91 lines
2.2 KiB
Factor
91 lines
2.2 KiB
Factor
! Copyright (C) 2008 Doug Coleman.
|
|
! See http://factorcode.org/license.txt for BSD license.
|
|
USING: arrays kernel make math math.order math.vectors sequences shuffle
|
|
splitting vectors ;
|
|
IN: math.polynomials
|
|
|
|
! Polynomials are vectors with the highest powers on the right:
|
|
! { 1 1 0 1 } -> 1 + x + x^3
|
|
! { } -> 0
|
|
|
|
: powers ( n x -- seq )
|
|
#! Output sequence has n elements, { 1 x x^2 x^3 ... }
|
|
<array> 1 [ * ] accumulate nip ;
|
|
|
|
<PRIVATE
|
|
|
|
: 2pad-left ( p p n -- p p ) [ 0 pad-left ] curry bi@ ;
|
|
: 2pad-right ( p p n -- p p ) [ 0 pad-right ] curry bi@ ;
|
|
: pextend ( p p -- p p ) 2dup [ length ] bi@ max 2pad-right ;
|
|
: pextend-left ( p p -- p p ) 2dup [ length ] bi@ max 2pad-left ;
|
|
: unempty ( seq -- seq ) [ { 0 } ] when-empty ;
|
|
: 2unempty ( seq seq -- seq seq ) [ unempty ] bi@ ;
|
|
|
|
PRIVATE>
|
|
|
|
: p= ( p p -- ? ) pextend = ;
|
|
|
|
: ptrim ( p -- p )
|
|
dup length 1 = [ [ zero? ] trim-right ] unless ;
|
|
|
|
: 2ptrim ( p p -- p p ) [ ptrim ] bi@ ;
|
|
: p+ ( p p -- p ) pextend v+ ;
|
|
: p- ( p p -- p ) pextend v- ;
|
|
: n*p ( n p -- n*p ) n*v ;
|
|
|
|
! convolution
|
|
: pextend-conv ( p p -- p p )
|
|
#! extend to: p_m + p_n - 1
|
|
2dup [ length ] bi@ + 1- 2pad-right [ >vector ] bi@ ;
|
|
|
|
: p* ( p p -- p )
|
|
#! Multiply two polynomials.
|
|
2unempty pextend-conv <reversed> dup length
|
|
[ over length pick <slice> pick [ * ] 2map sum ] map 2nip reverse ;
|
|
|
|
: p-sq ( p -- p-sq )
|
|
dup p* ;
|
|
|
|
<PRIVATE
|
|
|
|
: p/mod-setup ( p p -- p p n )
|
|
2ptrim
|
|
2dup [ length ] bi@ -
|
|
dup 1 < [ drop 1 ] when
|
|
[ over length + 0 pad-left pextend ] keep 1+ ;
|
|
|
|
: /-last ( seq seq -- a )
|
|
#! divide the last two numbers in the sequences
|
|
[ peek ] bi@ / ;
|
|
|
|
: (p/mod) ( p p -- p p )
|
|
2dup /-last
|
|
2dup , n*p swapd
|
|
p- >vector
|
|
dup pop* swap rest-slice ;
|
|
|
|
PRIVATE>
|
|
|
|
: p/mod ( a b -- / mod )
|
|
p/mod-setup [ [ (p/mod) ] times ] V{ } make
|
|
reverse nip swap 2ptrim pextend ;
|
|
|
|
: (pgcd) ( b a y x -- a d )
|
|
dup V{ 0 } clone p= [
|
|
drop nip
|
|
] [
|
|
tuck p/mod [ pick p* swap [ swapd p- ] dip ] dip (pgcd)
|
|
] if ;
|
|
|
|
: pgcd ( p p -- p q )
|
|
swap V{ 0 } clone V{ 1 } clone 2swap (pgcd) [ >array ] bi@ ;
|
|
|
|
: pdiff ( p -- p' )
|
|
#! Polynomial derivative.
|
|
dup length v* { 0 } ?head drop ;
|
|
|
|
: polyval ( p x -- p[x] )
|
|
#! Evaluate a polynomial.
|
|
[ dup length ] dip powers v. ;
|
|
|