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powers.m2
-- Copyright 1993-1999 by Daniel R. Grayson needs "methods.m2" needs "remember.m2" binomial(ZZ, ZZ) := ZZ => binomial0 binomial(Number, Number) := ZZ => memoize ( (n,i) -> ( if instance(numeric n, CC) or instance(numeric i, CC) then error "not yet implemented for complex numbers"; if instance(n, RRi) or instance(i, RRi) then error "not yet implemented for real intervals"; if i < 0 then 0 else if i === 0 then 1 else if n > 0 then ( if i > n then 0 else n! / (i! * (n-i)!) ) else if n === 0 then 0 else (-1)^i * binomial(-n+i-1,i) ) ) binomial(RingElement, ZZ):= (q,n)-> if n<0 then error "binomial undefined" else ( product(n, i-> q-i) * (promote(product(n, i->1+i),ring q))^(-1)) -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/m2 " -- End:
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