[GAP Forum] [$13.37] subscribing to eager-gen at listserv.dfn.de

[CHRISTOPHER MARY]

How I (almost) HACKED MICROSOFT ...

Proph Alejandro "NSERC boss" Adem ,

https://AnthropLOGIC.com ( https://鸡算计.中国 )

AnthropLOGIC.com WorkSchool 365 for art writing & filming (mathematics) via SurveyQuiz & EventReview

(1.) WorkSchool 365 App integrates the Customer Relationship Management (CRM) + Learning Management System (LMS) for your Business or University to engage/qualify/educate prospective users into paying/subscribed/grantee customers/students or paid reviewers/teachers via an integration of Stripe.com e-commerce payment (Card, AliPay, Wechat Pay, PayPal) + Microsoft.com Business Applications MBA (Azure AD, SharePoint Teams, Power Automate). 
(1.1.) WorkSchool 365 SurveyQuiz are Excel workbooks of auto-graded survey/quizzes with shareable transcripts of School, and 
(1.2.) WorkSchool 365 EventReview are SharePoint calendars of review-assignments for events/documents with shareable receipts of Work, and
(1.3.) WorkSchool 365 Users are passwordless sign-in/sign-up via Microsoft/Azure or Google or Facebook or Email. 
(1.4.) Buy from the Microsoft Commercial Marketplace: 
https://azuremarketplace.microsoft.com/en-us/marketplace/apps/anthroplogicworkschool3651593890930054.anthroplogic_workschool_365 

(2.) AnthropLOGIC.com is an instance of the WorkSchool 365 for end-users to trade/engage in art writing & filming ( mathematics ).
(2.1.) Advertisement 1: call for traders to sign-up via Google/Facebook/Github: https://sign.anthroplogic.com , via Microsoft/Outlook/Azure: https://sign-microsoft.anthroplogic.com , via Email: https://鸡算计.中国 : Cycle 1 ( Learners ) SurveyQuiz+EventReview is free; Cycle 3 ( Reviewers ) may create their own instances of paid non-free thematic Cycles 2 ( Seminarians ) ( video demo: https://www.youtube.com/watch?v=ZM9B7NFChOc ).
(2.2.) Advertisement 2: call for students/teachers to translate https://giam.southernct.edu into the SurveyQuiz ( vs WeBWorK ) workbooks survey-quizzes ( which also load the COQ/鸡算计 computer into Excel as the new COQ365 interactive add-in; demo: https://surveyquiz.anthroplogic.com ).
(2.3.) Advertisement 3: call for customers/reviewers to translate arxiv.org/researchseminars.org events/documents into the EventReview calendars review-assignments ( which has automatic graphical calendars + Gantt charts + Excel workbook views, passwordless security, auditable logs + compliance, data loss prevention + version history + personalized moderation/filtering; demo: https://eventreview.anthroplogic.com ). For example, I am assigning to any volunteer some review of http://www.cse.chalmers.se/~coquand/notes.txt for the pay amount of $13.37 due on Friday 13th November 6:49 PM CEST because it contains the usual bug that some of the descriptions ( involving sieves ) end up only global and not contextual ( ref 5.3. below )...

(3.) AnthropLOGIC.com WorkSchool 365 ​is a legal "business-university" name in Canada​ with tax id number 724573878, and as such is seeking the Natural Sciences and Engineering Research Council ( NSERC FORM 103CV ENGAGE GRANTS https://www.nserc-crsng.gc.ca/Professors-Professeurs/RPP-PP/F103CV_e.pdf ) review and funding. 
(3.1.) This WorkSchool outputs the shareable transcript/receipts records of learning-discovery-engineering-and-teaching/reviewing, and as such would pass the review by the Legislative Assembly or the Postsecondary Education Quality Assessment Board (PEQAB). 
(3.2.) I have personal knowledge that "possibly half" of the ( coward ) incumbent impersonators of the public money/infrastructure do forced/assault-fool/[intoxicated-by-bad-habits]-and-theft/lie/falsification of those transcripts/receipts records ( currencies ) without public review; for example, receipts of teaching ( professional "leadersheep" ) is falsified and transcripts of engineering ( other than "PDF" print ) is not recognized, and public review of those falsified/absent transcripts/receipts is prevented, and for sure this reality is mis-qualified and mis-framed. In short: https://readmyreply.online

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annenas ,

https://github.com/1337777/cartier/blob/master/cartierSolution10.v

New attempts at homotopical computational logic for geometry (COQ vs MODOS vs GAP/SINGULAR)

(1.) COQ computer is for reading and writing mathematical computations and proofs. Any collection of elements ( "datatype" ) may be presented constructively and inductively, and thereafter any function ( "program" ) may be defined on such datatype by case-analysis on the constructors and by recursion on this program itself. Moreover, the COQ computer extends mere computations (contrasted to OCAML) by allowing any datatype to be parameterized by elements from another datatype, therefore such parameterized datatypes become logical propositions and the programs defined thereon become proofs. Optionally, Coq allows many interface engineering in the form of transparent-opaque modularity, automation of proofs, and user interface...

(2.) GAP/SINGULAR computer is for computing in permutation groups and polynomial rings, whenever computational generators are possible, such as for the orbit-stabilizer algorithm ( "Schreier generators" ) or for the multiple-variables multiple-divisors division algorithm ( "Euclid/Gauss/Groebner basis" ). One technique in the algebra of group/ring-modules is to relativize to any general "zero" submodule, in particular to "primary" submodules which support/decompose this module. Dually to relativization is "parameterization", but now in the context of the spaces which are support/spectrum of any such relativized module. In short: the geometry vocabulary may be used while doing the GAP/SINGULAR computer algebra.

