I was working with some large Finitely Presented Groups in sage and encountered some unexpected behavior. For one particular group, a newline character is introduced to the string representation of the finitely presented group after calling the simplified()
function. I tried looking into the source code for the simplified function, but I am rather new to sage and GAP and nothing presented itself as an obvious source of this behavior.
I am running SageMath version 10.4 with Python 3.11.2.
It may also be worth noting that I have generated thousands of groups of this same type, many of which have been this size or larger, and never encountered this behavior before.
This is the group that produced the newline character:
G = FreeGroup(208)
L = [G([1])*G([12])**(-1), G([12])*G([204])**(-1), G([204])*G([1])**(-1), G([1])*G([11]), G([11])*G([202]), G([202])*G([1])**(-1), G([2])*G([9])**(-1), G([9])*G([127])**(-1), G([127])*G([2])**(-1), G([2])*G([9])**(-1), G([9])*G([100]), G([100])*G([2]), G([3])*G([10])**(-1), G([10])*G([96])**(-1), G([96])*G([3])**(-1), G([3])*G([10])**(-1), G([10])*G([92])**(-1), G([92])*G([3])**(-1), G([4])*G([11]), G([11])*G([86]), G([86])*G([4])**(-1), G([4])*G([12])**(-1), G([12])*G([87])**(-1), G([87])*G([4])**(-1), G([5])*G([13])**(-1), G([13])*G([70])**(-1), G([70])*G([5])**(-1), G([5])*G([14]), G([14])*G([104])**(-1), G([104])*G([5]), G([6])*G([15])**(-1), G([15])*G([172]), G([172])*G([6]), G([6])*G([15])**(-1), G([15])*G([174])**(-1), G([174])*G([6])**(-1), G([7])*G([14]), G([14])*G([176]), G([176])*G([7])**(-1), G([7])*G([13])**(-1), G([13])*G([207])**(-1), G([207])*G([7])**(-1), G([8])*G([16])**(-1), G([16])*G([208]), G([208])*G([8]), G([8])*G([16])**(-1), G([16])*G([206])**(-1), G([206])*G([8])**(-1), G([204])*G([199])**(-1), G([203])*G([204])**(-1)*G([201])**(-1)*G([204]), G([199])*G([198])**(-1), G([200])*G([199])*G([197])**(-1)*G([199])**(-1), G([194])*G([191])**(-1), G([193])*G([194])**(-1)*G([192])**(-1)*G([194]), G([190])*G([187])**(-1), G([189])*G([190])**(-1)*G([188])**(-1)*G([190]), G([186])*G([183])**(-1), G([185])*G([186])**(-1)*G([184])**(-1)*G([186]), G([183])*G([182])**(-1), G([184])*G([183])*G([181])**(-1)*G([183])**(-1), G([180])*G([181])**(-1), G([181])*G([182])**(-1), G([185])*G([188])**(-1), G([186])*G([185])**(-1)*G([187])**(-1)*G([185]), G([189])*G([192])**(-1), G([190])*G([189])**(-1)*G([191])**(-1)*G([189]), G([193])*G([196])**(-1), G([194])*G([193])**(-1)*G([195])**(-1)*G([193]), G([196])*G([197])**(-1), G([195])*G([196])*G([198])**(-1)*G([196])**(-1), G([200])*G([202])**(-1), G([201])*G([200])*G([145])**(-1)*G([200])**(-1), G([180])*G([181])**(-1), G([181])*G([182])**(-1), G([121])*G([118])**(-1), G([120])*G([121])**(-1)*G([119])**(-1)*G([121]), G([117])*G([114])**(-1), G([116])*G([117])**(-1)*G([78])**(-1)*G([117]), G([108])*G([106])**(-1), G([107])*G([108])**(-1)*G([105])**(-1)*G([108]), G([110])*G([112])**(-1), G([108])*G([110])**(-1)*G([111])**(-1)*G([110]), G([112])*G([113])**(-1), G([111])*G([112])*G([114])**(-1)*G([112])**(-1), G([167])*G([168])**(-1), G([166])*G([167])*G([169])**(-1)*G([167])**(-1), G([168])*G([172])**(-1), G([173])*G([168])**(-1)*G([109])**(-1)*G([168]), G([95])