(* testexamples for Poly, polynomials

    author: Matthias Goldgruber 2003

    (c) due to copyright terms

 use"../smltest/IsacKnowledge/poly.sml";

 use"poly.sml";

 ****************************************************************.*)

 (******************************************************************

   WN060104 'SPB' came into 'exp_IsacCore_Simp_Poly_Book.xml'

 	   'SPO' came into 'exp_IsacCore_Simp_Poly_Other.xml'

 *******************************************************************)

 "-----------------------------------------------------------------";

 "table of contents -----------------------------------------------";

 "-----------------------------------------------------------------";

 "-------- investigate new uniary minus ---------------------------";

 "-------- Bsple aus Schalk I -------------------------------------";

 "-------- Script 'simplification for_polynomials' ----------------";

 "-------- check pbl  'polynomial simplification' -----------------";

 "-------- me 'polynomial simplification' Schalk I p.63 No.267b ---";

 "-------- norm_Poly NOT COMPLETE ---------------------------------";

 "-------- ord_make_polynomial ------------------------------------";

 "-----------------------------------------------------------------";

 "-----------------------------------------------------------------";

 "-----------------------------------------------------------------";

 "-------- investigate new uniary minus ---------------------------";

 "-------- investigate new uniary minus ---------------------------";

 "-------- investigate new uniary minus ---------------------------";

 val t = (#prop o rep_thm) real_diff_0; (*"0 - ?x = - ?x"*)

 atomty t;

 (*** -------------

 *** Const ( Trueprop, bool => prop)

 *** . Const ( op =, [real, real] => bool)

 *** . . Const ( op -, [real, real] => real)

 *** . . . Const ( 0, real)

 *** . . . Var ((x, 0), real)

 *** . . Const ( uminus, real => real)

 *** . . . Var ((x, 0), real)              *)

 val t = (term_of o the o (parse thy)) "-1";

 atomty t;

 (*** -------------

 *** Free ( -1, real)                      *)

 val t = (term_of o the o (parse thy)) "- 1";

 atomty t;

 (*** -------------

 *** Const ( uminus, real => real)

 *** . Free ( 1, real)                     *)

 val t = (term_of o the o (parse thy)) "-x"; (*1-x  syntyx error !!!*)

 atomty t;

 (**** -------------

 *** Free ( -x, real)*)

 val t = (term_of o the o (parse thy)) "- x";

 atomty t;

 (**** -------------

 *** Free ( -x, real) !!!!!!!!!!!!!!!!!!!!!!!! is the same !!!*)

 val t = (term_of o the o (parse thy)) "-(x)";

 atomty t;

 (**** -------------

 *** Free ( -x, real)*)

 "-------- Bsple aus Schalk I -------------------------------------";

 "-------- Bsple aus Schalk I -------------------------------------";

 "-------- Bsple aus Schalk I -------------------------------------";

 (*SPB Schalk I p.63 No.267b*)

 val t = str2term

  	    "(5*x^^^2 + 3) * (2*x^^^7 + 3) - (3*x^^^5 + 8) * (6*x^^^4 - 1)";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = 

 "17 + 15 * x ^^^ 2 + -48 * x ^^^ 4 + 3 * x ^^^ 5 + 6 * x ^^^ 7 + -8 * x ^^^ 9"

 then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 1";

 (*SPB Schalk I p.63 No.275b*)

  val t = str2term

  	     "(3*x^^^2 - 2*x*y + y^^^2) * (x^^^2 - 2*y^^^2)";

  val Some (t,_) = rewrite_set_ thy false make_polynomial t;

  term2str t;

 if (term2str t) = 

 "3 * x ^^^ 4 + -2 * x ^^^ 3 * y + -5 * x ^^^ 2 * y ^^^ 2 + \

 \4 * x * y ^^^ 3 +\n-2 * y ^^^ 4"

 then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 2";

 (*SPB Schalk I p.63 No.279b*)

  val t = str2term

  	     "(x-a)*(x-b)*(x-c)*(x-d)";

  val Some (t,_) = rewrite_set_ thy false make_polynomial t;

  term2str t;

 (* Richtig! *)

 if (term2str t) = 

 "a * b * c * d + -1 * a * b * c * x + -1 * a * b * d * x + a * b * x ^^^ 2 +\n-1 * a * c * d * x +\na * c * x ^^^ 2 +\na * d * x ^^^ 2 +\n-1 * a * x ^^^ 3 +\n-1 * b * c * d * x +\nb * c * x ^^^ 2 +\nb * d * x ^^^ 2 +\n-1 * b * x ^^^ 3 +\nc * d * x ^^^ 2 +\n-1 * c * x ^^^ 3 +\n-1 * d * x ^^^ 3 +\nx ^^^ 4"

 then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 3";

