Isabelle2015->17: completed "normalise" cf. fb6f5ef2c647
authorWalther Neuper <wneuper@ist.tugraz.at>
Wed, 14 Feb 2018 06:06:27 +0100
changeset 59370b829919afd7b
parent 59369 5f9f07d37a1e
child 59371 3594fcedebe9
Isabelle2015->17: completed "normalise" cf. fb6f5ef2c647
src/Tools/isac/Knowledge/EqSystem.thy
src/Tools/isac/Knowledge/LinEq.thy
src/Tools/isac/Knowledge/PolyEq.thy
src/Tools/isac/Knowledge/Rational.thy
src/Tools/isac/Knowledge/RootEq.thy
src/Tools/isac/xmlsrc/pbl-met-hierarchy.sml
test/Tools/isac/ADDTESTS/course/SignalProcess/Build_Inverse_Z_Transform.thy
test/Tools/isac/ADDTESTS/course/SignalProcess/document/Build_Inverse_Z_Transform.tex
test/Tools/isac/Frontend/use-cases.sml
test/Tools/isac/Knowledge/Inverse_Z_Transform/inverse_z_transform.sml
test/Tools/isac/Knowledge/diffapp.sml
test/Tools/isac/Knowledge/eqsystem.sml
test/Tools/isac/Knowledge/rateq.sml
test/Tools/isac/Knowledge/rlang.sml
test/Tools/isac/Knowledge/rooteq.sml
test/Tools/isac/Knowledge/rootrat.sml
test/Tools/isac/Knowledge/system.sml
test/Tools/isac/Test_Isac.thy
     1.1 --- a/src/Tools/isac/Knowledge/EqSystem.thy	Tue Feb 13 16:17:59 2018 +0100
     1.2 +++ b/src/Tools/isac/Knowledge/EqSystem.thy	Wed Feb 14 06:06:27 2018 +0100
     1.3 @@ -48,7 +48,7 @@
     1.4      "[| [] from [bdv_1,bdv_2,bdv_3,bdv_4] occur_exactly_in a; Not (a=!=0) |] 
     1.5  		      			     ==>(a * b = c) = (b = c / a)" 
     1.6  axiomatization where (*..if replaced by "and" we get an error in 
     1.7 -  ---  rewrite in [EqSystem,normalize,2x2] --- step "--- 3---";*)
     1.8 +  ---  rewrite in [EqSystem,normalise,2x2] --- step "--- 3---";*)
     1.9    order_system_NxN:     "[a,b] = [b,a]"
    1.10    (*requires rew_ord for termination, eg. ord_simplify_Integral;
    1.11      works for lists of any length, interestingly !?!*)
    1.12 @@ -498,7 +498,7 @@
    1.13  
    1.14  ML {*
    1.15  (*this is for NTH only*)
    1.16 -val srls = Rls {id="srls_normalize_4x4", 
    1.17 +val srls = Rls {id="srls_normalise_4x4", 
    1.18  		preconds = [], 
    1.19  		rew_ord = ("termlessI",termlessI), 
    1.20  		erls = append_rls "erls_in_srls_IntegrierenUnd.." e_rls
    1.21 @@ -582,7 +582,7 @@
    1.22  	      [("#Given" ,["equalities e_s", "solveForVars v_s"]),
    1.23  		      ("#Find"  ,["solution ss'''"])],
    1.24  	      {rew_ord'="tless_true", rls' = Erls, calc = [], 
    1.25 -	        srls = append_rls "srls_normalize_2x2" e_rls
    1.26 +	        srls = append_rls "srls_normalise_2x2" e_rls
    1.27  				      [Thm ("hd_thm",num_str @{thm hd_thm}),
    1.28  				        Thm ("tl_Cons",num_str @{thm tl_Cons}),
    1.29  				        Thm ("tl_Nil",num_str @{thm tl_Nil})], 
    1.30 @@ -603,7 +603,7 @@
    1.31  	       [("#Given" ,["equalities e_s", "solveForVars v_s"]),
    1.32  	         ("#Find"  ,["solution ss'''"])],
    1.33  	       {rew_ord'="tless_true", rls' = Erls, calc = [], 
    1.34 -	         srls = append_rls "srls_normalize_4x4" srls
    1.35 +	         srls = append_rls "srls_normalise_4x4" srls
    1.36  	             [Thm ("hd_thm",num_str @{thm hd_thm}),
    1.37  	               Thm ("tl_Cons",num_str @{thm tl_Cons}),
    1.38  	               Thm ("tl_Nil",num_str @{thm tl_Nil})], 
     2.1 --- a/src/Tools/isac/Knowledge/LinEq.thy	Tue Feb 13 16:17:59 2018 +0100
     2.2 +++ b/src/Tools/isac/Knowledge/LinEq.thy	Wed Feb 14 06:06:27 2018 +0100
     2.3 @@ -16,7 +16,7 @@
     2.4                 ("((Script Solve'_lineq'_equation (_ _ =))// (_))" 9)
     2.5  
     2.6  axiomatization where
     2.7 -(*-- normalize --*)
     2.8 +(*-- normalise --*)
     2.9    (*WN0509 compare PolyEq.all_left "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)"*)
    2.10    all_left:          "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)" and
    2.11    makex1_x:          "a^^^1  = a" and
     3.1 --- a/src/Tools/isac/Knowledge/PolyEq.thy	Tue Feb 13 16:17:59 2018 +0100
     3.2 +++ b/src/Tools/isac/Knowledge/PolyEq.thy	Wed Feb 14 06:06:27 2018 +0100
     3.3 @@ -122,7 +122,7 @@
     3.4    plus_leq:              "(0 <= a + b) = ((-1)*b <= a)"(*Isa?*) and
     3.5    minus_leq:             "(0 <= a - b) = (     b <= a)"(*Isa?*) and
     3.6  
     3.7 -(*-- normalize --*)
     3.8 +(*-- normalise --*)
     3.9    (*WN0509 compare LinEq.all_left "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)"*)
    3.10    all_left:              "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)" and
    3.11    makex1_x:              "a^^^1  = a"   and
    3.12 @@ -928,14 +928,14 @@
    3.13  	          "((lhs e_e) has_degree_in v_v) = 4"]),
    3.14            ("#Find", ["solutions v_v'i'"])],
    3.15          PolyEq_prls, SOME "solve (e_e::bool, v_v)", [(*["PolyEq","solve_d4_polyeq_equation"]*)])),
    3.16 -    (*--- normalize ---*)
    3.17 +    (*--- normalise ---*)
    3.18      (Specify.prep_pbt thy "pbl_equ_univ_poly_norm" [] e_pblID
    3.19        (["normalise","polynomial","univariate","equation"],
    3.20          [("#Given", ["equality e_e","solveFor v_v"]),
    3.21            ("#Where", ["(Not((matches (?a = 0 ) e_e ))) |" ^
    3.22  	          "(Not(((lhs e_e) is_poly_in v_v)))"]),
    3.23            ("#Find", ["solutions v_v'i'"])],
    3.24 -        PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq","normalize_poly"]])),
    3.25 +        PolyEq_prls, SOME "solve (e_e::bool, v_v)", [["PolyEq","normalise_poly"]])),
    3.26      (*-------------------------expanded-----------------------*)
    3.27      (Specify.prep_pbt thy "pbl_equ_univ_expand" [] e_pblID
    3.28        (["expanded","univariate","equation"],
    3.29 @@ -974,7 +974,7 @@
    3.30            crls=PolyEq_crls, errpats = [], nrls = norm_Rational},
    3.31          "empty_script"),
