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Bertini :: makeWitnessSetFiles

makeWitnessSetFiles -- This function creates a witness point file and a slice file.

Synopsis

Description

This function does a track type 4 Bertini run creating a linear system file. The slice information for a positive dimensional run can be recovered from such a file.

i1 : makeB'InputFile(storeBM2Files,
       AffVariableGroup=>{x,y,z},
       B'Configs=>{{TrackType,1}},
       B'Polynomials=>{"(x^2+y^2+z^2-1)*y"})

o1 = /var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74577-0/0/input

o1 : File
i2 : runBertini(storeBM2Files)
~/bertini
i3 : makeWitnessSetFiles(storeBM2Files,2)--creats a witness point file for all dimension 2 components and a linear slice file for dimension 2 components.
~/bertini
i4 : L=importSliceFile(storeBM2Files)

o4 = {{{const1_1 ,  -3.239287744019561052720382862439986325636901712136234361
     ------------------------------------------------------------------------
     365626111788746715804140433755647346157390850987108829682410391509910505
     ------------------------------------------------------------------------
     593530609209546451420763631508332915037553602955751948548209786698389294
     ------------------------------------------------------------------------
     739961650518775314585062928665581758597009845922551400290672790402926601
     ------------------------------------------------------------------------
     703165829831663915070894904108118511275e-1+
     ------------------------------------------------------------------------
     6.9185474185812368614441871056705058870947628766773381377426433184148614
     ------------------------------------------------------------------------
     893067012422060406157449408061911012654677729208442639281006033731886959
     ------------------------------------------------------------------------
     112486758473765693446218732234130908094180656749554925359472906188330151
     ------------------------------------------------------------------------
     938448139225562769039696793128996653729683772865963513356039640589883955
     ------------------------------------------------------------------------
     64995196594202448736966e-1*ii}, {const1_2 ,
     ------------------------------------------------------------------------
     -5.674459140336796819121487552944459843392238906508557257831088818007926
     ------------------------------------------------------------------------
     342071901343234906065173117867149986370010512631431782112410826282992474
     ------------------------------------------------------------------------
     916834302424755141346677285573142424350204884949882333977759848878518838
     ------------------------------------------------------------------------
     553373091070843070364953993435758022847286333976243799862609070900806432
     ------------------------------------------------------------------------
     123407361261621534212667e-1+
     ------------------------------------------------------------------------
     4.3497986866019214205261217439655027330911320978550115019538835626309492
     ------------------------------------------------------------------------
     010951610560524377636490287402899704494238567167486894875105203002586514
     ------------------------------------------------------------------------
     163520991318526093313719121181819254269380676457305364868042944441095108
     ------------------------------------------------------------------------
     914995990681284669589462212351341216804979967630298206984513093349950897
     ------------------------------------------------------------------------
     18842419020658751451042e-1*ii}, {const1_3 ,
     ------------------------------------------------------------------------
     2.9976602455436688105330610106112661394877663849937987183846716637336908
     ------------------------------------------------------------------------
     554883349973997735208554732007334668052402729609072189733840113925217664
     ------------------------------------------------------------------------
     085616611374567235740240281830345827453922620319941105261618936053093504
     ------------------------------------------------------------------------
     607807426570897775994056235062519108391586431311339676345608181164059088
     ------------------------------------------------------------------------
     50561915924488163583939e-1+
     ------------------------------------------------------------------------
     7.1093016384542962048860332028296312582276037392193367559030825630099348
     ------------------------------------------------------------------------
     704927070517223440066730808732916172555828813332995612422358859631044434
     ------------------------------------------------------------------------
     912015128254287012509443801924907517537893833890418304594669907676162865
     ------------------------------------------------------------------------
     131470391670400527435686744637041646718342430871132359278201789308070635
     ------------------------------------------------------------------------
     10922446481231352630373e-1*ii}, {const1_4 ,
     ------------------------------------------------------------------------
     2.8280877934686583999171362205080048834422338723099910851799550652782036
     ------------------------------------------------------------------------
     576772838603890394797309319261218293203320255146658736892165491708917907
     ------------------------------------------------------------------------
     269069560080584144395977091340454621588767095057486937592221860880677524
     ------------------------------------------------------------------------
     849916084206427484319600674634767686322049326608001076732753431204046037
     ------------------------------------------------------------------------
     83458814897951965212722e-1-
     ------------------------------------------------------------------------
     6.4771368149221426637921554901436504502856126510331245698985507731360552
     ------------------------------------------------------------------------
     448970636607435823175800925925660589146653893758750025515984303113999262
     ------------------------------------------------------------------------
     010560801839295434279816297165216345741609917437289924523040381211845376
     ------------------------------------------------------------------------
     554971232834868459924453313268329940062503968777330176758124126031032531
     ------------------------------------------------------------------------