 (*SPB Schalk I p.63 No.291*)

  val t = str2term

  "(5+96*x^^^3+8*x*(-4+(7- 3*x)*4*x))*(5*(2- 3*x)- (-15*x*(-8*x- 5)))";

  val Some (t,_) = rewrite_set_ thy false make_polynomial t;

  term2str t;

 if (term2str t) = 

 "50 + -770 * x + 4520 * x ^^^ 2 + -16320 * x ^^^ 3 + -26880 * x ^^^ 4"

 then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 4";

 (*SPB Schalk I p.64 No.295c*)

  val t = str2term

  "(13*a^^^4*b^^^9*c - 12*a^^^3*b^^^6*c^^^9)^^^2";

  val Some (t,_) = rewrite_set_ thy false make_polynomial t;

  term2str t;

 if (term2str t) = 

 "169 * a ^^^ 8 * b ^^^ 18 * c ^^^ 2 + -312 * a ^^^ 7 * b ^^^ 15 * c ^^^ 10\

 \ +\n144 * a ^^^ 6 * b ^^^ 12 * c ^^^ 18"

 then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 5";

 (*SPB Schalk I p.64 No.299a*)

  val t = str2term

  "(x - y)*(x + y)";

  val Some (t,_) = rewrite_set_ thy false make_polynomial t;

  term2str t;

 if (term2str t) = 

 "x ^^^ 2 + -1 * y ^^^ 2"

 then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 6";

 (*SPB Schalk I p.64 No.300c*)

  val t = str2term

  "(3*x^^^2*y - 1)*(3*x^^^2*y + 1)";

  val Some (t,_) = rewrite_set_ thy false make_polynomial t;

  term2str t;

 if (term2str t) = 

 "-1 + 9 * x ^^^ 4 * y ^^^ 2"

 then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 7";

 (*SPB Schalk I p.64 No.302*)

 val t = str2term

  "(13*x^^^2 + 5)*(13*x^^^2 - 5) - (5*x^^^2 + 3)*(5*x^^^2 - 3) - (12*x^^^2 + 4)*(12*x^^^2 - 4)";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "0" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 8";

 (* Bei Berechnung sollte 3 mal real_plus_minus_binom1_p aus expand_poly verwendet werden *)

 (*SPB Schalk I p.64 No.306a*)

 val t = str2term "((x^^^2 + 1)*(x^^^2 - 1))^^^2";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "1 + 2 * x ^^^ 4 + 2 * -2 * x ^^^ 4 + x ^^^ 8" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial: not confluent \

 		 \2 * x ^^^ 4 + 2 * -2 * x ^^^ 4 = -2 * x ^^^ 4 works again";

 (*WN071729 when reducing "rls reduce_012_" for Schaerding,

 the above resulted in the term below ... but reduces from then correctly*)

 val t = str2term "1 + 2 * x ^^^ 4 + 2 * -2 * x ^^^ 4 + x ^^^ 8";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "1 + -2 * x ^^^ 4 + x ^^^ 8" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 9b";

 (*SPB Schalk I p.64 No.296a*)

 val t = str2term "(x - a)^^^3";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "-1 * a ^^^ 3 + 3 * a ^^^ 2 * x + -3 * a * x ^^^ 2 + x ^^^ 3"

 then () else raise error "poly.sml: diff.behav. in make_polynomial 10";

 (*SPB Schalk I p.64 No.296c*)

 val t = str2term "(-3*x - 4*y)^^^3";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = 

 "-27 * x ^^^ 3 + -108 * x ^^^ 2 * y + -144 * x * y ^^^ 2 + -64 * y ^^^ 3"

 then () else raise error "poly.sml: diff.behav. in make_polynomial 11";

 (*SPB Schalk I p.62 No.242c*)

 val t = str2term "x^^^(-4)*(x^^^(-4)*y^^^(-2))^^^(-1)*y^^^(-2)";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "1" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 12";

 (*SPB Schalk I p.60 No.209a*)

 val t = str2term "a^^^(7-x) * a^^^x";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "a ^^^ 7" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 13";

 (*SPB Schalk I p.60 No.209d*)

 val t = str2term "d^^^x * d^^^(x+1) * d^^^(2 - 2*x)";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "d ^^^ 3" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 14";

 (*---------------------------------------------------------------------*)

 (*------------------ Bsple bei denen es Probleme gibt------------------*)

 (*---------------------------------------------------------------------*)

