ukol1.sagews

%html
Priklad 1

Priklad 1

var('y')#deklarace promennych

y

((3*x^2+5*x*y-2*y^2)*(x-y)^3)^2 

(3*x^2 + 5*x*y - 2*y^2)^2*(x - y)^6

expand(_).show()#LaTeXova podoba vystupu

$\displaystyle 9 \, x^{10} - 24 \, x^{9} y - 32 \, x^{8} y^{2} + 172 \, x^{7} y^{3} - 146 \, x^{6} y^{4} - 188 \, x^{5} y^{5} + 484 \, x^{4} y^{6} - 428 \, x^{3} y^{7} + 193 \, x^{2} y^{8} - 44 \, x y^{9} + 4 \, y^{10}$

factor(_).show()

$\displaystyle {\left(3 \, x - y\right)}^{2} {\left(x + 2 \, y\right)}^{2} {\left(x - y\right)}^{6}$

%html
Priklad 2

Priklad 2

((x^2-1)/(3*x^3-11*x^2+13*x-5)).partial_fraction().show()

$\displaystyle \frac{4}{3 \, x - 5} - \frac{1}{x - 1}$

integrate(x^2*sin(x),x).show()#pokud zacnu psat nazev prikazu a dam tabulator, ukazou se mi moznosti, za vyraz dat jeste tecku

$\displaystyle -{\left(x^{2} - 2\right)} \cos\left(x\right) + 2 \, x \sin\left(x\right)$