    3.32      Specify.prep_met thy "met_polyeq_norm" [] e_metID
    3.33 -      (["PolyEq","normalize_poly"],
    3.34 +      (["PolyEq","normalise_poly"],
    3.35          [("#Given" ,["equality e_e","solveFor v_v"]),
    3.36            ("#Where" ,["(Not((matches (?a = 0 ) e_e ))) |(Not(((lhs e_e) is_poly_in v_v)))"]),
    3.37            ("#Find"  ,["solutions v_v'i'"])],
    3.38 @@ -1118,7 +1118,7 @@
    3.39            "             (Try (Rewrite_Set norm_Rational_parenthesized False))) e_e;" ^
    3.40            " (L_L::bool list) = ((Or_to_List e_e)::bool list)             " ^
    3.41            " in Check_elementwise L_L {(v_v::real). Assumptions} )"),
    3.42 -    (*.solves all expanded (ie. normalized) terms of degree 2.*) 
    3.43 +    (*.solves all expanded (ie. normalised) terms of degree 2.*) 
    3.44      (*Oct.02 restriction: 'eval_true 0 =< discriminant' ony for integer values
    3.45        by 'PolyEq_erls'; restricted until Float.thy is implemented*)
    3.46      Specify.prep_met thy "met_polyeq_complsq" [] e_metID
     4.1 --- a/src/Tools/isac/Knowledge/Rational.thy	Tue Feb 13 16:17:59 2018 +0100
     4.2 +++ b/src/Tools/isac/Knowledge/Rational.thy	Wed Feb 14 06:06:27 2018 +0100
     4.3 @@ -4,7 +4,7 @@
     4.4     Use is subject to license terms.
     4.5  
     4.6     depends on Poly (and not on Atools), because 
     4.7 -   fractions with _normalized_ polynomials are canceled, added, etc.
     4.8 +   fractions with _normalised_ polynomials are canceled, added, etc.
     4.9  *)
    4.10  
    4.11  theory Rational 
     5.1 --- a/src/Tools/isac/Knowledge/RootEq.thy	Tue Feb 13 16:17:59 2018 +0100
     5.2 +++ b/src/Tools/isac/Knowledge/RootEq.thy	Wed Feb 14 06:06:27 2018 +0100
     5.3 @@ -45,7 +45,7 @@
     5.4   
     5.5  axiomatization where
     5.6  
     5.7 -(* normalize *)
     5.8 +(* normalise *)
     5.9    makex1_x:            "a^^^1  = a"   and
    5.10    real_assoc_1:        "a+(b+c) = a+b+c" and
    5.11    real_assoc_2:        "a*(b*c) = a*b*c" and
    5.12 @@ -73,7 +73,7 @@
    5.13     (a = d + e*sqrt(f)) = (a + (-1) * d = e*sqrt(f))" and
    5.14    sqrt_isolate_r_add2: "[|bdv occurs_in f|] ==>
    5.15     (a = d + sqrt(f)) = (a + (-1) * d = sqrt(f))" and
    5.16 - (* small hack: thm 3,5,6 are not needed if rootnormalize is well done*)
    5.17 + (* small hack: thm 3,5,6 are not needed if rootnormalise is well done*)
    5.18    sqrt_isolate_r_add3: "[|bdv occurs_in f|] ==>
    5.19     (a = d + e*(g/sqrt(f))) = (a + (-1) * d = e*(g/sqrt(f)))" and
    5.20    sqrt_isolate_r_add4: "[|bdv occurs_in f|] ==>
    5.21 @@ -102,7 +102,7 @@
    5.22     ( (c*sqrt(a) = b) = (c^^^2*a = b^^^2))" and
    5.23    sqrt_square_equation_left_3: "[|bdv occurs_in a; 0 <= a; 0 <= b*c|] ==> 
    5.24     ( c/sqrt(a) = b) = (c^^^2 / a = b^^^2)" and
    5.25 -  (* small hack: thm 4-6 are not needed if rootnormalize is well done*)
    5.26 +  (* small hack: thm 4-6 are not needed if rootnormalise is well done*)
    5.27    sqrt_square_equation_left_4: "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d|] ==> 
    5.28     ( (c*(d/sqrt (a)) = b) = (c^^^2*(d^^^2/a) = b^^^2))" and
    5.29    sqrt_square_equation_left_5: "[|bdv occurs_in a; 0 <= a; 0 <= b*c*d|] ==> 
    5.30 @@ -115,7 +115,7 @@
    5.31     ( (a = c*sqrt (b)) = ((a^^^2) = c^^^2*b))" and
    5.32    sqrt_square_equation_right_3: "[|bdv occurs_in b; 0 <= a*c; 0 <= b|] ==> 
    5.33     ( (a = c/sqrt (b)) = (a^^^2 = c^^^2/b))" and
    5.34 - (* small hack: thm 4-6 are not needed if rootnormalize is well done*)
    5.35 + (* small hack: thm 4-6 are not needed if rootnormalise is well done*)
    5.36    sqrt_square_equation_right_4: "[|bdv occurs_in b; 0 <= a*c*d; 0 <= b|] ==> 
    5.37     ( (a = c*(d/sqrt (b))) = ((a^^^2) = c^^^2*(d^^^2/b)))" and
    5.38    sqrt_square_equation_right_5: "[|bdv occurs_in b; 0 <= a*c*d; 0 <= b|] ==> 
    5.39 @@ -156,7 +156,7 @@
    5.40      end;
    5.41  
    5.42  (* RL: 030518: Is in the rightest subterm of a term a sqrt with bdv,
    5.43 -and the subterm ist connected with + or * --> is normalized*)
    5.44 +and the subterm ist connected with + or * --> is normalised*)
    5.45   fun is_normSqrtTerm_in t v =
    5.46       let
    5.47  	fun coeff_in c v = member op = (vars c) v;
    5.48 @@ -501,7 +501,7 @@
    5.49              "  ((rhs e_e) is_normSqrtTerm_in (v_v::real))   )"]),
    5.50            ("#Find"  ,["solutions v_v'i'"])],
    5.51            RootEq_prls,  SOME "solve (e_e::bool, v_v)", [["RootEq","solve_sq_root_equation"]])),
    5.52 -    (* ---------normalize----------- *)
    5.53 +    (* ---------normalise----------- *)
    5.54      (Specify.prep_pbt thy "pbl_equ_univ_root_norm" [] e_pblID
    5.55        (["normalise","root'","univariate","equation"],
    5.56          [("#Given" ,["equality e_e","solveFor v_v"]),
    5.57 @@ -520,7 +520,7 @@
    5.58        (["RootEq"], [],
    5.59          {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
    5.60            crls=RootEq_crls, errpats = [], nrls = norm_Poly}, "empty_script"),
    5.61 -    (*-- normalize 20.10.02 --*)
    5.62 +    (*-- normalise 20.10.02 --*)
    5.63      Specify.prep_met thy "met_rooteq_norm" [] e_metID
    5.64        (["RootEq","norm_sq_root_equation"],
    5.65          [("#Given" ,["equality e_e","solveFor v_v"]),
    5.66 @@ -538,9 +538,7 @@
    5.67            "           (Try (Repeat (Rewrite_Set make_rooteq        False))) @@  " ^
    5.68            "           (Try (Rewrite_Set rooteq_simplify              True))) e_e " ^
    5.69            " in ((SubProblem (RootEq',[univariate,equation],                     " ^
    5.70 -          "      [no_met]) [BOOL e_e, REAL v_v])))")
