1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/Tools/isac/Knowledge/EqSystem.thy	Wed Aug 25 16:20:07 2010 +0200
     1.3 @@ -0,0 +1,72 @@
     1.4 +(* equational systems, minimal -- for use in Biegelinie
     1.5 +   author: Walther Neuper
     1.6 +   050826,
     1.7 +   (c) due to copyright terms
     1.8 +
     1.9 +remove_thy"EqSystem";
    1.10 +use_thy"Knowledge/EqSystem";
    1.11 +
    1.12 +use_thy_only"Knowledge/EqSystem";
    1.13 +
    1.14 +remove_thy"Typefix";
    1.15 +use_thy"Knowledge/Isac";
    1.16 +*)
    1.17 +
    1.18 +EqSystem = Rational + Root +
    1.19 +
    1.20 +consts
    1.21 +
    1.22 +  occur'_exactly'_in :: 
    1.23 +   "[real list, real list, 'a] => bool" ("_ from'_ _ occur'_exactly'_in _")
    1.24 +
    1.25 +  (*descriptions in the related problems*)
    1.26 +  solveForVars       :: real list => toreall
    1.27 +  solution           :: bool list => toreall
    1.28 +
    1.29 +  (*the CAS-command, eg. "solveSystem [x+y=1,y=2] [x,y]"*)
    1.30 +  solveSystem        :: "[bool list, real list] => bool list"
    1.31 +
    1.32 +  (*Script-names*)
    1.33 +  SolveSystemScript  :: "[bool list, real list,     bool list] \
    1.34 +						\=> bool list"
    1.35 +                  ("((Script SolveSystemScript (_ _ =))// (_))" 9)
    1.36 +
    1.37 +rules 
    1.38 +(*stated as axioms, todo: prove as theorems
    1.39 +  'bdv' is a constant handled on the meta-level 
    1.40 +   specifically as a 'bound variable'            *)
    1.41 +
    1.42 +  commute_0_equality  "(0 = a) = (a = 0)"
    1.43 +
    1.44 +  (*WN0510 see simliar rules 'isolate_' 'separate_' (by RL)
    1.45 +    [bdv_1,bdv_2,bdv_3,bdv_4] work also for 2 and 3 bdvs, ugly !*)
    1.46 +  separate_bdvs_add   
    1.47 +    "[| [] from_ [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a |]\
    1.48 +		      			   \ ==> (a + b = c) = (b = c + -1*a)"
    1.49 +  separate_bdvs0
    1.50 +    "[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in b; Not (b=!=0)  |]\
    1.51 +		      			   \ ==> (a = b) = (a + -1*b = 0)"
    1.52 +  separate_bdvs_add1  
    1.53 +    "[| some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in c |]\
    1.54 +		      			   \ ==> (a = b + c) = (a + -1*c = b)"
    1.55 +  separate_bdvs_add2
    1.56 +    "[| Not (some_of [bdv_1,bdv_2,bdv_3,bdv_4] occur_in a) |]\
    1.57 +		      			   \ ==> (a + b = c) = (b = -1*a + c)"
    1.58 +
    1.59 +
    1.60 +
    1.61 +  separate_bdvs_mult  
    1.62 +    "[| [] from_ [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a; Not (a=!=0) |]\
    1.63 +		      			   \  ==>(a * b = c) = (b = c / a)"
    1.64 +
    1.65 +  (*requires rew_ord for termination, eg. ord_simplify_Integral;
    1.66 +    works for lists of any length, interestingly !?!*)
    1.67 +  order_system_NxN     "[a,b] = [b,a]"
    1.68 +
    1.69 +(*
    1.70 +remove_thy"EqSystem";
    1.71 +use_thy_only"Knowledge/EqSystem";
    1.72 +use_thy"Knowledge/EqSystem";
    1.73 +use"Knowledge/EqSystem.ML";
    1.74 +  *)
    1.75 +end
    1.76 \ No newline at end of file