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Algebraic Geometry

Algebraic Geometry

Algebraic geometry is the study of the geometric properties of solutions to polynomial equations including solutions in dimensions beyond three. This branch of mathematics evolved from analytical geometry after 1850 when topology, complex analysis, and algebra were used to study algebraic curves. An algebraic curve is the graph of an equation f (x, y) =0 with f (x, y) considered a polynomial in two complex variables and cannot be factored. Curves are classified by a non-negative integer known as the genus (g) that cannot be calculated from their polynomial.

In the 20^th century, it was discovered that basic ideas of classical algebraic geometry could be applied to what are known as commutative rings with the algebra being the ring of polynomials and the geometry derived from the set of zeroes of polynomials called an algebraic variety. Commutative rings have units such as integers and the geometry of a commutative ring is determined by its algebraic structure: in particular its prime ideals. The mathematician Grothendieck defined schemes as these basic geometric objects which have the same relationship to the geometry of a ring as a manifold (a topological space that is Euclidean) to a coordinate chart (a way of expressing the points of a small neighborhood usually on a manifold).

At around the same period, the language of category theory emerged. Category theory is the branch of mathematics that formalizes a number of algebraic properties of collections of changes within mathematical objects such as binary relations, groups, sets, and topological spaces. This branch emerged from the increasingly abstract nature of algebraic geometry.

Some theorems that exist within algebraic geometry include Bezout’s theorem which states that two curves (C and D in a polynomial) are defined by equations of degrees M and N intersecting at MN points. In essence this theorem states that every two lines intersect at a unique point. Another theorem is the Riemann-Roch theorem which uses integrals along paths on C (algebraic curve) to characterize g (genus) analytically. Grothendieck extended the Riemann-Roch theorem in the 1950s by generalizing varieties (the solution set of r polynomial equations in n complex variables) to schemes.

Some disciplines within algebraic geometry include birational geometry, curves, algebraic groups, Abelian varieties, arithmetic algebraic geometry, and computational aspects. Birational geometry involves analysis of the isomorphic (corresponding or similar in form and relationship) class of an object. Algebraic groups discuss the symmetric groups of real objects and are essentially matrix group schemes and allow the various tools of algebraic geometry to be applied to their study. Abelian varieties help to generalize elliptic curves with such curves having led to advances within many fields of mathematics. Arithmetic algebraic geometry is the study of arithmetical problems using algebraic geometry. Computational aspects involve calculations with schemes in algebra.

Algebraic geometry can be applied to the field of integer programming or used in statistics within game theory, geometric modeling, matching graphs, and matching codes for error correction. The most significant application of algebraic geometry is with geometry as algebraic equations used instead of making exact graphs.

Sources

https://www.britannica.com/science/algebraic-geometry; accessed July 20 and 21
http://mathworld.wolfram.com/AlgebraicGeometry.html; accessed July 20 and 21
http://mathworld.wolfram.com/CategoryTheory.html; accessed July 20
http://mathworld.wolfram.com/Manifold.html; accessed July 20
http://mathworld.wolfram.com/CoordinateChart.html; accessed July 20
http://www.math.mcgill.ca/goren/AGwebpage/webpage2.htm; accessed July 21
https://web.archive.org/web/20040415021548/http://planetmath.org/encyclopedia/AlgebraicGeometry.html; accessed July 21
http://www.mathcaptain.com/geometry/algebraic-geometry.html; accessed July 23

