| Download
All published worksheets from http://sagenb.org
Project: sagenb.org published worksheets
Views: 168749Image: ubuntu2004
Sage Demo
Calculus
5
1/16*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*x) + (I - 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*x) - (I - 1)*sqrt(2)*erf(sqrt(-I)*x) + (I + 1)*sqrt(2)*erf((-1)^(1/4)*x))
\frac{1}{16} \, \sqrt{\pi} {\left(\left(i + 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} x\right) + \left(i - 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} x\right) - \left(i - 1\right) \, \sqrt{2} \operatorname{erf}\left(\sqrt{-i} x\right) + \left(i + 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(-1\right)^{\frac{1}{4}} x\right)\right)}
(a, b, c, X)
Linear Algebra
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WARNING: Output: 71997521 truncated by MAX_HTML_SIZE to 40000. Type 'smc?' to learn how to raise the output limit.
1627
400x300px 24-bit RGB image
600x414px 24-bit RGB image
Factoring
Error in lines 1-1
Traceback (most recent call last):
File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "<string>", line 1
time factor(next_prime(Integer(2)**Integer(40)) * next_prime(Integer(2)**Integer(300)),verbose=Integer(0))
^
SyntaxError: invalid syntax
[1099511627791, 2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397533]
CPU time: 0.25 s, Wall time: 0.82 s
[1237940039285380274899124357, 2475880078570760549798248507] 4.17
Elliptic Curves
Graph Theory
True
5
Multivariate Polynomial Rings
Time: CPU 2.46 s, Wall: 2.46 s
Time: CPU 0.29 s, Wall: 0.29 s
Sage/Singular 4.872305
Traceback (most recent call last): print 'MAGMA', magma.cputime(t)
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/interfaces/magma.py", line 349, in cputime
return float(self.eval('Cputime()'))
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/interfaces/magma.py", line 278, in eval
ans = Expect.eval(self, x).replace('\\\n','')
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/interfaces/expect.py", line 917, in eval
return '\n'.join([self._eval_line(L, **kwds) for L in code.split('\n') if L != ''])
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/interfaces/expect.py", line 613, in _eval_line
self._start()
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/interfaces/magma.py", line 285, in _start
Expect._start(self)
File "/usr/local/sage/local/lib/python2.5/site-packages/sage/interfaces/expect.py", line 450, in _start
self.__name, cmd, self._install_hints())
RuntimeError: Unable to start magma because the command 'magma -n' failed.
Combinatorics
Combinations of [0, 1, 2, 3, 4]
[[], [0], [1], [2], [3], [4], [0, 1], [0, 2], [0, 3], [0, 4], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4], [0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 3], [0, 2, 4], [0, 3, 4], [1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4], [0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 3, 4], [0, 2, 3, 4], [1, 2, 3, 4], [0, 1, 2, 3, 4]]
[1, 2]
Interfaces
1
176
176
176
176
<class 'sage.interfaces.gap.GapElement'>
[2, 4; 11, 1]
Curve Fitting
scipy.linalg.basic.lstsq curve fitting example
fitting data to quadratic equation y = a + bx + cx^2
yields: x data y data calc value error
5.357 0.376 0.355 -0.021
5.457 0.489 0.472 -0.017
5.797 0.874 0.882 0.008
5.936 1.049 1.055 0.006
6.161 1.327 1.341 0.014
6.697 2.054 2.054 0.000
6.731 2.077 2.101 0.024
6.775 2.138 2.162 0.024
8.442 4.744 4.688 -0.056
9.769 7.068 7.010 -0.058
9.861 7.104 7.181 0.077
3D Plotting
Sequences of Integers
Searching Sloane's online database...
40 The prime numbers.
41 a(n) = number of partitions of n (the partition numbers).