diff --git a/Manifest.toml b/Manifest.toml
index 458ec6b..09a2e96 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -2,7 +2,7 @@
 
 julia_version = "1.8.5"
 manifest_format = "2.0"
-project_hash = "5452e4eb8836d03e65c342a444826b894c3e14dc"
+project_hash = "46bad61f58c1a6b455db53aa91fae7351cb279ab"
 
 [[deps.AbstractAlgebra]]
 deps = ["GroupsCore", "InteractiveUtils", "LinearAlgebra", "MacroTools", "Markdown", "Random", "RandomExtensions", "SparseArrays", "Test"]
@@ -10,23 +10,6 @@ git-tree-sha1 = "29e65c331f97db9189ef00a4c7aed8127c2fd2d4"
 uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
 version = "0.27.10"
 
-[[deps.Accessors]]
-deps = ["Compat", "CompositionsBase", "ConstructionBase", "Dates", "InverseFunctions", "LinearAlgebra", "MacroTools", "Requires", "StaticArrays", "Test"]
-git-tree-sha1 = "beabc31fa319f9de4d16372bff31b4801e43d32c"
-uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
-version = "0.1.28"
-
-[[deps.Adapt]]
-deps = ["LinearAlgebra", "Requires"]
-git-tree-sha1 = "cc37d689f599e8df4f464b2fa3870ff7db7492ef"
-uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "3.6.1"
-
-[[deps.ArgCheck]]
-git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4"
-uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
-version = "2.3.0"
-
 [[deps.ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 version = "1.1.1"
@@ -34,20 +17,9 @@ version = "1.1.1"
 [[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 
-[[deps.BangBang]]
-deps = ["Compat", "ConstructionBase", "Future", "InitialValues", "LinearAlgebra", "Requires", "Setfield", "Tables", "ZygoteRules"]
-git-tree-sha1 = "7fe6d92c4f281cf4ca6f2fba0ce7b299742da7ca"
-uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
-version = "0.3.37"
-
 [[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
-[[deps.Baselet]]
-git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
-uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
-version = "0.1.1"
-
 [[deps.BenchmarkTools]]
 deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"]
 git-tree-sha1 = "d9a9701b899b30332bbcb3e1679c41cce81fb0e8"
@@ -113,48 +85,22 @@ deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 version = "1.0.1+0"
 
-[[deps.CompositionsBase]]
-git-tree-sha1 = "455419f7e328a1a2493cabc6428d79e951349769"
-uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
-version = "0.1.1"
-
-[[deps.ConstructionBase]]
-deps = ["LinearAlgebra"]
-git-tree-sha1 = "89a9db8d28102b094992472d333674bd1a83ce2a"
-uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
-version = "1.5.1"
-
 [[deps.Cyclotomics]]
 deps = ["LRUCache", "Memoize", "Primes", "SparseArrays", "Test"]
 git-tree-sha1 = "dc2e5fd64c188399434e83fa5c10c6fa4eff962a"
 uuid = "da8f5974-afbb-4dc8-91d8-516d5257c83b"
 version = "0.3.2"
 
-[[deps.DataAPI]]
-git-tree-sha1 = "e8119c1a33d267e16108be441a287a6981ba1630"
-uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
-version = "1.14.0"
-
 [[deps.DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
 git-tree-sha1 = "d1fff3a548102f48987a52a2e0d114fa97d730f0"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 version = "0.18.13"
 
-[[deps.DataValueInterfaces]]
-git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
-uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
-version = "1.0.0"
-
 [[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
-[[deps.DefineSingletons]]
-git-tree-sha1 = "0fba8b706d0178b4dc7fd44a96a92382c9065c2c"
-uuid = "244e2a9f-e319-4986-a169-4d1fe445cd52"
-version = "0.1.2"
-
 [[deps.DiffResults]]
 deps = ["StaticArraysCore"]
 git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621"
@@ -187,11 +133,6 @@ git-tree-sha1 = "d6863c556f1142a061532e79f611aa46be201686"
 uuid = "90fa49ef-747e-5e6f-a989-263ba693cf1a"
 version = "0.5.2"
 