*G([91])**(-1), G([94])*G([95])**(-1)*G([96])**(-1)*G([95]), G([88])*G([89])**(-1), G([89])*G([90])**(-1), G([89])*G([92])**(-1), G([90])*G([89])**(-1)*G([91])**(-1)*G([89]), G([71])*G([68])**(-1), G([69])*G([71])*G([70])**(-1)*G([71])**(-1), G([68])*G([67])**(-1), G([66])*G([68])**(-1)*G([69])**(-1)*G([68]), G([88])*G([89])**(-1), G([89])*G([90])**(-1), G([86])*G([85])**(-1), G([87])*G([86])*G([84])**(-1)*G([86])**(-1), G([85])*G([82])**(-1), G([84])*G([85])**(-1)*G([83])**(-1)*G([85]), G([82])*G([81])**(-1), G([83])*G([82])*G([80])**(-1)*G([82])**(-1), G([81])*G([63])**(-1), G([80])*G([81])**(-1)*G([65])**(-1)*G([81]), G([63])*G([62])**(-1), G([61])*G([63])**(-1)*G([64])**(-1)*G([63]), G([59])*G([53])**(-1), G([58])*G([59])**(-1)*G([60])**(-1)*G([59]), G([53])*G([52])**(-1), G([51])*G([53])**(-1)*G([54])**(-1)*G([53]), G([21])*G([20])**(-1), G([22])*G([21])*G([19])**(-1)*G([21])**(-1), G([17])*G([19])**(-1), G([19])*G([20])**(-1), G([24])*G([25])**(-1), G([23])*G([24])*G([26])**(-1)*G([24])**(-1), G([36])*G([37])**(-1), G([35])*G([36])*G([38])**(-1)*G([36])**(-1), G([40])*G([42])**(-1), G([21])*G([40])**(-1)*G([41])**(-1)*G([40]), G([57])*G([72])**(-1), G([73])*G([57])**(-1)*G([55])**(-1)*G([57]), G([72])*G([75])**(-1), G([74])*G([72])*G([73])**(-1)*G([72])**(-1), G([76])*G([78])**(-1), G([71])*G([76])*G([79])**(-1)*G([76])**(-1), G([116])*G([119])**(-1), G([117])*G([116])**(-1)*G([118])**(-1)*G([116]), G([120])*G([123])**(-1), G([121])*G([120])**(-1)*G([122])**(-1)*G([120]), G([123])*G([124])**(-1), G([122])*G([123])*G([125])**(-1)*G([123])**(-1), G([124])*G([129])**(-1), G([128])*G([124])*G([126])**(-1)*G([124])**(-1), G([129])*G([130])**(-1), G([131])*G([129])**(-1)*G([128])**(-1)*G([129]), G([133])*G([134])**(-1), G([135])*G([133])**(-1)*G([132])**(-1)*G([133]), G([203])*G([205])**(-1), G([206])*G([203])**(-1)*G([179])**(-1)*G([203]), G([205])*G([207])**(-1), G([208])*G([205])**(-1)*G([178])**(-1)*G([205]), G([66])*G([64])**(-1), G([65])*G([66])**(-1)*G([67])**(-1)*G([66]), G([61])*G([60])**(-1), G([59])*G([61])**(-1)*G([62])**(-1)*G([61]), G([58])*G([56])**(-1), G([57])*G([58])**(-1)*G([48])**(-1)*G([58]), G([51])*G([50])**(-1), G([49])*G([51])**(-1)*G([52])**(-1)*G([51]), G([50])*G([39])**(-1), G([41])*G([50])*G([49])**(-1)*G([50])**(-1), G([39])*G([38])**(-1), G([40])*G([39])*G([37])**(-1)*G([39])**(-1), G([35])*G([28])**(-1), G([36])*G([35])*G([34])**(-1)*G([35])**(-1), G([28])*G([26])**(-1), G([27])*G([28])**(-1)*G([18])**(-1)*G([28]), G([23])*G([18])**(-1), G([24])*G([23])*G([22])**(-1)*G([23])**(-1), G([27])*G([29])**(-1), G([30])*G([27])**(-1)*G([25])**(-1)*G([27]), G([29])*G([32])**(-1), G([31])*G([29])*G([30])**(-1)*G([29])**(-1), G([32])*G([33])**(-1), G([34])*G([32])**(-1)*G([31])**(-1)*G([32]), G([33])*G([43])**(-1), G([44])*G([33])**(-1)*G([42])**(-1)*G([33]), G([43])*G([46])**(-1), G([45])*G([43])*G([44])**(-1)*G([43])**(-1), G([46])*G([47])**(-1), G([48])*G([46])**(-1)*G([45])**(-1)*G([46]), G([47])*G([55])**(-1), G([54])*G([47])*G([56])**(-1)*G([47])**(-1), G([74])*G([77])**(-1), G([76])*G([74])*G([75])**(-1)*G([74])**(-1), G([77])*G([93])**(-1), G([79])*G([77])*G([94])**(-1)*G([77])**(-1), G([93])*G([98])**(-1