{{{id=1|
ring r1 = 0,(t,x,y,z),ls;
///
ring r1 = 0,(t,x,y,z),ls;
}}}

{{{id=4|
r1
ideal i1 = x-t2,y-t3,z;
///
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_8.py", line 10, in <module>
    exec compile(u"print _support_.syseval(singular, u'i1.category', __SAGE_TMP_DIR__)" + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sagenb-0.8.2-py2.6.egg/sagenb/misc/support.py", line 473, in syseval
    return system.eval(cmd, sage_globals, locals = sage_globals)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/interfaces/singular.py", line 549, in eval
    raise RuntimeError, 'Singular error:\n%s'%s
RuntimeError: Singular error:
i1[1]=x-t2
i1[2]=y-t3
i1[3]=z
   ? error occurred in or before STDIN line 31: `i1.category;`
   skipping text from `category`
}}}

{{{id=5|
i1.show
///
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_10.py", line 10, in <module>
    exec compile(u"print _support_.syseval(singular, u'i1.show', __SAGE_TMP_DIR__)" + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sagenb-0.8.2-py2.6.egg/sagenb/misc/support.py", line 473, in syseval
    return system.eval(cmd, sage_globals, locals = sage_globals)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/interfaces/singular.py", line 549, in eval
    raise RuntimeError, 'Singular error:\n%s'%s
RuntimeError: Singular error:
i1[1]=x-t2
i1[2]=y-t3
i1[3]=z
   ? error occurred in or before STDIN line 35: `i1.show;`
   skipping text from `show`
}}}

{{{id=43|
R.<r,s,t> = PolynomialRing(QQ)
///
}}}

{{{id=44|
R.objgens()
///
(Multivariate Polynomial Ring in r, s, t over Rational Field, (r, s, t))
}}}

{{{id=6|
def cuberoot2(c, prec):
    x = 1
    count = 0
    while (abs(x^3-c) > prec):
        x = (2*x^3+c)/(3*x^2)
        count = count + 1
    print 'did %s loops'%(count)
    return n(x);
///
}}}

{{{id=7|
time cuberoot2(500, 10^(-6))
///
did 13 loops
7.93700525984100
Time: CPU 7.92 s, Wall: 8.26 s
}}}

{{{id=8|
def cuberoot1(c, prec):
    s = sign(c);
    c = abs(c); 
    a = 0; 
    b = max(c, 1);
    count = 0;
    while (b-a > prec):
        m = (a+b)/2;
        if (m^3 < c): 
            a = m
        else:
            b = m
        count = count + 1
    print 'did %s loops'%(count)
    return n(s*m);
///
}}}

{{{id=41|
numerical_approx(pi)
///
3.14159265358979
}}}

{{{id=42|
pari('factor(15)')
///
[3, 1; 5, 1]
}}}

{{{id=9|
time cuberoot1(500, 10^(-6))
///
did 29 loops
7.93700572103262
Time: CPU 0.00 s, Wall: 0.00 s
}}}

{{{id=12|
poly = sum(Integer(round(random()*1000)))*x^i, i in range(10));
///
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_61.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cG9seSA9IHN1bShJbnRlZ2VyKHJvdW5kKHJhbmRvbSgpKjEwMDApKSkqeF5pLCBpIGluIHJhbmdlKDEwKSk7"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpbgDyXs/___code___.py", line 3
    poly = sum(Integer(round(random()*_sage_const_1000 )))*x**i, i in range(_sage_const_10 ));
                                                                                            ^
SyntaxError: invalid syntax
}}}

{{{id=13|
add(range(5))
///
10
}}}

{{{id=14|
p1 = PolynomialRing(QQ, 'x').random_element(degree=200)
///
}}}

{{{id=16|
type(p1)
///
<class 'sage.rings.polynomial.polynomial_element_generic.Polynomial_rational_dense'>
}}}

{{{id=15|
v = var('v')
p2 = p1 + v - v
///
}}}

{{{id=17|
type(p2)
///
<type 'sage.symbolic.expression.Expression'>
}}}

{{{id=18|
time t1 = p1*p1
///
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_100.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dCA9IHRpbWUgdDEgPSBwMSpwMQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpg51FF9/___code___.py", line 2
    t = time t1 = p1*p1
              ^
SyntaxError: invalid syntax
}}}

{{{id=19|
time t2 = expand(p2*p2)
///
Time: CPU 0.48 s, Wall: 0.48 s
}}}

{{{id=20|
expand(t1-t2)
///
0
}}}

{{{id=21|
def time_polymult(deg):
    res = [];
    d = 1;
    while (d < deg):
        p1 = PolynomialRing(QQ, 'x').random_element(degree=d)
        p2 = PolynomialRing(QQ, 'x').random_element(degree=d)
        t = cputime()
        p1 = p1*p2
        res.append((d,cputime(t)))
        d = ceil(11/10*d)
    return res
///
}}}

