w3+3/2)*x2y2+(-1/2w3-3/2)*xy3+y4+(-1/2w3-9/2)*x2+(5/2w3+13/2)*xy+(-1/2w3-9/2)*y2+(1/2w3+5/2) |
| 27 | | _[3]=x4+(1/2w3+1/2)*x3y+(-1/2w3-1/2)*x2y2+(1/2w3+1/2)*xy3+y4+(1/2w3-5/2)*x2+(-5/2w3-7/2)*xy+(1/2w3-5/2)*y2+(-1/2w3+1/2) |
| 28 | | [2]: |
| 29 | | 1,1,1 |
| 30 | | }}} |
| 31 | | The latter degree 4 polynomials are indeed irreducible over the given alg. extension. |
| 32 | | |
| 33 | | A further example with a bug (which I thought it had had gone away with the first revision 15434 |
| 34 | | but pops up after revision 15445): |
| | 1 | Just for notification: The following bug has also gone away: |
| 42 | | Note that the degree 5 algebraic extension is the same as the following with monic minpoly: |
| 43 | | Here factorize works fine: |
| | 9 | it now gives |
| | 10 | {{{ |
| | 11 | [1]: |
| | 12 | _[1]=1 |
| | 13 | _[2]=x-y |
| | 14 | _[3]=x2+(23861351480320871396437536/3555941291619449132439795402119947079a4+2308720746603927337762383479/3555941291619449132439795402119947079a3-83572375552814840574829353504768/3555941291619449132439795402119947079a2-30098631735440341391412583822199229/3555941291619449132439795402119947079a+37025313228575179485700296525884161128/3555941291619449132439795402119947079)*xy+y2+(20521806961427079037746577/3555941291619449132439795402119947079a4-10647469275139757833667715337/3555941291619449132439795402119947079a3-57531287778331120480082390876523/3555941291619449132439795402119947079a2+8177861685328503333952454386005122/3555941291619449132439795402119947079a+1380670094891985263615208035187416019/3555941291619449132439795402119947079) |
| | 15 | _[4]=x2+(-20521806961427079037746577/3555941291619449132439795402119947079a4+10647469275139757833667715337/3555941291619449132439795402119947079a3+57531287778331120480082390876523/3555941291619449132439795402119947079a2-8177861685328503333952454386005122/3555941291619449132439795402119947079a-8492552678130883528494798839427310177/3555941291619449132439795402119947079)*xy+y2+(-18387611948323442185368744/3555941291619449132439795402119947079a4-3340860258777304183289428224/3555941291619449132439795402119947079a3+66154788241129464190661517246912/3555941291619449132439795402119947079a2+21919012210843006290534984319222417/3555941291619449132439795402119947079a-38496582632396647662026559262563922174/3555941291619449132439795402119947079) |
| | 16 | _[5]=x2+(4382069856325522341261721/3555941291619449132439795402119947079a4+10190436453413217024043713792/3555941291619449132439795402119947079a3-20601768514030323541191311386180/3555941291619449132439795402119947079a2-29751993989608550084064951592359936/3555941291619449132439795402119947079a+14791025772214013503410987488469440018/3555941291619449132439795402119947079)*xy+y2+(-23861351480320871396437536/3555941291619449132439795402119947079a4-2308720746603927337762383479/3555941291619449132439795402119947079a3+83572375552814840574829353504768/3555941291619449132439795402119947079a2+30098631735440341391412583822199229/3555941291619449132439795402119947079a-44137195811814077750579887330124055286/3555941291619449132439795402119947079) |
| | 17 | _[6]=x2+(-26109226323542756885321424/3555941291619449132439795402119947079a4-26487486733934206378763240832/3555941291619449132439795402119947079a3+112797644529643507826599791261337/3555941291619449132439795402119947079a2+89947499621220401099964974119786704/3555941291619449132439795402119947079a-71152545080196609725323658231130371906/3555941291619449132439795402119947079)*xy+y2+(-4382069856325522341261721/3555941291619449132439795402119947079a4-10190436453413217024043713792/3555941291619449132439795402119947079a3+20601768514030323541191311386180/3555941291619449132439795402119947079a2+29751993989608550084064951592359936/3555941291619449132439795402119947079a-21902908355452911768290578292709334176/3555941291619449132439795402119947079) |
| | 18 | _[7]=x2+(18387611948323442185368744/3555941291619449132439795402119947079a4+3340860258777304183289428224/3555941291619449132439795402119947079a3-66154788241129464190661517246912/3555941291619449132439795402119947079a2-21919012210843006290534984319222417/3555941291619449132439795402119947079a+31384700049157749397146968458324028016/3555941291619449132439795402119947079)*xy+y2+(26109226323542756885321424/3555941291619449132439795402119947079a4+26487486733934206378763240832/3555941291619449132439795402119947079a3-112797644529643507826599791261337/3555941291619449132439795402119947079a2-89947499621220401099964974119786704/3555941291619449132439795402119947079a+64040662496957711460444067426890477748/3555941291619449132439795402119947079) |
| | 19 | [2]: |
| | 20 | 1,1,1,1,1,1,1 |
| | 21 | }}} |
| | 22 | Note,the degree 5 algebraic extension is the same as the following with monic minpoly: |