    5.71 -(*----- broke at Isabelle2015 \<longrightarrow> Isabelle2017, reason unknown -----
    5.72 -,
    5.73 +          "      [no_met]) [BOOL e_e, REAL v_v])))"),
    5.74      Specify.prep_met thy "met_rooteq_sq" [] e_metID
    5.75        (["RootEq","solve_sq_root_equation"],
    5.76          [("#Given" ,["equality e_e", "solveFor v_v"]),
    5.77 @@ -560,7 +558,7 @@
    5.78            "   (Try (Rewrite_Set rooteq_simplify                    True)) ) e_e;   " ^
    5.79            " (L_L::bool list) =                                                     " ^
    5.80            "   (if (((lhs e_e) is_sqrtTerm_in v_v) | ((rhs e_e) is_sqrtTerm_in v_v))" ^
    5.81 -          "    then (SubProblem (RootEq',[normalize,root',univariate,equation],   " ^
    5.82 +          "    then (SubProblem (RootEq',[normalise,root',univariate,equation],   " ^
    5.83            "                      [no_met]) [BOOL e_e, REAL v_v])                   " ^
    5.84            "    else (SubProblem (RootEq',[univariate,equation], [no_met])         " ^
    5.85            "                     [BOOL e_e, REAL v_v]))                             " ^
    5.86 @@ -581,7 +579,7 @@
    5.87            "    (Try (Repeat (Rewrite_Set make_rooteq                  False))) @@   " ^
    5.88            "    (Try (Rewrite_Set rooteq_simplify                       False))) e_e " ^
    5.89            " in if ((rhs e_e) is_sqrtTerm_in v_v)                                    " ^
    5.90 -          " then (SubProblem (RootEq',[normalize,root',univariate,equation],       " ^
    5.91 +          " then (SubProblem (RootEq',[normalise,root',univariate,equation],       " ^
    5.92            "       [no_met]) [BOOL e_e, REAL v_v])                                   " ^
    5.93            " else ((SubProblem (RootEq',[univariate,equation],                      " ^
    5.94            "        [no_met]) [BOOL e_e, REAL v_v])))"),
    5.95 @@ -601,13 +599,10 @@
    5.96            "  (Try (Repeat (Rewrite_Set make_rooteq                  False))) @@  " ^
    5.97            "  (Try (Rewrite_Set rooteq_simplify                       False))) e_e " ^
    5.98            " in if ((lhs e_e) is_sqrtTerm_in v_v)                                   " ^ 
    5.99 -          " then (SubProblem (RootEq',[normalize,root',univariate,equation],      " ^
   5.100 +          " then (SubProblem (RootEq',[normalise,root',univariate,equation],      " ^
   5.101            "       [no_met]) [BOOL e_e, REAL v_v])                                " ^
   5.102            " else ((SubProblem (RootEq',[univariate,equation],                    " ^
   5.103 -          "        [no_met]) [BOOL e_e, REAL v_v])))")
   5.104 ------ broke at Isabelle2015 \<longrightarrow> Isabelle2017, reason unknown  -------*)
   5.105 -] 
   5.106 -*}
   5.107 +          "        [no_met]) [BOOL e_e, REAL v_v])))")] *}
   5.108  
   5.109  setup {* KEStore_Elems.add_calcs
   5.110    [("is_rootTerm_in", ("RootEq.is'_rootTerm'_in", eval_is_rootTerm_in"")),
     6.1 --- a/src/Tools/isac/xmlsrc/pbl-met-hierarchy.sml	Tue Feb 13 16:17:59 2018 +0100
     6.2 +++ b/src/Tools/isac/xmlsrc/pbl-met-hierarchy.sml	Wed Feb 14 06:06:27 2018 +0100
     6.3 @@ -110,7 +110,7 @@
     6.4  fun pbl2term thy (pblRD: Specify.pblRD) = (*WN120405.TODO.txt*)
     6.5    str2term ("Problem (" ^ (get_thy o theory2domID) thy ^ "', " ^ (strs2str' o rev) pblRD ^ ")");
     6.6  (* term2str (pbl2term (Thy_Info_get_theory "Isac") ["equations","univariate","normalise"]);
     6.7 -val it = "Problem (Isac, [normalize, univariate, equations])" : string
     6.8 +val it = "Problem (Isac, [normalise, univariate, equations])" : string
     6.9  *)
    6.10  val i = indentation;
    6.11  
     7.1 --- a/test/Tools/isac/ADDTESTS/course/SignalProcess/Build_Inverse_Z_Transform.thy	Tue Feb 13 16:17:59 2018 +0100
     7.2 +++ b/test/Tools/isac/ADDTESTS/course/SignalProcess/Build_Inverse_Z_Transform.thy	Wed Feb 14 06:06:27 2018 +0100
     7.3 @@ -759,9 +759,9 @@
     7.4      (*Specify_Problem ["normalise","polynomial",
     7.5                         "univariate","equation"])*)
     7.6    val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
     7.7 -    (* Specify_Method["PolyEq","normalize_poly"]*)
     7.8 +    (* Specify_Method["PolyEq","normalise_poly"]*)
     7.9    val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
    7.10 -    (*Apply_Method["PolyEq","normalize_poly"]*)
    7.11 +    (*Apply_Method["PolyEq","normalise_poly"]*)
    7.12    val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
    7.13      (*Rewrite ("all_left","PolyEq.all_left")*)
    7.14    val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
    7.15 @@ -1412,9 +1412,9 @@
    7.16    val (p,_,f,nxt,_,pt) = me nxt p [] pt;
    7.17      (*Specify_Problem ["normalise","polynomial","univariate","equation"]*)
    7.18    val (p,_,f,nxt,_,pt) = me nxt p [] pt;
    7.19 -    (*Specify_Method ["PolyEq", "normalize_poly"]*)
    7.20 +    (*Specify_Method ["PolyEq", "normalise_poly"]*)
    7.21    val (p,_,f,nxt,_,pt) = me nxt p [] pt;
    7.22 -    (*Apply_Method ["PolyEq", "normalize_poly"]*)
    7.23 +    (*Apply_Method ["PolyEq", "normalise_poly"]*)
    7.24    val (p,_,f,nxt,_,pt) = me nxt p [] pt;
    7.25      (*Rewrite ("all_left", "PolyEq.all_left")*)
    7.26    val (p,_,f,nxt,_,pt) = me nxt p [] pt;
     8.1 --- a/test/Tools/isac/ADDTESTS/course/SignalProcess/document/Build_Inverse_Z_Transform.tex	Tue Feb 13 16:17:59 2018 +0100
     8.2 +++ b/test/Tools/isac/ADDTESTS/course/SignalProcess/document/Build_Inverse_Z_Transform.tex	Wed Feb 14 06:06:27 2018 +0100
     8.3 @@ -1480,12 +1480,12 @@
     8.4  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