), G([95])*G([93])**(-1)*G([97])**(-1)*G([93]), G([98])*G([99])**(-1), G([97])*G([98])*G([100])**(-1)*G([98])**(-1), G([99])*G([126])**(-1), G([125])*G([99])*G([127])**(-1)*G([99])**(-1), G([131])*G([132])**(-1), G([133])*G([131])**(-1)*G([130])**(-1)*G([131]), G([135])*G([136])**(-1), G([137])*G([135])**(-1)*G([134])**(-1)*G([135]), G([136])*G([139])**(-1), G([138])*G([136])*G([137])**(-1)*G([136])**(-1), G([139])*G([140])**(-1), G([141])*G([139])**(-1)*G([138])**(-1)*G([139]), G([140])*G([143])**(-1), G([142])*G([140])*G([141])**(-1)*G([140])**(-1), G([143])*G([144])**(-1), G([145])*G([143])**(-1)*G([142])**(-1)*G([143]), G([156])*G([159])**(-1), G([158])*G([156])*G([157])**(-1)*G([156])**(-1), G([160])*G([162])**(-1), G([154])*G([160])*G([163])**(-1)*G([160])**(-1), G([162])*G([165])**(-1), G([163])*G([162])**(-1)*G([164])**(-1)*G([162]), G([165])*G([170])**(-1), G([169])*G([165])*G([171])**(-1)*G([165])**(-1), G([101])*G([102])**(-1), G([102])*G([103])**(-1), G([102])*G([105])**(-1), G([103])*G([102])**(-1)*G([104])**(-1)*G([102]), G([107])*G([109])**(-1), G([110])*G([107])**(-1)*G([106])**(-1)*G([107]), G([173])*G([175])**(-1), G([174])*G([173])*G([170])**(-1)*G([173])**(-1), G([176])*G([171])**(-1), G([177])*G([176])*G([175])**(-1)*G([176])**(-1), G([166])*G([164])**(-1), G([167])*G([166])*G([113])**(-1)*G([166])**(-1), G([153])*G([150])**(-1), G([152])*G([153])**(-1)*G([151])**(-1)*G([153]), G([115])*G([146])**(-1), G([146])*G([147])**(-1), G([147])*G([148])**(-1), G([146])*G([147])*G([149])**(-1)*G([147])**(-1), G([148])*G([151])**(-1), G([149])*G([148])**(-1)*G([150])**(-1)*G([148]), G([152])*G([155])**(-1), G([153])*G([152])**(-1)*G([154])**(-1)*G([152]), G([155])*G([157])**(-1), G([156])*G([155])*G([144])**(-1)*G([155])**(-1), G([158])*G([161])**(-1), G([160])*G([158])*G([159])**(-1)*G([158])**(-1), G([161])*G([178])**(-1), G([179])*G([161])**(-1)*G([177])**(-1)*G([161]), G([17])*G([19])**(-1), G([19])*G([20])**(-1), G([115])*G([146])**(-1), G([146])*G([147])**(-1), G([101])*G([102])**(-1), G([102])*G([103])**(-1)]
F = G/L
K = F.simplified() # has a newline in it and I don't know why
K.simplified() # still works, so somehow despite the newline character the group behaves well in GAP
Displaying F produces the expected output:
Finitely presented group < x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207 | x0*x11^-1, x11*x203^-1, x203*x0^-1, x0*x10, x10*x201, x201*x0^-1, x1*x8^-1, x8*x126^-1, x126*x1^-1, x1*x8^-1, x8*x99, x99*x1, x2*x9^-1, x9*x95^-1, x95*x2^-1, x2*x9^-1, x9*x91^-1, x91*x2^-1, x3*x10, x10*x85, x85*x3^-1, x3*x11^-1, x11*x86^-1, x86*x3^-1, x4*x12^-1, x12*x69^-1, x69*x4^-1, x4*x13, x13*x103^-1, x103*x4, x5*x14^-1, x14*x171, x171*x5, x5*x14^-1, x14*x173^-1, x173*x5^-1, x6*x13, x13*x175, x175*x6^-1, x6*x12^-1, x12*x206^-1, x206*x6^-1, x7*x15^-1, x15*x207, x207*x7, x7*x15^-1, x15*x205^-1, x205*x7^-1, x203*x198^-1, x202*x203^-1*x200^-1*x203, x198*x197^-1, x199*x198*x196^-1*x198^-1, x193*x190^-1, x192*x193^-1*x191^-1*x193, x189*x186^-1, x188*x189^-1*x187^-1*x189, x185*x182^-1, x184*x185^-1*x183^-1*x185, x182*x181^-1, x183*x182*x180^-1*x182^-1, x179*x180^-1, x180*x181^-1, x184*x187^-1, x185*x184^-1*x186^-1*x184, x