author | ballarin |
Thu, 03 Aug 2006 14:57:26 +0200 | |
changeset 20318 | 0e0ea63fe768 |
child 21423 | 6cdd0589aa73 |
permissions | -rw-r--r-- |
20318
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Restructured algebra library, added ideals and quotient rings.
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(* |
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Restructured algebra library, added ideals and quotient rings.
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Ideals for commutative rings |
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Restructured algebra library, added ideals and quotient rings.
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$Id$ |
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Restructured algebra library, added ideals and quotient rings.
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Author: Clemens Ballarin, started 24 September 1999 |
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Restructured algebra library, added ideals and quotient rings.
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*) |
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Restructured algebra library, added ideals and quotient rings.
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0e0ea63fe768
Restructured algebra library, added ideals and quotient rings.
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theory Ideal2 imports Ring2 begin |
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Restructured algebra library, added ideals and quotient rings.
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Restructured algebra library, added ideals and quotient rings.
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consts |
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Restructured algebra library, added ideals and quotient rings.
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ideal_of :: "('a::ring) set => 'a set" |
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Restructured algebra library, added ideals and quotient rings.
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is_ideal :: "('a::ring) set => bool" |
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Restructured algebra library, added ideals and quotient rings.
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is_pideal :: "('a::ring) set => bool" |
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Restructured algebra library, added ideals and quotient rings.
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0e0ea63fe768
Restructured algebra library, added ideals and quotient rings.
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defs |
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Restructured algebra library, added ideals and quotient rings.
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is_ideal_def: "is_ideal I == (ALL a: I. ALL b: I. a + b : I) & |
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Restructured algebra library, added ideals and quotient rings.
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(ALL a: I. - a : I) & 0 : I & |
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Restructured algebra library, added ideals and quotient rings.
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(ALL a: I. ALL r. a * r : I)" |
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Restructured algebra library, added ideals and quotient rings.
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ideal_of_def: "ideal_of S == Inter {I. is_ideal I & S <= I}" |
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Restructured algebra library, added ideals and quotient rings.
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is_pideal_def: "is_pideal I == (EX a. I = ideal_of {a})" |
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Restructured algebra library, added ideals and quotient rings.
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Restructured algebra library, added ideals and quotient rings.
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text {* Principle ideal domains *} |
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Restructured algebra library, added ideals and quotient rings.
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Restructured algebra library, added ideals and quotient rings.
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axclass pid < "domain" |
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Restructured algebra library, added ideals and quotient rings.
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pid_ax: "is_ideal I ==> is_pideal I" |
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Restructured algebra library, added ideals and quotient rings.
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Restructured algebra library, added ideals and quotient rings.
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end |