tcal_rs 0.2.0

Number theory functions library - Rust port of libqalculate number theory module
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/set approximation exact
/set fr 2

5^x = 3
	x = ln(3) / ln(5)

x^3 + x^2 + x = 5
	x = 2 / (3 * cbrt(3 * sqrt(561) - 71)) - 1/3 - cbrt(3 * sqrt(561) - 71) / 3

x^4 + 20x^3 + 150x^2 + 500x + 625 = 0
	x = -5

x^(1/3) + x^(2/3) = 3
	x = 2 * sqrt(13) - 5

ln(x) + x = 3
	x = lambertw(e^3)

2^(3x) + 4x = 5
	x = 5/4 - lambertw(6 * 8^(1/4) * ln(2)) / (3 * ln(2))

x^(-3x) = 2
	x = e^lambertw(-ln(2) / 3) or x = e^lambertw(-ln(2) / 3, -1)

1/3 * sin(3x) - 1/3 = 0
	x = (2/3) * pi * n + pi / 6

2/3 * sin(3x) - 1/3 = 0
	x = (2/3) * pi * n + (5/18) * pi or x = (2/3) * pi * n + pi / 18

sin(x) + cos(x) = 1
	x = 2 pi * n or x = 2 pi * n + pi / 2

sin(x) = 1 + cos(x)
	x = 2 pi * n + pi or x = 2 pi * n + pi / 2

sqrt(2) * cos(3x + pi/6) = 1
	x = (2/3) * pi * n + pi / 36 or x = (2/3) * pi * n - (5/36) * pi

2 * sin(3x/4) = 1
	x = (8/3) * pi * n + (10/9) * pi or x = (8/3) * pi * n + (2/9) * pi

tan(x/4 + pi/3) = sqrt(3)
	x = 4 pi * n

sqrt(3) * sin(x) + cos(x) = sqrt(3)
	x = 2 pi * n + pi / 2 or x = 2 pi * n + pi / 6

sin(x)^2 = sin(x)^3
	x = pi * n or x = 2 pi * n + pi / 2

sin(x) = sin(x/2)
	x = 2 pi * n or x = 4 pi * n + (2/3) * pi or x = 4 pi * n - (2/3) * pi

sin(4x) + cos(2x) = 0
	x = pi * n + (7/12) * pi or x = pi * n - pi / 12 or x = (pi * n) / 2 - pi / 4

/set approximation try exact

newtonsolve(Ei(x) = 3, 1)
	1.397510842

secantsolve(Ei(x) = 3, 1, 4)
	1.397510842

newtonsolve(Ei(x) = 3i, 1)
	-1.160849461 + 1.034283360i

/set unicode 1

x^7 - x^5 + 3x^2 + 5x = 3
	x ≈ 0.4706753153

x^(5x) = 5
	x ≈ 1.284730245

1 * 2^(3x) + 4x = 5
	x ≈ 0.5171781450

x^(-3x) = 2
	x ≈ 0.7280844118 or x ≈ 0.1006083268





#(sqrt(3) + 1) * cos(x) - (sqrt(3) - 1) * sin(x) = 2
#	x = 2 pi * n - pi/3 or x = 2 pi * n + pi/6

#3*sin(7x) - 2*sin(4x) + 3*sin(x) = 0
#	x = 2 pi * n or ...

#tan(x + pi/4) - tan(x - pi/4) = 4
#	x = pi * n - pi/6 or x = pi * n + pi/6

#solve(cos(3x) = sin(x))
#	x = pi * n - 7 pi/8 or x = pi * n - 3 pi/8 or x = pi * n - pi/4

#sin(7x) + sin(3x) = 0
#	x = 2 pi * n or ...

#sin(x) + sin(2x) = sin(3x)
#	x = pi * n or x = 2 pi * n - 2 pi/3 or x = 2 pi * n + 2 pi/3

#sin(2x + pi/4) = cos(pi/6 - x)
#	x = 2 pi * n - 19 pi/36 or ...

#sin(5x) + sin(3x) = sin(8x)
#	x = 2 pi * n or ...

#2(cos(x)^2) + sqrt(3) * sin(x) = 1
#	x = pi * n - pi/3 or ...

#cos(2x) + 4*(sin(x)^2) - cos(x) = 2
#	x = pi * n - pi / 2

#sin(x)^2 + sin(2x)^2 = sin(3x)^2
#	x = pi * n or x = pi * n - x = pi / 2 or x = pi * n - 5 pi/6 or x = pi * n - pi / 6