| Download
Github repo cloud-examples: https://github.com/sagemath/cloud-examples
Project: Support and Testing
Views: 7921License: MIT
%md #### %auto The %auto decorator sets a cell so that it will be automatically executed when the Sage process first starts. Thus %auto allows you to initialize functions, variables, interacts, etc., e.g., when loading a worksheet. NOTE: The %auto decorator just calls salvus.auto(True), which sets a cell metatag. You *must* execute the cell containing %auto at least once in order for it to work. ︠7bce0e7f-535c-4d04-9716-35ae475712c4︠ %md #### %axiom Create an instance of the Axiom interpreter. For further documentation, view [this page](http://www.axiom-developer.org/axiom-website/documentation.html). Note that you must have Axiom installed in order to use it on Sage Math Cloud. TESTS: sage: axiom == loads(dumps(axiom)) True ︠54f5a9cd-7d4e-4560-bb60-0677c6a7f3a7︠ %md #### %capture Capture or ignore the output from evaluating the given code. (SALVUS only). Use capture as a block decorator by placing either %capture or %capture(optional args) at the beginning of a cell or at the beginning of a line. If you use just plane %capture then stdout and stderr are completely ignored. If you use %capture(args) you can redirect or echo stdout and stderr to variables or files. For example if you start a cell with this line:: ︠01d1941c-6049-4e00-825c-87a3f375bfe9︠ %capture(stdout='output', stderr=open('error','w'), append=True, echo=True) ︠82ded579-f66a-4063-a0e6-64e373ff2f76︠ %md then stdout is appended (because append=True) to the global variable output, stderr is written to the file 'error', and the output is still displayed in the output portion of the cell (echo=True). INPUT: - stdout -- string (or object with write method) to send stdout output to (string=name of variable) - stderr -- string (or object with write method) to send stderr output to (string=name of variable) - append -- (default: False) if stdout/stderr are a string, append to corresponding variable - echo -- (default: False) if True, also echo stdout/stderr to the output cell. ︠24561ad1-0a2e-4e06-b3d3-5029ef50d037︠ %md #### %coffeescript Execute code using CoffeeScript. For example: ︠323dc6a0-90d0-400c-86f2-72bb6c54f633︠ %coffeescript console.log 'hi' ︠021fb959-d3a7-48f5-980a-3e64c262fdde︠ %md or ︠490a600d-b35d-4378-827a-9788d54147c5︠ coffeescript("console.log 'hi'") ︠44fbdbeb-dc0f-4193-8378-f2fd4022b0bb︠ %md You may either pass in a string or use this as a cell decorator, i.e., put %coffeescript at the top of a cell. If you set once=False, the code will be executed every time the output of the cell is rendered, e.g., on load, like with %auto: ︠3e52e4a6-b047-46ec-a379-f30fcd066530︠ coffeescript('console.log("hi")', once=False) ︠a321c3a1-5c27-41b2-9d61-45394a2a0520︠ %md or ︠e240fdb5-3e03-4093-b1cc-9235e3e00804︠ %coffeescript(once=False) console.log("hi") ︠7b5dfaad-c7b4-4cb6-bb4d-593fd76a9919︠ %md To send code from Javascript back to the Python process to be executed use the worksheet.execute_code function: ︠58b699a3-30ce-4cd4-a444-111da42f9db2︠ %javascript worksheet.execute_code(string_to_execute) ︠23021163-f3f2-4468-9373-3badad497207︠ %md You may also use a more general call format of the form: ︠65009715-a04f-4676-bf14-17018ab004ea︠ %javascript worksheet.execute_code({code:string_to_execute, data:jsonable_object, preparse:true or false, cb:function}); ︠0d8bfd5a-a117-4a29-9c51-1e10ad43ca71︠ %md The data object is available when the string_to_execute is being evaluated as salvus.data. For example, if you execute this code in a cell: ︠e8b8f58a-db83-4f51-af42-50fcb666fefc︠ javascript(''' worksheet.execute_code({code:"a = salvus.data['b']/2; print a", data:{b:5}, preparse:false, cb:function(mesg) { console.log(mesg)} }); ''') ︠4b9a52a8-e950-421d-aab7-e517bd1eafc6︠ %md then the Python variable a is set to 2, and the Javascript console log will display: Object {done: false, event: "output", id: "..."} Object {stdout: "2n", done: true, event: "output", id: "..."} You can also send an interrupt signal to the Python process from Javascript by calling worksheet.interrupt(), and kill the process with worksheet.kill(). For example, here the a=4 never happens (but a=2 does): ︠3acef502-2c4b-4913-8c4e-60413256d146︠ %javascript worksheet.execute_code({code:'a=2; sleep(100); a=4;', cb:function(mesg) { worksheet.interrupt(); console.log(mesg)}}) ︠d206e0fd-fb4d-4504-b342-f95e484c0dfe︠ %md or using CoffeeScript (a Javascript preparser): ︠86f325e2-4400-47bb-9411-11a22faf20f0︠ %coffeescript worksheet.execute_code code : 'a=2; sleep(100); a=4;' cb : (mesg) -> worksheet.interrupt() console.log(mesg) ︠51325018-d41a-4d23-8ac3-c1f7c7e00156︠ %md The Javascript code is evaluated with numerous standard Javascript libraries available, including jQuery, Twitter Bootstrap, jQueryUI, etc. ︠5fea33a7-3d0f-4372-8701-54de0b5105c4︠ %md #### %cython Block decorator to easily include Cython code in the Salvus notebook. For full documentation, please visit [this page](http://docs.cython.org/src/tutorial/cython_tutorial.html). Just put %cython at the top of a cell, and the rest is compiled as Cython code. You can pass options to cython by typing "%cython(... var=value...)" instead. This is a