Rosetta Code

Pell's equation: Difference between revisions

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Line 1,025:
{lambda {:n}
{let { {:n :n}
{:x {BN.intPart {BN.sqrt :n}}} // x=int(sqrt(n))
} {pell.r :n :x :x 1 {* 2 :x} 1 0 0 1}
}}}
Line 1,032:
{def pell.r
{lambda {:n :x :y :z :r :e1 :e2 :f1 :f2}
{let { {:n :n} {:x :x} {:z :z} {:r :r} // no closure ->
{:e1 :e1} {:e2 :e2} {:f1 :f1} {:f2 :f2} // must reassign :(
{:y {BN.- {BN.* :r :z} :y}} // y=rz-y
} {let { {:n :n} {:x :x} {:y :y} {:r :r}
{:e1 :e1} {:e2 :e2} {:f1 :f1} {:f2 :f2}
{:z {BN.intPart {BN./ {BN.- :n {BN.* :y :y}} :z}}} // z=int((n-y*y)/z)
{BN./ {BN.- :n {BN.* :y :y}} :z}}} // z=(n-y*y)//z
} {let { {:n :n} {:x :x} {:y :y} {:z :z}
{:e1 :e1} {:e2 :e2} {:f1 :f1} {:f2 :f2}
{:r {BN.intPart {BN./ {BN.+ :x :y} :z}}} // r= int((x+y)//z)
} {let { {:n :n} {:x :x} {:y :y} {:z :z} {:r :r}
{:e1 :e2} // e1=e2
Line 1,050 ⟶ 1,051:
{:a {BN.+ :e2 {BN.* :x :f2}}} // a=e2+x*f2
{:b :f2} // b=f2
} {if {= {BN.compare {BN.- {BN.* :a :a} // a*a-n*b*b == 1
{BN.* :n {BN.* :b :b}}}
1}
0} // a*a-n*b*b == 1
then {div}x{sup 2} - n*y{sup 2} = 1 for n=:n, x=:a, y=:b
else {pell.r :n :x :y :z :r :e1 :e2 :f1 :f2} // do it again
Line 1,061 ⟶ 1,062:
{S.map pell 61 109 181 277}
->
x2x^2 - n*y2y^2 = 1 for n=61, x=1766319049, y=226153980
x2x^2 - n*y2y^2 = 1 for n=109, x=158070671986249, y=15140424455100
x2x^2 - n*y2y^2 = 1 for n=181, x=2469645423824185801, y=183567298683461940
x2x^2 - n*y2y^2 = 1 for n=277, x=159150073798980475849, y=9562401173878027020
</syntaxhighlight>
 
=={{header|langur}}==
{{trans|D}}
<syntaxhighlight lang="langur">val .fun = f [.b, .b x .c + .a]▼
{{works with|langur|0.10}}
val fun = fn a, b, c: [b, b * c + a]
Prior to 0.10, multi-variable declaration/assignment would use parentheses around variable names and values.
 
val .solvePell = ffn(.n) {▼
▲<syntaxhighlight lang="langur">val .fun = f [.b, .b x .c + .a]
val x = trunc(n ^/ 2)
 
var .y, .z, .r = .x, 1, .x x* 2▼
▲val .solvePell = f(.n) {
valvar .xe1, e2, f1, f2 = truncate1, .n0, ^/0, 21
▲ var .y, .z, .r = .x, 1, .x x 2
var .e1, .e2, .f1, .f2 = 1, 0, 0, 1
 
for {
.y = .r x* .z - .y
.z = (.n - .y x* .y) \ .z
.r = (.x + .y) \ .z
.e1, .e2 = .fun(.e1, .e2, .r)
.f1, .f2 = .fun(.f1, .f2, .r)
val .b, .a = .fun(.e2, .f2, .x)
if .a^2 - .n x* .b^2 == 1: return [.a, .b]
}
}
 
val .C = ffn(.x) {
# format number string with commas
var .neg, .s = "", toString .x -> string
if .s[1] == '-' {
.neg, .s = "-", rest .s -> rest
}
.neg ~ join (",", split (-3, .s))
}
 
for .n in [61, 109, 181, 277, 8941] {
val .x, .y = .solvePell(.n)
writeln $"x² - \.{{n;}}y² = 1 for:\n\tx = \.{{x:.fn C;}}\n\ty = \.{{y:.fn C;}}\n"
}
</syntaxhighlight>
Line 1,871 ⟶ 1,870:
{{libheader|Wren-big}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./big" for BigInt
import "./fmt" for Fmt
 
var solvePell = Fn.new { |n|
Retrieved from "https://rosettacode.org/wiki/Pell%27s_equation"