{{{id=22|
timing = time_polymult(5000)
///
}}}

{{{id=23|
plot_step_function(timing)
///
<html><font color='black'><img src='cell://sage0.png'></font></html>
}}}

{{{id=24|
time mathematica(p1*p2)
///
WARNING: Output truncated!  
<html><a target='_new' href='/home/admin/6/cells/24/full_output.txt' class='file_link'>full_output.txt</a></html>



Exception RuntimeError: 'maximum recursion depth exceeded in __subclasscheck__' in <type 'exceptions.RuntimeError'> ignored
Exception RuntimeError: 'maximum recursion depth exceeded in __subclasscheck__' in <type 'exceptions.RuntimeError'> ignored
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_141.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dGltZSBtYXRoZW1hdGljYShwMSpwMik="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpN60Kig/___code___.py", line 2, in <module>
    exec compile(u'__time__=misc.cputime(); __wall__=misc.walltime(); mathematica(p1*p2); print "Time: CPU %.2f s, Wall: %.2f s"%(misc.cputime(__time__), misc.walltime(__wall__))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1034, in __call__
    return self._coerce_from_special_method(x)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/interfaces/expect.py", line 1058, in _coerce_from_special_method
    return (x.__getattribute__(s))(self)
  File "sage_object.pyx", line 542, in sage.structure.sage_object.SageObject._mathematica_ (sage/structure/sage_object.c:5739)
  File "expression.pyx", line 423, in sage.symbolic.expression.Expression._interface_ (sage/symbolic/expression.cpp:3239)
  File "sage_object.pyx", line 379, in sage.structure.sage_object.SageObject._interface_ (sage/structure/sage_object.c:3374)
  File "sage_object.pyx", line 547, in sage.structure.sage_object.SageObject._mathematica_init_ (sage/structure/sage_object.c:5832)
  File "expression.pyx", line 462, in sage.symbolic.expression.Expression._interface_init_ (sage/symbolic/expression.cpp:3510)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)

...

    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/ckoutsch/sage-4.5.3/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 505, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "expression.pyx", line 3568, in sage.symbolic.expression.Expression.operands (sage/symbolic/expression.cpp:16014)
  File "pynac.pyx", line 948, in sage.symbolic.pynac.py_numer (sage/symbolic/pynac.cpp:8561)
RuntimeError: maximum recursion depth exceeded in __instancecheck__
}}}

{{{id=26|
test = 3
///
}}}

{{{id=25|
test.str()
///
'3'
}}}

{{{id=28|
2.sqrt().n()
///
1.41421356237310
}}}

{{{id=29|
def f(x): return x^2
///
}}}

{{{id=30|
type(f)
///
<type 'function'>
}}}

{{{id=31|
g(x,y) = x^2+y^3
///
}}}

{{{id=32|
type(g(x))
///
<type 'sage.symbolic.expression.Expression'>
}}}

{{{id=33|
h = function('h', x)
///
}}}

{{{id=34|
g.diff()
///
x |--> 2*x
}}}

{{{id=35|
desolve(diff(h,x)+h-1, [h,x])
///
(c + e^x)*e^(-x)
}}}

{{{id=36|
p1 = plot(f, (-2,2))
///
}}}

{{{id=37|
p2 = circle((0,0), 1, rgbcolor=(1,1,0))
///
}}}

{{{id=38|
show(p1+p2)
///
<html><font color='black'><img src='cell://sage0.png'></font></html>
}}}

{{{id=39|
R = PolynomialRing(QQ, 2, "xy")
R
///
Multivariate Polynomial Ring in x, y over Rational Field
}}}

{{{id=45|
x,y = R.gens()
///
}}}

{{{id=46|
f = x^2+y^2+1; g = x^3+2*x*y-y^3
///
}}}

{{{id=47|
id1 = (f,g)*R
///
}}}

{{{id=48|
id1.groebner_basis()
///
[y^4 - 3/2*x*y + y^2 + x - y + 1/2, x*y^2 + y^3 - 2*x*y + x, x^2 + y^2 + 1]
}}}

{{{id=49|
x = var('x')
def ff(x):
       if x<2:
           return 0
       else:
           return x-2
///
}}}

{{{id=50|
plot(ff, (0, 4))
///
<html><font color='black'><img src='cell://sage0.png'></font></html>
}}}

{{{id=51|
x
///
x
}}}

{{{id=52|

///
}}}