wrapper around Sage's cython function, whose docstring is: Compile a Cython file. This converts a Cython file to a C (or C++ file), and then compiles that. The .c file and the .so file are created in a temporary directory. INPUTS: * "filename" - the name of the file to be compiled. Should end with 'pyx'. * "verbose" (bool, default False) - if True, print debugging information. * "compile_message" (bool, default False) - if True, print "'Compiling <filename>...'" to the standard error. * "use_cache" (bool, default False) - if True, check the temporary build directory to see if there is already a corresponding .so file. If so, and if the .so file is newer than the Cython file, don't recompile, just reuse the .so file. * "create_local_c_file" (bool, default False) - if True, save a copy of the .c file in the current directory. * "annotate" (bool, default True) - if True, create an html file which annotates the conversion from .pyx to .c. By default this is only created in the temporary directory, but if "create_local_c_file" is also True, then save a copy of the .html file in the current directory. * "sage_namespace" (bool, default True) - if True, import "sage.all". * "create_local_so_file" (bool, default False) - if True, save a copy of the compiled .so file in the current directory. TESTS: Before http://trac.sagemath.org/12975, it would have beeen needed to write "#clang c++", but upper case "C++" has resulted in an error: sage: code = [ ... "#clang C++", ... "#cinclude %s/include/singular %s/include/factory"%(SAGE_LOCAL, SAGE_LOCAL), ... "#clib m readline singular givaro ntl gmpxx gmp", ... "from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomial_libsingular", ... "from sage.libs.singular.polynomial cimport singular_polynomial_pow", ... "def test(MPolynomial_libsingular p):", ... " singular_polynomial_pow(&p._poly, p._poly, 2, p._parent_ring)"] sage: cython(os.linesep.join(code)) The function "test" now manipulates internal C data of polynomials, squaring them: sage: P.<x,y>=QQ[] sage: test(x) sage: x x^2 ︠e1402121-9fba-4b05-a89d-2e211482d7c9︠ %md #### %default_mode md(hide=False) Set the default mode for cell evaluation. This is equivalent to putting %mode at the top of any cell that does not start with %. Use default_mode() to return the current mode. Use default_mode("") to have no default mode. EXAMPLES: Make Pari/GP the default mode: ︠949f2525-ceaa-4840-ae4f-a0bdba3377d3︠ default_mode("gp") default_mode() # outputs "gp" ︠a26f4592-0bfb-47bc-8079-cff3e15194d2︠ %md Then switch back to Sage: ︠05ef0e09-9609-4bb5-b7ff-d3a10d51d6bd︠ default_mode("") # or default_mode("sage") ︠a27897a2-beeb-4e5a-b05b-964b02223212︠ ︠5f034b67-62f2-494e-babd-8c968e0816f5︠ %md You can also use default_mode as a line decorator: ︠b0958699-bd59-4d94-9ac7-c05d2b83792e︠ %default_mode gp # equivalent to default_mode("gp") ︠3dd10217-ee9c-496a-8978-3165d591d3dc︠ %md #### %exercise Use the %exercise cell decorator to create interactive exercise sets. Put %exercise at the top of the cell, then write Sage code in the cell that defines the following (all are optional): - a ``question`` variable, as an HTML string with math in dollar signs - an ``answer`` variable, which can be any object, or a pair (correct_value, interact control) -- see the docstring for interact for controls. - an optional callable ``check(answer)`` that returns a boolean or a 2-tuple (True or False, message), where the first argument is True if the answer is correct, and the optional second argument is a message that should be displayed in response to the given answer. NOTE: Often the input "answer" will be a string, so you may have to use Integer, RealNumber, or sage_eval to evaluate it, depending on what you want to allow the user to do. - hints -- optional list of strings to display in sequence each time the user enters a wrong answer. The last string is displayed repeatedly. If hints is omitted, the correct answer is displayed after three attempts. NOTE: The code that defines the exercise is executed so that it does not impact (and is not impacted by) the global scope of your variables elsewhere in your session. Thus you can have many %exercise cells in a single worksheet with no interference between them. The following examples further illustrate how %exercise works. An exercise to test your ability to sum the first $n$ integers:: ︠17bd52ca-8577-42c8-ae70-02cc38a70e6b︠ %exercise title = "Sum the first n integers, like Gauss did." n = randint(3, 100) question = "What is the sum $1 + 2 + \\cdots + %s$ of the first %s positive integers?"%(n,n) answer = n*(n+1)//2 ︠4fa7b6a1-3a91-4b8f-b4bd-0b14fb1f0cba︠ %md Transpose a matrix:: ︠29a6590d-deaf-4d4a-a011-4eb8b427d07f︠ %exercise title = r"Transpose a $2 \times 2$ Matrix" A = random_matrix(ZZ,2) question = "What is the transpose of $%s?$"%latex(A) answer = A.transpose() ︠3f74167f-17a2-4cb1-8ab7-bb296c3fd3b1︠ %md Add together a few numbers:: ︠e8477bde-d7ee-468b-9bde-60a664bfa464︠ %exercise k = randint(2,5) title = "Add %s numbers"%k v = [randint(1,10) for _ in range(k)] question = "What is the sum $%s$?"