 (*Schalk I p.64 No.303*)

 val t = str2term "(a + 2*b)*(a^^^2 + 4*b^^^2)*(a - 2*b) - (a - 6*b)*(a^^^2 + 36*b^^^2)*(a + 6*b)";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "1280 * b ^^^ 4" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 14b";

 (* Richtig - aber Binomische Formel wurde nicht verwendet! *)

 (*--------------------------------------------------------------------*)

 (*----------------------- Eigene Beispiele ---------------------------*)

 (*--------------------------------------------------------------------*)

 (*SPO*)

 val t = str2term "a^^^2*a^^^(-2)";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "1" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 15";

 (*SPO*)

 val t = str2term "a + a + a";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "3 * a" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 16";

 (*SPO*)

 val t = str2term "a + b + b + b";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "a + 3 * b" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 17";

 (*SPO*)

 val t = str2term "a^^^2*b*b^^^(-1)";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "a ^^^ 2" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 18";

 (*SPO*)

 val t = str2term "a^^^2*a^^^(-2)";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "1" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 19";

 (*SPO*)

 val t = str2term "b + a - b";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "a" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 20";

 (*SPO*)

 val t = str2term "b * a * a";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "a ^^^ 2 * b" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 21";

 (*SPO*)

 val t = str2term "(a^^^2)^^^3";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "a ^^^ 6" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 22";

 (*SPO*)

 val t = str2term "x^^^2 * y^^^2 + x * x^^^2 * y";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if term2str t = "x ^^^ 3 * y + x ^^^ 2 * y ^^^ 2" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 23";

 (*SPO*)

 val t = (term_of o the o (parse thy)) "a^^^2 * (-a)^^^2";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "a ^^^ 4" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 24";

 (*SPO*)

 val t = str2term "a * b * b^^^(-1) + a";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "2 * a" then ()

 else raise error "poly.sml: diff.behav. in make_polynomial 25";

 (*SPO*)

 val t = str2term "a*c*b^^^(2*n) + 3*a + 5*b^^^(2*n)*c*b";

 val Some (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;

 if (term2str t) = "3 * a + 5 * b ^^^ (1 + 2 * n) * c + a * b ^^^ (2 * n) * c"

 then () else raise error "poly.sml: diff.behav. in make_polynomial 26";

 (*MG.27.6.03 -------------vvv-: Verschachtelte Terme -----------*)

 (*SPO*)

 val t = str2term "(1 + (x*y*a) + x)^^^(1 + (x*y*a) + x)";

  val Some (t,_) = rewrite_set_ thy false make_polynomial t;

  term2str t;

 if term2str t = "(1 + x + a * x * y) ^^^ (1 + x + a * x * y)"

  then () else raise error "poly.sml: diff.behav. in make_polynomial 27";(*SPO*)

 val t = str2term "(1 + x*(y*z)*zz)^^^(1 + x*(y*z)*zz)";

  val Some (t,_) = rewrite_set_ thy false make_polynomial t;

  term2str t;

 if term2str t = "(1 + x * y * z * zz) ^^^ (1 + x * y * z * zz)"

  then () else raise error "poly.sml: diff.behav. in make_polynomial 28";

 "-------- Script 'simplification for_polynomials' ----------------";

 "-------- Script 'simplification for_polynomials' ----------------";

 "-------- Script 'simplification for_polynomials' ----------------";

 val str = 

 "Script SimplifyScript (t_::real) =                \

 \  ((Rewrite_Set norm_Poly False) t_)";

 val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;

 atomty sc;

 "-------- check pbl  'polynomial simplification' -----------------";

 "-------- check pbl  'polynomial simplification' -----------------";

 "-------- check pbl  'polynomial simplification' -----------------";

 val fmz = ["term ((5*x^^^2 + 3) * (2*x^^^7 + 3) \

 	   \- (3*x^^^5 + 8) * (6*x^^^4 - 1))",

 	   "normalform N"];

 (*0*)

 case refine fmz ["polynomial","simplification"]of

     [Matches (["polynomial", "simplification"], _)] => ()

   | _ => raise error "poly.sml diff.behav. in check pbl, refine";

 (*...if there is an error, then ...*)

 (*1*)

 print_depth 7;

 val pbt = get_pbt ["polynomial","simplification"];

 print_depth 3;

 (*if there is ...