     8.5  \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Theory\ {\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
     8.6  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
     8.7 -\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
     8.8 +\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
     8.9  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.10  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.11 -\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\ Specify{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.12 +\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\ Specify{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.13  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.14 -\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.15 +\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.16  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.17  \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{2E}{\isachardot}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.18  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.19 @@ -1519,7 +1519,7 @@
    8.20  \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}Postcond\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
    8.21  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.22  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.23 -\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}Postcond\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
    8.24 +\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}Postcond\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
    8.25  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.26  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.27  \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}End{\isaliteral{5F}{\isacharunderscore}}Proof{\isaliteral{27}{\isacharprime}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.28 @@ -2527,11 +2527,11 @@
    8.29  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.30  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.31  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.32 -\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.33 +\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.34  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.35 -\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.36 +\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.37  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.38 -\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.39 +\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.40  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    8.41  \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{2E}{\isachardot}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    8.42  \ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
     9.1 --- a/test/Tools/isac/Frontend/use-cases.sml	Tue Feb 13 16:17:59 2018 +0100
     9.2 +++ b/test/Tools/isac/Frontend/use-cases.sml	Wed Feb 14 06:06:27 2018 +0100
     9.3 @@ -615,9 +615,9 @@
     9.4   setNextTactic 1 (Specify_Problem ["normalise","polynomial",
     9.5  				   "univariate","equation"]);
     9.6   autoCalculate 1 (Step 1); fetchProposedTactic 1;
     9.7 - setNextTactic 1 (Specify_Method ["PolyEq","normalize_poly"]);
     9.8 + setNextTactic 1 (Specify_Method ["PolyEq","normalise_poly"]);
     9.9   autoCalculate 1 (Step 1); fetchProposedTactic 1;
    9.10 - setNextTactic 1 (Apply_Method ["PolyEq","normalize_poly"]);
    9.11 + setNextTactic 1 (Apply_Method ["PolyEq","normalise_poly"]);
    9.12   autoCalculate 1 (Step 1); fetchProposedTactic 1;
    9.13   setNextTactic 1 (Rewrite ("all_left", num_str @{thm all_left}));
    9.14   autoCalculate 1 (Step 1); fetchProposedTactic 1;
    9.15 @@ -742,11 +742,11 @@
    9.16  (*and Specify_Theory skipped by fetchProposedTactic ?!?*)
    9.17  
    9.18   fetchProposedTactic 1;
    9.19 - setNextTactic 1 (Specify_Method ["PolyEq","normalize_poly"]);
    9.20 + setNextTactic 1 (Specify_Method ["PolyEq","normalise_poly"]);
    9.21   autoCalculate 1 (Step 1);
    9.22  
    9.23   fetchProposedTactic 1;
    9.24 - setNextTactic 1 (Apply_Method ["PolyEq","normalize_poly"]);
    9.25 + setNextTactic 1 (Apply_Method ["PolyEq","normalise_poly"]);
    9.26  
    9.27   autoCalculate 1 CompleteCalc;
    9.28  
    9.29 @@ -765,7 +765,7 @@
    9.30   autoCalculate 1 (Step 1);
    9.31  
    9.32   fetchProposedTactic 1;
    9.33 - setNextTactic 1 (Specify_Method ["PolyEq","normalize_poly"]);
    9.34 + setNextTactic 1 (Specify_Method ["PolyEq","normalise_poly"]);
    9.35   autoCalculate 1 (Step 1);
    9.36  
    9.37   fetchProposedTactic 1;
    10.1 --- a/test/Tools/isac/Knowledge/Inverse_Z_Transform/inverse_z_transform.sml	Tue Feb 13 16:17:59 2018 +0100
    10.2 +++ b/test/Tools/isac/Knowledge/Inverse_Z_Transform/inverse_z_transform.sml	Wed Feb 14 06:06:27 2018 +0100
    10.3 @@ -109,7 +109,7 @@
    10.4  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
    10.5  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
    10.6  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
    10.7 -val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (*Apply_Method ["PolyEq", "normalize_poly"]*)
    10.8 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (*Apply_Method ["PolyEq", "normalise_poly"]*)
    10.9  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
   10.10  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
   10.11  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
   10.12 @@ -140,7 +140,7 @@
   10.13  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
   10.14  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