%(' + '.join([str(x) for x in v])) answer = sum(v) ︠09000ffb-3148-4dee-b39f-aaa57cb6e86b︠ %md ︠68d0173d-dc85-493a-a8af-249f1335b81a︠ The trace of a matrix:: ︠4ea138bb-99f8-4fd9-a2f4-048ac1a750cb︠ %exercise title = "Compute the trace of a matrix." A = random_matrix(ZZ, 3, x=-5, y = 5)^2 question = "What is the trace of $$%s?$$"%latex(A) answer = A.trace() ︠1894db9a-d6e8-4178-b35c-56b3e7cd1335︠ %md Some basic arithmetic with hints and dynamic feedback:: ︠5f411aa9-2389-45d0-b06c-2c9b72a7e93e︠ %exercise k = randint(2,5) title = "Add %s numbers"%k v = [randint(1,10) for _ in range(k)] question = "What is the sum $%s$?"%(' + '.join([str(x) for x in v])) answer = sum(v) hints = ['This is basic arithmetic.', 'The sum is near %s.'%(answer+randint(1,5)), "The answer is %s."%answer] def check(attempt): c = Integer(attempt) - answer if c == 0: return True if abs(c) >= 10: return False, "Gees -- not even close!" if c < 0: return False, "too low" if c > 0: return False, "too high" ︠7b3abe5e-f60f-42ef-a1e0-19214b5cd626︠ %md #### %file Block decorator to write to a file. Use as follows: ︠6c6b4e1a-6450-4025-9f51-b61c8cdb60c0︠ %file('filename') put this line in the file ︠5890dff4-0db3-409d-9738-a5fe58ed7a73︠ %md or ︠4d56517d-ccf0-48b2-bba3-1488a22b2691︠ %file('filename') ︠e03fe68a-4b16-4895-960a-2c259fa1c98d︠ %md everything in the rest of the cell goes into the file with given name. As with all block decorators in Salvus, the arguments to file can be an arbitrary expression. For examples, ︠64de8ae1-6b25-4cda-b333-cb90ad706be0︠ a = 'file'; b = ['name', 'txt'] ︠db1e29e9-fc4b-46ff-9233-ecd24be3af1b︠ %file(a+b[0]+'.'+b[1]) rest of line goes in 'filename.txt' ︠473e5adf-5bd7-4d5d-b0b0-67390bbab847︠ %md #### %fork The %fork block decorator evaluates its code in a forked subprocess that does not block the main process. WARNING: This is highly experimental and possibly flakie. Use with caution. All (picklelable) global variables that are set in the forked subprocess are set in the parent when the forked subprocess terminates. However, the forked subprocess has no other side effects, except what it might do to file handles and the filesystem. To see currently running forked subprocesses, type fork.children(), which returns a dictionary {pid:execute_uuid}. To kill a given subprocess and stop the cell waiting for input, type fork.kill(pid). This is currently the only way to stop code running in %fork cells. ︠e120851f-a5fa-462d-8743-a4a349b04849︠ %md #### %fortran Compile Fortran code and make it available to use. For further documentation, view [this page](http://www.math.utah.edu/~beebe/software/fortran-documentation.html). INPUT: * x -- a string containing code Use this as a decorator. For example, put this in a cell and evaluate it: %fortran C FILE: FIB1.F SUBROUTINE FIB(A,N) C C CALCULATE FIRST N FIBONACCI NUMBERS C INTEGER N REAL*8 A(N) DO I=1,N IF (I.EQ.1) THEN A(I) = 0.0D0 ELSEIF (I.EQ.2) THEN A(I) = 1.0D0 ELSE A(I) = A(I-1) + A(I-2) ENDIF ENDDO END C END FILE FIB1.F In the next cell, evaluate this: import numpy n = numpy.array(range(10),dtype=float) fib(n,int(10)) n This will produce this output: array([ 0., 1., 1., 2., 3., 5., 8., 13., 21., 34.]). ︠5c0c0124-b97e-4603-8115-f2508fd0eb32︠ %md #### %fricas Interface to a FriCAS interpreter. For further documentation, visit [this page](http://fricas.sourceforge.net/doc/). Note that you must have FriCAS installed to use it on SMC. ︠44cc1309-91ef-4976-b6b4-8eecf9ab13c6︠ %md #### %gap Interface to the GAP interpreter. For further documentation, visit [this page](http://www.gap-system.org/Doc/doc.html). Note that you must have GAP installed to use it on SMC. ︠9022ac04-8e3b-4f59-843f-0c737f54dea1︠ %md #### %gap3 A simple Expect interface to GAP3. For further documentation, visit [this page](http://www.gap-system.org/Gap3/Doc3/doc.html). Note that you must have GAP3 installed to use it on SMC. EXAMPLES: sage: from sage.interfaces.gap3 import Gap3 sage: gap3 = Gap3(command='gap3') TESTS: sage: gap3(2) == gap3(3) #optional - gap3 False sage: gap3(2) == gap3(2) #optional - gap3 True sage: gap3.trait_names() #optional - gap3 [] We test the interface behaves correctly after a keyboard interrupt: sage: gap3(2) #optional - gap3 2 sage: try: ... gap3._keyboard_interrupt() ... except KeyboardInterrupt: ... pass #optional - gap3 Interrupting Gap3... sage: gap3(2) #optional - gap3 2 We test that the interface busts out of GAP3's break loop correctly: sage: f = gap3('function(L) return L[0]; end;;') #optional - gap3 sage: f([1,2,3]) #optional - gap3 Traceback (most recent call last): ... RuntimeError: Gap3 produced error output Error, List Element: <position> must be a positive integer at return L[0] ... ︠24f5aeef-eb72-42cb-ab0c-8ca89c01c40a︠ %md #### %giac Interface to the Giac interpreter. You must have the optional Giac interpreter installed and available as the command "giac" in your PATH in order to use this interface. Try the command: print giac._install_hints() for more informations on giac installation. Type "giac.[tab]" for a list of all the functions available from your Giac install. Type "giac.