Formal power series: Difference between revisions
→{{header|Kotlin}}: Added preamble, code and output.
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=={{header|Kotlin}}==
This is a translation of the Java entry except that it uses fractions rather than double precision floating point numbers. The Frac class from the [[Arithmetic/Rational]] task has been embedded in the program for this purpose.
<lang scala>// version 1.2.10
fun gcd(a: Long, b: Long): Long = if (b == 0L) a else gcd(b, a % b)
class Frac : Comparable<Frac> {
val num: Long
val denom: Long
companion object {
val ZERO = Frac(0, 1)
val ONE = Frac(1, 1)
}
constructor(n: Long, d: Long) {
require(d != 0L)
var nn = n
var dd = d
if (nn == 0L) {
dd = 1
}
else if (dd < 0) {
nn = -nn
dd = -dd
}
val g = Math.abs(gcd(nn, dd))
if (g > 1) {
nn /= g
dd /= g
}
num = nn
denom = dd
}
constructor(n: Int, d: Int) : this(n.toLong(), d.toLong())
operator fun plus(other: Frac) =
Frac(num * other.denom + denom * other.num, other.denom * denom)
operator fun unaryPlus() = this
operator fun unaryMinus() = Frac(-num, denom)
operator fun minus(other: Frac) = this + (-other)
operator fun times(other: Frac) =
Frac(this.num * other.num, this.denom * other.denom)
operator fun rem(other: Frac) = this - Frac((this / other).toLong(), 1) * other
operator fun inc() = this + ONE
operator fun dec() = this - ONE
fun inverse(): Frac {
require(num != 0L)
return Frac(denom, num)
}
operator fun div(other: Frac) = this * other.inverse()
fun abs() = if (num >= 0) this else -this
override fun compareTo(other: Frac): Int {
val diff = this.toDouble() - other.toDouble()
return when {
diff < 0.0 -> -1
diff > 0.0 -> +1
else -> 0
}
}
override fun equals(other: Any?): Boolean {
if (other == null || other !is Frac) return false
return this.compareTo(other) == 0
}
override fun hashCode() = num.hashCode() xor denom.hashCode()
override fun toString() = if (denom == 1L) "$num" else "$num/$denom"
fun toDouble() = num.toDouble() / denom
fun toLong() = num / denom
}
interface Gene {
fun coef(n: Int): Frac
}
class Term(private val gene: Gene) {
private val cache = mutableListOf<Frac>()
operator fun get(n: Int): Frac {
if (n < 0) return Frac.ZERO
if (n >= cache.size) {
for (i in cache.size..n) cache.add(gene.coef(i))
}
return cache[n]
}
}
class FormalPS {
private lateinit var term: Term
private companion object {
const val DISP_TERM = 12
const val X_VAR = "x"
}
constructor() {}
constructor(term: Term) {
this.term = term
}
constructor(polynomial: List<Frac>) :
this(Term(object : Gene {
override fun coef(n: Int) =
if (n < 0 || n >= polynomial.size)
Frac.ZERO
else
polynomial[n]
}))
fun copyFrom(other: FormalPS) {
term = other.term
}
fun inverseCoef(n: Int): Frac {
val res = Array(n + 1) { Frac.ZERO }
res[0] = term[0].inverse()
for (i in 1..n) {
for (j in 0 until i) res[i] += term[i - j] * res[j]
res[i] *= -res[0]
}
return res[n]
}
operator fun plus(other: FormalPS) =
FormalPS(Term(object : Gene {
override fun coef(n: Int) = term[n] + other.term[n]
}))
operator fun minus(other: FormalPS) =
FormalPS(Term(object : Gene {
override fun coef(n: Int) = term[n] - other.term[n]
}))
operator fun times(other: FormalPS) =
FormalPS(Term(object : Gene {
override fun coef(n: Int): Frac {
var res = Frac.ZERO
for (i in 0..n) res += term[i] * other.term[n - i]
return res
}
}))
operator fun div(other: FormalPS) =
FormalPS(Term(object : Gene {
override fun coef(n: Int): Frac {
var res = Frac.ZERO
for (i in 0..n) res += term[i] * other.inverseCoef(n - i)
return res
}
}))
fun diff() =
FormalPS(Term(object : Gene {
override fun coef(n: Int) = term[n + 1] * Frac(n + 1, 1)
}))
fun intg() =
FormalPS(Term(object : Gene {
override fun coef(n: Int) =
if (n == 0) Frac.ZERO else term[n - 1] * Frac(1, n)
}))
override fun toString() = toString(DISP_TERM)
private fun toString(dpTerm: Int): String {
val sb = StringBuilder()
var c = term[0]
if (c != Frac.ZERO) sb.append(c.toString())
for (i in 1 until dpTerm) {
c = term[i]
if (c != Frac.ZERO) {
if (c > Frac.ZERO && sb.length > 0) sb.append(" + ")
sb.append (when {
c == Frac.ONE -> X_VAR
c == -Frac.ONE -> " - $X_VAR"
c.num < 0 -> " - ${-c}$X_VAR"
else -> "$c$X_VAR"
})
if (i > 1) sb.append("^$i")
}
}
if (sb.length == 0) sb.append("0")
sb.append(" + ...")
return sb.toString()
}
}
fun main(args: Array<String>) {
var cos = FormalPS()
val sin = cos.intg()
cos.copyFrom(FormalPS(listOf(Frac.ONE)) - sin.intg())
println("SIN(x) = $sin")
println("COS(x) = $cos")
}</lang>
{{out}}
<pre>
SIN(x) = x - 1/6x^3 + 1/120x^5 - 1/5040x^7 + 1/362880x^9 - 1/39916800x^11 + ...
COS(x) = 1 - 1/2x^2 + 1/24x^4 - 1/720x^6 + 1/40320x^8 - 1/3628800x^10 + ...
</pre>
=={{header|jq}}==
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