   10.15  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
   10.16 -val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (*Apply_Method ["PolyEq", "normalize_poly"]*)
   10.17 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (*Apply_Method ["PolyEq", "normalise_poly"]*)
   10.18  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
   10.19  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
   10.20  val (p,_,fb,nxt,_,pt) = me nxt p [] pt; (**)
    11.1 --- a/test/Tools/isac/Knowledge/diffapp.sml	Tue Feb 13 16:17:59 2018 +0100
    11.2 +++ b/test/Tools/isac/Knowledge/diffapp.sml	Wed Feb 14 06:06:27 2018 +0100
    11.3 @@ -340,11 +340,11 @@
    11.4  ### assod: NotAss m= Subproblem'  ,
    11.5   stac= Substitute
    11.6   [(b, (rhs o hd)
    11.7 -       (Subproblem (thy, [normalize, polynomial, univariate, equation])))]
    11.8 +       (Subproblem (thy, [normalise, polynomial, univariate, equation])))]
    11.9   (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))
   11.10  *** stac2tac_ TODO: no match for Substitute
   11.11  ***  [(b, (rhs o hd)
   11.12 -***        (Subproblem (thy, [normalize, polynomial, univariate, equation])))]
   11.13 +***        (Subproblem (thy, [normalise, polynomial, univariate, equation])))]
   11.14  ***  (hd (filterVar A [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]))
   11.15  Exception- ERROR raised
   11.16  
   11.17 @@ -364,7 +364,7 @@
   11.18  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   11.19  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   11.20  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   11.21 -(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalize_poly"])*)
   11.22 +(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalise_poly"])*)
   11.23  
   11.24  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   11.25  (*val f = Form' (FormKF (~1,EdUndef,3,Nundef,"A = a * b"))*)
    12.1 --- a/test/Tools/isac/Knowledge/eqsystem.sml	Tue Feb 13 16:17:59 2018 +0100
    12.2 +++ b/test/Tools/isac/Knowledge/eqsystem.sml	Wed Feb 14 06:06:27 2018 +0100
    12.3 @@ -10,15 +10,15 @@
    12.4  "----------- occur_exactly_in ------------------------------------";
    12.5  "----------- problems --------------------------------------------";
    12.6  "----------- rewrite-order ord_simplify_System -------------------";
    12.7 -"----------- rewrite in [EqSystem,normalize,2x2] -----------------";
    12.8 -"----------- rewrite example from 2nd [EqSystem,normalize,2x2] ---";
    12.9 +"----------- rewrite in [EqSystem,normalise,2x2] -----------------";
   12.10 +"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
   12.11  "----------- rewrite in [EqSystem,top_down_substitution,2x2] -----";
   12.12 -"----------- rewrite in [EqSystem,normalize,4x4] -----------------";
   12.13 +"----------- rewrite in [EqSystem,normalise,4x4] -----------------";
   12.14  "----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";
   12.15  "----------- refine [linear,system]-------------------------------";
   12.16  "----------- refine [2x2,linear,system] search error--------------";
   12.17 -"----------- me [EqSystem,normalize,2x2] -------------------------";
   12.18 -"----------- me [linear,system] ..normalize..top_down_sub..-------";
   12.19 +"----------- me [EqSystem,normalise,2x2] -------------------------";
   12.20 +"----------- me [linear,system] ..normalise..top_down_sub..-------";
   12.21  "----------- all systems from Biegelinie -------------------------";
   12.22  "----------- 4x4 systems from Biegelinie -------------------------";
   12.23  "-----------------------------------------------------------------";
   12.24 @@ -145,9 +145,9 @@
   12.25  then () else error "integrate.sml, (. * .) < (. * .) not#6";
   12.26  
   12.27  
   12.28 -"----------- rewrite in [EqSystem,normalize,2x2] -----------------";
   12.29 -"----------- rewrite in [EqSystem,normalize,2x2] -----------------";
   12.30 -"----------- rewrite in [EqSystem,normalize,2x2] -----------------";
   12.31 +"----------- rewrite in [EqSystem,normalise,2x2] -----------------";
   12.32 +"----------- rewrite in [EqSystem,normalise,2x2] -----------------";
   12.33 +"----------- rewrite in [EqSystem,normalise,2x2] -----------------";
   12.34  val t = str2term"[0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2,\
   12.35  	        \0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2]";
   12.36  val bdvs = [(str2term"bdv_1",str2term"c"),
   12.37 @@ -169,9 +169,9 @@
   12.38  then () else error "eqsystem.sml rewrite in 2x2 simplify_System_par.3";
   12.39  "--- 4---";
   12.40  
   12.41 -"----------- rewrite example from 2nd [EqSystem,normalize,2x2] ---";
   12.42 -"----------- rewrite example from 2nd [EqSystem,normalize,2x2] ---";
   12.43 -"----------- rewrite example from 2nd [EqSystem,normalize,2x2] ---";
   12.44 +"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
   12.45 +"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
   12.46 +"----------- rewrite example from 2nd [EqSystem,normalise,2x2] ---";
   12.47  val thy = @{theory "Isac"} (*because of Undeclared constant "Biegelinie.EI*);
   12.48  val t = 
   12.49      str2term"[0 = c_2 + c * 0 + 1 / EI * (L * q_0 / 12 * 0 ^^^ 3 +         \
   12.50 @@ -234,10 +234,10 @@
   12.51  trace_rewrite:=false;
   12.52  
   12.53  
   12.54 -"----------- rewrite in [EqSystem,normalize,4x4] -----------------";
   12.55 -"----------- rewrite in [EqSystem,normalize,4x4] -----------------";
   12.56 -"----------- rewrite in [EqSystem,normalize,4x4] -----------------";
   12.57 -(*STOPPED.WN06?: revise rewrite in [EqSystem,normalize,4x4] from before 0609*)
   12.58 +"----------- rewrite in [EqSystem,normalise,4x4] -----------------";