[tab]?" for Giac's help about a given function. Type "giac(...)" to create a new Giac object. Full html documentation for giac is avaible from your giac installation at "$PREFIX"/share/giac/doc/en/cascmd_en/index.html EXAMPLES: Any Giac instruction can be evaluated as a string by the giac command. You can access the giac functions by adding the "giac." prefix to the usual Giac name. sage: l=giac('normal((y+sqrt(2))^4)'); l # optional - giac y^4+4*sqrt(2)*y^3+12*y^2+8*sqrt(2)*y+4 sage: f=giac('(u,v)->{ if (u<v){ [u,v] } else { [v,u] }}');f(1,2),f(3,1) # optional - giac ([1,2], [1,3]) The output of the giac command is a Giac object, and it can be used for another giac command. sage: l.factors() #optional - giac [y+sqrt(2),4] sage: giac('(x^12-1)').factor( ) # optional - giac (x-1)*(x+1)*(x^2+1)*(x^2-x+1)*(x^2+x+1)*(x^4-x^2+1) sage: giac('assume(y>0)'); giac('y^2=3').solve('y') #optional - giac y [sqrt(3)] You can create some Giac elements and avoid many quotes like this: sage: x,y,z=giac('x,y,z');type(y) # optional - giac <class 'sage.interfaces.giac.GiacElement'> sage: I1=(1/(cos(2*y)+cos(y))).integral(y,0,pi/4).simplify() #optional - giac sage: (I1-((-2*ln((sqrt(3)-3*tan(1/8*pi))/(sqrt(3)+3*tan(1/8*pi)))*sqrt(3)-3*tan(1/8*pi))/9)).normal() # optional - giac 0 sage: ((y+z*sqrt(5))*(y-sqrt(5)*z)).normal() # optional - giac y^2-5*z^2 Polynomials or elements of SR can be evaluated directly by the giac interface. sage: R.<a,b>=QQ[];f=(2+a+b);p=giac.gcd(f^3+5*f^5,f^2+f^5);p;R(p); #optional - giac a^2+2*a*b+4*a+b^2+4*b+4 a^2 + 2*a*b + b^2 + 4*a + 4*b + 4 Variable names in python and giac are independant. sage: a=sqrt(2);giac('Digits:=30;a:=5');a,giac('a'),giac(a),giac(a).evalf() # optional - giac [...] (sqrt(2), 5, sqrt(2), 1.414213562373095048801688724209) ︠50cd0aac-e3ff-43b8-a6a4-03f6a7a9b098︠ %md #### %gp Interface to the PARI gp interpreter. For full documentation, please visit [this page](http://pari.math.u-bordeaux.fr/doc.html). Type "gp.[tab]" for a list of all the functions available from your Gp install. Type "gp.[tab]?" for Gp's help about a given function. Type "gp(...)" to create a new Gp object, and "gp.eval(...)" to evaluate a string using Gp (and get the result back as a string). INPUT: * "stacksize" (int, default 10000000) -- the initial PARI stacksize in bytes (default 10MB) * "maxread" (int, default 100000) -- ?? * "script_subdirectory" (string, default None) -- name of the subdirectory of SAGE_EXTCODE/pari from which to read scripts * "logfile" (string, default None) -- log file for the pexpect interface * "server" -- name of remote server * "server_tmpdir" -- name of temporary directory on remote server * "init_list_length" (int, default 1024) -- length of initial list of local variables. EXAMPLE: ︠2fa2db56-fea5-4bb3-8443-6030c3d6566c︠ %gp Gp() ︠863362f6-2750-438b-a1ab-5544ec375efe︠ %md PARI/GP interpreter ︠79f4c871-b704-4b2a-a78e-c6ef30b653ce︠ %md #### %hide Hide a component of a cell. By default, hide hides the the code editor part of the cell, but you can hide other parts by passing in an optional argument: 'input', 'output' Use the cell.show(...) function to reveal a cell component. ︠04b583d1-7d81-4e5d-9297-1fe07d383f92︠ %md #### %html Cell mode that renders everything after %html as HTML then hides the input (unless you pass in hide=False).\n ︠876ffdd1-e87b-4fbc-adb8-dc74dcbb662f︠ %html <h1>A Title</h1> <h2>Subtitle</h2> ︠679bfd8c-f491-41f7-b1d7-8939e5f20ddc︠ %html(hide=False) <h1>A Title</h1> <h2>Subtitle</h2> ︠a87ec0e6-4292-4745-9259-24988eae781d︠ %html(hide=False) <h1>Title</h1> ︠950da5c7-774a-48cc-a0a0-e52e07febf1f︠ %md #### %java script Execute code using JavaScript. For example: ︠ef6dafd5-af8d-4c39-aa69-d6ec72ebb983︠ %javascript console.log('hi') ︠39deb4f0-9dda-47cc-a511-2b19c50eebb5︠ %md or ︠4ebe3ea8-6598-4534-95e9-920b3c5db65c︠ javascript("console.log('hi')") ︠5d229873-bf9a-4808-994e-6adb004d4070︠ %md You may either pass in a string or use this as a cell decorator, i.e., put %javascript at the top of a cell. If you set once=False, the code will be executed every time the output of the cell is rendered, e.g., on load, like with %auto: javascript('.. some code ', once=False) or %javascript(once=False) ... some code WARNING: If once=True, then this code is likely to get executed *before* the rest of the output for this cell has been rendered by the client. To send code from Javascript back to the Python process to be executed use the worksheet.execute_code function: %javascript worksheet.execute_code(string_to_execute) You may also use a more general call format of the form: %javascript worksheet.execute_code({code:string_to_execute, data:jsonable_object, preparse:true or false, cb:function}); The data object is available when the string_to_execute is being evaluated as salvus.data. For example, if you execute this code in a cell: javascript(''' worksheet.execute_code({code:"a = salvus.data['b']/2; print a", data:{b:5}, preparse:false, cb:function(mesg) { console.log(mesg)} }); ''') then the Python variable a is set to 2, and the Javascript console log will display: Object {done: false, event: "output", id: "..."} Object {stdout: "2n", done: true, event: "output", id: "..."