     31382054968784923842848e-1*ii}, {const2_1 ,
     ------------------------------------------------------------------------
     1.3770506983382267219724095721901028629241228459654655957923415858232337
     ------------------------------------------------------------------------
     825381829409649632267392757736545575383023443747805068502096071346869802
     ------------------------------------------------------------------------
     693893424369290653854890410562790634243679575166867501655239622414316772
     ------------------------------------------------------------------------
     446840529445525745543197675429122672884580152993750055831522223776934864
     ------------------------------------------------------------------------
     51491439496415526617500e-1-
     ------------------------------------------------------------------------
     8.8352978300290629566630055534540638107998400252240576017159572691846892
     ------------------------------------------------------------------------
     555946202179369197284719086196186645773026775426450783393362957441281817
     ------------------------------------------------------------------------
     622921316057948240219788187671654448363554821479205181347667512484486563
     ------------------------------------------------------------------------
     778249267968213671701300749763148661606970207278036157512056933566162398
     ------------------------------------------------------------------------
     81647634873690550352171e-1*ii}, {const2_2 ,
     ------------------------------------------------------------------------
     -5.655818052182300428445072313101048561677808880480178518257597163289321
     ------------------------------------------------------------------------
     179773186941589110891256290993517606501415523998167421883733887428205501
     ------------------------------------------------------------------------
     995206452732276831902261245133730180086776305469356354363917903284445921
     ------------------------------------------------------------------------
     905179550839070519581102359309466866111191535422195967666741564937919826
     ------------------------------------------------------------------------
     370662068367913270935816e-1+
     ------------------------------------------------------------------------
     7.7002142892830731908581520785978969156959964948756496930477270060501513
     ------------------------------------------------------------------------
     690946655984760563992008813588342118658634809427073604010387589743577632
     ------------------------------------------------------------------------
     105123105630333813158618614653453311858418194632125181793887732351054002
     ------------------------------------------------------------------------
     547899393894687009270248417107129839661716248132016361350219068304253194
     ------------------------------------------------------------------------
     57099971666282780490799e-1*ii}, {const2_3 ,
     ------------------------------------------------------------------------
     -1.563521356248019203529130506599858455038001141657251694085065163321257
     ------------------------------------------------------------------------
     169623273383733052953894335522376686432851147799379579665693951594724088
     ------------------------------------------------------------------------
     536919251615699809842843342097806897881251077153138935629484651226379311
     ------------------------------------------------------------------------
     861710400109099830206379762369203421879233668722598118599513914164765279
     ------------------------------------------------------------------------
     457107974292373503170968e-1+
     ------------------------------------------------------------------------
     8.6997653673199135978157703499843481125355486628322468936566137061034641
     ------------------------------------------------------------------------
     972590530171604448978191326195592776754023395235835981561985396096391122
     ------------------------------------------------------------------------
     822361160486354775981447697896633299831979247272085130807206754765029577
     ------------------------------------------------------------------------
     955962316647342316511970385258289321842543232908358121577571233101260346
     ------------------------------------------------------------------------
     56173701557294868106020e-1*ii}, {const2_4 ,
     ------------------------------------------------------------------------
     -8.059314936395580188183900499209940458964958550913777703792496061524382
     ------------------------------------------------------------------------
     402375926127553077305040712112868470902420304083104051202280207701456453
     ------------------------------------------------------------------------
     146607307920950638248376850683177134610379544910541358253550294305126877
     ------------------------------------------------------------------------
     699961184778586122635959194334543069736071699429508210937541881451871712
     ------------------------------------------------------------------------
     582598010295504945680879e-1+
     ------------------------------------------------------------------------
     5.3063415447470915749276699451943394924748847737303707210824706231520739
     ------------------------------------------------------------------------
     053740151691600907265789167328392777037889751794986121454298916499660456
     ------------------------------------------------------------------------
     843224867403287288659504191049004017575492402141984654677522919822838657
     ------------------------------------------------------------------------
     069407137521988825292340584770317006703966863306061361211997428053937113
     ------------------------------------------------------------------------
     74297797430072630367781e-1*ii}}, {{linear1 ,  const1_1 + const1_2*x +
     ------------------------------------------------------------------------
     const1_3*y + const1_4*z}, {linear2 ,  const2_1 + const2_2*x + const2_3*y
     ------------------------------------------------------------------------
     + const2_4*z}}}

o4 : List
i5 : makeWitnessSetFiles(storeBM2Files,2,
       NameSolutionsFile=>"custom_name_witness_points",--creates a witness point file with a custom name.
       SpecifyComponent=>0)  --Component indexing begins at 0. The function creates a witness point file for only a particular component.
~/bertini
i6 : L1=importSliceFile(storeBM2Files)