   12.59 +"----------- rewrite in [EqSystem,normalise,4x4] -----------------";
   12.60 +"----------- rewrite in [EqSystem,normalise,4x4] -----------------";
   12.61 +(*STOPPED.WN06?: revise rewrite in [EqSystem,normalise,4x4] from before 0609*)
   12.62  val t = str2term"[0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c_3 + c_4,\
   12.63  	        \0 = -1 * q_0 * L ^^^ 2 / 2 + L * c_3 + c_4,\
   12.64  		\c + c_2 + c_3 + c_4 = 0,\
   12.65 @@ -328,7 +328,7 @@
   12.66  				        Correct "solveForVars [c, c_2]"],
   12.67  				     Where = [],
   12.68  				     Relate = []})] => ()
   12.69 -| _ => error "eqsystem.sml refine ['normalize','2x2'...]";
   12.70 +| _ => error "eqsystem.sml refine ['normalise','2x2'...]";
   12.71  
   12.72  "===== case 2 =====";
   12.73  val fmz = ["equalities [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]", 
   12.74 @@ -504,9 +504,9 @@
   12.75  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   12.76  *)
   12.77  
   12.78 -"----------- me [EqSystem,normalize,2x2] -------------------------";
   12.79 -"----------- me [EqSystem,normalize,2x2] -------------------------";
   12.80 -"----------- me [EqSystem,normalize,2x2] -------------------------";
   12.81 +"----------- me [EqSystem,normalise,2x2] -------------------------";
   12.82 +"----------- me [EqSystem,normalise,2x2] -------------------------";
   12.83 +"----------- me [EqSystem,normalise,2x2] -------------------------";
   12.84  val fmz = ["equalities [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,\
   12.85  	               \0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2]", 
   12.86  	   "solveForVars [c, c_2]", "solution LL"];
   12.87 @@ -520,7 +520,7 @@
   12.88  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   12.89  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   12.90  case nxt of ("Specify_Method",_) => ()
   12.91 -	  | _ => error "eqsystem.sml [EqSystem,normalize,2x2] specify";
   12.92 +	  | _ => error "eqsystem.sml [EqSystem,normalise,2x2] specify";
   12.93  
   12.94  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   12.95  val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   12.96 @@ -530,7 +530,7 @@
   12.97  val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   12.98  case nxt of
   12.99      (_, Subproblem ("Biegelinie", ["triangular", "2x2", "LINEAR",_])) => ()
  12.100 -  | _ => error "eqsystem.sml me [EqSystem,normalize,2x2] SubProblem";
  12.101 +  | _ => error "eqsystem.sml me [EqSystem,normalise,2x2] SubProblem";
  12.102  
  12.103  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  12.104  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  12.105 @@ -567,9 +567,9 @@
  12.106      (_, End_Proof') => ()
  12.107    | _ => error "eqsystem.sml me [EqSys...2x2] finished End_Proof'";
  12.108  
  12.109 -"----------- me [linear,system] ..normalize..top_down_sub..-------";
  12.110 -"----------- me [linear,system] ..normalize..top_down_sub..-------";
  12.111 -"----------- me [linear,system] ..normalize..top_down_sub..-------";
  12.112 +"----------- me [linear,system] ..normalise..top_down_sub..-------";
  12.113 +"----------- me [linear,system] ..normalise..top_down_sub..-------";
  12.114 +"----------- me [linear,system] ..normalise..top_down_sub..-------";
  12.115  val fmz = 
  12.116      ["equalities\
  12.117       \[0 = c_2 + c * 0 + 1 / EI * (L * q_0 / 12 * 0 ^^^ 3 +                \
  12.118 @@ -765,9 +765,9 @@
  12.119  
  12.120  val SOME (t, _) = rewrite_set_ thy false order_system t;
  12.121  if term2str t = "[c = -1 * L * q_0 / -1, L * c + c_2 = q_0 * L ^^^ 2 / 2, c_3 = 0, c_4 = 0]"
  12.122 -then () else error "eqsystem.sml: exp 7.70 normalize 4x4 by rewrite changed";
  12.123 +then () else error "eqsystem.sml: exp 7.70 normalise 4x4 by rewrite changed";
  12.124  
  12.125 -"----- 7.70 with met normalize: ";
  12.126 +"----- 7.70 with met normalise: ";
  12.127  val fmz = ["equalities" ^
  12.128    "[L * q_0 = c, " ^
  12.129    "0 = (2 * c_2 + 2 * L * c + -1 * L ^^^ 2 * q_0) / 2, " ^
  12.130 @@ -792,7 +792,7 @@
  12.131  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  12.132  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
  12.133  case nxt of (_,Apply_Method ["EqSystem", "normalise", "4x4"]) => ()
  12.134 -	  | _ => error "eqsystem.sml [EqSystem,normalize,4x4] specify";
  12.135 +	  | _ => error "eqsystem.sml [EqSystem,normalise,4x4] specify";
  12.136  val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
  12.137  
  12.138  "----- outcommented before Isabelle2002 --> 2011 -------------------------";
  12.139 @@ -808,7 +808,7 @@
  12.140  val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
  12.141  val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
  12.142  if f2str f ="[c = L * q_0, L * c + c_2 = q_0 * L ^^^ 2 / 2, c_3 = 0, c_4 = 0]" 
  12.143 -then () else error "eqsystem.sml: exp 7.70 normalize 4x4 by met changed";
  12.144 +then () else error "eqsystem.sml: exp 7.70 normalise 4x4 by met changed";
  12.145  --------------------------------------------------------------------------*)
  12.146  
  12.147  "----- 7.70 with met top_down_: me";
    13.1 --- a/test/Tools/isac/Knowledge/rateq.sml	Tue Feb 13 16:17:59 2018 +0100
    13.2 +++ b/test/Tools/isac/Knowledge/rateq.sml	Wed Feb 14 06:06:27 2018 +0100
    13.3 @@ -76,7 +76,7 @@
    13.4  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    13.5  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    13.6  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    13.7 -(*val nxt = Apply_Method ["PolyEq", "normalize_poly"])*)
    13.8 +(*val nxt = Apply_Method ["PolyEq", "normalise_poly"])*)