} You can also send an interrupt signal to the Python process from Javascript by calling worksheet.interrupt(), and kill the process with worksheet.kill(). For example, here the a=4 never happens (but a=2 does): %javascript worksheet.execute_code({code:'a=2; sleep(100); a=4;', cb:function(mesg) { worksheet.interrupt(); console.log(mesg)}}) or using CoffeeScript (a Javascript preparser): %coffeescript worksheet.execute_code code : 'a=2; sleep(100); a=4;' cb : (mesg) -> worksheet.interrupt() console.log(mesg) The Javascript code is evaluated with numerous standard Javascript libraries available, including jQuery, Twitter Bootstrap, jQueryUI, etc. ︠c433b0a2-2af9-429c-84d9-24df2d3338c0︠ %md #### %kash Use %kash to interface with KASH code, which is the command line of KANT software. For further docuementation, visit [this page](http://page.math.tu-berlin.de/~kant/publications.html#docu). Currently, this command appears to be experiencing a bug in which it returns the values from previous calls of %kash. Examples of KASH: Basic operations: ︠5cf41652-69ce-4828-aa92-c9c0fe6af5dd︠ %kash kash% x_z3 := pAdicRing(3,30); ︠128954dc-a5df-4086-ad67-243126a2397f︠ %md Rings: ︠78d42022-b6ee-4407-9b67-fae4085ec6d8︠ %kash kash% 12345/25; ︠a986aeeb-3b9c-4eb4-970e-d45669544da1︠ %md #### %latex Return a "LatexExpr" built out of the argument "x". For full documentation, please visit [this page](http://latex-project.org/guides/). INPUT: * "x" -- a Sage object * "combine_all" -- boolean (Default: "False") If "combine_all" is "True" and the input is a tuple, then it does not return a tuple and instead returns a string with all the elements separated by a single space. OUTPUT: A "LatexExpr" built from "x" EXAMPLES: ︠2bd379f2-157d-49ac-9e61-c4713e900162︠ latex(Integer(3)) # indirect doctest latex(1==0) print latex([x,2]) ︠d4331e4b-8eb1-470e-9548-14420b11512b︠ %md Check that http://trac.sagemath.org/11775 is fixed: ︠d7263b93-f809-4390-9d03-729d404c34bf︠ latex((x,2), combine_all=True) ︠7d127345-fede-44e1-bc01-2b1033a0a78a︠ %md #### %lie Use %lie to interface with the LiE package. Type lie.[tab] for a list of all the functions available from your LiE install. Type lie.[tab]? for LiE's help about a given function. Type lie(...) to create a new LiE object, and lie.eval(...) to run a string using LiE (and get the result back as a string). For further information, view [this page](http://www-math.univ-poitiers.fr/~maavl/LiEman/manual.pdf). ︠3ef4b314-4471-4166-aa6f-373bd8a171e6︠ %md #### %lisp Use %lisp to interface with lisp code. For further documentation, visit [this page](http://www.paulgraham.com/lispcode.html). Examples: ︠acf12a30-298b-49ea-b359-6407eec1ce70︠ %md Subtracting 6 from 4: ︠8dbc2eaa-2931-4eca-94e1-2cddc6f1ef3b︠ %lisp (- 4 6)
-2
%md Finding the minimum value of a collection of numbers: ︠38919d14-07da-424d-b256-7c0b4ee34bc4︠ %lisp (min 4 -2 1 4) ︠610291bc-bf7a-44f8-91d2-6c0f4d900bc4︠ %md Note that sometimes lisp can hang while awaiting user input, among other things. Use ︠3be08e83-162d-4e76-a852-c7885cd18268︠ lisp.quit() ︠d6c63909-d641-416f-8b30-0b2967da5d23︠ %md to restart the lisp system. ︠f7fe05d2-7221-40fa-a332-5638aa9d64b6︠ %md #### %load Load Sage object from the file with name filename, which will have an .sobj extension added if it doesn't have one. Or, if the input is a filename ending in .py, .pyx, or .sage, load that file into the current running session. Loaded files are not loaded into their own namespace, i.e., this is much more like Python's "execfile" than Python's "import". You may also load an sobj or execute a code file available on the web by specifying the full URL to the file. (Set "verbose = False" to supress the download progress indicator.) INPUT: * args -- any number of filename strings with any of the following extensions: .sobj, .sage, .py, .pyx, .html, .css, .js, .coffee, .pdf * "verbose" -- (default: True) load file over the network. If you load and of the web types (.html, .css, .js, .coffee), they are loaded into the web browser DOM (or Javascript session), not the Python process. If you load a pdf, it is displayed in the output of the worksheet. The extra options are passed to salvus.pdf -- see the docstring for that. In SageMathCloud you may also use load as a decorator, with filename separated by whitespace or commas: %load foo.sage bar.py a.pyx, b.pyx The following are all valid ways to use load: %load a.html %load a.css %load a.js %load a.coffee %load a.css a.js a.coffee a.html load('a.css', 'a.js', 'a.coffee', 'a.html') load('a.css a.js a.coffee a.html') load(['a.css', 'a.js', 'a.coffee', 'a.html']) ALIAS: %runfile is the same as %load, for compatibility with IPython. ︠3d1a0cae-15e0-439a-abf0-000be315cb12︠ %md #### %macaulay2 Use %macaulay2 to interface with Macaulay2 code. For further documentation, visit [this page](http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.6/share/doc/Macaulay2/Macaulay2Doc/html/). Examples: Addition: ︠f6e56ba4-905f-4bdf-a12c-0b392afbc521︠ %macaulay2 2 + 2 ︠2aeab117-9f64-4b0f-bf3b-ffa06c4e3951︠ %md Strings: ︠3ea3890e-ee43-4e3a-9436-b8a8b68e1b54︠ %macaulay2 s = "hi there" ︠8eb8180f-b145-45e7-8e98-8474e9be410e︠ %md Elementary uses of Groebner bases ︠593fad15-ddbe-4239-93e0-a53897ec9d4f︠ %macaulay2 KK = ZZ/31991 R = KK[x,y,z,w] I = ideal(x^2*y,x*y^2+x^3) J = gens gb I ︠44f0eb3b-7131-471a-94d6-abce36a76823︠ %md #### %magics Type %magics to print all SageMathCloud magic commands or magics() to get a list of them. To use a magic command, either type %command <a line of code> or %command [rest of cell] Create your own magic command by dedefining a function that takes a string as input and outputs a string. (Yes, it is that simple.) ︠d8ae92a6-31b5-4462-a813-cc95e0cef0b6︠ %md #### %magma Type "magma.