# Category:Jq/polynomials.jq

module { "name": "polynomials", "description": "Polynomials as JSON arrays", "version": "0.0.1", "homepage": "https://rosettacode.org/w/index.php?title=Category:Jq/polynomials.jq", "license": "MIT", "author": "pkoppstein at gmail dot com", }; # Except for the above `module` declaration, this module is intended for use with jq, gojq and jaq, # namely the C, Go and Rust implementations of jq. # In this module, a point (x, y) in the Euclidean plane is represented by the JSON array [x, y], # and the polynomial SIGMA a[i] * x^i is represented by the JSON array a. # The canonical representation of a polynomical of degree n has length n+1, # for example 2x is represented by [0,2]. # Unless otherwise indicated, all filters expect the canonical JSON representation # of a polynomial as input. # The canonical form of the possibly non-canonical input polynomial def canonical: if length == 0 then [0] elif length == 1 then . elif .[-1] == 0 then .[:-1]|canonical else . end; # degree of the input polynomial, it being understood that # [] | degree #=> null def degree: canonical | length | if . == 0 then null else . - 1 end; # Evaluate the input polynomial at $x # The input need not be canonical. def eval($x): . as $p | reduce range(0; length) as $i ({power: 1, ans: 0}; .ans += $p[$i] * .power | .power *= $x ) | .ans; # Add two polynomials and emit the canonical result. def add($p1; $p2): ([($p1|length), ($p2|length)]|max) as $max | reduce range(0;$max) as $i ([range(0;$max)|0]; .[$i] = $p1[$i] + $p2[$i]) | canonical ; # Multiply two polynomials. If they are canonical, the result will be too. def multiply($p1; $p2): if $p1 == [0] or $p2 == [0] then [0] else reduce range(0;$p1|length) as $i ( [range(0; ($p1|length) + ($p2|length)) | 0]; reduce range(0;$p2|length) as $j (.; .[$i+$j] += $p1[$i] * $p2[$j])) end; # Multiply the input polynomial by a scalar. def scalarMultiply($x): if $x == 0 then [0] else map($x * .) end; # Divide the input polynomial by a scalar not 0 def scalarDivide($x): map(./$x); # The derivative of an arbitrary polynomial. def derivative: . as $p | if length == 1 then [0] else reduce range(0; length-1) as $i (.[1:]; .[$i] = $p[$i+1] * ($i + 1) ) end; def pp: def digits: tostring | explode[] | [.] | implode | tonumber; def superscript: if . <= 1 then "" else ["\u2070", "\u00b9", "\u00b2", "\u00b3", "\u2074", "\u2075", "\u2076", "\u2077", "\u2078", "\u2079"] as $ss | reduce digits as $d (""; . + $ss[$d] ) end; . as $p | if length == 1 then .[0] | tostring else reduce range(0; length) as $i ([]; if $p[$i] != 0 then (if $i > 0 then "x" else "" end) as $x | ( if $i > 0 and ($p[$i]|length) == 1 then (if $p[$i] == 1 then "" else "-" end) else ($p[$i]|tostring) end ) as $c | . + ["\($c)\($x)\($i|superscript)"] else . end ) | reverse | join("+") | gsub("\\+-"; "-") end ;

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