-[[deps.ExternalDocstrings]]
-git-tree-sha1 = "1224740fc4d07c989949e1c1b508ebd49a65a5f6"
-uuid = "e189563c-0753-4f5e-ad5c-be4293c83fb4"
-version = "0.1.1"
-
 [[deps.FastRounding]]
 deps = ["ErrorfreeArithmetic", "LinearAlgebra"]
 git-tree-sha1 = "6344aa18f654196be82e62816935225b3b9abe44"
@@ -201,27 +142,17 @@ version = "0.3.1"
 [[deps.FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 
-[[deps.Folds]]
-deps = ["Accessors", "BangBang", "Baselet", "DefineSingletons", "Distributed", "ExternalDocstrings", "InitialValues", "MicroCollections", "Referenceables", "Requires", "Test", "ThreadedScans", "Transducers"]
-git-tree-sha1 = "638109532de382a1f99b1aae1ca8b5d08515d85a"
-uuid = "41a02a25-b8f0-4f67-bc48-60067656b558"
-version = "0.2.8"
-
 [[deps.ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
 git-tree-sha1 = "00e252f4d706b3d55a8863432e742bf5717b498d"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
 version = "0.10.35"
 
-[[deps.Future]]
-deps = ["Random"]
-uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
-
 [[deps.Groups]]
-deps = ["Folds", "GroupsCore", "KnuthBendix", "LinearAlgebra", "Logging", "OrderedCollections", "PermutationGroups", "StaticArrays"]
-git-tree-sha1 = "5dbf642ee0048e6ad5f0bda11af17e40b8e8dd2f"
+deps = ["GroupsCore", "KnuthBendix", "LinearAlgebra", "Logging", "OrderedCollections", "PermutationGroups", "Random", "StaticArrays"]
+git-tree-sha1 = "47967c88672431b6d3624d1cb200abdc15aa0b47"
 uuid = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
-version = "0.7.5"
+version = "0.7.6"
 
 [[deps.GroupsCore]]
 deps = ["Markdown", "Random"]
@@ -229,11 +160,6 @@ git-tree-sha1 = "9e1a5e9f3b81ad6a5c613d181664a0efc6fe6dd7"
 uuid = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
 version = "0.4.0"
 
-[[deps.InitialValues]]
-git-tree-sha1 = "4da0f88e9a39111c2fa3add390ab15f3a44f3ca3"
-uuid = "22cec73e-a1b8-11e9-2c92-598750a2cf9c"
-version = "0.3.1"
-
 [[deps.IntegerMathUtils]]
 git-tree-sha1 = "f366daebdfb079fd1fe4e3d560f99a0c892e15bc"
 uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
@@ -249,6 +175,12 @@ git-tree-sha1 = "c1c88395d09366dae431556bcb598ad08fa1392b"
 uuid = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 version = "0.20.8"
 
+[[deps.IntervalMatrices]]
+deps = ["IntervalArithmetic", "LinearAlgebra", "Random", "Reexport", "SparseArrays"]
+git-tree-sha1 = "b5a981918e38fb40aeea659ec6511187fa488c14"
+uuid = "5c1f47dc-42dd-5697-8aaa-4d102d140ba9"
+version = "0.8.3"
+
 [[deps.InverseFunctions]]
 deps = ["Test"]
 git-tree-sha1 = "49510dfcb407e572524ba94aeae2fced1f3feb0f"
@@ -260,11 +192,6 @@ git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 version = "0.2.2"
 
-[[deps.IteratorInterfaceExtensions]]
-git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
-uuid = "82899510-4779-5014-852e-03e436cf321d"
-version = "1.0.0"
-
 [[deps.JLLWrappers]]
 deps = ["Preferences"]
 git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
@@ -279,9 +206,9 @@ version = "0.21.3"
 
 [[deps.JuMP]]
 deps = ["LinearAlgebra", "MathOptInterface", "MutableArithmetics", "OrderedCollections", "Printf", "SnoopPrecompile", "SparseArrays"]
-git-tree-sha1 = "611b9f12f02c587d860c813743e6cec6264e94d8"
+git-tree-sha1 = "4ec0e68fecbbe1b78db2ddf1ac573963ed5adebc"
 uuid = "4076af6c-e467-56ae-b986-b466b2749572"
-version = "1.9.0"
+version = "1.10.0"
 
 [[deps.KnuthBendix]]
 deps = ["MacroTools", "ProgressMeter"]
@@ -341,9 +268,9 @@ uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
 [[deps.MathOptInterface]]
 deps = ["BenchmarkTools", "CodecBzip2", "CodecZlib", "DataStructures", "ForwardDiff", "JSON", "LinearAlgebra", "MutableArithmetics", "NaNMath", "OrderedCollections", "Printf", "SnoopPrecompile", "SparseArrays", "SpecialFunctions", "Test", "Unicode"]
-git-tree-sha1 = "f219b62e601c2f2e8adb7b6c48db8a9caf381c82"
+git-tree-sha1 = "88551cb56065a7bf9276af1d1970d2bd0d4b6ed4"
 uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
-version = "1.13.1"
+version = "1.14.0"
 
