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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | --Copyright The Numerical Algorithms Group Limited 1991.
-- Examples used in Algebra document: ALGFACOB SCRIPT
)set history on
)clear all
-- The Algebra of Factored Integers
(w,x,y,z): FR INT
x := 2**8 * 78**7 * 111**3 * 74534
y := nilFactor(2,10) * nilFactor(3,20) * nilFactor(5,30)
x*y
w := x+y
expand w
f := x/y
g := (x**9)/y
f*g
h := (f*g)/(g*nilFactor(2,200))
)clear all
-- The Algebra of Factored Polynomials
(u,v,w) : FR POLY INT
u := factor (x**4 - y**4)
v := nilFactor(x-y,2) * nilFactor(x+y,2) * nilFactor(x**2 + y**2,1)
w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * nilFactor(x-y,2)
nthFactor(u,1)
nthFactor(u,2)
nthFactor(u,3)
nthFactor(u,4)
gcd(u,v)
u + v
lcm(u,v)
u * v * w
expand %
u/w
w/(u*v)
%%(-1) * %%(-2)
%%(-1) + %%(-2)
)clear all
-- Some Notes on Using Factored Objects
f : FR INT := 144000
nthFactor(f,1)
nthExponent(f,1)
nthFlag(f,1)
nthFlag(nilFactor(20,4),1)
nthFlag(primeFactor(7,9),1)
factors f
numberOfFactors f
f
reduce(*,[nthFactor(f,i) :: (FR INT) for i in 1..numberOfFactors(f)])
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