(3.) MODOS computer are new attempts at homotopical computational logic for geometry, moved by some alternative reformulation of categorical-algebra, which mathematicians ( except Kosta Dosen , Pierre Cartier ... ) have failed to notice since the past half-century. Some programming techniques ( "cut-elimination" , "confluence" , "dependent-typed functional programming" ... ) from the electrical circuits generalize to categorical-algebras ( "adjunctions" , "comonads" , "products" ... ). In contrast to GAP/SINGULAR which does the inner computational-algebra corresponding to the affine-projective aspects of geometry, the MODOS aims at the outer logical/categorical-algebra corresponding to the parameterized-schematic aspects of geometry; this contrast is similar as the OCAML-COQ contrast. In short: MODOS does the computational-logic of the coherent sheaf modules over some base topological ringed scheme; dually the relative support/spectrum of such modules/algebras are schemes parameterized over this base scheme.

(4.) ALGEBRA-GEOMETRY reminder: An affine variety corresponds to its coordinate ring which is any quotient of some polynomial ring by any fixed ideal; the points of the variety correspond to the maximal ideals of the coordinate ring. Some notion of "regular functions" on the variety are defined such that the space of regular local-functions/germs near some point (or away from the zero locus of some polynomial) correspond to the localization/fraction of the coordinate ring near this maximal ideal (or away from this polynomial). In other words, any regular function can be locally-specified by some fraction of polynomials; and for example: the locally-constant functions are more than the constant functions on the two-points-space.
(4.1.) Now the affine schemes say the same story with general/opaque coordinate rings, but the "points" (prime ideals) are more than mere singletons: they are morphisms of irreducible closed subschemes into the base scheme. This angle of view of "point-as-morphism" is the same behind the cut-elimination technique where cuts/composition are "accumulated" into grammatical-constructors which operate on morphisms instead of singletons.
(4.2.) The logical/categorical aspects have thus already started, but further intensify when some base topological ringed space is fixed and the sheaf modules over this base are grammatically-constructed; dually the relative support/spectrum of such sheaf modules/algebras define the schemes which are parameterized over this base scheme: https://stacks.math.columbia.edu/tag/01LQ
(4.3.) Those grammatical constructions are such that the resulting elements ( "functions" ) are always locally-specified ( "sheafification" ) by the source elements/functions; therefore the only-global view may cause loss of data ( "cohomology of sheaves" ).
(4.4.) The question of topos is, assuming that categories are presentable-by-generators with pullback/substitution-distributing-over-colimits ( for example, sets or presheaves of sets or pullbacks/colimits-preserving reflection of those ), the same as the question of morphisms-classifier ( "universe" / "type of types" ). For computations, those morphisms/fibrations should be finitely-compact and should be over some varying context whose elements are non-uniformly locally-specified; therefore each element/code in the contextual ( in the slice over any context ) universe should itself/internally carry the open-cover / truthness-sieve where it is locally-specified. Moreover the phrasing of "locally" as saying "near the prime ideal, for every prime ideal" would require some computational reformulations.

(5.) MODOS computer has solved the critical techniques behind those questions, even if the production-grade engineering is still lacking.
(5.1.) For example in "cartierSolution8.v", some grammatical-constructors accumulate morphisms ( "point-as-morphism" ) during cut-elimination, and the sheafification is based on the "plus construction" where each element of the sheaf ( itself/internally ) carry the open-cover data where it is locally-specified. Now this suggests that even the elements of any presheaf can carry such open-cover data. Another motivation for this suggestion is that any locally-free sheaf module must carry the open-cover where it is locally-free; and such sheaf is itself some element of the sheaf universe of sheaves. This reformulation comes with some continuity-condition on the morphisms of sheaf modules/algebras such that dually the morphisms of the relative-spectra/support would be continuous. And the sense for this refomulated grammar mimicks the usual forcing-semantics of the topos internal-language.
(5.2.) CONTRAST: Joyal who failed to see that the generalized elements ( arrows ) should remain internalized/accumulated (  "point-as-morphism" / polymorphism ) and not become variables/terms as in the usual internal-language...
(5.3.) CONTRAST: Coquand who failed to see that the the universe should remain contextual ( in the slice over any varying context ) and not become global ( ref the lost "Sieve : Context -> Covers" ), therefore any single descent-data modality shall already mix the sieves for this context...
(5.4.) Another example in "cartierSolution6.v" shows that cut-elimination holds for 2-fold categories with sense in some homotopy/model-category; this suggests some homotopical computational logic for derived algebraic geometry
(5.5.) Also the cut-eliminations in "cartierSolution5.v" ( enriched categories ) and "cartierSolution4.v" ( internal categories ) hint at how linear-actions may be presented such to upgrade from the sheaves of sets to the sheaves of modules and such to relativize modulo zero/submodules ( in other words, computations in abelian category with general kernel/cokernel and with the extracted addition operation ).
(5.6.) Recently "cartierSolution10.v" ( fibred category with local internal products ) outlines how "dependent types" ( with polymorph context-extension ) can be upgraded into "coverings over parameterizations" and "relaxations under relativizations" ( or maybe Cisinski cocartesian fibrations / "petit vs gros category theory" ); memo that the associativity-coherence ( "coherence2.v" ) was used there, rounding off the full circle of this SOLUTION PROGRAMME...