 [[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -356,12 +283,6 @@ git-tree-sha1 = "2b1dfcba103de714d31c033b5dacc2e4a12c7caa"
 uuid = "c03570c3-d221-55d1-a50c-7939bbd78826"
 version = "0.4.4"
 
-[[deps.MicroCollections]]
-deps = ["BangBang", "InitialValues", "Setfield"]
-git-tree-sha1 = "629afd7d10dbc6935ec59b32daeb33bc4460a42e"
-uuid = "128add7d-3638-4c79-886c-908ea0c25c34"
-version = "0.1.4"
-
 [[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
@@ -402,9 +323,9 @@ uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
 version = "0.5.5+0"
 
 [[deps.OrderedCollections]]
-git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
+git-tree-sha1 = "d321bf2de576bf25ec4d3e4360faca399afca282"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
-version = "1.4.1"
+version = "1.6.0"
 
 [[deps.Parsers]]
 deps = ["Dates", "SnoopPrecompile"]
@@ -469,17 +390,10 @@ git-tree-sha1 = "261dddd3b862bd2c940cf6ca4d1c8fe593e457c8"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 version = "1.3.3"
 
-[[deps.Referenceables]]
-deps = ["Adapt"]
-git-tree-sha1 = "e681d3bfa49cd46c3c161505caddf20f0e62aaa9"
-uuid = "42d2dcc6-99eb-4e98-b66c-637b7d73030e"
-version = "0.1.2"
-
-[[deps.Requires]]
-deps = ["UUIDs"]
-git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
-uuid = "ae029012-a4dd-5104-9daa-d747884805df"
-version = "1.3.0"
+[[deps.Reexport]]
+git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
+uuid = "189a3867-3050-52da-a836-e630ba90ab69"
+version = "1.2.2"
 
 [[deps.RoundingEmulator]]
 git-tree-sha1 = "40b9edad2e5287e05bd413a38f61a8ff55b9557b"
@@ -498,12 +412,6 @@ git-tree-sha1 = "d7a25e439d07a17b7cdf97eecee504c50fedf5f6"
 uuid = "3cc68bcd-71a2-5612-b932-767ffbe40ab0"
 version = "0.2.1"
 
-[[deps.Setfield]]
-deps = ["ConstructionBase", "Future", "MacroTools", "StaticArraysCore"]
-git-tree-sha1 = "e2cc6d8c88613c05e1defb55170bf5ff211fbeac"
-uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
-version = "1.1.1"
-
 [[deps.SnoopPrecompile]]
 deps = ["Preferences"]
 git-tree-sha1 = "e760a70afdcd461cf01a575947738d359234665c"
@@ -523,12 +431,6 @@ git-tree-sha1 = "ef28127915f4229c971eb43f3fc075dd3fe91880"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
 version = "2.2.0"
 
-[[deps.SplittablesBase]]
-deps = ["Setfield", "Test"]
-git-tree-sha1 = "e08a62abc517eb79667d0a29dc08a3b589516bb5"
-uuid = "171d559e-b47b-412a-8079-5efa626c420e"
-version = "0.1.15"
-
 [[deps.StarAlgebras]]
 deps = ["LinearAlgebra", "SparseArrays"]
 git-tree-sha1 = "265b89a5dfb38fe94ad48b997a253b2393fce6f1"
@@ -537,9 +439,9 @@ version = "0.2.0"
 
 [[deps.StaticArrays]]
 deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
-git-tree-sha1 = "6aa098ef1012364f2ede6b17bf358c7f1fbe90d4"
+git-tree-sha1 = "b8d897fe7fa688e93aef573711cb207c08c9e11e"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.5.17"
+version = "1.5.19"
 
 [[deps.StaticArraysCore]]
 git-tree-sha1 = "6b7ba252635a5eff6a0b0664a41ee140a1c9e72a"
@@ -552,7 +454,7 @@ uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[deps.SymbolicWedderburn]]
 deps = ["Cyclotomics", "GroupsCore", "LinearAlgebra", "PermutationGroups", "Primes", "SparseArrays", "StarAlgebras"]
-git-tree-sha1 = "3a098aae261c4c57d6ee41dab62973065f0cb68b"
+git-tree-sha1 = "7afdc5576b8fc49032c1f765c1514e5369fb77fe"
 repo-rev = "enh/towards_simple_projections"
 repo-url = "https://github.com/kalmarek/SymbolicWedderburn.jl.git"
 uuid = "858aa9a9-4c7c-4c62-b466-2421203962a2"
@@ -563,18 +465,6 @@ deps = ["Dates"]
 uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 version = "1.0.0"
 
