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ubuntu2004
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%typeset_mode True
##### úkol číslo 1
CC = ComplexField()
v = x^2+1
#e.expand()
assume(v, "complex")
print(assume(v, "complex"))
v.rectform()
expand(x^2+1, "complex")
Error in lines 4-4 Traceback (most recent call last): File "/cocalc/lib/python3.10/site-packages/smc_sagews/sage_server.py", line 1244, in execute exec( File "", line 1, in <module> File "/ext/sage/9.8/src/sage/symbolic/assumptions.py", line 676, in assume x.assume() File "sage/symbolic/expression.pyx", line 2380, in sage.symbolic.expression.Expression.assume raise TypeError("self (=%s) must be a relational expression" % self) TypeError: self (=x^2 + 1) must be a relational expression 
##### úkol číslo 2
reset()
var('y')
def f(x,y):
    if x<y: return 6
    else: return 5
f(9,2)
f(0,1)
y\displaystyle y
5\displaystyle 5
6\displaystyle 6
##### úkol číslo 3
reset()
var('y')
vyr = y^3 + 2*y + 1 + y/(y+1)^3;vyr
vyr.subs(vyr.operands()[2] == vyr.operands()[2].simplify_full())
y\displaystyle y
y3+2 y+y(y+1)3+1\displaystyle y^{3} + 2 \, y + \frac{y}{{\left(y + 1\right)}^{3}} + 1
y3+2 y+yy3+3 y2+3 y+1+1\displaystyle y^{3} + 2 \, y + \frac{y}{y^{3} + 3 \, y^{2} + 3 \, y + 1} + 1
##### úkol číslo 4
reset()
eqn = cos(x)==0;eqn
res = solve(eqn, x);res
check = eqn.subs(res);check
#chybí další řešení
cos⁡(x)=0\displaystyle \cos\left(x\right) = 0
[x=12 π\displaystyle x = \frac{1}{2} \, \pi]
0=0\displaystyle 0 = 0
#### úkol číslo 5
reset()
var('x,y')
implicit_plot((x - 1)^2+y^2==9, (x,-2,4), (y,-3,4))
(x\displaystyle x, y\displaystyle y)