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| This page was first created for Google Summer of Code by Alexis Newton, with mentorship by Mckenzie West. | This page was first created for Google Summer of Code 2021 by Alexis Newton, with mentorship by Mckenzie West. |
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| The main function of this page is to demonstrate the improved capabilities that we have developed for SageMath during the GSOC Summer 2021. The trac ticket for those developments can be found here: https://trac.sagemath.org/ticket/32196#comment:5. Note that this ticket has not yet been approved, so in many cases we have defined our main function "order_n" in the Sage cell to be a more rudimentary version of the what is contained in the trac ticket. We do this in order to demonstrate how it may be used. Once the ticket has been pushed through the Sage development process, we will update the page to remove this extraneous code. |
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| GAP is a system...explanation of what we are doing (calling GAP), what gap is and what its limitations are We rely heavily on the Small Group and All Small Groups GAP commands within this page. The documentation for these can be found on the GAP System website. |
GAP is a system for computational discrete algebra, which provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, rings, vector spaces, algebras, combinatorial structures, and more. Using Sage, we are able to interface with the GAP System call groups of different types. This is extremely useful for finding and demonstrating examples in undergraduate algebra courses. Learn more about interfacing with GAP via Sage here: https://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/gap.html. We rely heavily on the Small Group and All Small Groups GAP commands within this page. The documentation for these can be found on the GAP System website: https://www.gap-system.org/Manuals/pkg/SmallGrp/doc/chap1.html. |
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| def foo(n = input_box(default='10', label="Order:"), m = input_box(default='1', label= "Group Number:")): | def order_n1(n = input_box(default='10', label="Order:"), m = input_box(default='1', label= "Group Number:")): |
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| def foo(n = input_box(default='10', label="Order:"), Parameter = | def order_n1(n = input_box(default='10', label="Order:"), Parameter = |
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| def foo(n = input_box(default='10', label="Order:")): | def order_n1(n = input_box(default='10', label="Order:")): |
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| def foo(n = input_box(default='10', label="Order:"), Parameter = | def order_n1(n = input_box(default='10', label="Order:"), Parameter = |
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| def foo(n = input_box(default='32', label="Order:")): | def order_n1(n = input_box(default='32', label="Order:")): |
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| explanation part 2 | The current configuration for calling information from GAP only allows for you to call one group at a time, but we aim to allow for lists of groups which meet certain parameters. The some of the group properties we aim to address include abelian, solvable, nilpotent, given order, dihedral, semi-direct products, alternating, symmetric, and simple. |
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| def foo(n = input_box(default='10', label="Upper Bound:")): | def order_n1(n = input_box(default='10', label="Upper Bound:")): |
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| def foo(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:")): | def order_n1(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:")): |
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| def foo(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:"), Parameter = | def order_n1(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:"), Parameter = |
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| def foo(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:"), Parameter = | def order_n1(m = input_box(default='1', label="Lower Bound:"), n = input_box(default='10', label="Upper Bound:"), Parameter = |
Sage Interactions - Groups Using the GAP System
This page was first created for Google Summer of Code 2021 by Alexis Newton, with mentorship by Mckenzie West.
If you have interactions that you are interested in adding to this page, please do so. You can also contact Alexis Newton at [email protected].
The main function of this page is to demonstrate the improved capabilities that we have developed for SageMath during the GSOC Summer 2021. The trac ticket for those developments can be found here: https://trac.sagemath.org/ticket/32196#comment:5.
Note that this ticket has not yet been approved, so in many cases we have defined our main function "order_n" in the Sage cell to be a more rudimentary version of the what is contained in the trac ticket. We do this in order to demonstrate how it may be used. Once the ticket has been pushed through the Sage development process, we will update the page to remove this extraneous code.
goto interact main page
Contents
Calling Groups from GAP
GAP is a system for computational discrete algebra, which provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, rings, vector spaces, algebras, combinatorial structures, and more.
Using Sage, we are able to interface with the GAP System call groups of different types. This is extremely useful for finding and demonstrating examples in undergraduate algebra courses. Learn more about interfacing with GAP via Sage here: https://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/gap.html.
We rely heavily on the Small Group and All Small Groups GAP commands within this page. The documentation for these can be found on the GAP System website: https://www.gap-system.org/Manuals/pkg/SmallGrp/doc/chap1.html.
Group of Order n
Use this interact to call a group of order n from the GAP library.
Group of Order n of a Certain Type
Use this interact to specify a type of group to call.
All Groups of Order n
Use this interact to call all groups of order n from the GAP library.
All Groups of Order n of a Certain Type
Use this interact to specify a type of group to call.
Small Group Info
Use this interact to learn information about the small groups of order n contained in the GAP library.
Calling a List of Groups from GAP
The current configuration for calling information from GAP only allows for you to call one group at a time, but we aim to allow for lists of groups which meet certain parameters. The some of the group properties we aim to address include abelian, solvable, nilpotent, given order, dihedral, semi-direct products, alternating, symmetric, and simple.
Groups Order Less Than or Equal to n
Use this interact to call all groups from the GAP library that have order less than or equal to your desired value.
Groups Order Between m and n
Use this interact to call all the groups from the GAP library that have order between m and n
Groups of a Certain Type
Use this interact to call all groups of a certain type from the GAP library that have order between m and n
Direct or Semidirect Product Groups
Use this interact to specify groups that contain direct or semidirect products.