Formal power series: Difference between revisions
Content added Content deleted
(Added Wren) |
(→{{header|Wren}}: Corrected previously unused inverseCoef method and added more examples.) |
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| Line 3,175: | Line 3,175: | ||
var res = List.filled(n+1, null) |
var res = List.filled(n+1, null) |
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res[0] = _term[0].inverse |
res[0] = _term[0].inverse |
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if (n > 0) { |
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for ( |
for (i in 1..n) { |
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res[i] = Rat.zero |
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for (j in 0...i) res[i] = res[i] + _term[i - j] * res[j] |
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res[i] = -res[0] * res[i] |
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} |
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} |
} |
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return res[n] |
return res[n] |
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| Line 3,224: | Line 3,227: | ||
_fps = fps |
_fps = fps |
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_other = other |
_other = other |
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} |
} |
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coef(n) { |
coef(n) { |
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var res = Rat.zero |
var res = Rat.zero |
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| Line 3,254: | Line 3,257: | ||
var c = _term[0] |
var c = _term[0] |
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Rat.showAsInt = true |
Rat.showAsInt = true |
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var supers = ["⁰", "¹", "²", "³", "⁴", "⁵", "⁶", "⁷", "⁸", "⁹", "¹⁰", "¹¹"] |
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if (c != Rat.zero) sb = sb + c.toString |
if (c != Rat.zero) sb = sb + c.toString |
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for (i in 1...dpTerm) { |
for (i in 1...dpTerm) { |
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| Line 3,264: | Line 3,268: | ||
(c == Rat.minusOne) ? " - %(xvar)" : |
(c == Rat.minusOne) ? " - %(xvar)" : |
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(c.num < 0) ? " - %(-c)%(xvar)" : "%(c)%(xvar)") |
(c.num < 0) ? " - %(-c)%(xvar)" : "%(c)%(xvar)") |
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if (i > 1) sb = sb + " |
if (i > 1) sb = sb + "%(supers[i])" |
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} |
} |
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} |
} |
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| Line 3,277: | Line 3,281: | ||
var cos = FormalPS.new() |
var cos = FormalPS.new() |
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var sin = cos.intg() |
var sin = cos.intg() |
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var tan = sin/cos |
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cos.copyFrom(FormalPS.fromPolynomial([Rat.one]) - sin.intg()) |
cos.copyFrom(FormalPS.fromPolynomial([Rat.one]) - sin.intg()) |
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System.print(" |
System.print("sin(x) = %(sin)") |
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System.print(" |
System.print("cos(x) = %(cos)") |
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System.print("tan(x) = %(tan)") |
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System.print("sin'(x) = %(sin.diff())") |
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var exp = FormalPS.new() |
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exp.copyFrom(FormalPS.fromPolynomial([Rat.one]) + exp.intg()) |
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System.print("exp(x) = %(exp)")</lang> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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sin(x) = x - 1/6x³ + 1/120x⁵ - 1/5040x⁷ + 1/362880x⁹ - 1/39916800x¹¹ + ... |
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cos(x) = 1 - 1/2x² + 1/24x⁴ - 1/720x⁶ + 1/40320x⁸ - 1/3628800x¹⁰ + ... |
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tan(x) = x + 1/3x³ + 2/15x⁵ + 17/315x⁷ + 62/2835x⁹ + 1382/155925x¹¹ + ... |
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sin'(x) = 1 - 1/2x² + 1/24x⁴ - 1/720x⁶ + 1/40320x⁸ - 1/3628800x¹⁰ + ... |
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exp(x) = 1 + x + 1/2x² + 1/6x³ + 1/24x⁴ + 1/120x⁵ + 1/720x⁶ + 1/5040x⁷ + 1/40320x⁸ + 1/362880x⁹ + 1/3628800x¹⁰ + 1/39916800x¹¹ + ... |
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</pre> |
</pre> |
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