neuper@37906
|
1 |
(* testexamples for Poly, polynomials
|
neuper@37906
|
2 |
author: Matthias Goldgruber 2003
|
neuper@37906
|
3 |
(c) due to copyright terms
|
neuper@37906
|
4 |
|
neuper@38022
|
5 |
12345678901234567890123456789012345678901234567890123456789012345678901234567890
|
neuper@38022
|
6 |
10 20 30 40 50 60 70 80
|
neuper@42395
|
7 |
LEGEND:
|
neuper@42395
|
8 |
WN060104: examples marked with 'SPB' came into 'exp_IsacCore_Simp_Poly_Book.xml'
|
neuper@42395
|
9 |
examples marked with 'SPO' came into 'exp_IsacCore_Simp_Poly_Other.xml'
|
neuper@38022
|
10 |
*)
|
neuper@42395
|
11 |
|
neuper@38022
|
12 |
"--------------------------------------------------------";
|
neuper@38022
|
13 |
"--------------------------------------------------------";
|
neuper@38022
|
14 |
"table of contents --------------------------------------";
|
neuper@38022
|
15 |
"--------------------------------------------------------";
|
neuper@38022
|
16 |
"-------- check is'_polyexp is_polyexp ------------------";
|
neuper@42395
|
17 |
"-------- investigate (new 2002) uniary minus -----------";
|
neuper@38036
|
18 |
"-------- check make_polynomial with simple terms -------";
|
neuper@38036
|
19 |
"-------- fun is_multUnordered --------------------------";
|
neuper@38036
|
20 |
"-------- examples from textbook Schalk I ---------------";
|
neuper@38022
|
21 |
"-------- check pbl 'polynomial simplification' --------";
|
neuper@38022
|
22 |
"-------- me 'poly. simpl.' Schalk I p.63 No.267b -------";
|
neuper@38036
|
23 |
"-------- interSteps for Schalk 299a --------------------";
|
neuper@38022
|
24 |
"-------- norm_Poly NOT COMPLETE ------------------------";
|
neuper@38022
|
25 |
"-------- ord_make_polynomial ---------------------------";
|
neuper@38022
|
26 |
"--------------------------------------------------------";
|
neuper@38022
|
27 |
"--------------------------------------------------------";
|
neuper@38022
|
28 |
"--------------------------------------------------------";
|
neuper@37906
|
29 |
|
neuper@37906
|
30 |
|
neuper@38022
|
31 |
"-------- check is'_polyexp is_polyexp ------------------";
|
neuper@38022
|
32 |
"-------- check is'_polyexp is_polyexp ------------------";
|
neuper@38022
|
33 |
"-------- check is'_polyexp is_polyexp ------------------";
|
neuper@38022
|
34 |
if is_polyexp @{term "x / x"}
|
neuper@38031
|
35 |
then error "poly.sml: check is'_polyexp is_polyexp" else ();
|
neuper@38022
|
36 |
|
neuper@42395
|
37 |
"-------- investigate (new 2002) uniary minus -----------";
|
neuper@42395
|
38 |
"-------- investigate (new 2002) uniary minus -----------";
|
neuper@42395
|
39 |
"-------- investigate (new 2002) uniary minus -----------";
|
neuper@42395
|
40 |
(*---------------------------------------------- vvvvvvvvvvvvvv -----------------------*)
|
neuper@38036
|
41 |
val t = (#prop o rep_thm) @{thm real_diff_0}; (*"0 - ?x = - ?x"*)
|
neuper@37906
|
42 |
atomty t;
|
wneuper@59117
|
43 |
(*
|
wneuper@59117
|
44 |
*** Const (HOL.Trueprop, bool => prop)
|
wneuper@59117
|
45 |
*** . Const (HOL.eq, real => real => bool)
|
wneuper@59117
|
46 |
*** . . Const (Groups.minus_class.minus, real => real => real)
|
wneuper@59117
|
47 |
*** . . . Const (Groups.zero_class.zero, real)
|
neuper@37906
|
48 |
*** . . . Var ((x, 0), real)
|
wneuper@59117
|
49 |
*** . . Const (Groups.uminus_class.uminus, real => real)
|
wneuper@59117
|
50 |
*** . . . Var ((x, 0), real)
|
