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### SageMathCloud™ collaborative computational mathematics

#### SageMath, IPython, LaTeX, and terminals in your browser

- Mathematics: SageMath, R, IPython, Numpy/Scipy/Matplotlib, Octave, Cython, GAP, Pari, Macaulay2, Singular, and much more
- Collaborate: edit Sage worksheets, LaTeX documents and IPython notebooks with realtime sync
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SMC is run by SageMath, Inc., and receives grant funding from the National Science Foundation (awards 1161226, 1147802, 1020378 1015114) and Google.
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## Terminal (settings applied to newly opened terminals)

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## Editor (settings apply to newly (re-)opened files)

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## Keyboard shortcuts

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### SageMathCloud™ collaborative computational mathematics

#### SageMath, Python, LaTeX, and terminals in your browser

### Support

- In case of problems with the SageMathCloud platform, do not hesitate to immediately email us at help@sagemath.com. We want to know if anything isn't working! Include a link (the address in your browser) to any project or document you are asking about.
- Getting started with SageMathCloud
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- Github issue tracker (you may also email bug reports to us)
- Sage-cloud support mailing list and developer mailing list.
- Frequently Asked Questions
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- Install the Chrome App

### About

- LEGAL: Terms of Service, Pricing, Copyright and Privacy policies
- William Stein is the founder and main architect of SageMathCloud, and Harald Schilly does marketing and QA testing. Also, Keith Clawson has done hardware, and Jon Lee, Andy Huchala, and Nicholas Ruhland have done web development. SageMathCloud has received support from SageMath, Inc., the National Science Foundation (awards 1161226, 1147802, 1020378 and 1015114), and Google's Education Grant program.
- SageMathCloud first launched in April, 2013.
- SageMath, Inc. (a Delaware C Corporation) was incorporated on Feb 2, 2015.

### Usage

- 266 people are connected right now actively modifying 20 projects. Users modified 1263 projects in the last day and 4562 projects in the last week.
- accounts and projects.
- Being used by over 60 courses during Spring 2015...
- More usage data...

### Getting started with SageMathCloud

### Create an account

video

Navigate to https://cloud.sagemath.com. If you're already signed in, first sign out by clicking on your email address by the icon in the upper right, and clicking "Sign out". Click on "create an account", then agree to the terms of usage. Next either enter your name, email address, and password for the new account you would like to create, or login using your Google, Github, Facebook, etc., account. You may change your name, email address or password at any time later, and also reset your password in case you forget it.

#### Technical Notes

- Please use a strong password or login via Google, Github or another provider, especially when you start using the SageMathCloud frequently.
- Only the hash of your password is stored by the server, which uses 1000 iterations of a sha-512 hash function, with a salt length of 32. This makes it more difficult for a hacker to brute-force your password, even if they have the database of password hashes, since every guess takes much more work to make.

### Change your name, email address, or password

video

Log into https://cloud.sagemath.com, then click in the upper right corner on your email address by the icon. Change your first or last name in the settings tab that appears, then click save.

To change your password, click the "Change password" link, enter your old password, then enter a new password.

To change the email account that is linked to your SageMathCloud account, click on the "change" link next to your email address, type in the password (to your SageMathCloud account), then enter a new email address.

#### Technical Notes

- Changing your first or last name at any time is pretty harmless, since it only changes the name other people see when collaborating with you on projects.
- The primary purpose of providing an email address is that you can use it to reset your password when you forget it.

### Get a bunch of examples

To easily copy our collection of examples into a project, just click "+New", paste in this link

    https://github.com/sagemath/cloud-examples.git

and click "From Web". In a few seconds you'll find a directory

    sage-cloud-templates

in your project, full of examples.

#### Technical Notes

- The collection of examples is a Github repository, which we regularly update. In a terminal in the sage-cloud-templates directory, you can type

      git pull

  to get the latest changes and examples (you may have to type "git commit -a" first, if you have made changes). You can also see what's new in the Github repository.

### Watch a March 2015 talk about all of the main features of SageMathCloud

William Stein (lead developer of SageMathCloud) gave the following one-hour talk in March 2015 at the UW eScience Institute:

video

###
Using

- video1
- video2
- and Vincent Knight's 21 videos introducing

is a system for creating professional quality documents, with excellent support for typesetting mathematical formulas like
. There are two main ways to use latex in the SageMathCloud:

1. In chats or in worksheet cells that start with %html or %md, enclose mathematical formulas in single or double dollar signs and they will be typeset (using MathJax) when you submit them. In addition to dollar signs, you can use the other standard latex equation wrappers \[ \] and \( \). In worksheets, if f is some object, you can type show(f) to see f nicely typeset using the latex generated by latex(f). In a worksheet, type typeset_mode(True) to show the nicely typeset version of objects by default. You may also use MathJax in Markdown cells in Jupyter notebooks.
2. You can edit a full LaTeX document by creating or uploading a file with an extension of .tex, then opening it. The tex file appears on the left, and there is a preview of the compiled version on the right, which is updated whenever you save the file (ctrl+s). By clicking , you can split the tex editor so that you can see two parts of the file at once. You can also use inverse and forward search to easily move back and forth between the tex file and the preview. In addition the preview, there is an error and warning log with buttons to jump to the corresponding issue in the tex file or preview. There's also a button to show or download the final high-quality PDF. In addition, you can see the output of running pdflatex, bibtex, and use SageTex (which should "just work"), make any of those programs re-run, and customize the latex build command. If necessary, you can do extremely sophisticated processing of tex files in a Terminal ( New --> Terminal).

### Use R in SageMath worksheets

video

In a project, click New then the "Sage" button. In the worksheet that appears, type

    %default_mode r

then press shift+enter. For the reset of the worksheet, type normal R commands, followed by shift+enter. Plotting should just work as usual in R. See these example worksheets.

### Use Jupyter notebooks

video

In a project, click New then the "Jupyter" button, or just open an ipynb file. The notebook will be opened using Jupyter's html-based client, with support for embedded graphics. To support the collaborative nature of the SageMathCloud, we've enhanced the Jupyter notebook with realtime sync, so if you open the same notebook on multiple computers (or if multiple people open the same notebook), they will stay in sync. Also, if you want to use the Sage preparser, type %load_ext sage into a notebook cell.

#### Technical Notes

- You can also run a normal version of the Jupyter notebook server (no sync, not integrated into cloud) by (1) finding your project's id in project settings, then (2) visiting https://cloud.sagemath.com/[project_id]/port/jupyter (you will possibly have to refresh your browser if this takes too long the first time). Any collaborator on your project can securely use the Jupyter notebook server by visiting this link, but nobody else can.

###

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## Create a New Project

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# Data
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## Wizard

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### Task Lists

Use task lists to help organize your work on a SageMathCloud project.

#### Editing the Description (Markdown)

Click or use the cursor keys (and press enter) to edit a task, or create a new task. Use Github style markdown to describe your task, use LaTeX to typeset mathematics (use `\$` for a dollar sign), use `[ ]` and `[x]` to create checklists, and press shift+enter to save your changes. The editor respects the themes you select in account settings, and external links open in another browser tab. You can toggle showing the full description or only everything up to the first blank line. Of course simultaneous synchronized editing of tasks by multiple clients is fully supported.

#### Moving tasks

In custom order (the default) click and drag to change the order of the tasks. You can also click and to move the currently selected task to the top or bottom of the currently visible task.

#### Due date

Each task has an optional due date (and time), which you can set by clicking on the due date (or none). You can see when the task is due, when you last edited it, and click the due column to sort by due date. View finished tasks by selecting the done checkbox.

#### Hashtags

Put `#tag` anywhere in the description of a task to create a hashtag, with no space between the hash symbol and the tag identifier. A corresponding button will appear at the top of the screen. Click on the bottom or the hashtag in a task to toggle showing only tasks with that hashtag.

#### Search

Enter terms in the search box in the upper left to show only tasks containing all search terms.

#### Keyboard shortcuts

Let mod be any of control, alt, or command. Use mod+s to save, mod+f to find, mod+n to make a new task, mod+space to toggle done state, and mod+arrow to move a task up or down the list. Use arrows (or j and k) to change which task is selected, enter to start editing a task description, and shift+enter to stop editing.

#### File format

A task list is stored as a file with extension `.tasks` that contains one JSON line per task. You can directly edit this file with other tools (e.g., vim on the command line) and changes should appear in the task list within a few seconds. You can have many task lists, store them in revision control, recover them from snapshots, etc. You can also create a task list by creating a file `foo.tasks` that has one description per line (as a string):

                "the first task"
                        "another task"

Or, with one JSON line per task:

                {"desc":"the first task"}
                        {"desc":"another task"}

Additional optional fields are `position`, which is a float that determines sort order, `done`, `due` and `last_edited`, which are the number of milliseconds since the epoch in the UTC time zone, and `task_id` which is a v4 UUID.
``
Extract Files...

### Contents

Students Assignments Settings Help

### Title and Description

####

### Options

Show deleted students
Show deleted assignments
Create all Projects...
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Enter an email address (or several separated by commas) to invite a student who does not have an account.

#### Loading student list...

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Add new students to this course by entering their email address (or name) in the box above to the right and clicking the button.
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Create a folder using New (upper left) that contains materials for an assignment. Then search for that folder in the box above to the right.
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### Course Help

Courses allow you to manage a list of students, create projects for each of them, share homework and folders with them, collect homework, and grade and return it to students.

