1 (* Title: Knowledge/polyeq-1.sml
2 testexamples for PolyEq, poynomial equations and equational systems
3 Author: Richard Lang 2003
4 (c) due to copyright terms
5 WN030609: some expls dont work due to unfinished handling of 'expanded terms';
6 others marked with TODO have to be checked, too.
9 "-----------------------------------------------------------------";
10 "table of contents -----------------------------------------------";
11 "-----------------------------------------------------------------";
12 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
13 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
14 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
15 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
16 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
17 "----------- rls make_polynomial_in ------------------------------";
18 "----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
19 "----------- rls d2_polyeq_bdv_only_simplify ---------------------";
20 "-----------------------------------------------------------------";
21 "-----------------------------------------------------------------";
24 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
25 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
26 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
27 val fmz = ["equality (a*b - (a+b)*x + x^^^2 = 0)",
28 "solveFor x","solutions L"];
30 ("PolyEq",["degree_2","expanded","univariate","equation"],
31 ["PolyEq","complete_square"]);
32 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
33 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
34 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
35 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
36 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
37 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
38 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
39 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
40 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
41 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
42 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
43 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
44 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
45 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
46 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
47 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
48 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
49 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
50 val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
51 (*WN.2.5.03 TODO FIXME Matthias ?
56 "[x = (a + b) / 2 + -1 * sqrt ((a + b) ^^^ 2 / 2 ^^^ 2 - a * b),\n x = (a + b) / 2 + sqrt ((a + b) ^^^ 2 / 2 ^^^ 2 - a * b)]"))
58 | _ => error "polyeq.sml: diff.behav. in a*b - (a+b)*x + x^^^2 = 0";
59 this will be simplified [x = a, x = b] to by Factor.ML*)
62 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
63 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
64 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
65 val fmz = ["equality (-64 + x^^^2 = 0)",(*Schalk 2, S.66 Nr.1.a~*)
66 "solveFor x","solutions L"];
68 ("PolyEq",["degree_2","expanded","univariate","equation"],
69 ["PolyEq","complete_square"]);
70 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
71 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
72 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
73 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
74 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
75 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
76 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
77 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
78 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
79 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
80 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
81 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
82 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
83 val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
84 (*WN.2.5.03 TODO "[x = sqrt (0 - -64), x = -1 * sqrt (0 - -64)]"
85 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 8, x = -8]")) => ()
86 | _ => error "polyeq.sml: diff.behav. in [x = 8, x = -8]";
89 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
90 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
91 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
92 val fmz = ["equality (-147 + 3*x^^^2 = 0)",(*Schalk 2, S.66 Nr.1.b*)
93 "solveFor x","solutions L"];
95 ("PolyEq",["degree_2","expanded","univariate","equation"],
96 ["PolyEq","complete_square"]);
97 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
98 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
99 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
