Add regression test

On my system In [2]: %time count_roots(expr) # with GMPY CPU times: user 900 ms, sys: 8 ms, total: 908 ms Wall time: 968 ms In [2]: %time count_roots(expr) # without GMPY CPU times: user 14.5 s, sys: 16 ms, total: 14.5 s Wall time: 14.8 s Closes sympy/sympy#12602
skirpichev · Oct 6, 2018 · 82ee3b6 · 82ee3b6
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diff --git a/diofant/polys/tests/test_polytools.py b/diofant/polys/tests/test_polytools.py
@@ -2715,6 +2715,12 @@ def test_count_roots():
     pytest.raises(PolynomialError, lambda: count_roots(1))
 
 
+def test_sympyissue_12602():
+    expr = 11355363812949950368319856364342755712460471081301053527133568171268803160551855579764764406412332136789657466300880824616465555590045220022768132246969281371700283178427904690172215428157788636395727*t**14/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 1182614101238502509994197939548011046110362591360244720959032955996959698293886871005468894084128139099293801809189908060595593758885614886473934547400040763077455747185622083724725964710198605960741*t**13/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 12922822504467751142249299122933324184092020356108036157731097049497758652003692943810675925067800052327142015387959211427374009396705154181837176763552511140169473943304565171121276347837419884681487*t**12/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 2247204646780185719430022273864876084706708953097666720876560045907791931848809022047384483255204086759310635258105261945382035979316693256857004274231432751741774866992749719943120236265693542959121*t**11/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 48361843519832766388699493325560944345496391872452676523436328806727211606456243561884964568166128629309073817110912281835520854136140406763166099011063597874739148993632932049857510934073377073756943*t**10/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 80164052804759260531194459240730834126540153423610579212661871973340813173703351959915044156338949310408408075892534630817446213642840221172696829016781427774802300251456296296549939454943896121381103*t**9/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 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10574051936471402714931747549059296527795248964344182731742838740900131997560377847217760142735497446739729085272580576056569967115897852649538335744262984346103108139783500273358254849041434565692381*t**4/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 7621024600438344015600198602526834713218087596509021419939455089811715884880919464619193508300267251654333701818067555976498078593210932512841643006106774171602557804624587725019604901643333157908251*t**3/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 810596792271328855063337004546095119237768466927680286629788036582515398849767422695474356109018097281604030779219064519000249092915587584571381512608327847454533913096943271752401133736953700148513*t**2/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 7250440010579498280072969338541700246700434564503594127678121996192953098480655821398616200867454166215020508242889954318334847876038061179796990134727332078272146610064625333734530143125317393151907*t/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 1
+    expr = 11355363812949950368319856364342755712460471081301053527133568171268803160551855579764764406412332136789657466300880824616465555590045220022768132246969281371700283178427904690172215428157788636395727*t**14/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 1182614101238502509994197939548011046110362591360244720959032955996959698293886871005468894084128139099293801809189908060595593758885614886473934547400040763077455747185622083724725964710198605960741*t**13/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 12922822504467751142249299122933324184092020356108036157731097049497758652003692943810675925067800052327142015387959211427374009396705154181837176763552511140169473943304565171121276347837419884681487*t**12/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 2247204646780185719430022273864876084706708953097666720876560045907791931848809022047384483255204086759310635258105261945382035979316693256857004274231432751741774866992749719943120236265693542959121*t**11/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 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11820298688854366697091577677719451524251323356734720588058286064886307168520540386661816641085576247246659191024148765432674755172844550760156289246049795015707597236348994207857339854655564489007679*t**8/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 14908242237501135776503697900202844008307102016637953004464689811953233096672981556176039254271036473296837438230462049062156575391853236190707958824171141585643979204278060814079164562347710212783143*t**7/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 4004804534801340363315980630036975745885352263060800540982728634021250371208042415913703863593076428445232409745085269553713246947392078483528154594010983406996758112107177357774230732091992176355051*t**6/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 14405532019175131023474809758591882760843355517617477976264800133366074549575009123545658907344444270748700666056555232135755778765629022007752913521423634118196613981546114590366304386999628027814879*t**5/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 10574051936471402714931747549059296527795248964344182731742838740900131997560377847217760142735497446739729085272580576056569967115897852649538335744262984346103108139783500273358254849041434565692381*t**4/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 7621024600438344015600198602526834713218087596509021419939455089811715884880919464619193508300267251654333701818067555976498078593210932512841643006106774171602557804624587725019604901643333157908251*t**3/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 810596792271328855063337004546095119237768466927680286629788036582515398849767422695474356109018097281604030779219064519000249092915587584571381512608327847454533913096943271752401133736953700148513*t**2/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 7250440010579498280072969338541700246700434564503594127678121996192953098480655821398616200867454166215020508242889954318334847876038061179796990134727332078272146610064625333734530143125317393151907*t/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 1
+    assert count_roots(expr) == 0
+
+
 def test_Poly_root():
     f = Poly(2*x**3 - 7*x**2 + 4*x + 4)
 

diff --git a/docs/release/notes-0.10.rst b/docs/release/notes-0.10.rst
@@ -115,3 +115,4 @@ These Sympy issues also were addressed:
 * :sympyissue:`7047` Python and gmpy ground type specific stuff from "from sympy import \*"
 * :sympyissue:`15323` limit of the derivative of (1-1/x)^x as x --> 1+ gives wrong answer
 * :sympyissue:`15344` mathematica_code gives wrong output with Max
+* :sympyissue:`12602` count_roots is extremely slow with Python ground types