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27 x Illuminate\Database\Events\StatementPrepared (6.39%)	38.42ms
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1 x Illuminate\Routing\Events\Routing (0.09%)	513μs
1 x eloquent.booting: App\Models\User\Tutor (0.08%)	504μs
6 x composing: components.tutors-card (0.07%)	450μs
4 x eloquent.retrieved: App\Models\Twill\TwillFaq (0.07%)	437μs
1 x creating: components.canonical (0.07%)	427μs
1 x creating: site.blocks.how-it-works (0.07%)	399μs
1 x eloquent.booting: App\Models\Twill\TwillFaq (0.07%)	399μs
1 x eloquent.booting: App\Models\User\TutorAttributes\TutorDegree (0.06%)	388μs
4 x creating: components.faq-item (0.06%)	381μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)	356μs
1 x creating: site.headers.header (0.06%)	352μs
6 x eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (0.06%)	332μs
1 x creating: site.blocks.text-with-image (0.05%)	330μs
1 x creating: components.forms.contact-us (0.05%)	300μs
1 x creating: components.breadcrumbs (0.05%)	296μs
6 x eloquent.retrieved: App\Models\User\Tutor (0.05%)	278μs
1 x composing: components.forms.free-tool-download (0.05%)	278μs
1 x composing: components.homework-blocks (0.04%)	263μs
1 x eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (0.04%)	263μs
4 x composing: components.faq-item (0.04%)	263μs
1 x creating: site.layouts.app (0.04%)	241μs
1 x creating: components.homework-blocks (0.04%)	239μs
1 x creating: site.blocks.work-with-tutors (0.04%)	235μs
1 x eloquent.booted: App\Models\User\Tutor (0.04%)	231μs
1 x Illuminate\Routing\Events\RouteMatched (0.04%)	230μs
1 x creating: components.tutors-cards (0.04%)	229μs
1 x creating: components.open-graph (0.04%)	214μs
1 x eloquent.booting: App\Models\Subject (0.03%)	194μs
1 x eloquent.booted: App\Models\Twill\TwillFaq (0.03%)	188μs
1 x eloquent.booting: App\Models\Meta (0.03%)	182μs
1 x composing: components.forms.contact-us (0.03%)	182μs
1 x composing: subjects.show (0.03%)	176μs
1 x composing: components.breadcrumbs (0.03%)	174μs
1 x creating: components.forms.get-started (0.03%)	168μs
1 x creating: site.blocks.submit-homework (0.03%)	168μs
1 x creating: components.forms.claim-free-worksheet (0.03%)	164μs
4 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)	163μs
1 x eloquent.booting: App\Models\SubjectCat (0.03%)	158μs
1 x creating: site.blocks.subject-tutors (0.03%)	156μs
1 x creating: subjects.show (0.03%)	154μs
1 x creating: components.forms.free-tool-download (0.02%)	140μs
1 x creating: components.forms.tutor-subscription-join (0.02%)	135μs
1 x creating: components.forms.tutor-subscription-waitlist (0.02%)	134μs
1 x creating: components.forms.tutor-support (0.02%)	133μs
1 x composing: components.tutors-cards (0.02%)	128μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)	127μs
1 x creating: site.blocks.faq (0.02%)	123μs
1 x eloquent.retrieved: App\Models\Meta (0.02%)	104μs
1 x composing: components.canonical (0.02%)	99μs
1 x composing: components.footer (0.02%)	97μs
1 x composing: site.headers.header (0.02%)	91μs
1 x eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (0.01%)	84μs
1 x composing: components.open-graph (0.01%)	82μs
1 x composing: components.forms.get-started (0.01%)	82μs
1 x creating: components.footer (0.01%)	79μs
1 x composing: components.forms.claim-free-worksheet (0.01%)	78μs
1 x composing: components.forms.tutor-subscription-waitlist (0.01%)	74μs
1 x composing: components.forms.tutor-subscription-join (0.01%)	74μs
1 x composing: components.forms.tutor-support (0.01%)	74μs
1 x eloquent.booted: App\Models\User\TutorAttributes\TutorDegree (0.01%)	62μs
1 x eloquent.booted: App\Models\Meta (0.01%)	58μs
1 x eloquent.booted: App\Models\SubjectCat (0.01%)	55μs
1 x eloquent.booted: App\Models\Subject (0.01%)	49μs
1 x composing: site.blocks.faq (0.01%)	32μs
1 x composing: site.blocks.how-it-works (0%)	25μs
1 x composing: site.blocks.subject-homework (0%)	24μs
1 x composing: site.blocks.reviews (0%)	24μs
1 x composing: site.blocks.text-with-image (0%)	22μs
1 x composing: site.layouts.app (0%)	22μs
1 x composing: site.blocks.submit-homework (0%)	21μs
1 x composing: site.blocks.work-with-tutors (0%)	21μs
1 x composing: site.blocks.subject-tutors (0%)	19μs

