2629-Basic examples of Sage.sagews

Basic examples of Sage

Multiplying Two Numbers

$\displaystyle 24536*5768$

24536*5768

Evaluating Sine

$\displaystyle \sin \frac {\pi}2$

sin(pi/2)

Evaluating Natural Logarithm

$\displaystyle \ln 2$

log(2)

Finding a Numerical Approximation to Natural Logarithm

$\displaystyle \ln 2$

n(log(2))

Finding a Limit

$\displaystyle \lim_{x \to 0} \frac {\sin x}x$

limit(sin(x)/x, x=0)

Evaluating a Sum

$\displaystyle \sum_1^5 \sqrt{n^2 +1}$

sum(sqrt(n^2 +1) for n in [1..5])

Finding a Numerical Approximation to a Sum

$\displaystyle \sum_1^5 \sqrt{n^2 +1}$

n(sum(sqrt(n^2 +1) for n in [1..5]))

Finding the Derivative of a Function of One Variable

$\displaystyle \frac d{dx} [\sin (x^2 + 6x - 2)]$

diff(sin(x^2 + 6*x - 2), x)

Finding the Indefinite Integral of a Function of One Variable

$\displaystyle \int \ln x\, dx$

integral(ln(x), x)

Finding the Definite Integral of a Function of One Variable

$\displaystyle \int_3^5 \ln x\, dx$

integral(ln(x), x, 3, 5)

Finding a Numerical Approximation to a Definite Integral of a Function of One Variable

$\displaystyle \int_3^5 \ln x\, dx$

n(integral(ln(x), x, 3, 5))

Plotting the Graph of a Function of One Variable

$\displaystyle f(x) = 4x - 6x^{\frac 23} + 2$

x = var('x')
plot(4*x - 6*((x^2)^(1/3)) + 2, (x,-5,5))

Plotting the Graphs of Two Functions of One Variable

The graph of $\displaystyle f(x) = x^2$ is in blue.

The graph of $\displaystyle g(x) = - \cos x$ is in red.

x = var('x')
P = plot(x^2, (x,-5,5))
Q = plot(-cos(x), (x,-5,5), color='red')
P + Q