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Project: calcul-formel
Views: 35
License: GPL3
Image: ubuntu2204
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matrix(2, 3, [1,pi,3, e,5,6])
[ 1 pi 3] [ e 5 6] 
vector([pi, 2, 3, e])
(pi, 2, 3, e) 
matrix(2, 2, [1,2, 3,4]).charpoly()
x^2 - 5*x - 2 
import numpy
numpy.array([[1,2,3], [4,5,6]], dtype=float)
array([[1., 2., 3.], [4., 5., 6.]]) 
[n+1 for n in range(10) if n%2==0]
len([1, 2, 5, 6, 10])




show(cube(color=['red', 'blue', 'green'], frame_thickness=2,
         frame_color='brown', opacity=0.8), frame=False)
from sage.plot.plot3d.shapes import Torus
inner_radius = .3; outer_radius = 1
show(Torus(outer_radius, inner_radius, color='orange'), aspect_ratio=1, spin=3)
text3d("Text in 3D", (1,1, 1), color="darkred", fontsize=20)
[1, 3, 5, 7, 9] 5
3D rendering not yet implemented
3D rendering not yet implemented
3D rendering not yet implemented



@interact
def interactive_function(a = slider(0, 10, .05, default=4),
                         b = (-3, 3, .1)):
    f(x) = b * x + sin(a * x)
    plot(f, (x, -5, 5)).show()
Mod(5, 12)
Interact: please open in CoCalc


Mod(5, 12)
prime_range(100)
factor(2015)
5 [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97] 78498 5 * 13 * 31 

prime_pi(10^6)
BinaryQF([1,2,3])
EllipticCurve([1,2,3,4,5])
78498 x^2 + 2*x*y + 3*y^2 Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational Field 
CC
CDF
R.<x,y,z> = QQ[x,y,z]
Complex Field with 53 bits of precision Complex Double Field 
a=2*3+7^3

a;a==9;
349 False 
b=a%13
A=13*(a//13)+b
A==a
True 
 R.<x> = PolynomialRing(ZZ,'x')
 R
P = 6*x^4 + 6*x^3 - 6*x^2 - 12*x - 12; P.factor()
Univariate Polynomial Ring in x over Integer Ring 2 * 3 * (x^2 - 2) * (x^2 + x + 1) 
P2 = P.change_ring(QQ)
P2.factor()
(6) * (x^2 - 2) * (x^2 + x + 1) 
P3 = P.change_ring(QQbar)
P3.factor()
(6) * (x - 1.414213562373095?) * (x + 0.500000000000000? - 0.866025403784439?*I) * (x + 0.500000000000000? + 0.866025403784439?*I) * (x + 1.414213562373095?) 
bool(arctan(1+abs(x)) == pi/2 - arctan(1/(1+abs(x))))
False 


bool(arctan(1/sqrt(2))+arctan(sqrt(2))==pi/2)
False 

d=7^2; d; d==7^2
49 True 
 reset(); print('d')
d 
33+
22
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python3.11/site-packages/smc_sagews/sage_server.py", line 1245, in execute compile(block + '\n', File "<string>", line 1 Integer(33)+ ^ SyntaxError: invalid syntax 
1+2+3+4+5+ \
 6+7
28 
1+2+3+4+5+ 
6+7
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python3.11/site-packages/smc_sagews/sage_server.py", line 1245, in execute compile(block + '\n', File "<string>", line 1 Integer(1)+Integer(2)+Integer(3)+Integer(4)+Integer(5)+ ^ SyntaxError: invalid syntax 
10/2
5 
10/3
10/3 
20/30
2/3 
sqrt(20)
2*sqrt(5) 
A1
3 
 20/10; 10/20; sqrt(9); sqrt(20)
2 1/2 3 2*sqrt(5) 
 n(sqrt(20));  N(sqrt(20));  numerical_approx(sqrt(20))
4.47213595499958 4.47213595499958 4.47213595499958 
N(sqrt(20),digits=6);n(sqrt(20),digits=6);  numerical_approx(sqrt(20),prec=6)
4.47214 4.47214 4.5 
sqrt(20).n(); sqrt(20).n(digits=6); sqrt(20).numerical_approx(); sqrt(20).numerical_approx(prec=6)
4.47213595499958 4.47214 4.47213595499958 4.5 
10./20
0.500000000000000 

d=7^2; d; d==7^2
49 True 
reset(); d==7^2
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python3.11/site-packages/smc_sagews/sage_server.py", line 1244, in execute exec( File "", line 1, in <module> NameError: name 'd' is not defined 



sqrt(9); sqrt(20)
3 2*sqrt(5)