100 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
101 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
102 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
103 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
104 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
105 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
106 (*WN.2.5.03 TODO "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]"
107 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 7, x = -7]")) => ()
108 | _ => error "polyeq.sml: diff.behav. in [x = 7, x = -7]";
110 if f2str f = "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]" then ()
111 else error "polyeq.sml CORRECTED?behav. in [x = 7, x = -7]";
114 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
115 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
116 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
117 (*EP-17 Schalk_I_p86_n5*)
118 val fmz = ["equality ((3::real)*x - 1 - (5*x - (2 - 4*x)) = -11)","solveFor x","solutions L"];
119 (* Refine.refine fmz ["univariate","equation"];
121 val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
122 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
123 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
126 Model_Problem ["normalise","polynomial","univariate","equation"])
128 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
129 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
130 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
131 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
132 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
135 Subproblem ("PolyEq",["polynomial","univariate","equation"]))
137 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
140 Model_Problem ["degree_1","polynomial","univariate","equation"])
142 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
143 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
144 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
145 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
146 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
147 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
148 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
149 case f of Test_Out.FormKF "[x = 2]" => ()
150 | _ => error "polyeq.sml: diff.behav. in [x = 2]";
153 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
154 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
155 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
156 (*is in rlang.sml, too*)
157 val fmz = ["equality ((x+1)*(x+2) - (3*x - 2)^^^2=(2*x - 1)^^^2+(3*x - 1)*(x+1))",
158 "solveFor x","solutions L"];
159 val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
160 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
161 (*val nxt = ("Refine_Tacitly",Refine_Tacitly ["univariate","equation"])*)
162 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
165 Model_Problem ["normalise","polynomial","univariate","equation"])
167 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
168 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
169 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
170 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
171 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
172 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
175 Subproblem ("PolyEq",["polynomial","univariate","equation"]))
177 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
180 Model_Problem ["abcFormula","degree_2","polynomial","univariate","equation"])
182 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
183 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
184 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
185 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
186 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
187 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
188 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
189 case f of Test_Out.FormKF "[x = 2 / 15, x = 1]" => ()
190 | _ => error "polyeq.sml: diff.behav. in [x = 2 / 15, x = 1]";
196 val fmz = ["equality ( -4 + x^^^2 =0)", "solveFor x","solutions L"];
197 (* val fmz = ["equality (1 + x^^^2 =0)", "solveFor x","solutions L"];*)
198 (*val fmz = ["equality (0 =0)", "solveFor x","solutions L"];*)
199 val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
200 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
202 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
203 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
204 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
205 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
206 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
207 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
208 val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