o6 = {{{const1_1 ,  -3.239287744019561052720382862439986325636901712136234361
     ------------------------------------------------------------------------
     365626111788746715804140433755647346157390850987108829682410391509910505
     ------------------------------------------------------------------------
     593530609209546451420763631508332915037553602955751948548209786698389294
     ------------------------------------------------------------------------
     739961650518775314585062928665581758597009845922551400290672790402926601
     ------------------------------------------------------------------------
     703165829831663915070894904108118511275e-1+
     ------------------------------------------------------------------------
     6.9185474185812368614441871056705058870947628766773381377426433184148614
     ------------------------------------------------------------------------
     893067012422060406157449408061911012654677729208442639281006033731886959
     ------------------------------------------------------------------------
     112486758473765693446218732234130908094180656749554925359472906188330151
     ------------------------------------------------------------------------
     938448139225562769039696793128996653729683772865963513356039640589883955
     ------------------------------------------------------------------------
     64995196594202448736966e-1*ii}, {const1_2 ,
     ------------------------------------------------------------------------
     -5.674459140336796819121487552944459843392238906508557257831088818007926
     ------------------------------------------------------------------------
     342071901343234906065173117867149986370010512631431782112410826282992474
     ------------------------------------------------------------------------
     916834302424755141346677285573142424350204884949882333977759848878518838
     ------------------------------------------------------------------------
     553373091070843070364953993435758022847286333976243799862609070900806432
     ------------------------------------------------------------------------
     123407361261621534212667e-1+
     ------------------------------------------------------------------------
     4.3497986866019214205261217439655027330911320978550115019538835626309492
     ------------------------------------------------------------------------
     010951610560524377636490287402899704494238567167486894875105203002586514
     ------------------------------------------------------------------------
     163520991318526093313719121181819254269380676457305364868042944441095108
     ------------------------------------------------------------------------
     914995990681284669589462212351341216804979967630298206984513093349950897
     ------------------------------------------------------------------------
     18842419020658751451042e-1*ii}, {const1_3 ,
     ------------------------------------------------------------------------
     2.9976602455436688105330610106112661394877663849937987183846716637336908
     ------------------------------------------------------------------------
     554883349973997735208554732007334668052402729609072189733840113925217664
     ------------------------------------------------------------------------
     085616611374567235740240281830345827453922620319941105261618936053093504
     ------------------------------------------------------------------------
     607807426570897775994056235062519108391586431311339676345608181164059088
     ------------------------------------------------------------------------
     50561915924488163583939e-1+
     ------------------------------------------------------------------------
     7.1093016384542962048860332028296312582276037392193367559030825630099348
     ------------------------------------------------------------------------
     704927070517223440066730808732916172555828813332995612422358859631044434
     ------------------------------------------------------------------------
     912015128254287012509443801924907517537893833890418304594669907676162865
     ------------------------------------------------------------------------
     131470391670400527435686744637041646718342430871132359278201789308070635
     ------------------------------------------------------------------------
     10922446481231352630373e-1*ii}, {const1_4 ,
     ------------------------------------------------------------------------
     2.8280877934686583999171362205080048834422338723099910851799550652782036
     ------------------------------------------------------------------------
     576772838603890394797309319261218293203320255146658736892165491708917907
     ------------------------------------------------------------------------
     269069560080584144395977091340454621588767095057486937592221860880677524
     ------------------------------------------------------------------------
     849916084206427484319600674634767686322049326608001076732753431204046037
     ------------------------------------------------------------------------
     83458814897951965212722e-1-
     ------------------------------------------------------------------------
     6.4771368149221426637921554901436504502856126510331245698985507731360552
     ------------------------------------------------------------------------
     448970636607435823175800925925660589146653893758750025515984303113999262
     ------------------------------------------------------------------------
     010560801839295434279816297165216345741609917437289924523040381211845376
     ------------------------------------------------------------------------
     554971232834868459924453313268329940062503968777330176758124126031032531
     ------------------------------------------------------------------------
     31382054968784923842848e-1*ii}, {const2_1 ,
     ------------------------------------------------------------------------
     1.3770506983382267219724095721901028629241228459654655957923415858232337
     ------------------------------------------------------------------------
     825381829409649632267392757736545575383023443747805068502096071346869802
     ------------------------------------------------------------------------
     693893424369290653854890410562790634243679575166867501655239622414316772
     ------------------------------------------------------------------------
