its working! itsss woorking!!!

.idea/dictionaries/allem.xml

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+<component name="ProjectDictionaryState">
+  <dictionary name="allem">
+    <words>
+      <w>coset</w>
+      <w>cosets</w>
+      <w>ngens</w>
+    </words>
+  </dictionary>
+</component>

.idea/inspectionProfiles/profiles_settings.xml

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+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/misc.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="JavaScriptSettings">
+    <option name="languageLevel" value="ES6" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Pipenv (tc-fast)" project-jdk-type="Python SDK" />
+</project>

.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/tc-fast.iml" filepath="$PROJECT_DIR$/.idea/tc-fast.iml" />
+    </modules>
+  </component>
+</project>

.idea/tc-fast.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+  <component name="TestRunnerService">
+    <option name="PROJECT_TEST_RUNNER" value="Unittests" />
+  </component>
+</module>

.idea/workspace.xml

@@ -0,0 +1,132 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ChangeListManager">
+    <list default="true" id="d9bcf4a3-5128-4140-a8b2-98cb9536d00e" name="Default Changelist" comment="" />
+    <option name="EXCLUDED_CONVERTED_TO_IGNORED" value="true" />
+    <option name="SHOW_DIALOG" value="false" />
+    <option name="HIGHLIGHT_CONFLICTS" value="true" />
+    <option name="HIGHLIGHT_NON_ACTIVE_CHANGELIST" value="false" />
+    <option name="LAST_RESOLUTION" value="IGNORE" />
+  </component>
+  <component name="DatabaseView">
+    <option name="SHOW_INTERMEDIATE" value="true" />
+    <option name="GROUP_DATA_SOURCES" value="true" />
+    <option name="GROUP_SCHEMA" value="true" />
+    <option name="GROUP_CONTENTS" value="false" />
+    <option name="SORT_POSITIONED" value="false" />
+    <option name="SHOW_EMPTY_GROUPS" value="false" />
+    <option name="AUTO_SCROLL_FROM_SOURCE" value="false" />
+    <option name="HIDDEN_KINDS">
+      <set />
+    </option>
+    <expand />
+    <select />
+  </component>
+  <component name="FileTemplateManagerImpl">
+    <option name="RECENT_TEMPLATES">
+      <list>
+        <option value="Python Script" />
+      </list>
+    </option>
+  </component>
+  <component name="ProjectId" id="1UrBzU5LBS1twz9GRL9IT4R6RuY" />
+  <component name="PropertiesComponent">
+    <property name="WebServerToolWindowFactoryState" value="false" />
+    <property name="settings.editor.selected.configurable" value="preferences.lookFeel" />
+  </component>
+  <component name="RunDashboard">
+    <option name="ruleStates">
+      <list>
+        <RuleState>
+          <option name="name" value="ConfigurationTypeDashboardGroupingRule" />
+        </RuleState>
+        <RuleState>
+          <option name="name" value="StatusDashboardGroupingRule" />
+        </RuleState>
+      </list>
+    </option>
+  </component>
+  <component name="RunManager">
+    <configuration name="speedy_gonzolas" type="PythonConfigurationType" factoryName="Python" temporary="true">
+      <module name="tc-fast" />
+      <option name="INTERPRETER_OPTIONS" value="" />
+      <option name="PARENT_ENVS" value="true" />
+      <envs>
+        <env name="PYTHONUNBUFFERED" value="1" />
+      </envs>
+      <option name="SDK_HOME" value="" />