[tab]" for a list of all the functions available from your Magma install. Type "magma.Function?" for Magma's help about a given "Function" Type "magma(...)" to create a new Magma object, and "magma.eval(...)" to run a string using Magma (and get the result back as a string). Note: If you do not own a local copy of Magma, try using the "magma_free" command instead, which uses the free demo web interface to Magma. You must use nvals = 0 to call a function that doesn't return anything, otherwise you'll get an error. (nvals is the number of return values.) **Note that Magma is proprietary and is not installed by default**
%md #### %maple Use %maple to run maple code. For full Maple documentation, please visit [this page](http://www.maplesoft.com/documentation_center/). **Note that Maple is proprietary and is not installed by default** ︠a82d6c94-827a-44a3-8826-9cb489a6bd05︠ %md #### %mathematica Use %mathematica to interface with Mathematica code. Mathematica software utilizes symbolic mathematics and is further documented on [this page](http://reference.wolfram.com/mathematica/guide/Mathematica.html). **Note that Mathematica is proprietary and is not installed by default** ︠f9e3e771-1553-4f8e-9840-7ead8437e1c6︠ %md #### %matlab Use %matlab to run MATLAB code. MATLAB is a language which provides an interactive environment for numerical computation. For full documentation, view [this page](http://www.mathworks.com/products/matlab/). **Note that MATLAB is proprietary and is not installed by default** ︠fb6a3bf6-ac6a-4023-a8ee-0b05c49d3d4e︠ %md #### %maxima Interface to the Maxima interpreter. For full documentation, please visit [this page](http://maxima.sourceforge.net/documentation.html). EXAMPLES: ︠b7469fdd-cf09-42e2-add5-299e70c9592c︠ m = Maxima() m == maxima 2 ^ 3 ^ 4 2 ^ (3 ^ 4) (2 ^ 3) ^ 4 ︠9428f318-12a3-441c-8d49-06fe52355a23︠ %md #### %md Cell mode that renders everything after %md as markdown and hides the input by default. EXAMPLES: ︠61034462-7a10-426a-9906-c2e5996683d5︠ %md A Title A subheading ︠39e67d33-d27b-4055-9e8e-4664c98f4e99︠ %md(hide=False) A title - a list ︠37f1ad85-7f53-45d3-835e-ff9f02a9f134︠ md("# A title", hide=False) ︠0af2e93a-d079-47d3-b089-25a03a5852e9︠ %md(hide=False) `some code` ︠5260025b-598c-4302-ba8d-c8f3a97ba1ad︠ %md This uses the Python markdown2 library with the following extras enabled: 'code-friendly', 'footnotes', 'smarty-pants', 'wiki-tables' See https://github.com/trentm/python-markdown2/wiki/Extras We also use markdown2Mathjax so that LaTeX will be properly typeset if it is wrapped in $'s and $$'s, \(, \), \[, \], \begin{equation}, \end{equation}, \begin{align}, \end{align}., ︠da2cb4ad-c9fc-4a54-98c2-4680b5bbe83b︠ %md #### %mupad Use %mupad to run mupad code. MuPAD operates using symbolic mathematic expressions. For full documentation, view [this page](http://www.mathworks.com/discovery/mupad.html). **Note that MuPAD is proprietary and is not installed by default** ︠fd0793ab-8707-4a7c-8218-05a23329697c︠ %md #### %mwrank Use %mwrank to run mwrank code. Written in C++, mwrank is used to compute Mordell-Weil groups of elliptic curves over Q via 2-descent. For full documentation, view [this page](http://homepages.warwick.ac.uk/~masgaj/mwrank/). Example code: ︠f3ee9c4c-c919-4a17-b7af-5c6f01636c39︠ M = Mwrank('-v 0 -l') print M('0 0 1 -1 0') ︠0c78d683-65a3-47a0-8c9c-5b9de1d82071︠ %md #### %octave Interface to the Octave interpreter. For full documentation, visit [this page](http://www.gnu.org/software/octave/doc/interpreter/Simple-Examples.html#Help-and-Documentation). EXAMPLES: ︠cad4a8de-31f2-4cfa-96f5-eba4c0129dd0︠ octave.eval("a = [ 1, 1, 2; 3, 5, 8; 13, 21, 33 ]") # optional - octave ︠27a6b13d-0760-4c91-9d8b-4821ff9bb449︠ octave.eval("b = [ 1; 3; 13]") # optional - octave ︠ece99dbe-3e07-4739-9f70-16217b009c32︠ octave.eval("c=a b") # solves linear equation: a*c = b # optional - octave; random output ︠e212a78f-8a16-42ce-8de3-9169472c82e4︠ octave.eval("c") # optional - octave; random output ︠e059d8d6-398f-4cba-97e1-ff453f1229f3︠ %md #### %perl Block decorator to run code in a Perl session. For full documentation, visit [this page](http://perldoc.perl.org/). To use this, put %perl by itself in a cell so that it applies to the rest of the cell, or put it at the beginning of a line to run just that line using perl. EXAMPLE: A perl cell: ︠fd550f6b-4522-490f-b465-e926d8ec4431︠ %perl $apple_count = 5; $count_report = "There are $apple_count apples."; print "The report is: $count_report"; ︠58de064e-c4be-43de-99f1-767f29f70cc8︠ %md Or use %perl on one line: ︠98397638-8c7f-456b-b168-c01e0a6a8718︠ %perl $apple_count = 5; $count_report = "There are $apple_count apples."; print "The report is: $count_report"; ︠9b8e51b2-03af-41f7-b1c5-c6e7249bbdb4︠ %md You can combine %perl with capture, if you would like to capture the output to a variable. For example: ︠967e06c1-6860-4a28-bd00-5d729382ad81︠ %capture(stdout='p') %perl print "hi" ︠cc44e6c6-b087-48c1-9c62-5049c416a3bc︠ %md Afterwards, p contains 'hi'. NOTE: No state is preserved between