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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | )abbrev category LORER LeftOreRing
++ References:
++ Dele06 Noncommutative Symmetric functions and W-polynomials,
++ Bron96a An introduction to pseudo-linear algebra
++ Description:
++ This is the category of left ore rings, that is noncommutative
++ rings without zero divisors where we can compute the least left
++ common multiple.
LeftOreRing() : Category == SIG where
SIG ==> EntireRing with
lcmCoef : (%, %) -> Record(llcm_res : %, coeff1 : %, coeff2 : %)
++ lcmCoef(c1, c2) computes (llcm_res, coeff1, coeff2) such that
++ llcm_res is least left common multiple of c1 and c2
++ and llcm_res = coeff1*c1 = coeff2*c2
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