author chaieb Wed, 31 Oct 2007 12:19:35 +0100 changeset 25250 b3a485b98963 parent 25249 76b9892020d5 child 25251 759bffe1d416
(1) added axiom to ringb and theorems to enable algebra to prove the ideal membership problem; (2) Method algebra now calls algebra_tac which first tries to solve a universal formula, then in case of failure trie to solve the ideal membership problem (see HOL/Tools/Groebner_Basis/groebner.ML)
```--- a/src/HOL/Groebner_Basis.thy	Wed Oct 31 12:19:33 2007 +0100
+++ b/src/HOL/Groebner_Basis.thy	Wed Oct 31 12:19:35 2007 +0100
@@ -301,6 +301,12 @@
thus "False" using add_mul_solve nz cnd by simp
qed

+lemma add_r0_iff: " x = add x a \<longleftrightarrow> a = r0"
+proof-
+qed
+
declare "axioms" [normalizer del]

lemma "axioms" [normalizer
@@ -311,7 +317,8 @@

end

-locale ringb = semiringb + gb_ring
+locale ringb = semiringb + gb_ring +
+  assumes subr0_iff: "sub x y = r0 \<longleftrightarrow> x = y"
begin

declare "axioms" [normalizer del]
@@ -321,11 +328,13 @@
semiring rules: semiring_rules
ring ops: ring_ops
ring rules: ring_rules
"ringb add mul pwr r0 r1 sub neg" by fact

end

+
lemma no_zero_divirors_neq0:
assumes az: "(a::'a::no_zero_divisors) \<noteq> 0"
and ab: "a*b = 0" shows "b = 0"
@@ -349,7 +358,6 @@
thus "w = x"  by simp
qed

-
declaration {* normalizer_funs @{thm class_ringb.axioms} *}

interpretation natgb: semiringb
@@ -386,7 +394,8 @@
semiring rules: semiring_rules
ring ops: ring_ops
ring rules: ring_rules
"fieldgb add mul pwr r0 r1 sub neg divide inverse" by unfold_locales
end

@@ -424,8 +433,8 @@
((Scan.optional (keyword addN |-- thms) []) --
(Scan.optional (keyword delN |-- thms) [])) src
#> (fn ((add_ths, del_ths), ctxt) =>
-       Method.SIMPLE_METHOD' (Groebner.ring_tac add_ths del_ths ctxt))
+       Method.SIMPLE_METHOD' (Groebner.algebra_tac add_ths del_ths ctxt))
end
-*} "solve polynomial equations over (semi)rings using Groebner bases"
+*} "solve polynomial equations over (semi)rings and ideal membership problems using Groebner bases"

end```