+      <option name="WORKING_DIRECTORY" value="$PROJECT_DIR$" />
+      <option name="IS_MODULE_SDK" value="true" />
+      <option name="ADD_CONTENT_ROOTS" value="true" />
+      <option name="ADD_SOURCE_ROOTS" value="true" />
+      <EXTENSION ID="PythonCoverageRunConfigurationExtension" runner="coverage.py" />
+      <option name="SCRIPT_NAME" value="$PROJECT_DIR$/speedy_gonzolas.py" />
+      <option name="PARAMETERS" value="" />
+      <option name="SHOW_COMMAND_LINE" value="false" />
+      <option name="EMULATE_TERMINAL" value="false" />
+      <option name="MODULE_MODE" value="false" />
+      <option name="REDIRECT_INPUT" value="false" />
+      <option name="INPUT_FILE" value="" />
+      <method v="2" />
+    </configuration>
+    <recent_temporary>
+      <list>
+        <item itemvalue="Python.speedy_gonzolas" />
+      </list>
+    </recent_temporary>
+  </component>
+  <component name="SvnConfiguration">
+    <configuration />
+  </component>
+  <component name="TaskManager">
+    <task active="true" id="Default" summary="Default task">
+      <changelist id="d9bcf4a3-5128-4140-a8b2-98cb9536d00e" name="Default Changelist" comment="" />
+      <created>1576105095293</created>
+      <option name="number" value="Default" />
+      <option name="presentableId" value="Default" />
+      <updated>1576105095293</updated>
+      <workItem from="1576105097677" duration="8305000" />
+    </task>
+    <servers />
+  </component>
+  <component name="TypeScriptGeneratedFilesManager">
+    <option name="version" value="1" />
+  </component>
+  <component name="XDebuggerManager">
+    <breakpoint-manager>
+      <breakpoints>
+        <line-breakpoint enabled="true" suspend="THREAD" type="python-line">
+          <url>file://$PROJECT_DIR$/speedy_gonzolas.py</url>
+          <line>90</line>
+          <option name="timeStamp" value="11" />
+        </line-breakpoint>
+        <line-breakpoint enabled="true" suspend="THREAD" type="python-line">
+          <url>file://$PROJECT_DIR$/speedy_gonzolas.py</url>
+          <line>100</line>
+          <option name="timeStamp" value="14" />
+        </line-breakpoint>
+        <line-breakpoint enabled="true" suspend="THREAD" type="python-line">
+          <url>file://$PROJECT_DIR$/speedy_gonzolas.py</url>
+          <line>145</line>
+          <option name="timeStamp" value="16" />
+        </line-breakpoint>
+      </breakpoints>
+      <default-breakpoints>
+        <breakpoint type="python-exception">
+          <properties notifyOnTerminate="true" exception="BaseException">
+            <option name="notifyOnTerminate" value="true" />
+          </properties>
+        </breakpoint>
+      </default-breakpoints>
+    </breakpoint-manager>
+    <watches-manager>
+      <configuration name="PythonConfigurationType">
+        <watch expression="cosets.data.__len__()" />
+        <watch expression="idx" />
+      </configuration>
+    </watches-manager>
+  </component>
+  <component name="com.intellij.coverage.CoverageDataManagerImpl">
+    <SUITE FILE_PATH="coverage/tc_fast$speedy_gonzolas.coverage" NAME="speedy_gonzolas Coverage Results" MODIFIED="1576113402777" SOURCE_PROVIDER="com.intellij.coverage.DefaultCoverageFileProvider" RUNNER="coverage.py" COVERAGE_BY_TEST_ENABLED="true" COVERAGE_TRACING_ENABLED="false" WORKING_DIRECTORY="$PROJECT_DIR$" />
+  </component>
+</project>