    13.9  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.10  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.11  (* val nxt = (_,Subproblem ("PolyEq",["polynomial","univariate","equation"]=======*)
   13.12 @@ -239,8 +239,8 @@
   13.13  val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.14  val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.15  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.16 -case nxt of ("Apply_Method", Apply_Method ["PolyEq", "normalize_poly"]) => ()
   13.17 -| _ => error "55b normalize_poly specification broken";
   13.18 +case nxt of ("Apply_Method", Apply_Method ["PolyEq", "normalise_poly"]) => ()
   13.19 +| _ => error "55b normalise_poly specification broken";
   13.20  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.21  val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.22  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.23 @@ -251,7 +251,7 @@
   13.24  val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.25  val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.26  case nxt of ("Apply_Method", Apply_Method ["PolyEq", "solve_d2_polyeq_bdvonly_equation"]) => ()
   13.27 -| _ => error "55b normalize_poly specification broken";
   13.28 +| _ => error "55b normalise_poly specification broken";
   13.29  val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.30  val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.31  val (p,_,f,nxt,_,pt) = me nxt p [1] pt; val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   13.32 @@ -260,16 +260,16 @@
   13.33  f2str f = "[x = 0, x = 6 / 5]";                                                        (*= GUI*)
   13.34  case snd nxt of Check_elementwise "Assumptions" => () | _ => ((*not checked before*)); (*= GUI*)
   13.35  if terms2str (get_assumptions_ pt p) =
   13.36 -("[\"<not> matches (?a = 0)\n" ^
   13.37 -   "   ((3 + -1 * x + x ^^^ 2) * x = 1 * (9 * x + -6 * x ^^^ 2 + x ^^^ 3)) |\n" ^
   13.38 -   "<not> lhs ((3 + -1 * x + x ^^^ 2) * x =\n   " ^
   13.39 -   "    1 * (9 * x + -6 * x ^^^ 2 + x ^^^ 3)) is_poly_in x\"," ^
   13.40 -   "\"x = 6 / 5\"," ^
   13.41 -   "\"x = 0\"," ^
   13.42 -   "\"lhs (-6 * x + 5 * x ^^^ 2 = 0) is_poly_in x\"," ^
   13.43 -   "\"lhs (-6 * x + 5 * x ^^^ 2 = 0) has_degree_in x = 2\"," ^
   13.44 -   "\"9 * x + -6 * x ^^^ 2 + x ^^^ 3 ~= 0\"," ^
   13.45 -   "\"x / (x ^^^ 2 - 6 * x + 9) - 1 / (x ^^^ 2 - 3 * x) =\n1 / x is_ratequation_in x\"]")
   13.46 +("[\"\<not> matches (?a = 0)\n        " ^
   13.47 +  "((3 + -1 * x + x ^^^ 2) * x =\n         " ^
   13.48 +  "1 * (9 * x + -6 * x ^^^ 2 + x ^^^ 3)) \<or>\n\<not> lhs ((3 + -1 * x + x ^^^ 2) * x =\n            " ^
   13.49 +  "1 * (9 * x + -6 * x ^^^ 2 + x ^^^ 3)) is_poly_in x\"," ^
   13.50 +  "\"x = 6 / 5\"," ^
   13.51 +  "\"x = 0\"," ^
   13.52 +  "\"lhs (-6 * x + 5 * x ^^^ 2 = 0) is_poly_in x\"," ^
   13.53 +  "\"lhs (-6 * x + 5 * x ^^^ 2 = 0) has_degree_in x = 2\"," ^
   13.54 +  "\"9 * x + -6 * x ^^^ 2 + x ^^^ 3 \<noteq> 0\"," ^
   13.55 +  "\"x / (x ^^^ 2 - 6 * x + 9) - 1 / (x ^^^ 2 - 3 * x) =\n1 / x is_ratequation_in x\"]")
   13.56  then () else error "rateq.sml: diff.behav. in I s.87 Bsp 55b [x = 6 / 5], asms";
   13.57  
   13.58  (*
    14.1 --- a/test/Tools/isac/Knowledge/rlang.sml	Tue Feb 13 16:17:59 2018 +0100
    14.2 +++ b/test/Tools/isac/Knowledge/rlang.sml	Wed Feb 14 06:06:27 2018 +0100
    14.3 @@ -522,7 +522,7 @@
    14.4  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    14.5  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    14.6  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
    14.7 -(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalize_poly"])*)
    14.8 +(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalise_poly"])*)
    14.9  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   14.10  val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
   14.11  (*val nxt =Subproblem ("PolyEq",["polynomial","univariate","equation"]))*)
   14.12 @@ -1698,7 +1698,7 @@
   14.13  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.14  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.15  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.16 -(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalize_poly"])*)
   14.17 +(*val nxt = ("Apply_Method",Apply_Method ["PolyEq","normalise_poly"])*)
   14.18  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.19  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.20  (*val nxt = Subproblem ("PolyEq",["polynomial","univariate","equation"])*)
   14.21 @@ -1775,7 +1775,7 @@
   14.22  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.23  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.24  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.25 -(*val nxt = Apply_Method ["PolyEq","normalize_poly"])     *)
   14.26 +(*val nxt = Apply_Method ["PolyEq","normalise_poly"])     *)
   14.27  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.28  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   14.29  (*val nxt = Subproblem ("PolyEq",["polynomial","univariate","equation"]))*)
    15.1 --- a/test/Tools/isac/Knowledge/rooteq.sml	Tue Feb 13 16:17:59 2018 +0100
    15.2 +++ b/test/Tools/isac/Knowledge/rooteq.sml	Wed Feb 14 06:06:27 2018 +0100
    15.3 @@ -282,7 +282,7 @@
    15.4  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
    15.5  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
    15.6  val (p,_,f,nxt,_,pt) = me nxt p c pt;
    15.7 -(*val p = ([6],Pbl)val nxt = Specify_Method ["PolyEq","normalize_poly"])*)
    15.8 +(*val p = ([6],Pbl)val nxt = Specify_Method ["PolyEq","normalise_poly"])*)
    15.9  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.10  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.11  (*val p = ([6,2],Res) val f = Form' (FormKF (~1,EdUndef,2,Nundef,"0 = 0"))
