In the spirit of the StackOverflow threads of "hidden" language features, we can use this thread (community wiki) to aggregate useful but little-known features or tricks of Sage. Perhaps these can be collected and added to the documentation in the future.
In the command line, the underscore is a variable holding the result of the last output. This is very useful, e.g., for the following:
sage: integrate(cos(x), x)
sin(x)
sage: diff(_, x)
cos(x)
The import_statements() function, which allows to know what import statement should we do to use an object.
sage: import_statements('RDF')
from sage.rings.real_double import RDF
By the way, it would be http://www.faqtory.co/sky/ (useful) (if it doesn't already exist) to have a function to render LaTeX code to an image just large enough to fit the expression
The preparser() function which allows to understand differences between Python and Sage parsers, and between .py and .sage files:
sage: 2^2
4
sage: preparser(False)
sage: 2^2
0
sage: 2**2
4
Conversely, the preparse() function tells you how Sage preparses the input:
sage: preparse('1.0+2^2')
"RealNumber('1.0')+Integer(2)**Integer(2)"
It is possible to delete user-defined variables, and reset Sage variables back to their default:
sage: a = 1 ; a
1
sage: reset()
sage: a
NameError: name 'a' is not defined
It is also possible to reset only a few things:
sage: a = b = c = 1
sage: reset(['a','b'])
sage: c
1
To create a tuple of variables x0,...,xk you can use var("x", n=k), e.g.
sage: var("x", n=10)
(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
A very hidden feature of Python!
For faster code using itertools you may delete the reference at the end of the loop
sage: from itertools import combinations
sage: sage: timeit('for p in combinations(range(18),5): pass')
625 loops, best of 3: 615 µs per loop
sage: sage: timeit('for p in combinations(range(18),5): del p')
625 loops, best of 3: 322 µs per loop
The reason is that the iterators in itertools recycle the objects they return if they are the only one to reference it! But is it relevant to optimize Python code?
Wow, this is really cool! Is there any documentation anywhere for this?
Actually not ! You have to read the sources of Python to discover that fact. I wrote few months ago to the developer of itertools which told me that it was a minor speedup (if you want speed you will not use Python).
Locally disable the preparser with the suffix r
It's not really disabling the preparser (the input is still preparsed), but telling the preparser not to process some of the (numerical) input by marking this input as raw (by appending the letter r).
sage: type(12)
<type 'sage.rings.integer.Integer'>
sage: type(12r)
<type 'int'>
sage: type(42.42)
<type 'sage.rings.real_mpfr.RealLiteral'>
sage: type(42.42r)
<type 'float'>
Also works for Python complex numbers:
sage: type(1j)
<type 'sage.rings.complex_number.ComplexNumber'>
sage: type(1jr)
<type 'complex'>
It's a bit similar to specifying some strings as raw by prepending an r to '...' or "..." or '''...''' or """..."""; for instance in '\t' the backslash-t produces a tab, but in r'\t' it stays backslash-t.
The function sage_input (sometimes) alows to get the Sage code to reconstruct an object you like.
sage: m = random_matrix(ZZ,3)
sage: m
[-1 1 -1]
[-2 -2 -1]
[ 1 -5 0]
I like that one, how could i reconstruct it ?
sage: sage_input(m)
matrix(ZZ, [[-1, 1, -1], [-2, -2, -1], [1, -5, 0]])
sage: m == eval(str(sage_input(m)))
True
Another example:
sage: e = m.eigenvalues()[0]
sage: sage_input(e)
R.<x> = QQbar[]
QQbar.polynomial_root(AA.common_polynomial(x^3 + 3*x^2 + 8), CIF(RIF(-RR(3.6128878647175449), -RR(3.6128878647175444)), RIF(RR(0))))
sage: sage_input(e, preparse=False)
R = QQbar['x']
x = R.gen()
QQbar.polynomial_root(AA.common_polynomial(x**3 + 3*x**2 + 8), CIF(RIF(-RR(3.6128878647175449), -RR(3.6128878647175444)), RIF(RR(0))))
To know whether Sage is running from the notebook or the command line, use the misc.embedded() function:
sage: misc.embedded()
False
Symbolic variables can be created from the command line as follows, faster than typing out var('x y z'):
,var x y z
Asked: 2013-04-29 01:09:50 +0200
Seen: 3,566 times
Last updated: Oct 15 '20
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