Polynomial long division: Difference between revisions
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Compute: (2x^7 - 24x^6 + 2x^5 - 108x^4 + 3x^3 - 120x^2 - 126) / (2x^4 + 2x^2 + 3) = x^3 - 12x^2 - 42 reminder 0
Test: (x^3 - 12x^2 - 42) * (2x^4 + 2x^2 + 3) + (0) = 2x^7 - 24x^6 + 2x^5 - 108x^4 + 3x^3 - 120x^2 - 126
</pre>
=={{header|jq}}==
{{works with|jq}}
'''Also works with gojq, the Go implementation of jq, and with fq'''
'''Adapted from the second version in the [[#Wren|Wren]] entry.'''
In this entry, polynomials are represented by JSON arrays exactly as
in the task description; that is, using jq notation, `.[$i]` corresponds to
the coefficient of {\displaystyle x^i}.
<syntaxhighlight lang=jq>
# Emit the canonical form of the polynomical represented by the input array
def canonical:
if length == 0 then .
elif .[-1] == 0 then .[:-1]|canonical
else .
end;
# string representation
def poly2s: "Polynomial(\(join(",")))";
# Polynomial division
# Output [ quotient, remainder]
def divrem($divisor):
($divisor|canonical) as $divisor
| { curr: canonical}
| .base = ((.curr|length) - ($divisor|length))
| until( .base < 0;
(.curr[-1] / $divisor[-1]) as $res
| .result += [$res]
| .curr |= .[0:-1]
| reduce range (0;$divisor|length-1) as $i (.;
.curr[.base + $i] += (- $res * $divisor[$i]) )
| .base += -1
)
| (.result | reverse), (.curr | canonical)];
def demo($num; $den):
{$num, $den,
res: ($num | divrem($den)) }
| .quot = .res[0]
| .rem = .res[1]
| del(.res)
| map_values(poly2s)
| "\(.num) / \(.den) = \(.quot) remainder \(.rem)";
demo( [-42, 0, -12, 1]; [-3, 1, 0, 0])
</syntaxhighlight>
{{output}}
<pre>
Polynomial(-42,0,-12,1) / Polynomial(-3,1,0,0) = Polynomial(-27,-9,1)
remainder Polynomial(-123)
</pre>
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