188*x191^-1, x189*x188^-1*x190^-1*x188, x192*x195^-1, x193*x192^-1*x194^-1*x192, x195*x196^-1, x194*x195*x197^-1*x195^-1, x199*x201^-1, x200*x199*x144^-1*x199^-1, x179*x180^-1, x180*x181^-1, x120*x117^-1, x119*x120^-1*x118^-1*x120, x116*x113^-1, x115*x116^-1*x77^-1*x116, x107*x105^-1, x106*x107^-1*x104^-1*x107, x109*x111^-1, x107*x109^-1*x110^-1*x109, x111*x112^-1, x110*x111*x113^-1*x111^-1, x166*x167^-1, x165*x166*x168^-1*x166^-1, x167*x171^-1, x172*x167^-1*x108^-1*x167, x94*x90^-1, x93*x94^-1*x95^-1*x94, x87*x88^-1, x88*x89^-1, x88*x91^-1, x89*x88^-1*x90^-1*x88, x70*x67^-1, x68*x70*x69^-1*x70^-1, x67*x66^-1, x65*x67^-1*x68^-1*x67, x87*x88^-1, x88*x89^-1, x85*x84^-1, x86*x85*x83^-1*x85^-1, x84*x81^-1, x83*x84^-1*x82^-1*x84, x81*x80^-1, x82*x81*x79^-1*x81^-1, x80*x62^-1, x79*x80^-1*x64^-1*x80, x62*x61^-1, x60*x62^-1*x63^-1*x62, x58*x52^-1, x57*x58^-1*x59^-1*x58, x52*x51^-1, x50*x52^-1*x53^-1*x52, x20*x19^-1, x21*x20*x18^-1*x20^-1, x16*x18^-1, x18*x19^-1, x23*x24^-1, x22*x23*x25^-1*x23^-1, x35*x36^-1, x34*x35*x37^-1*x35^-1, x39*x41^-1, x20*x39^-1*x40^-1*x39, x56*x71^-1, x72*x56^-1*x54^-1*x56, x71*x74^-1, x73*x71*x72^-1*x71^-1, x75*x77^-1, x70*x75*x78^-1*x75^-1, x115*x118^-1, x116*x115^-1*x117^-1*x115, x119*x122^-1, x120*x119^-1*x121^-1*x119, x122*x123^-1, x121*x122*x124^-1*x122^-1, x123*x128^-1, x127*x123*x125^-1*x123^-1, x128*x129^-1, x130*x128^-1*x127^-1*x128, x132*x133^-1, x134*x132^-1*x131^-1*x132, x202*x204^-1, x205*x202^-1*x178^-1*x202, x204*x206^-1, x207*x204^-1*x177^-1*x204, x65*x63^-1, x64*x65^-1*x66^-1*x65, x60*x59^-1, x58*x60^-1*x61^-1*x60, x57*x55^-1, x56*x57^-1*x47^-1*x57, x50*x49^-1, x48*x50^-1*x51^-1*x50, x49*x38^-1, x40*x49*x48^-1*x49^-1, x38*x37^-1, x39*x38*x36^-1*x38^-1, x34*x27^-1, x35*x34*x33^-1*x34^-1, x27*x25^-1, x26*x27^-1*x17^-1*x27, x22*x17^-1, x23*x22*x21^-1*x22^-1, x26*x28^-1, x29*x26^-1*x24^-1*x26, x28*x31^-1, x30*x28*x29^-1*x28^-1, x31*x32^-1, x33*x31^-1*x30^-1*x31, x32*x42^-1, x43*x32^-1*x41^-1*x32, x42*x45^-1, x44*x42*x43^-1*x42^-1, x45*x46^-1, x47*x45^-1*x44^-1*x45, x46*x54^-1, x53*x46*x55^-1*x46^-1, x73*x76^-1, x75*x73*x74^-1*x73^-1, x76*x92^-1, x78*x76*x93^-1*x76^-1, x92*x97^-1, x94*x92^-1*x96^-1*x92, x97*x98^-1, x96*x97*x99^-1*x97^-1, x98*x125^-1, x124*x98*x126^-1*x98^-1, x130*x131^-1, x132*x130^-1*x129^-1*x130, x134*x135^-1, x136*x134^-1*x133^-1*x134, x135*x138^-1, x137*x135*x136^-1*x135^-1, x138*x139^-1, x140*x138^-1*x137^-1*x138, x139*x142^-1, x141*x139*x140^-1*x139^-1, x142*x143^-1, x144*x142^-1*x141^-1*x142, x155*x158^-1, x157*x155*x156^-1*x155^-1, x159*x161^-1, x153*x159*x162^-1*x159^-1, x161*x164^-1, x162*x161^-1*x163^-1*x161, x164*x169^-1, x168*x164*x170^-1*x164^-1, x100*x101^-1, x101*x102^-1, x101*x104^-1, x102*x101^-1*x103^-1*x101, x106*x108^-1, x109*x106^-1*x105^-1*x106, x172*x174^-1, x173*x172*x169^-1*x172^-1, x175*x170^-1, x176*x175*x174^-1*x175^-1, x165*x163^-1, x166*x165*x112^-1*x165^-1, x152*x149^-1, x151*x152^-1*x150^-1*x152, x114*x145^-1, x145*x146^-1, x146*x147^-1, x145*x146*x148^-1*x146^-1, x147*x150^-1, x148*x147^-1*x149^-1*x147, x151*x154^-1, x152*x151^-1*x153^-1*x151, x154*x156^-1, x155*x154*x143^-1*x154^-1, x157*x160^-1, x159*x157*x158^-1*x157^-1, x160*x177^-1, x178*x160^-1*x176^-1*x160, x16*x18^-1, x18*x19^-1, x114*x145^-1, x145*x146^-1, x100*x101^-1, x101*x102^-1 >
