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Magične naredbe

Osim dekoratora %md, %html i %latex, postoji još cijeli niz dekoratora, koje možemo izlistati s %magics

%magics
%auto %axiom %capture %coffeescript %command %cython %default %default_mode %exercise %file %fork %fortran %fricas %gap %gap3 %giac %go %gp %hide %hideall %html %javascript %julia %kash %lie %lisp %load %macaulay2 %magics %magma %maple %mathematica %matlab %maxima %md %mupad %mwrank %octave %pandoc %perl %prun %python %r %reset %ruby %runfile %sage0 %scilab %script %sh %singular %time %timeit %typeset_mode %var %wiki

Za neke, kao npr. %mathematica, potrebno je da je na računalu instaliran odgovarajući program.

%r omogućava korištenje programskog jezika R

%r
x <- c(1,2,3,4,5,6)
y <- x^2
print(y)
mean(y)
var(y)
[1] 1 4 9 16 25 36 [1] 15.16667 [1] 178.9667

%fortran omogućuje kompajliranje Fortran koda te njegovo korištenje.

%fortran
            SUBROUTINE FIB(A,N)
            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

import numpy
n = numpy.array(range(10),dtype=float)
fib(n,int(10))
n
array([ 0., 1., 1., 2., 3., 5., 8., 13., 21., 34.]) 
%cython
cimport cython
from libc.math cimport sqrt
cdef double cy_funkcija(double x):
    return sqrt(1-x**2)

def cy_integral4pi(int n):
    cdef double korak, rez
    cdef int i
    korak = 1.0/n
    rez = (cy_funkcija(0)+cy_funkcija(1))/2
    for i in range(n):
        rez += cy_funkcija(i*korak)
    return 4*rez*korak

%timeit cy_integral4pi(10**7)
5 loops, best of 3: 71.4 ms per loop 
%cython
def is2pow(unsigned int n):
    while n != 0 and n%2 == 0:
        n = n >> 1
    return n == 1

%time [n for n in range(10^5) if is2pow(n)]
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536] CPU time: 0.08 s, Wall time: 0.08 s 
%python
def slow_is2pow(n):
    while n != 0 and n%2 == 0:
        n = n >> 1
    return n == 1

%time [n for n in range(10^5) if slow_is2pow(n)]
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536] CPU time: 0.11 s, Wall time: 0.11 s 
%octave
x = [1; 3; 2]
A = [1, 1, 2; 3, 5, 8; 13, 21, 34]
A'*x
x = 1 3 2 A = 1 1 2 3 5 8 13 21 34 ans = 36 58 94

%exercise omogućava kreiranje sučelja za vježbanje.

Varijable:

title: naslov

question: pitanje

answer: odgovor

hints: upute (opcionalno)

attempt: odgovor korisnika

Ovdje možete pogledati kako je %exercise implementiran.

%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"
Interact: please open in CoCalc

Jednostavniji primjer.

%exercise
title = r"Transpose a $2 x 2$ Matrix"
A = random_matrix(ZZ,2)
question = "What is the transpose of $%s?$"%latex(A)
answer = A.transpose()
Interact: please open in CoCalc