3847.sagews

def sveikasis(skaicius):
    sveikoji = int(skaicius)
    sveikoji_bin = bin(sveikoji)
    return sveikoji_bin[2:]
def trupmena(skaicius):
    while True:
        skaicius *= 2
        yield int(skaicius)
        if skaicius >= 1:
            skaicius -= 1
def eile(skaicius):
    if skaicius >= 1:
        return len(sveikasis(skaicius))-1
    else:
        temp = 0
        po_kablelio = trupmena(skaicius-int(skaicius))
        for i in range(2048):
            temp -= 1
            if po_kablelio.next() == 1:
                break
        return temp

def mantise(skaicius):
    temp = sveikasis(skaicius)[1:]
    trupmenoj = trupmena(skaicius-int(skaicius))
    for i in range(23-len(temp)):
        temp += str(trupmenoj.next())
    return temp
print(mantise(12.34))

10001010111000010100011

bin(eile(12.34)+127)

'0b10000010'

def trumpas(skaicius):
    eilute = ''
    if skaicius > 0:
        eilute += '0'
    else:
        eilute += '1'
        skaicius *= -1

    charakteristika = eile(skaicius)+127
    charakteristika_bin = bin(charakteristika)[2:]
    eilute += '0'*(8-len(charakteristika_bin))
    eilute += charakteristika_bin
    eilute += mantise(skaicius)
    return eilute

hex(int(trumpas(12.34), 2))

'0x414570a3'

mantise(0.34)

'01010111000010100011110'

trumpas(4.25)

'01000000100010000000000000000000'

mantise(4.25/8)

'10001000000000000000000'

mantise(0.25)

'01000000000000000000000'

bin(130)

'0b10000010'

12.34/8

1.54250000000000

listas = trupmena(.34)
temp = ''
for i in range(23):
    temp += str(listas.next())
temp

'01010111000010100011110'

def mantise_ilg(skaicius):
    temp = sveikasis(skaicius)[1:]
    trupmenoj = trupmena(skaicius-int(skaicius))
    for i in range(52-len(temp)):
        temp += str(trupmenoj.next())
    return temp

def ilgas(skaicius):
    eilute = ''
    if skaicius > 0:
        eilute += '0'
    else:
        eilute += '1'
        skaicius *= -1

    charakteristika = eile(skaicius)+1023
    charakteristika_bin = bin(charakteristika)[2:]
    eilute += '0'*(11-len(charakteristika_bin))
    eilute += charakteristika_bin
    eilute += mantise_ilg(skaicius)
    return eilute

hex(int(ilgas(12.34),2))

'0x4028ae147ae147ae'

var('x y')
solve((x-3*y+4)/sqrt(10)==0, y)

[y == 1/3*x + 4/3]

var('x y r')
r = 2
equ1 = abs((x-3*y+4)/sqrt(10))==r
equ2 = sqrt((-1-x)**2+(1-y)**2)==r
a=solve([equ1, equ2], x, y)
pretty_print(a)

$\renewcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x = -\frac{1}{5} \, \sqrt{10} - 1, y = \frac{3}{5} \, \sqrt{2} \sqrt{5} + 1\right], \left[x = \frac{1}{5} \, \sqrt{10} - 1, y = -\frac{3}{5} \, \sqrt{2} \sqrt{5} + 1\right]\right]$

var('y')
r=2
a=r==(sqrt(10)*r+3*y-4)**2+2*(sqrt(10)*r+3*y-4)+1+y**2-2*y+1

a

2 == (3*y + 2*sqrt(10) - 4)^2 + y^2 + 4*y + 4*sqrt(10) - 6

pretty_print(expand(a))

$\renewcommand{\Bold}[1]{\mathbf{#1}}2 = 4 \, \sqrt{10} + y^{2} + 12 \, \sqrt{10} y - 16 \, \sqrt{10} + 9 \, y^{2} - 20 \, y + 50$

b=expand(a)
b=simplify(b)
pretty_print(b)

$\renewcommand{\Bold}[1]{\mathbf{#1}}2 = -12 \, \sqrt{10} + 10 \, y^{2} + 12 \, \sqrt{10} y - 20 \, y + 50$

pretty_print(solve(b, y))

$\renewcommand{\Bold}[1]{\mathbf{#1}}\left[y = -\frac{1}{5} i \, \sqrt{5} - \frac{3}{5} \, \sqrt{10} + 1, y = \frac{1}{5} i \, \sqrt{5} - \frac{3}{5} \, \sqrt{10} + 1\right]$

400/16

25

400/25

16

25+16

41