34 templates were rendered

1x subjects.showshow.blade.phpblade
1x components.breadcrumbsbreadcrumbs.blade.phpblade
1x site.blocks.how-it-workshow-it-works.blade.phpblade
1x site.blocks.subject-tutorssubject-tutors.blade.phpblade
1x components.tutors-cardstutors-cards.blade.phpblade
6x components.tutors-cardtutors-card.blade.phpblade
1x site.blocks.subject-homeworksubject-homework.blade.phpblade
1x components.homework-blockshomework-blocks.blade.phpblade
1x site.blocks.reviewsreviews.blade.phpblade
1x site.blocks.submit-homeworksubmit-homework.blade.phpblade
1x site.blocks.faqfaq.blade.phpblade
4x components.faq-itemfaq-item.blade.phpblade
1x site.blocks.text-with-imagetext-with-image.blade.phpblade
1x site.blocks.work-with-tutorswork-with-tutors.blade.phpblade
1x site.layouts.appapp.blade.phpblade
1x components.canonicalcanonical.blade.phpblade
1x components.open-graphopen-graph.blade.phpblade
1x site.headers.headerheader.blade.phpblade
1x components.footerfooter.blade.phpblade
1x components.forms.contact-uscontact-us.blade.phpblade
1x components.forms.get-startedget-started.blade.phpblade
1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
1x components.forms.tutor-supporttutor-support.blade.phpblade

uri: GET subjects/{categoryUri}/{subjectUri?}
middleware: web, utm.parameters
controller: App\Http\Controllers\SubjectController@show
namespace
where
as: subjects.show
file: app/Http/Controllers/SubjectController.php:43-96

27 statements were executed, 2 of which were duplicates, 25 unique. Show only duplicated59.8ms

Connection Establishedtwenty4_siteSubjectRepository.php#123

Backtrace

13. app/Repositories/SubjectRepository.php:123
14. app/Http/Controllers/SubjectController.php:54
15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `subjects` where `urlFriendlyTitle` = 'Algebraic-Geometry' limit 1

8.74mstwenty4_siteSubjectRepository.php#123

Bindings	0: Algebraic-Geometry
Backtrace	15. app/Repositories/SubjectRepository.php:123 16. app/Http/Controllers/SubjectController.php:54 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `subject_cats` where `subject_cats`.`id` in (1)

910μstwenty4_siteSubjectRepository.php#123

Backtrace

20. app/Repositories/SubjectRepository.php:123
21. app/Http/Controllers/SubjectController.php:54
22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `meta` where `meta`.`id` = 3 limit 1

910μstwenty4_siteMetaService.php#118

Bindings	0: 3
Backtrace	19. app/Services/MetaService.php:118 20. app/Services/MetaService.php:108 21. app/Services/MetaService.php:81 22. app/Http/Controllers/SubjectController.php:89 23. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54

Connection Establishedtwenty4_siteTutorRepository.php#40

Backtrace

13. app/Repositories/TutorRepository.php:40
14. app/View/Components/TutorsCards.php:28
15. app/View/Components/TutorsCards.php:22
17. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
18. vendor/laravel/framework/src/Illuminate/Container/Container.php:770

select count(*) as aggregate from `users` where (`subjectsQualified` like '%|160|%' or `DSF_subjectsQualified` like '%|160|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor'

5.45mstwenty4_siteTutorsCards.php#35

Bindings	0: %\|160\|% 1: %\|160\|% 2: 1 3: 0 4: 5: 1 6: 0 7: 0 8: 9: tutor
Backtrace	15. app/View/Components/TutorsCards.php:35 16. app/View/Components/TutorsCards.php:22 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933

select * from `users` where (`subjectsQualified` like '%|160|%' or `DSF_subjectsQualified` like '%|160|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor' order by `completed_requests` desc limit 6 offset 0

11.23mstwenty4_siteTutorsCards.php#35

Bindings	0: %\|160\|% 1: %\|160\|% 2: 1 3: 0 4: 5: 1 6: 0 7: 0 8: 9: tutor
Backtrace	15. app/View/Components/TutorsCards.php:35 16. app/View/Components/TutorsCards.php:22 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 6531 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

960μstwenty4_siteTutor.php#361

Bindings	0: 6531
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 10818 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

930μstwenty4_siteTutor.php#361

Bindings	0: 10818
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 76351 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

2.64mstwenty4_siteTutor.php#361

Bindings	0: 76351
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `subject_cats` where `subject_cats`.`id` = 42 limit 1

1.31mstwenty4_siteSubject.php#100

Bindings	0: 42
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 69722 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

970μstwenty4_siteTutor.php#361

Bindings	0: 69722
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 71870 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

1.11mstwenty4_siteTutor.php#361

Bindings	0: 71870
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `subject_cats` where `subject_cats`.`id` = 2 limit 1

1.01mstwenty4_siteSubject.php#100

Bindings	0: 2
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 88731 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