209 case f of Test_Out.FormKF "[x = 2, x = -2]" => ()
210 | _ => error "polyeq.sml: diff.behav. in [x = 2, x = -2]";
212 "----------- rls make_polynomial_in ------------------------------";
213 "----------- rls make_polynomial_in ------------------------------";
214 "----------- rls make_polynomial_in ------------------------------";
215 (*Punkte aus dem TestBericht, die ich in rlang.sml nicht zuordnen konnte:*)
217 (*3(b)*)val (bdv,v) = (str2term "''bdv''", str2term "R1");
218 val t = str2term "-1 * (R * R2) + R2 * R1 + -1 * (R * R1) = 0";
219 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
220 if UnparseC.term t' = "-1 * R * R2 + R2 * R1 + -1 * R * R1 = 0" then ()
221 else error "make_polynomial_in (-1 * (R * R2) + R2 * R1 + -1 * (R * R1) = 0)";
222 "-1 * R * R2 + (R2 + -1 * R) * R1 = 0";
225 (*3(c)*)val (bdv,v) = (str2term "bdv", str2term "p");
226 val t = str2term "y ^^^ 2 + -2 * (x * p) = 0";
227 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
228 if UnparseC.term t' = "y ^^^ 2 + -2 * x * p = 0" then ()
229 else error "make_polynomial_in (y ^^^ 2 + -2 * (x * p) = 0)";
231 (*3(d)*)val (bdv,v) = (str2term "''bdv''", str2term "x2");
233 "A + x1 * (y3 * (1 / 2)) + x3 * (y2 * (1 / 2)) + -1 * (x1 * (y2 * (1 / 2))) + -1 * (x3 * (y1 * (1 / 2 ))) + y1 * (1 / 2 * x2) + -1 * (y3 * (1 / 2 * x2)) = 0";
234 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
235 if UnparseC.term t' =
236 "A + x1 * y3 * (1 / 2) + x3 * y2 * (1 / 2) + -1 * x1 * y2 * (1 / 2) +\n-1 * x3 * y1 * (1 / 2) +\ny1 * (1 / 2) * x2 +\n-1 * y3 * (1 / 2) * x2 =\n0"
238 else error "make_polynomial_in (A + x1 * (y3 * (1 / 2)) + x3 * (y2 * (1 / 2)) + -1...";
239 "A + x1 * y3 * (1 / 2) + x3 * y2 * (1 / 2) + - x1 * y2 * (1 / 2) + - x3 * y1 * (1 / 2) + (y1 * (1 / 2) + - y3 * (1 / 2)) * x2 = 0";
241 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_ratpoly_in t;
242 if UnparseC.term t' =
243 "A / 1 + x1 * y3 / 2 + x3 * y2 / 2 + -1 * x1 * y2 / 2 + -1 * x3 * y1 / 2 +\ny1 * x2 / 2 +\n-1 * y3 * x2 / 2 =\n0"
245 else error "make_ratpoly_in (A + x1 * (y3 * (1 / 2)) + x3 * (y2 * (1 / 2)) + -1...";
246 "A + x1 * y3 * (1 / 2) + x3 * y2 * (1 / 2) + -1 * x1 * y2 * (1 / 2) + -1 * x3 * y1 * (1 / 2) + (y1 * (1 / 2) + -1 * y3 * (1 / 2)) * x2 = 0";
248 (*3(e)*)val (bdv,v) = (str2term "bdv", str2term "a");
250 "A ^^^ 2 + c ^^^ 2 * (c / d) ^^^ 2 + (-4 * (c / d) ^^^ 2) * a ^^^ 2 = 0";
251 val NONE = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
252 (* the invisible parentheses are as expected *)
254 val t = str2term "(x + 1) * (x + 2) - (3 * x - 2) ^^^ 2 - ((2 * x - 1) ^^^ 2 + (3 * x - 1) * (x + 1)) = 0";
255 Rewrite.trace_on:=(*true*)false;
256 rewrite_set_ thy false expand_binoms t;
257 Rewrite.trace_on:=false;
260 "----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
261 "----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
262 "----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
265 [(["equality ((3::real)*x - 1 - (5*x - (2 - 4*x)) = -11)","solveFor x","solutions L"],
266 ("PolyEq",["univariate","equation"],["no_met"]))];
270 autoCalculate 1 CompleteCalc;
271 val ((pt,p),_) = get_calc 1; show_pt pt;
272 interSteps 1 ([1],Res)
273 (*BEFORE Isabelle2002 --> 2011: <ERROR> no Rewrite_Set... </ERROR> ?see fun prep_rls?*);
276 "----------- rls d2_polyeq_bdv_only_simplify ---------------------";
277 "----------- rls d2_polyeq_bdv_only_simplify ---------------------";
278 "----------- rls d2_polyeq_bdv_only_simplify ---------------------";
279 val t = str2term "-6 * x + 5 * x ^^^ 2 = (0::real)";
280 val subst = [(str2term "(bdv::real)", str2term "(x::real)")];
281 val SOME (t''''', _) = rewrite_set_inst_ thy true subst d2_polyeq_bdv_only_simplify t;
282 (* steps in rls d2_polyeq_bdv_only_simplify:*)
284 (*-6 * x + 5 * x ^ 2 = 0 : Rewrite_Inst (["(''bdv'',x)"],("d2_prescind1","")) --> x * (-6 + 5 * x) = 0*)
285 t |> UnparseC.term; t |> atomty;
286 val thm = ThmC.numerals_to_Free @{thm d2_prescind1};
287 thm |> Thm.prop_of |> UnparseC.term; thm |> Thm.prop_of |> atomty;
288 val SOME (t', _) = rewrite_inst_ thy e_rew_ord Rule_Set.empty true subst thm t; UnparseC.term t';
290 (*x * (-6 + 5 * x) = 0 : Rewrite_Inst (["(''bdv'',x)"],("d2_reduce_equation1",""))
291 --> x = 0 | -6 + 5 * x = 0*)
292 t' |> UnparseC.term; t' |> atomty;
293 val thm = ThmC.numerals_to_Free @{thm d2_reduce_equation1};
294 thm |> Thm.prop_of |> UnparseC.term; thm |> Thm.prop_of |> atomty;
295 val SOME (t'', _) = rewrite_inst_ thy e_rew_ord Rule_Set.empty true subst thm t'; UnparseC.term t'';
296 (* NONE with d2_reduce_equation1: "(bdv*(a +b*bdv)=0) = ((bdv=0)|(a+b*bdv=0))"
297 instead d2_reduce_equation1: "(bdv*(a +b*bdv)=0) = ((bdv=0)|(a+b*bdv=(0::real)))"
299 if UnparseC.term t'' = "x = 0 \<or> -6 + 5 * x = 0" then ()
300 else error "rls d2_polyeq_bdv_only_simplify broken";