   15.12 @@ -334,7 +334,7 @@
   15.13  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.14  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.15  val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.16 -(*val nxt = ("Specify_Method",Specify_Method ["PolyEq","normalize_poly"])*)
   15.17 +(*val nxt = ("Specify_Method",Specify_Method ["PolyEq","normalise_poly"])*)
   15.18  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.19  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.20  (*val p = ([3,2],Res)val f = Form' (FormKF (~1,EdUndef,2,Nundef,"-1 + x = 0"))
   15.21 @@ -391,7 +391,7 @@
   15.22  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.23  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.24  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.25 -(*val p = ([2],Pbl) val nxt = Specify_Method ["PolyEq","normalize_poly"])*)
   15.26 +(*val p = ([2],Pbl) val nxt = Specify_Method ["PolyEq","normalise_poly"])*)
   15.27  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.28  val (p,_,f,nxt,_,pt) = me nxt p c pt;val (p,_,f,nxt,_,pt) = me nxt p c pt;
   15.29  (*val p = ([2,2],Res) val f = Form' (FormKF (~1,EdUndef,2,Nundef,"0 = 0"))
    16.1 --- a/test/Tools/isac/Knowledge/rootrat.sml	Tue Feb 13 16:17:59 2018 +0100
    16.2 +++ b/test/Tools/isac/Knowledge/rootrat.sml	Wed Feb 14 06:06:27 2018 +0100
    16.3 @@ -48,7 +48,7 @@
    16.4  
    16.5  val SOME (t,asm) = rewrite_set_ thy true rls ttt;
    16.6  if term2str t =
    16.7 -"-1 * x = -1 + sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8) |\nx = -1 * (-1 + -1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))"
    16.8 +"-1 * x = -1 + sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8) \<or>\nx = -1 * (-1 + -1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))"
    16.9  (*"-1 * x = -1 + sqrt (1 ^^^ 2 - -8) | x = -1 * (-1 + -1 * sqrt (1 ^^^ 2 - -8))"*)
   16.10  then () else error "val rls = calculate_Rational GOON";
   16.11  
    17.1 --- a/test/Tools/isac/Knowledge/system.sml	Tue Feb 13 16:17:59 2018 +0100
    17.2 +++ b/test/Tools/isac/Knowledge/system.sml	Wed Feb 14 06:06:27 2018 +0100
    17.3 @@ -9,16 +9,16 @@
    17.4  "-----------------------------------------------------------------";
    17.5  "table of contents -----------------------------------------------";
    17.6  "-----------------------------------------------------------------";
    17.7 -"----------- normalize system ------------------------------------";
    17.8 +"----------- normalise system ------------------------------------";
    17.9  "----------- me --------------------------------------------------";
   17.10  "-----------------------------------------------------------------";
   17.11  "-----------------------------------------------------------------";
   17.12  "-----------------------------------------------------------------";
   17.13  
   17.14  
   17.15 -"----------- normalize system ------------------------------------";
   17.16 -"----------- normalize system ------------------------------------";
   17.17 -"----------- normalize system ------------------------------------";
   17.18 +"----------- normalise system ------------------------------------";
   17.19 +"----------- normalise system ------------------------------------";
   17.20 +"----------- normalise system ------------------------------------";
   17.21  val t = str2term "[0 = c*0 + -1*q_0*(0^^^2 / 2) + c_2,\
   17.22  		 \ 0 = c*L + -1*q_0*(L^^^2 / 2) + c_2]";
   17.23  val SOME (t,_) = rewrite_set_ thy false norm_Poly t;
    18.1 --- a/test/Tools/isac/Test_Isac.thy	Tue Feb 13 16:17:59 2018 +0100
    18.2 +++ b/test/Tools/isac/Test_Isac.thy	Wed Feb 14 06:06:27 2018 +0100
    18.3 @@ -195,6 +195,15 @@
    18.4    ML_file "Knowledge/atools.sml"
    18.5    ML_file "Knowledge/simplify.sml"
    18.6    ML_file "Knowledge/poly.sml"
    18.7 +  ML_file "Knowledge/gcd_poly_ml.sml"
    18.8 +  ML_file "Knowledge/gcd_poly_winkler.sml" (*must be after gcd_poly_ml.sml: redefines functions*)
    18.9 +  ML_file "Knowledge/rational.sml"
   18.10 +  ML_file "Knowledge/equation.sml"
   18.11 +  ML_file "Knowledge/root.sml"
   18.12 +  ML_file "Knowledge/lineq.sml"
   18.13 +(*ML_file "Knowledge/rooteq.sml"    some complicated equations not recovered from 2002 *)
   18.14 +  ML_file "Knowledge/rateq.sml"   (*some complicated equations not recovered from 2002 *)
   18.15 +  ML_file "Knowledge/rootrat.sml"
   18.16  
   18.17  ML {*
   18.18  "~~~~~ fun xxx, args:"; val () = ();
   18.19 @@ -203,17 +212,8 @@
   18.20  *} ML {*
   18.21  *}
   18.22  
   18.23 -  ML_file "Knowledge/gcd_poly_ml.sml"
   18.24 -  ML_file "Knowledge/gcd_poly_winkler.sml" (*must be after gcd_poly_ml.sml: redefines functions*)
   18.25 -  ML_file "Knowledge/rational.sml"
   18.26 +  ML_file "Knowledge/rootrateq.sml"(*ome complicated equations not recovered from 2002 *)
   18.27  (*---------------------- check test file by testfile -------------------------------------------
   18.28 -  ML_file "Knowledge/equation.sml"
   18.29 -  ML_file "Knowledge/root.sml"
   18.30 -  ML_file "Knowledge/lineq.sml"
   18.31 -(*ML_file "Knowledge/rooteq.sml"    some complicated equations not recovered from 2002 *)
   18.32 -  ML_file "Knowledge/rateq.sml"   (*some complicated equations not recovered from 2002 *)
   18.33 -  ML_file "Knowledge/rootrat.sml"
   18.34 -  ML_file "Knowledge/rootrateq.sml"(*ome complicated equations not recovered from 2002 *)
   18.35    ML_file "Knowledge/partial_fractions.sml"
   18.36    ML_file "Knowledge/polyeq.sml"
   18.37  (*ML_file "Knowledge/rlang.sml"     much to clean up, similar tests in other files     *)