#### Add Students

To add a student to your course, click on the Students tab, then type a student's name or email address in the "Add student" box to the right and press enter or click the button. Searching for an email address is best, since you can be certain that the person you're adding is really a student in your course (instead of an unknown SageMathCloud user with the same name); moreover, if your student doesn't already have an account, they will receive an invitation via email. To add many students at once, just paste in a list of email addresses separated by commas.

Once you add a student, click on Create Project next to your student's name to create their project (or click Create all Projects... to create 2 or more student projects). You own the project, and they will be added as a collaborator, and invited by email if they do not yet have an account. Don't worry if you have 100s of studnets, since student projects are hidden by default from your main project listing.

To delete a student, click to the right of the student. You can toggle whether deleted students are shown in settings.

#### Add Assignments

To create an assignment, first click New in the upper left of your project to create a new folder, and create or add files to it, as usual. Click on the Assignments tab of the course, then search for the folder by typing some part of its name in the box on the far right. Click to select the folder and it will be added to your list of assignments. To make copies of this folder available to all of your students whose projects you have created, click the Assign all... button.
(NOTE: Students will not be explicitly notified that you have made an assignment available.) (NOTE: You can share arbitrary folders with any contents with your students -- folders don't have to contain "assignments", and may contain anything, Sage worksheets, IPython notebooks, LaTeX documents, etc.)

#### Collecting and Grading Assignments

To collect an assignment from your students, click Collect all... to the right of an assignment to collect it from all students. (NOTE: There is currently no way to schedule collection to happen at a specific time -- it happens when you click the button. Click it again to update the collected files.)

Once the assignments are collected, click
and select a student to jump to the folder that contains the collected version of a student's assignment. Edit the files there, indicating grades on each problem, etc. (NOTE: There is no special support yet for recording grades, knowing which homework you have graded already, etc.)

When you are done grading, click Return Graded to return the graded homework to the students. If the homework folder is called `homework1`, then the graded version will appear in the student's project as `homework1-graded`.

#### Course Settings

Set the title and description of the course in the Settings tab. When you change these, the new title and description propagates automatically to all student projects for this course.

#### Other

- Video Tutorial
- Blog Post

#### Technical Remarks

The underlying file format of a .course file is a plain text file with one line in JSON format for each student, shared assignment, and for settings.
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### Opening...

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`%sage`
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# Data
Control
Program
Plots
Calculus
Linear
Graphs
Number Theory
Rings
#
Control
Stats
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# Control
…
$ $$
82
1

2

    ## RUN the thing!!

3

    ​

4

    ​

5

    print "Rubik cube \n \n"

6

    ​

7

    S48=SymmetricGroup(48)

8

    R=S48("(25,27,32,30)(26,29,31,28)(3,38,43,19)(5,36,45,21)(8,33,48,24)")

9

    L=S48("(9,11,16,14)(10,13,15,12)(1,17,41,40)(4,20,44,37)(6,22,46,35)")

10

    U=S48("(1,3,8,6)(2,5,7,4)(9,33,25,17)(10,34,26,18)(11,35,27,19)")

11

    D=S48("(41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40)")

12

    F=S48("(17,19,24,22)(18,21,23,20)(6,25,43,16)(7,28,42,13)(8,30,41,11)")

13

    B=S48("(33,35,40,38)(34,37,39,36)(3,9,46,32)(2,12,47,29)(1,14,48,27)")

14

    RC3=S48.subgroup([R,L,U,D,F,B]) # define Rubik’s cube group to be RC3

15

    RC3.order()

16

    ​

17

    S48("(7,18)") in RC3

18

    S48("(7,18)(5,26)") in RC3

19

    RC3.is_subgroup(S48)

20

    ​

21

    rubik = CubeGroup()

22

    print "rubik diagram \n"

23

    rubik.display2d("")

24

    rubik.order()  # same as RC3

25

    ​

26

    R=rubik.R()

27

    L=rubik.L()

28

    U=rubik.U()

29

    D=rubik.D()

30

    F=rubik.F()

31

    B=rubik.B()

32

    ​

33

    show(R)

34

    ​

35

    print "solve the 'word problem' \n"

36

    state = rubik("(7,18)(5,26)")

37

    rubik.solve(state) # calls the word solve algorithm

38

    print "\n"

39

    ​

40

    B^(-1)

41

    F^2 * R^2 * B^(-1) * F^(-1) * D^(-1) * F * D * B * R^2 * F^(-1) * R^(-1) * F^(-1) * R

42

    F^3

43

    rubik.is_subgroup(S48)

44

    state in S48

45

    Permutation('(1,2,6,5)') in S48

46

    show(Permutation('(1,2,6,5)'))

12

    F=S48("(17,19,24,22)(18,21,23,20)(6,25,43,16)(7,28,42,13)(8,30,41,11)")

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