Formal power series: Difference between revisions

Line 1,911:

=={{header|Perl 6}}==

Much less broken, <code>sin</code> and <code>cos</code> working. <code>tan</code> a WIP...

<lang perl6>class DerFPS { ... }

class IntFPS { ... }

Line 1,925:

Line 1,923:

sub super($i) { $i.trans('0123456789' => '⁰¹²³⁴⁵⁶⁷⁸⁹') }

my $str = $.coeffs[0].perl;

for 1..$n Z $.coeffs[1..$n] -> $i, $_ {

for flat 1..$n Z $.coeffs[1..$n] -> $p, $c {

when * > 0 { $str ~= " + {(+$_).perl}∙x{super($i)}" }

when $c > 0 { $str ~= " + {(+$c).perl}∙x{super($p)}" }

when * < 0 { $str ~= " - {(-$_).perl}∙x{super($i)}" }

when $c < 0 { $str ~= " - {(-$c).perl}∙x{super($p)}" }

}

$str;

Line 1,970:

Line 1,968:

class IntFPS does FPS {

has FPS $.x;

method coeffs { 0, (0..*).map: { $.x.coeffs[$_] / ($_+1) } }

method coeffs { 0, |(0..*).map: { $.x.coeffs[$_] / ($_+1) } }

}

Line 1,985:

Line 1,983:

# an example of a mixed-type operator:

multi infix:<->(Numeric $x, FPS $y) { ExplicitFPS.new(:coeffs($x, 0 xx *)) - $y }

multi infix:<->(Numeric $x, FPS $y) { ExplicitFPS.new(:coeffs(flat $x, 0 xx 9)) - $y }

# define sine and cosine in terms of each other

Line 1,993:

Line 1,991:

# define tangent in terms of sine and cosine

my $tan = $sin / $cos;

#my $tan = $sin / $cos;

say 'sin(x) ≈ ', $sin.pretty(10);

say 'cos(x) ≈ ', $cos.pretty(10);

say 'tan(x) ≈ ', $tan.pretty(10);</lang>

#say 'tan(x) ≈ ', $tan.pretty(10);</lang>

<pre>sin(x) ≈ 0 + 1/1∙x¹ - 1/6∙x³ + 1/120∙x⁵ - 1/5040∙x⁷ + 1/362880∙x⁹

cos(x) ≈ 1 - 1/2∙x² + 1/24∙x⁴ - 1/720∙x⁶ + 1/40320∙x⁸ - 1/3628800∙x¹⁰

cos(x) ≈ 1 - 1/2∙x² + 1/24∙x⁴ - 1/720∙x⁶ + 1/40320∙x⁸ - 1/3628800∙x¹⁰</pre>

tan(x) ≈ 0/1 + 1/1∙x¹ + 1/3∙x³ + 2/15∙x⁵ + 17/315∙x⁷ + 62/2835∙x⁹~~</pre~~>

=={{header|Phix}}==