930μstwenty4_siteTutor.php#361

Bindings	0: 88731
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select `subjects`.*, `subject_cats`.`title` as `category_title`, `subject_cats`.`id` as `category_id` from `subjects` inner join `subject_cats` on `subject_cats`.`id` = `subjects`.`catID` where `subjects`.`id` in (430, 419, 16, 142, 18, 15, 385, 136, 440, 258, 72, 259, 344, 140, 207, 143, 361, 54, 296, 30, 211, 212, 240, 262, 264, 45, 44, 149, 2, 160, 1, 6, 127, 257, 3, 349, 9, 66, 41, 8, 4, 184, 75, 505)

8.81mstwenty4_siteTutor.php#214

Bindings	0: 430 1: 419 2: 16 3: 142 4: 18 5: 15 6: 385 7: 136 8: 440 9: 258 10: 72 11: 259 12: 344 13: 140 14: 207 15: 143 16: 361 17: 54 18: 296 19: 30 20: 211 21: 212 22: 240 23: 262 24: 264 25: 45 26: 44 27: 149 28: 2 29: 160 30: 1 31: 6 32: 127 33: 257 34: 3 35: 349 36: 9 37: 66 38: 41 39: 8 40: 4 41: 184 42: 75 43: 505
Backtrace	14. app/Models/User/Tutor.php:214 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 18. app/Models/User/Tutor.php:216 24. app/Models/User/Tutor.php:267

select * from `subject_cats` where `subject_cats`.`id` in (1, 3, 5, 9, 11, 31, 33, 41)

1.69mstwenty4_siteTutor.php#214

Backtrace

19. app/Models/User/Tutor.php:214
20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
23. app/Models/User/Tutor.php:216
29. app/Models/User/Tutor.php:267

select count(*) as aggregate from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 160 and `status` = 'published' and `price` > 0

940μstwenty4_siteHomeworkBlocks.php#27

Bindings	0: 160 1: published 2: 0
Backtrace	15. app/View/Components/HomeworkBlocks.php:27 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.subject-homework:4 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 160 and `status` = 'published' and `price` > 0 order by `purchase_count` desc limit 6 offset 0

1.64mstwenty4_siteHomeworkBlocks.php#27

Bindings	0: 160 1: published 2: 0
Backtrace	15. app/View/Components/HomeworkBlocks.php:27 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.subject-homework:4 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `subjects` where `subjects`.`id` in (160)

1.02mstwenty4_siteHomeworkBlocks.php#27

Backtrace

20. app/View/Components/HomeworkBlocks.php:27
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.subject-homework:4
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `subject_cats` where `subject_cats`.`id` in (1)

1.01mstwenty4_siteHomeworkBlocks.php#27

Backtrace

25. app/View/Components/HomeworkBlocks.php:27
26. vendor/laravel/framework/src/Illuminate/View/Component.php:102
27. view::site.blocks.subject-homework:4
29. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
30. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-homework-in-less-than-24-hours' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1

1.09mstwenty4_siteFaqItem.php#15

Bindings	0: can-you-help-me-with-my-homework-in-less-than-24-hours 1: 1 2: en
Backtrace	15. app/View/Components/FaqItem.php:15 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.faq:7 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (1) and `twill_faq_slugs`.`deleted_at` is null

940μstwenty4_siteFaqItem.php#15

Backtrace

20. app/View/Components/FaqItem.php:15
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.faq:7
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-examquiztest' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1

1.01mstwenty4_siteFaqItem.php#15

Bindings	0: can-you-help-me-with-my-examquiztest 1: 1 2: en
Backtrace	15. app/View/Components/FaqItem.php:15 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.faq:24 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (2) and `twill_faq_slugs`.`deleted_at` is null

960μstwenty4_siteFaqItem.php#15

Backtrace

20. app/View/Components/FaqItem.php:15
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.faq:24
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'how-much-will-it-cost' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1

1.01mstwenty4_siteFaqItem.php#15

Bindings	0: how-much-will-it-cost 1: 1 2: en
Backtrace	15. app/View/Components/FaqItem.php:15 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.faq:41 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (3) and `twill_faq_slugs`.`deleted_at` is null

870μstwenty4_siteFaqItem.php#15

Backtrace

20. app/View/Components/FaqItem.php:15
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.faq:41
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'what-kind-of-payments-do-you-accept' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1

900μstwenty4_siteFaqItem.php#15

Bindings	0: what-kind-of-payments-do-you-accept 1: 1 2: en
Backtrace	15. app/View/Components/FaqItem.php:15 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.faq:58 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (4) and `twill_faq_slugs`.`deleted_at` is null

810μstwenty4_siteFaqItem.php#15

Backtrace

20. app/View/Components/FaqItem.php:15
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.faq:58
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
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