src/HOL/Groebner_Basis.thy
 author huffman Tue Mar 27 15:34:36 2012 +0200 (2012-03-27) changeset 47161 8a32c2294498 parent 47160 8ada79014cb2 child 47165 9344891b504b permissions -rw-r--r--
remove duplicate [algebra] declarations
```     1 (*  Title:      HOL/Groebner_Basis.thy
```
```     2     Author:     Amine Chaieb, TU Muenchen
```
```     3 *)
```
```     4
```
```     5 header {* Groebner bases *}
```
```     6
```
```     7 theory Groebner_Basis
```
```     8 imports Semiring_Normalization
```
```     9 uses
```
```    10   ("Tools/groebner.ML")
```
```    11 begin
```
```    12
```
```    13 subsection {* Groebner Bases *}
```
```    14
```
```    15 lemmas bool_simps = simp_thms(1-34)
```
```    16
```
```    17 lemma dnf:
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```    18     "(P & (Q | R)) = ((P&Q) | (P&R))" "((Q | R) & P) = ((Q&P) | (R&P))"
```
```    19     "(P \<and> Q) = (Q \<and> P)" "(P \<or> Q) = (Q \<or> P)"
```
```    20   by blast+
```
```    21
```
```    22 lemmas weak_dnf_simps = dnf bool_simps
```
```    23
```
```    24 lemma nnf_simps:
```
```    25     "(\<not>(P \<and> Q)) = (\<not>P \<or> \<not>Q)" "(\<not>(P \<or> Q)) = (\<not>P \<and> \<not>Q)" "(P \<longrightarrow> Q) = (\<not>P \<or> Q)"
```
```    26     "(P = Q) = ((P \<and> Q) \<or> (\<not>P \<and> \<not> Q))" "(\<not> \<not>(P)) = P"
```
```    27   by blast+
```
```    28
```
```    29 lemma PFalse:
```
```    30     "P \<equiv> False \<Longrightarrow> \<not> P"
```
```    31     "\<not> P \<Longrightarrow> (P \<equiv> False)"
```
```    32   by auto
```
```    33
```
```    34 ML {*
```
```    35 structure Algebra_Simplification = Named_Thms
```
```    36 (
```
```    37   val name = @{binding algebra}
```
```    38   val description = "pre-simplification rules for algebraic methods"
```
```    39 )
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```    40 *}
```
```    41
```
```    42 setup Algebra_Simplification.setup
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```    43
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```    44 use "Tools/groebner.ML"
```
```    45
```
```    46 method_setup algebra = Groebner.algebra_method
```
```    47   "solve polynomial equations over (semi)rings and ideal membership problems using Groebner bases"
```
```    48
```
```    49 declare dvd_def[algebra]
```
```    50 declare dvd_eq_mod_eq_0[symmetric, algebra]
```
```    51 declare mod_div_trivial[algebra]
```
```    52 declare mod_mod_trivial[algebra]
```
```    53 declare div_by_0[algebra]
```
```    54 declare mod_by_0[algebra]
```
```    55 declare zmod_zdiv_equality[symmetric,algebra]
```
```    56 declare zdiv_zmod_equality[symmetric, algebra]
```
```    57 declare div_minus_minus[algebra]
```
```    58 declare mod_minus_minus[algebra]
```
```    59 declare div_minus_right[algebra]
```
```    60 declare mod_minus_right[algebra]
```
```    61 declare div_0[algebra]
```
```    62 declare mod_0[algebra]
```
```    63 declare mod_by_1[algebra]
```
```    64 declare div_by_1[algebra]
```
```    65 declare mod_minus1_right[algebra]
```
```    66 declare div_minus1_right[algebra]
```
```    67 declare mod_mult_self2_is_0[algebra]
```
```    68 declare mod_mult_self1_is_0[algebra]
```
```    69 declare zmod_eq_0_iff[algebra]
```
```    70 declare dvd_0_left_iff[algebra]
```
```    71 declare zdvd1_eq[algebra]
```
```    72 declare zmod_eq_dvd_iff[algebra]
```
```    73 declare nat_mod_eq_iff[algebra]
```
```    74
```
```    75 end
```