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SIGNIFICANT DEPENDENCIES BETWEEN SECTIONS
THE APL LANGUAGE
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abelian group algebra algorithm APL expression APL proposition arrays assume basis bijection binary operation characteristic vector CLASSLIB coefﬁcient coefficients column commutative ring components compute congruence contains Corollary cosets deﬁned deﬁnition denote determine divides entries equivalence relation Euclidean domain example Exercise factor ﬁeld ﬁnd ﬁnite ﬁrst function gcd(a graph greatest common divisor group G group table ideal identity element integral domain inverse irreducible irreducible polynomials isomorphic kernel left R-module LEMMA Let f Let G linearly independent m-by-n matrix minimal polynomial module monic multiplication nonnegative nonzero notation permutation positive integer prime procedure proof of Theorem Prove quotient R-module real numbers right cosets ring homomorphism root row equivalent row operations row reduced row-echelon form Section Show solution subgroup of G submodule subring subset Suppose surjective terminal unique unit variables vector of length vector space Write an APL