     446840529445525745543197675429122672884580152993750055831522223776934864
     ------------------------------------------------------------------------
     51491439496415526617500e-1-
     ------------------------------------------------------------------------
     8.8352978300290629566630055534540638107998400252240576017159572691846892
     ------------------------------------------------------------------------
     555946202179369197284719086196186645773026775426450783393362957441281817
     ------------------------------------------------------------------------
     622921316057948240219788187671654448363554821479205181347667512484486563
     ------------------------------------------------------------------------
     778249267968213671701300749763148661606970207278036157512056933566162398
     ------------------------------------------------------------------------
     81647634873690550352171e-1*ii}, {const2_2 ,
     ------------------------------------------------------------------------
     -5.655818052182300428445072313101048561677808880480178518257597163289321
     ------------------------------------------------------------------------
     179773186941589110891256290993517606501415523998167421883733887428205501
     ------------------------------------------------------------------------
     995206452732276831902261245133730180086776305469356354363917903284445921
     ------------------------------------------------------------------------
     905179550839070519581102359309466866111191535422195967666741564937919826
     ------------------------------------------------------------------------
     370662068367913270935816e-1+
     ------------------------------------------------------------------------
     7.7002142892830731908581520785978969156959964948756496930477270060501513
     ------------------------------------------------------------------------
     690946655984760563992008813588342118658634809427073604010387589743577632
     ------------------------------------------------------------------------
     105123105630333813158618614653453311858418194632125181793887732351054002
     ------------------------------------------------------------------------
     547899393894687009270248417107129839661716248132016361350219068304253194
     ------------------------------------------------------------------------
     57099971666282780490799e-1*ii}, {const2_3 ,
     ------------------------------------------------------------------------
     -1.563521356248019203529130506599858455038001141657251694085065163321257
     ------------------------------------------------------------------------
     169623273383733052953894335522376686432851147799379579665693951594724088
     ------------------------------------------------------------------------
     536919251615699809842843342097806897881251077153138935629484651226379311
     ------------------------------------------------------------------------
     861710400109099830206379762369203421879233668722598118599513914164765279
     ------------------------------------------------------------------------
     457107974292373503170968e-1+
     ------------------------------------------------------------------------
     8.6997653673199135978157703499843481125355486628322468936566137061034641
     ------------------------------------------------------------------------
     972590530171604448978191326195592776754023395235835981561985396096391122
     ------------------------------------------------------------------------
     822361160486354775981447697896633299831979247272085130807206754765029577
     ------------------------------------------------------------------------
     955962316647342316511970385258289321842543232908358121577571233101260346
     ------------------------------------------------------------------------
     56173701557294868106020e-1*ii}, {const2_4 ,
     ------------------------------------------------------------------------
     -8.059314936395580188183900499209940458964958550913777703792496061524382
     ------------------------------------------------------------------------
     402375926127553077305040712112868470902420304083104051202280207701456453
     ------------------------------------------------------------------------
     146607307920950638248376850683177134610379544910541358253550294305126877
     ------------------------------------------------------------------------
     699961184778586122635959194334543069736071699429508210937541881451871712
     ------------------------------------------------------------------------
     582598010295504945680879e-1+
     ------------------------------------------------------------------------
     5.3063415447470915749276699451943394924748847737303707210824706231520739
     ------------------------------------------------------------------------
     053740151691600907265789167328392777037889751794986121454298916499660456
     ------------------------------------------------------------------------
     843224867403287288659504191049004017575492402141984654677522919822838657
     ------------------------------------------------------------------------
     069407137521988825292340584770317006703966863306061361211997428053937113
     ------------------------------------------------------------------------
     74297797430072630367781e-1*ii}}, {{linear1 ,  const1_1 + const1_2*x +
     ------------------------------------------------------------------------
     const1_3*y + const1_4*z}, {linear2 ,  const2_1 + const2_2*x + const2_3*y
     ------------------------------------------------------------------------
     + const2_4*z}}}

o6 : List
i7 : S0=importSolutionsFile(storeBM2Files,NameSolutionsFile=>"custom_name_witness_points")

o7 = {{-.282176-.371394*ii, -3.66001e-17+6.68835e-18*ii, 1.01251-.438602*ii}}

o7 : List
i8 : makeWitnessSetFiles(storeBM2Files,2,
       NameSolutionsFile=>"custom_name_witness_points")
~/bertini
i9 : S=importSolutionsFile(storeBM2Files,NameSolutionsFile=>"custom_name_witness_points")

o9 = {{.599223-.417343*ii, -.534718-.594863*ii, .942471-.072154*ii},
     ------------------------------------------------------------------------
     {-1.01248-.752022*ii, .148031+.73152*ii, 1.24243-.699997*ii},
     ------------------------------------------------------------------------
     {-.282176-.371394*ii, -3.66001e-17+6.68835e-18*ii, 1.01251-.438602*ii}}

o9 : List

Ways to use makeWitnessSetFiles :