1035.sagews

Solve the equations in Sage
Veikko Keränen -2009
Rovaniemi University of Applied Sciences
[e-mail]
Edited by Shijing Zhang
[e-mail]

For example there is a linear polynomial, we can calculate the equation like this

solve(x^2+x-12==0,x)

[x == 3, x == -4]

solve(x^4-2*x^2+1==0,x)

[x == -1, x == 1]

Also there is another way to solve like this

x=var('x')

eqn=10*x==1000

eqn.show()

10 \, x = 1000

\newcommand{\Bold}[1]{\mathbf{#1}}\hbox{}

eqn1=eqn.multiply_both_sides(1/10)

eqn1.show()

x = 100

\newcommand{\Bold}[1]{\mathbf{#1}}\hbox{}

If there are more than one variable, please do like this

x,y=var('x,y')

solve([x+y==6, x-y==4],x,y)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x = 5, y = 1\right]\right]

solve([x+y==10, x-y==3],x,y)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x = \left(\frac{13}{2}\right), y = \left(\frac{7}{2}\right)\right]\right]

solve(2^x==6,x)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \frac{\log\left(6\right)}{\log\left(2\right)}\right]

Differential equation

diff(x^2,x)

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, x

diff(x^3,x)

\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2}

diff(sin(2*x),x)

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \cos\left(2 \, x\right)

Limit value

var('x')

\newcommand{\Bold}[1]{\mathbf{#1}}x

f=(x**2+x-6)/(x-2)

f.show()

\frac{{(x^{2} + x - 6)}}{{(x - 2)}}

\newcommand{\Bold}[1]{\mathbf{#1}}\hbox{}

f.limit(x=2)

\newcommand{\Bold}[1]{\mathbf{#1}}5

f=(sqrt(x+2)-3)/(x-7)

f.show()

\frac{{(\sqrt{x + 2} - 3)}}{{(x - 7)}}

\newcommand{\Bold}[1]{\mathbf{#1}}\hbox{}

f.limit(x=7)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{6}

f.numerator()

\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{x + 2} - 3

fn=f.numerator()*(sqrt(x+2)+3)

fn.show()

{(\sqrt{x + 2} - 3)} {(\sqrt{x + 2} + 3)}

\newcommand{\Bold}[1]{\mathbf{#1}}\hbox{}

fn.expand().show()

x - 7

\newcommand{\Bold}[1]{\mathbf{#1}}\hbox{}

f.denominator()

\newcommand{\Bold}[1]{\mathbf{#1}}x - 7