The output from K and K.simplified() are identical, and both have a newline character in the relations:
Finitely presented group < x7, x40, x55, x105 | x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105^-1*x40*x55*(x40*x55*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105)^2*x40*x55*x40^-1*x55^-1*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*x55^-1*x40^-1, x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x7*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x7^-1*x105*x7*x40*x55*x40*(x55^-1*x40^-1)^2*x7^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x7*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x7*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x7^-1*x105^-1*x7*x40*x55*x40*(x55^-1*x40^-1)^2*x7^-1, (x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x7*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x7^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2)^2*x105*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x7*x40*x55*x40*(x55^-1*x40^-1)^2*x7^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x7*x40*x55*x40*(x55^-1*x40^-1)^2, x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*(x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1)^2*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*(x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1)^2*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^\
-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105 >
Calling K.relations() also prints this character (at the end of the second-to-last line):
(x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105^-1*x40*x55*(x40*x55*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105)^2*x40*x55*x40^-1*x55^-1*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*x55^-1*x40^-1,
x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x7*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x7^-1*x105*x7*x40*x55*x40*(x55^-1*x40^-1)^2*x7^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x7*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x7*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x7^-1*x105^-1*x7*x40*x55*x40*(x55^-1*x40^-1)^2*x7^-1,
(x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x7*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x7^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2)^2*x105*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x7*x40*x55*x40*(x55^-1*x40^-1)^2*x7^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x7*x40*x55*x40*(x55^-1*x40^-1)^2,
x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*(x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1)^2*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*(x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1)^2*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55^-1*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40^-1*x105^-1*(x40*x55)^2*x40^-1*x55^\
-1*x40^-1*x105^-1*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x55*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105*x40*x105^-1*(x40*x55)^2*x40^-1*x55^-1*x40^-1*x105*x40*x55*x40*(x55^-1*x40^-1)^2*x105)