CoCalc -- 1637.sagews

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x=var('x') 
n=var('n') 
n=8 
f=sqrt(x) 
p1=plot(f,(x,0,4)) 
p1

x=var('x') 
n=var('n') 
n=8 
f=sqrt(x) 
p1=plot(f,(x,0,4)) 
for i in range(0,n,1):p1+=polygon([(i/2,0), (i/2+4/n,0), (i/2+4/n,f(i/2+4/n)), (i/2,f(i/2+4/n))], rgbcolor=(1/8,3/4,1/2)) 
p1

__main__:1: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)

import numpy 
import pylab 
        	
t = numpy.arange(0.0, 1.0, 0.01) 
s = numpy.cos(2*2*numpy.pi*t) 
z = numpy.sin(2*2*numpy.pi*t) 
pylab.plot(t, s, 'ro-', t, z, 'bx-') 
pylab.xlabel('time (s)') 
pylab.ylabel('voltage (mV)') 
pylab.title('About as simple as it gets, folks') 
pylab.grid(True) 
pylab.savefig('simple_plot') 
pylab.legend(('sin','cos')) 
pylab.show()

u, v = var('u,v') 
fx = (1+cos(v))*cos(u) 
fy = (1+cos(v))*sin(u) 
fz = -tanh((2/3)*(u-pi))*sin(v) 
parametric_plot3d([fx, fy, fz], (u, 0, 2*pi), (v, 0, 2*pi), frame=False, color="red")

a=var('a')
b=var('b')
c=var('c')
x = -1/2*(b + sqrt(-4*a*c + b^2))/a

-1/2*(b + sqrt(-4*a*c + b^2))/a

var('a b c d')

(a, b, c, d)

-1/2*(b + sqrt(-4*a*c + b^2))/a

-1/2*(b + sqrt(-4*a*c + b^2))/a

q = solve(a*x^2+b*x+c==0,x);q

[-1/2*(b + sqrt(-4*a*c + b^2))/a == -1/2*(b + sqrt(-4*a*c + b^2))/a]

show(q[0])

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, \frac{{\left(b + \sqrt{-4 \, a c + b^{2}}\right)}}{a} = -\frac{1}{2} \, \frac{{\left(b + \sqrt{-4 \, a c + b^{2}}\right)}}{a}

var('a1 b1 c1 d1')

(a1, b1, c1, d1)

d1 = solve(a1*x^2+b1*x+c1==0,x);d1

[]

show(d1)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\right]

q = solve(a*x^3+b*x^2+c*x+d==0,x);q

[]

show(q[0].simplify_full())

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_18.py", line 9, in <module>
    exec compile(ur'open("___code___.py","w").write("# -*- coding: utf-8 -*-\n" + _support_.preparse_worksheet_cell(base64.b64decode("c2hvdyhxWzBdLnNpbXBsaWZ5X2Z1bGwoKSk="),globals())+"\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpBNvZaB/___code___.py", line 3, in <module>
    exec compile(ur'show(q[_sage_const_0 ].simplify_full())' + '\n', '', 'single')
  File "", line 1, in <module>
    
IndexError: list index out of range

var('a b c d');show(sqrt(a+sqrt(b+sqrt(c+sqrt(d)))))

(a, b, c, d)(a, b, c, d)
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{a + \sqrt{b + \sqrt{c + \sqrt{d

}}}

var('u v');plot3d(sin(u^2) - cos(v^2), (u,-2,2),(v,-2,2))

(u, v)