This first verifies that the conditions are either all partitions or all brackets, and that they form a Schubert problem on Gr(k,n).
Then it creates a list of random square invertible matrices that represent flags for the Schubert problem.
i1 : randomSchubertProblemInstance({{1},{1},{1},{1}},2,4)
o1 = {({1}, | .781262-.624203i -.462954-.886382i -.272832+.962062i
| .9868+.161945i -.219207-.975678i .778029-.628229i
| -.971549+.236839i .157598-.987503i .841103-.540875i
| .893324+.449414i .360485-.932765i -.651048+.759036i
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-.670948-.741504i |), ({1}, | .696205+.717843i -.028156+.999604i
.118767+.992922i | | -.58234+.812945i -.924052-.382267i
-.396553+.918012i | | .486335-.873772i -.970803-.23988i
-.272372-.962192i | | -.783999-.620762i .577597-.816322i
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-.056229-.998418i .776937+.629579i |), ({1}, | -.746312-.665596i
.023444+.999725i .570649+.821194i | | -.936289-.351232i
.701149-.713015i -.863646+.504099i | | -.164243+.98642i
.357971+.933733i -.820726+.571321i | | .85817-.513365i
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.995687+.092774i .168661+.985674i -.765803+.643076i |), ({1}, |
.701342-.712825i -.286823-.957983i -.415126-.909764i | |
-.78761-.616174i .976163-.21704i -.416188-.909278i | |
.759918-.650019i .482783+.87574i .975922-.218119i | |
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.918399+.395655i .719639-.694348i .9772+.212322i -.998741-.050173i
.58629+.810101i -.554833-.831962i .454813+.890587i -.698649-.715464i
-.590887+.806754i -.726792+.686857i .080013+.996794i .742918+.669382i
-.939129+.343564i -.616052-.787706i .339065+.940763i -.99319-.116506i
------------------------------------------------------------------------
|)}
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o1 : List
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i2 : randomSchubertProblemInstance({{2,4},{2,4},{2,4},{2,4}},2,4)
o2 = {({2, 4}, | .996754-.080509i -.909393-.415938i .398424+.917201i
| -.531694+.846937i .92457+.381011i -.976915+.213627i
| .51095+.859611i -.227376-.973807i .842765-.538281i
| -.341238+.939977i -.110622-.993863i -.923063-.384649i
------------------------------------------------------------------------
-.688353+.725376i |), ({2, 4}, | -.991977+.126418i .398109-.917338i
-.81898+.573823i | | .91893+.394421i -.210222+.977654i
-.915156-.403101i | | -.834955-.550318i .491643-.870797i
-.684587-.728932i | | -.978842+.204616i .097639-.995222i
------------------------------------------------------------------------
.989783-.142579i .930733+.365699i |), ({2, 4}, | .276727+.960949i
.990088-.140449i .233835+.972276i | | .74405-.668124i
-.999969-.007811i .565772+.824562i | | -.191573+.981478i
-.344326+.93885i -.974074-.226228i | | .476077+.879404i
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-.166675+.986012i .824149+.566373i -.788618-.614883i |), ({2, 4}, |
.936252-.351329i .869663+.493645i .794218+.607632i | |
-.987864+.155324i .68453+.728985i -.990213-.139564i | |
-.535925+.844266i .415186-.909737i .194585-.980886i | |
------------------------------------------------------------------------
.109319-.994007i .560285+.8283i .990856+.13492i -.211093+.977466i
.984107-.177574i .000053+i .978795+.20484i .241807+.970324i
-.764815-.64425i -.64519-.764022i .93104+.364917i .923802+.382872i
-.129853+.991533i .889567+.456804i -.872433-.488734i -.636591-.771201i
------------------------------------------------------------------------
|)}
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o2 : List
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The output consists of random numerical matrices that are assumed invertible. The code does not check for this invertibility condition.