Pell's equation: Difference between revisions
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Line 1,018:
x^2 - 181 * y^2 = 1 for x = 2,469,645,423,824,185,801 and y = 183,567,298,683,461,940
x^2 - 277 * y^2 = 1 for x = 159,150,073,798,980,475,849 and y = 9,562,401,173,878,027,020</pre>
=={{header|Lambdatalk}}==
Computing big numbers requires the lib_BN library.
{def pell
{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}
}}}
-> pell
{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=(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= (x+y)//z
} {let { {:n :n} {:x :x} {:y :y} {:z :z} {:r :r}
{:e1 :e2} // e1=e2
{:e2 {BN.+ {BN.* :r :e2} :e1}} // e2=r*e2+e1
{:f1 :f2} // f1=f2
{:f2 {BN.+ {BN.* :r :f2} :f1}} // f2=r*f2+f1
} {let { {:n :n} {:x :x} {:y :y} {:z :z} {:r :r}
{:e1 :e1} {:e2 :e2} {:f1 :f1} {:f2 :f2}
{:a {BN.+ :e2 {BN.* :x :f2}}} // a=e2+x*f2
{:b :f2} // b=f2
} {if {= {BN.compare {BN.- {BN.* :a :a}
{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
}}}}}}}}
-> pell.r
{S.map pell 61 109 181 277}
->
x^2 - n*y^2 = 1 for n=61, x=1766319049, y=226153980
x^2 - n*y^2 = 1 for n=109, x=158070671986249, y=15140424455100
x^2 - n*y^2 = 1 for n=181, x=2469645423824185801, y=183567298683461940
x^2 - n*y^2 = 1 for n=277, x=159150073798980475849, y=9562401173878027020
</syntaxhighlight>
=={{header|langur}}==
{{trans|D}}
<syntaxhighlight lang="langur">val .fun = fn(.a, .b, .c) { [.b, .b * .c + .a] }
▲<syntaxhighlight lang="langur">val .fun = f [.b, .b x .c + .a]
val .solvePell =
val .x =
var .y, .z, .r = .x, 1, .x
var .e1, .e2, .f1, .f2 = 1, 0, 0, 1
for {
.y = .r
.z = (.n - .y
.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
}
}
val .C =
# format number string with commas
var .neg, .s = "",
if .s[1] == '-' {
.neg, .s = "-", rest .s
Line 1,053 ⟶ 1,099:
for .n in [61, 109, 181, 277, 8941] {
val .x, .y = .solvePell(.n)
writeln $"x² - \.n;y² = 1 for:\n\tx = \.x:
}
</syntaxhighlight>
Line 1,823 ⟶ 1,869:
{{libheader|Wren-big}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
var solvePell = Fn.new { |n|
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