add tests for intervals

Author: Remi Prebet

test/algorithms/solvers.jl

@@ -12,9 +12,18 @@
         [1611414365//8589934592, 673053615//8589934592, 632173751//8589934592, 708759148891639684402860468800417934359477//2787593149816327892691964784081045188247552],
         [2863311531//8589934592, 0, 0, 14518714321960041107770649917088777022123//43556142965880123323311949751266331066368]
                             ]
+    inter_sols = Vector{Vector{QQFieldElem}}[
+        [[2431274387//4294967296, 607818597//1073741824], [320390731//2147483648, 640781463//4294967296], [1097534103//4294967296, 137191763//536870912], [-16357136847304379909836796974131395209669//87112285931760246646623899502532662132736, -4089284211826094977459199243532848802417//21778071482940061661655974875633165533184]],
+        [[1889817751//4294967296, 236227219//536870912], [1319238065//4294967296, 659619033//2147483648], [113559211//1073741824, 454236845//4294967296], [-46316921746739551124221118038944540401681//348449143727040986586495598010130648530944, -2894807609171221945263819877434033775105//21778071482940061661655974875633165533184]],
+        [[1, 1], [0, 0], [0, 0], [0, 0]].
+        [[3205239737//4294967296, 1602619869//2147483648], [501382663//2147483648, 1002765327//4294967296], [-792885089//4294967296, -24777659//134217728], [3478667982170137579718084770105695880909725//44601490397061246283071436545296723011960832, 27829343857361100637744678160845567047277801//356811923176489970264571492362373784095686656]],
+        [[402853591//2147483648, 805707183//4294967296], [336526807//4294967296, 42065851//536870912], [316086875//4294967296, 79021719//1073741824], [177189787222909921100715117200104483589869//696898287454081973172991196020261297061888, 354379574445819842201430234400208967179739//1393796574908163946345982392040522594123776]],
+        [[1431655765//4294967296, 715827883//2147483648], [-1//4294967296, 1//4294967296], [-1//4294967296, 1//4294967296], [7259357160980020553885324958544388511061//21778071482940061661655974875633165533184, 3629678580490010276942662479272194255531//10889035741470030830827987437816582766592]]
+                                            ]
     rat_sols = Vector{QQFieldElem}[[49, 0, 0, 0], [49//3, 0, 0, 1//3]]
 
     @test sols == real_solutions(I)
+    @test inter_sols == inter_solutions(I)
     @test rat_sols == rational_solutions(I)
     @test I.real_sols == real_solutions(I)
 
@@ -45,10 +54,12 @@
 
     I = Ideal([x1^2-x2, x1*x3-x4, x2*x4-12, x4^3-x3^2])
     real_solutions(I)
+    inter_solutions(I)
     @test I.rat_param.vars == Symbol[]
 
     I = Ideal([x1^2-x2, x1*x3, x2-12])
 	@test_throws ErrorException real_solutions(I)
+    @test_throws ErrorException inter_solutions(I)
 	@test_throws ErrorException rational_solutions(I)
 
     # check variable permutation