calls. Each call is a separate process. ︠2454c251-70cf-46f6-ad3f-45afa3890d1f︠ %md #### %prun Use %prun followed by a block of code to profile execution of that code. This will display the resulting profile, along with a menu to select how to sort the data. EXAMPLES: Profile computing a tricky integral (on a single line): ︠b5e03a19-76a1-4bd4-b42d-2a2467b3e006︠ %prun integrate(sin(x^2),x) ︠4378a004-63b7-4759-afbc-dc676b6f39c9︠ %md Profile a block of code:: ︠0835bebf-a214-4d4c-9857-377c8bc9955f︠ %prun E = EllipticCurve([1..5]) v = E.anlist(10^5) r = E.rank() ︠64026a2b-d854-47b4-a10f-5d7eef669193︠ %md #### %python Block decorator to run code in pure Python mode, without it being preparsed by the Sage preparser. Otherwise, nothing changes. To use this, put %python by itself in a cell so that it applies to the rest of the cell, or put it at the beginning of a line to disable preparsing just for that line. ︠587e7ae9-8260-4ab7-ba25-2bdc4b3bda21︠ %python print "hello world" for i in range(0, 10, 2): print i ︠8e778cce-f140-400c-9dfe-e0026a786b8e︠ %md #### %r An interface to the R interpreter. R is a comprehensive collection of methods for statistics, modelling, bioinformatics, data analysis and much more. For more details, see http://www.r-project.org/about.html EXAMPLES: sage: r.summary(r.c(1,2,3,111,2,3,2,3,2,5,4)) Min. 1st Qu. Median Mean 3rd Qu. Max. 1.00 2.00 3.00 12.55 3.50 111.00 TESTS: sage: r == loads(dumps(r)) True ︠caa74c25-eddc-4a78-bbf2-bedaae7c6878︠ %md #### %reset If vars is specified, just restore the value of vars and leave all other variables alone. In SageCloud, you can also use reset as a line decorator:: ︠c205f496-bbf3-4f16-9058-ecee76fc2f9d︠ %reset x, pi, sin # comma-separated %reset x pi sin # commas are optional ︠487b2d88-374b-4a30-a2a6-02bcd2acb278︠ %md If vars is not given, delete all user-defined variables, reset all global variables back to their default states, and reset all interfaces to other computer algebra systems. ︠fc50cb15-a71a-49aa-833a-91efcde4f5fc︠ %md #### %ruby Block decorator to run code in a Ruby session. To use this, put %ruby by itself in a cell so that it applies to the rest of the cell, or put it at the beginning of a line to run just that line using ruby. EXAMPLE: A ruby cell: ︠e283e1af-90cd-4744-9a17-2878ba1e9094︠ %ruby lang = "ruby" print "Hello from #{lang}!" ︠62d3e7db-f29b-466f-93c1-1279e3b3a408︠ %md Or use %ruby on one line: ︠5b5acf48-be41-45ae-8ce3-02cfe5ebbf7b︠ %ruby lang = "ruby"; print "Hello from #{lang}!" ︠52072002-1d2a-4c43-a1e2-56816bcbd35d︠ %md You can combine %ruby with capture, if you would like to capture the output to a variable. For example: ︠a8fb8b70-1cd6-4cd7-bb9f-c9ece289738c︠ %capture(stdout='p') %ruby lang = "ruby"; print "Hello from #{lang}!" ︠5e511672-e13e-48b4-b2e8-4df7639b3510︠ %md Afterwards, p contains 'Hello from ruby!'. NOTE: No state is preserved between calls. Each call is a separate process. ︠958e7011-b19f-4742-8236-b0217bc53722︠ %md #### %runfile Load Sage object from the file with name filename, which will have an .sobj extension added if it doesn't have one. Or, if the input is a filename ending in .py, .pyx, or .sage, load that file into the current running session. Loaded files are not loaded into their own namespace, i.e., this is much more like Python's "execfile" than Python's "import". You may also load an sobj or execute a code file available on the web by specifying the full URL to the file. (Set "verbose = False" to supress the download progress indicator.) INPUT: * args -- any number of filename strings with any of the following extensions: .sobj, .sage, .py, .pyx, .html, .css, .js, .coffee, .pdf * "verbose" -- (default: True) load file over the network. If you load and of the web types (.html, .css, .js, .coffee), they are loaded into the web browser DOM (or Javascript session), not the Python process. If you load a pdf, it is displayed in the output of the worksheet. The extra options are passed to salvus.pdf -- see the docstring for that. In SageMathCloud you may also use load as a decorator, with filename separated by whitespace or commas: %load foo.sage bar.py a.pyx, b.pyx The following are all valid ways to use load: %load a.html %load a.css %load a.js %load a.coffee %load a.css a.js a.coffee a.html load('a.css', 'a.js', 'a.coffee', 'a.html') load('a.css a.js a.coffee a.html') load(['a.css', 'a.js', 'a.coffee', 'a.html']) ALIAS: %runfile is the same as %load, for compatibility with IPython. ︠d46b6591-0b59-45bc-b72a-8581dad2b496︠ %md #### %sage0 Load Sage object from the file with name filename, which will have an .sobj extension added if it doesn't have one. Or, if the input is a filename ending in .py, .pyx, or .sage, load that file into the current running session. Loaded files are not loaded into their own namespace, i.e., this is much more like Python's "execfile" than Python's "import". You may also load an sobj or execute a code file available on the web by specifying the full URL to the file. (Set "verbose = False" to supress the download progress indicator.) INPUT: * args -- any number of filename strings with any of the following extensions: .sobj, .sage, .py, .pyx, .html, .css, .js, .coffee, .pdf * "verbose" -- (default: True) load