-[[deps.TableTraits]]
-deps = ["IteratorInterfaceExtensions"]
-git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
-uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
-version = "1.0.1"
-
-[[deps.Tables]]
-deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"]
-git-tree-sha1 = "1544b926975372da01227b382066ab70e574a3ec"
-uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
-version = "1.10.1"
-
 [[deps.Tar]]
 deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
@@ -584,24 +474,12 @@ version = "1.10.1"
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
-[[deps.ThreadedScans]]
-deps = ["ArgCheck"]
-git-tree-sha1 = "ca1ba3000289eacba571aaa4efcefb642e7a1de6"
-uuid = "24d252fe-5d94-4a69-83ea-56a14333d47a"
-version = "0.1.0"
-
 [[deps.TranscodingStreams]]
 deps = ["Random", "Test"]
 git-tree-sha1 = "94f38103c984f89cf77c402f2a68dbd870f8165f"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
 version = "0.9.11"
 
-[[deps.Transducers]]
-deps = ["Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "Setfield", "SplittablesBase", "Tables"]
-git-tree-sha1 = "c42fa452a60f022e9e087823b47e5a5f8adc53d5"
-uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
-version = "0.4.75"
-
 [[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
@@ -614,12 +492,6 @@ deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 version = "1.2.12+3"
 
-[[deps.ZygoteRules]]
-deps = ["MacroTools"]
-git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
-uuid = "700de1a5-db45-46bc-99cf-38207098b444"
-version = "0.2.2"
-
 [[deps.libblastrampoline_jll]]
 deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
 uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
diff --git a/Project.toml b/Project.toml
index 75f97da..c13977e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,6 +6,7 @@ version = "0.4.0"
 [deps]
 Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
 IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
+IntervalMatrices = "5c1f47dc-42dd-5697-8aaa-4d102d140ba9"
 JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
@@ -17,6 +18,7 @@ SymbolicWedderburn = "858aa9a9-4c7c-4c62-b466-2421203962a2"
 COSMO = "0.8"
 Groups = "0.7"
 IntervalArithmetic = "0.20"
+IntervalMatrices = "0.8"
 JuMP = "1.3"
 ProgressMeter = "1.7"
 SCS = "1.1"
diff --git a/src/PropertyT.jl b/src/PropertyT.jl
index d4a664a..60b0aef 100644
--- a/src/PropertyT.jl
+++ b/src/PropertyT.jl
@@ -3,7 +3,6 @@ module PropertyT
 using LinearAlgebra
 using SparseArrays
 
-using IntervalArithmetic
 using JuMP
 
 using Groups
diff --git a/src/certify.jl b/src/certify.jl
index 43648aa..b93c843 100644
--- a/src/certify.jl
+++ b/src/certify.jl
@@ -1,3 +1,6 @@
+import IntervalArithmetic
+import IntervalMatrices
+
 function augment_columns!(Q::AbstractMatrix)
     for c in eachcol(Q)
         c .-= sum(c) ./ length(c)
@@ -63,7 +66,7 @@ function sufficient_λ(residual::StarAlgebras.AlgebraElement, λ; halfradius)
     suff_λ = λ - 2.0^(2ceil(log2(halfradius))) * L1_norm
 
     eq_sign = let T = eltype(residual)
-        if T <: Interval
+        if T <: IntervalArithmetic.Interval
             "∈"
         elseif T <: Union{Rational,Integer}
             "="
@@ -119,8 +122,10 @@ function certify_solution(
         return false, λ_flpoint
     end
 
-    λ_int = @interval(λ)
-    Q_int = [@interval(q) for q in Q]
+    λ_int = IntervalArithmetic.@interval(λ)
+    Q_int = IntervalMatrices.IntervalMatrix([
+        IntervalArithmetic.@interval(q) for q in Q
+    ])
 
     check, sos_int = @time if should_we_augment
         @info("Projecting columns of Q to the augmentation ideal...")
@@ -141,5 +146,5 @@ function certify_solution(
     λ_certified =
         sufficient_λ(elt, orderunit, λ_int, sos_int; halfradius = halfradius)
 
-    return check && inf(λ_certified) > 0.0, λ_certified
+    return check && IntervalArithmetic.inf(λ_certified) > 0.0, λ_certified
 end