 > val NoMatch' {Given=gi, Where=wh, Find=fi,...} = match_pbl fmz pbt;

 ... then trace_rewrite:*)

 (*2*)

 trace_rewrite:=true; 

 match_pbl fmz pbt;

 trace_rewrite:=false;

 (*... if there is no rewrite, then there is something wrong with prls*)

 (*3*)

 print_depth 7;

 val prls = (#prls o get_pbt) ["polynomial","simplification"];

 print_depth 3;

 val t = str2term "((5*x^^^2 + 3) * (2*x^^^7 + 3) \

 		 \- (3*x^^^5 + 8) * (6*x^^^4 - 1)) is_polyexp";

 trace_rewrite:=true; 

 val Some (t',_) = rewrite_set_ thy false prls t;

 trace_rewrite:=false;

 if t' = HOLogic.true_const then () 

 else raise error "poly.sml: diff.behav. in check pbl 'polynomial..";

 (*... if this works, but (*1*) does still NOT work, check types:*)

 (*4*)

 show_types:=true;

 (*

 > val NoMatch' {Given=gi, Where=wh, Find=fi,...} = match_pbl fmz pbt;

 val wh = [False "(t_::real => real) (is_polyexp::real)"]

 ......................^^^^^^^^^^^^...............^^^^*)

 val Matches' _ = match_pbl fmz pbt;

 show_types:=false;

 "-------- me 'polynomial simplification' Schalk I p.63 No.267b ---";

 "-------- me 'polynomial simplification' Schalk I p.63 No.267b ---";

 "-------- me 'polynomial simplification' Schalk I p.63 No.267b ---";

 val fmz = ["term ((5*x^^^2 + 3) * (2*x^^^7 + 3) \

 	   \- (3*x^^^5 + 8) * (6*x^^^4 - 1))",

 	   "normalform N"];

 val (dI',pI',mI') =

   ("Poly.thy",["polynomial","simplification"],

    ["simplification","for_polynomials"]);

 val p = e_pos'; val c = []; 

 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 (writeln o (itms2str_ ctxt)) (get_obj g_pbl pt (fst p));

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt;

 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;

 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;

 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;

 if f2str f = 

 "17 + 15 * x ^^^ 2 + -48 * x ^^^ 4 + 3 * x ^^^ 5 + 6 * x ^^^ 7 + -8 * x ^^^ 9"

 then () else raise error "poly.sml diff.behav. in me Schalk I p.63 No.267b";

 "-------- interSteps for Schalk 299a -----------------------------";

 "-------- interSteps for Schalk 299a -----------------------------";

 "-------- interSteps for Schalk 299a -----------------------------";

 states:=[];

 CalcTree

 [(["term ((x - y)*(x + y))", "normalform N"], 

   ("Poly.thy",["polynomial","simplification"],

   ["simplification","for_polynomials"]))];

 Iterator 1;

 moveActiveRoot 1;

 autoCalculate 1 CompleteCalc;

 val ((pt,p),_) = get_calc 1; show_pt pt;

 interSteps 1 ([1],Res)(*<ERROR> syserror in detailstep </ERROR>*);

 val ((pt,p),_) = get_calc 1; show_pt pt;

 if existpt' ([1,1], Frm) pt then ()

 else raise error "poly.sml: interSteps doesnt work again 1";

 interSteps 1 ([1,1],Res)(*<ERROR> syserror in detailstep </ERROR>*);

 val ((pt,p),_) = get_calc 1; show_pt pt;

 if existpt' ([1,1,1], Frm) pt then ()

 else raise error "poly.sml: interSteps doesnt work again 2";

 "-------- norm_Poly NOT COMPLETE ---------------------------------";

 "-------- norm_Poly NOT COMPLETE ---------------------------------";

 "-------- norm_Poly NOT COMPLETE ---------------------------------";

 trace_rewrite:=true;

 val Some (f',_) = rewrite_set_ thy false norm_Poly 

 (str2term "L = k - 2 * q + (k - 2 * q) + (k - 2 * q) + (k - 2 * q) + senkrecht + oben")(*see poly.sml: -- norm_Poly NOT COMPLETE -- TODO MG*);

 trace_rewrite:=false;

 term2str f';

 "-------- ord_make_polynomial ------------------------------------";

 "-------- ord_make_polynomial ------------------------------------";

 "-------- ord_make_polynomial ------------------------------------";

 val t1 = str2term "2 * b + (3 * a + 3 * b)";

 val t2 = str2term "3 * a + 3 * b + 2 * b";

 if ord_make_polynomial true Poly.thy [] (t1, t2) then ()

 else raise error "poly.sml: diff.behav. in ord_make_polynomial";

 (*WN071202: ^^^ why then is there no rewriting ...*)

 val term = str2term "2*b + (3*a + 3*b)";

 val None = rewrite_set_ Isac.thy false order_add_mult term;

 (*or why is there no rewriting this way...*)

 val t1 = str2term "2 * b + (3 * a + 3 * b)";

 val t2 = str2term "3 * a + (2 * b + 3 * b)";