file over the network. If you load and of the web types (.html, .css, .js, .coffee), they are loaded into the web browser DOM (or Javascript session), not the Python process. If you load a pdf, it is displayed in the output of the worksheet. The extra options are passed to salvus.pdf -- see the docstring for that. In SageMathCloud you may also use load as a decorator, with filename separated by whitespace or commas: %load foo.sage bar.py a.pyx, b.pyx The following are all valid ways to use load: %load a.html %load a.css %load a.js %load a.coffee %load a.css a.js a.coffee a.html load('a.css', 'a.js', 'a.coffee', 'a.html') load('a.css a.js a.coffee a.html') load(['a.css', 'a.js', 'a.coffee', 'a.html']) ALIAS: %runfile is the same as %load, for compatibility with IPython. ︠cbf9435d-3716-43be-899e-9464c4c1aad3︠ %md #### %scilab Interface to the Scilab interpreter. EXAMPLES: sage: a = scilab('[ 1, 1, 2; 3, 5, 8; 13, 21, 33 ]') # optional - scilab sage: b = scilab('[ 1; 3; 13]') # optional - scilab sage: c = a * b # optional - scilab sage: print c # optional - scilab 30. 122. 505. **Note that Scilab is not proprietary and is not installed by default** ︠832dc33b-a67e-42c7-a22c-5508df8a4b35︠ %md #### %script Block decorator to run an arbitrary shell command with input from a cell in Salvus. Put %script('shell command line') or %script(['command', 'arg1', 'arg2', ...]) by itself on a line in a cell, and the command line is run with stdin the rest of the contents of the cell. You can also use script in single line mode, e.g.,:: ︠2507f9c2-4de3-40a0-93d6-63729ea34831︠ %script('gp -q') factor(2^97 - 1) ︠1e416d2e-3988-4d13-9877-3a1843bbd7ad︠ %md or ︠19e80634-30d6-43b0-b65a-5ce535810f8d︠ %script(['gp', '-q']) factor(2^97 - 1) ︠1c4bceda-f4ec-4698-b21a-d023fabdf55f︠ %md will launch a gp session, feed 'factor(2^97-1)' into stdin, and display the resulting factorization. NOTE: the result is stored in the attribute "stdout", so you can do:: ︠6a5401ae-b1e5-46de-8845-2c9cda0f27d3︠ s = script('gp -q') %s factor(2^97-1) s.stdout '\n[11447 1]\n\n[13842607235828485645766393 1]\n\n' ︠0f41567c-70c5-48ae-94c5-c98faff5b7b1︠ %md and s.stdout will now be the output string. You may also specify the shell environment with the env keyword. ︠d1e7aac5-fd74-4eb4-903f-86c6780ed149︠ %md ####%sh Run a bash script in Salvus. EXAMPLES: Use as a block decorator on a single line:: ︠3ca8491c-a57f-4682-8d6d-603f4b475989︠ %sh pwd ︠a46c3e48-6821-4b48-bb6e-ee550f8cbedf︠ %md and multiline ︠d27de9b9-359b-41be-bf6b-7e590d7a7963︠ %sh echo "hi" pwd ls -l ︠0f08064c-ca51-433b-a21b-08d0780f10a8︠ %md You can also just directly call it:: ︠f36c02e3-59d4-4e7e-9fba-a3b401b396cd︠ sh('pwd') ︠0889fddb-f614-4ca1-bb5d-8c940290bcb0︠ %md The output is printed. To capture it, use capture ︠72ef5343-5a14-4f8c-a8dd-808fa8211ce1︠ %capture(stdout='output') %sh pwd ︠0527d4e7-558b-4287-9857-2b3fa6bd0544︠ %md After that, the variable output contains the current directory ︠b7b8a7a7-0b7c-4d09-acac-d77630d897f4︠ %md #### %singular Interface to the Singular interpreter. EXAMPLES: A Groebner basis example. sage: R = singular.ring(0, '(x0,x1,x2)', 'lp') sage: I = singular.ideal([ 'x0*x1*x2 -x0^2*x2', 'x0^2*x1*x2-x0*x1^2*x2-x0*x1*x2^2', 'x0*x1-x0*x2-x1*x2']) sage: I.groebner() x1^2*x2^2, x0*x2^3-x1^2*x2^2+x1*x2^3, x0*x1-x0*x2-x1*x2, x0^2*x2-x0*x2^2-x1*x2^2 ︠6df69528-974b-4072-a93e-eb1d67ee87c3︠ %md #### %time Time execution of code exactly once in Salvus by: - putting %time at the top of a cell to time execution of the entire cell - put %time at the beginning of line to time execution of just that line - write time('some code') to executation of the contents of the string. If you want to time repeated execution of code for benchmarking purposes, use the timeit command instead. ︠7e888feb-4856-4776-9529-4fce1c02c930︠ %md #### %timeit Time execution of a command or block of commands. This command has been enhanced for Salvus so you may use it as a block decorator as well, e.g., ︠e7af31dd-bc0e-4cb2-8108-91be6afe3d77︠ %timeit 2+3 ︠8be55fbe-6d54-456e-90bf-452b40a5057f︠ %md and ︠3cae7b1c-ff00-47b0-8b56-06aab96ee64c︠ %timeit(number=10, preparse=False) 2^3 ︠51b152be-ec4d-4217-a506-ec99447d8d53︠ %md and ︠b99f4b7a-f339-4123-b113-770b5f1ab7c0︠ %timeit(preparse=False) ︠0b670cdf-2b8b-4c49-8a2f-bdfc03ff31d9︠ %md [rest of the cell] ︠d740a1b5-5eef-4cae-9412-a94ccfd346cc︠ %md #### %typeset_mode Turn typeset mode on or off. When on, each output is typeset using LaTeX. EXAMPLES:: ︠ebe73d6a-82d9-4366-a573-558fe2b1647b︠ typeset_mode() # turns typesetting on typeset_mode(False) # turn typesetting off typeset_mode(True, display=False) # typesetting mode on, but do not make output big and centered ︠de6ec6db-a41d-48fe-ac53-10e2a1066a52︠ %md #### %var Create symbolic variables and inject them into the global namespace. NOTE: In SageCloud, you can use var as a line decorator:: %var x %var a,b,theta # separate with commas %var x y z t # separate with spaces Here is the docstring for var in Sage: if len(args)==1: name = args[0] else: name = args G = salvus.namespace v = sage.all.SR.var(name, **kwds) if isinstance(v, tuple): for x in v: G[repr(x)] = x else: G[repr(v)] = v return v var.__doc__ += sage.all.var.__doc__ ︠7c7486d7-5b22-4d52-aaad-9f0ea4eae65e︠