Pipfile

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+[[source]]
+name = "pypi"
+url = "https://pypi.org/simple"
+verify_ssl = true
+
+[dev-packages]
+
+[packages]
+
+[requires]
+python_version = "3.8"

speedy_gonzolas.py

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+from typing import List
+
+
+class Cosets:
+    def __init__(self, ngens, data=()):
+        assert len(data) % ngens == 0, 'invalid length starting row'
+
+        self.ngens = ngens
+        self.data = list(data)
+        self.len = len(data) // ngens
+
+    def add_row(self):
+        self.len += 1
+        self.data.extend(-1 for _ in range(self.ngens))
+
+    def put(self, idx, target):
+        coset, gen = divmod(idx, self.ngens)
+        self.data[idx] = target
+        self.data[target * self.ngens + gen] = coset
+
+    def get(self, idx):
+        return self.data[idx]
+
+    def __getitem__(self, key):
+        coset, gen = key
+        return self.data[coset * self.ngens + gen]
+
+    def __setitem__(self, key, target):
+        coset, gen = key
+        self.data[coset * self.ngens + gen] = target
+        self.data[target * self.ngens + gen] = coset
+
+    def __len__(self):
+        return self.len
+
+    def __repr__(self):
+        return '\n'.join(
+            f'{i // self.ngens:>3} | ' +
+            ' '.join(
+                f'{e:>3}' for e in self.data[i:i + self.ngens])
+            for i in range(0, len(self.data), self.ngens))
+
+
+class RelTable:
+    def __init__(self, gens: List[int], mul: int):
+        self.gens = gens
+        self.mul = mul
+
+        self.fam = []
+        self.gen = []
+        self.lst = []
+
+    def add_row(self):
+        idx = len(self.fam)
+        self.fam.append(-1)
+        self.gen.append(-1)
+        self.lst.append(-1)
+        return idx
+
+
+def solve(cosets: Cosets, rel_tables: List[RelTable]):
+    if len(cosets) < 1:
+        cosets.add_row()
+
+    for rel in rel_tables:
+        idx = rel.add_row()
+
+        count = 0
+        for g in rel.gens:
+            if cosets.get(g) == 0:
+                count += 1
+
+        rel.fam[idx] = 0
+        rel.gen[idx] = 0
+        rel.lst[idx] = 0
+
+        if count == 1:
+            rel.gen[idx] = -1
+
+    idx = 0
+    while True:
+        while idx < len(cosets.data) and cosets.get(idx) >= 0:
+            idx += 1
+
+        if idx == len(cosets.data):
+            break
+
+        # print()
+        # print(cosets)
+        # print()
+        coset, gen = divmod(idx, cosets.ngens)
+        target = len(cosets)
+
+        cosets.add_row()
+
+        for rel in rel_tables:
+            rel.add_row()
+
+        facts = [(coset, gen)]
+
+        while facts:
+            coset, gen = facts.pop()
+            cosets[coset, gen] = target
+
+            for rel in rel_tables:
+                if gen in rel.gens and rel.fam[target] == -1:
+                    rel.fam[target] = rel.fam[coset]
+                    rel.gen[target] = rel.gen[coset] + 1
+
+                    if rel.gen[coset] < 0:
+                        rel.gen[target] -= 2
+
+                    if rel.gen[target] == rel.mul:  # forward learn
+                        lst = rel.lst[rel.fam[target]]
+                        gen_ = rel.gens[rel.gens[0] == gen]
+                        facts.append((lst, gen_))
+                    elif rel.gen[target] == -rel.mul:  # stationary learn
+                        gen_ = rel.gens[rel.gens[0] == gen]
+                        facts.append((target, gen_))
+                    elif rel.gen[target] == rel.mul - 1:
+                        rel.lst[rel.fam[target]] = target
+
+            # print('=====================')
+            # for rel in rel_tables:
+            #     print(rel.gens)
+            #     print('fam', rel.fam)
+            #     print('gen', rel.gen)
+            #     print('lst', rel.lst)
+            #     print()
+
+            facts.sort(reverse=True)
+
+        for rel in rel_tables:
+            if rel.fam[target] == -1:
+                rel.fam[target] = target
+                rel.gen[target] = 0
+
+                count = 0
+                for g in rel.gens:
+                    if cosets[target, g] == target:
+                        count += 1
+
+                if count == 1:
+                    rel.gen[target] = -1
+
+        # print('=====================')
+        # for rel in rel_tables:
+        #     print(rel.gens)
+        #     print('fam', rel.fam)
+        #     print('gen', rel.gen)
+        #     print('lst', rel.lst)
+        #     print()
+
+
+if __name__ == '__main__':
+    # cosets = Cosets(3)
+    # mults = [((0, 1), 50000), ((1, 2), 2), ((0, 2), 2)]
+
+    cosets = Cosets(4)
+    n = 100
+    mults = [((0, 1), 5), ((1, 2), 3), ((2, 3), 3),
+             ((0, 2), 2), ((1, 3), 2), ((0, 3), 2)]
+
+    rel_tables = [RelTable(*args) for args in mults]
+
+    solve(cosets, rel_tables)
+
+    print(len(cosets))
+    if len(cosets) < 20:
+        print(cosets)
+    else:
+        print('--')