Dan Bron wrote:
> Given two polynomials, what is the simplest (most succinct) J phrase which
> gives their intersection?
The examples already given are probably the best way to do it for 2
polynomials. If you want the common intersection of several, here is a
non-succinct method.
You can test whether f0,f1,... are all equal by
forming the sum of (fi-fj)^2 and setting it to zero.
ppr =: +//.@(*/) NB. polynomial product
pdiff=: -/@,: NB. polynomial difference
pps =: ppr~ NB. polynomial square
comb=: 4 : 0
k=. i.>:d=.y-x
z=. (d$<i.0 0),<i.1 0
for. i.x do. z=. k ,.&.> ,&.>/\. >:&.> z end.
; z
)
NB. g <list of boxes of coefficients>
NB. returns x-coordinates of common intersection points
g=:3 : 0
a=.>y
c=.2 comb #a
~. (#~ (= +)) 1{:: p. +/ [EMAIL PROTECTED] /"2 c { a
)
a=:0 0 1
b=:2 0 _1
c=:1
]r=:g a;b;c
1 _1
a p. r
1 1
b p. r
1 1
c p. r
1 1
Best wishes,
John
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