wneuper@59117
|
51 |
*)
|
neuper@42395
|
52 |
case t of
|
neuper@42395
|
53 |
Const ("HOL.Trueprop", _) $
|
wneuper@59117
|
54 |
(Const ("HOL.eq", _) $
|
wneuper@59117
|
55 |
(Const ("Groups.minus_class.minus", _) $ Const ("Groups.zero_class.zero", _) $
|
wneuper@59117
|
56 |
Var (("x", 0), _)) $
|
wneuper@59117
|
57 |
(Const ("Groups.uminus_class.uminus", _) $ Var (("x", 0), _))) => ()
|
neuper@42395
|
58 |
| _ => error "internal representation of \"0 - ?x = - ?x\" changed";
|
neuper@37906
|
59 |
|
neuper@42395
|
60 |
(*----------------------------------- vvvv --------------------------------------------*)
|
neuper@37906
|
61 |
val t = (term_of o the o (parse thy)) "-1";
|
neuper@37906
|
62 |
atomty t;
|
neuper@37906
|
63 |
(*** -------------
|
neuper@37906
|
64 |
*** Free ( -1, real) *)
|
neuper@42395
|
65 |
case t of
|
neuper@42395
|
66 |
Free ("-1", _) => ()
|
neuper@42395
|
67 |
| _ => error "internal representation of \"-1\" changed";
|
neuper@42395
|
68 |
(*----------------------------------- vvvvv -------------------------------------------*)
|
neuper@37906
|
69 |
val t = (term_of o the o (parse thy)) "- 1";
|
neuper@37906
|
70 |
atomty t;
|
wneuper@59117
|
71 |
(*
|
wneuper@59117
|
72 |
***
|
wneuper@59117
|
73 |
*** Free (-1, real)
|
wneuper@59117
|
74 |
***
|
wneuper@59117
|
75 |
*)
|
neuper@42395
|
76 |
case t of
|
wneuper@59117
|
77 |
Free ("-1", _) => ()
|
neuper@42395
|
78 |
| _ => error "internal representation of \"- 1\" changed";
|
neuper@37906
|
79 |
|
neuper@42395
|
80 |
"======= these external values all have the same internal representation";
|
neuper@42395
|
81 |
(* "1-x" causes syntyx error --- binary minus detected by blank inbetween !!!*)
|
neuper@42395
|
82 |
(*----------------------------------- vvvvv -------------------------------------------*)
|
neuper@42395
|
83 |
val t = (term_of o the o (parse thy)) "-x";
|
neuper@37906
|
84 |
atomty t;
|
neuper@37906
|
85 |
(**** -------------
|
neuper@37906
|
86 |
*** Free ( -x, real)*)
|
neuper@42395
|
87 |
case t of
|
neuper@42395
|
88 |
Const ("Groups.uminus_class.uminus", _) $ Free ("x", _) => ()
|
neuper@42395
|
89 |
| _ => error "internal representation of \"-x\" changed";
|
neuper@42395
|
90 |
(*----------------------------------- vvvvv -------------------------------------------*)
|
neuper@37906
|
91 |
val t = (term_of o the o (parse thy)) "- x";
|
neuper@37906
|
92 |
atomty t;
|
neuper@37906
|
93 |
(**** -------------
|
neuper@37906
|
94 |
*** Free ( -x, real) !!!!!!!!!!!!!!!!!!!!!!!! is the same !!!*)
|
neuper@42395
|
95 |
case t of
|
neuper@42395
|
96 |
Const ("Groups.uminus_class.uminus", _) $ Free ("x", _) => ()
|
neuper@42395
|
97 |
| _ => error "internal representation of \"- x\" changed";
|
neuper@42395
|
98 |
(*----------------------------------- vvvvvv ------------------------------------------*)
|
neuper@37906
|
99 |
val t = (term_of o the o (parse thy)) "-(x)";
|
neuper@37906
|
100 |
atomty t;
|
neuper@37906
|
101 |
(**** -------------
|
neuper@37906
|
102 |
*** Free ( -x, real)*)
|
neuper@42395
|
103 |
case t of
|
neuper@42395
|
104 |
Const ("Groups.uminus_class.uminus", _) $ Free ("x", _) => ()
|
neuper@42395
|
105 |
| _ => error "internal representation of \"-(x)\" changed";
|
neuper@37906
|
106 |
|
neuper@38036
|
107 |
"-------- check make_polynomial with simple terms -------";
|
neuper@38036
|
108 |
"-------- check make_polynomial with simple terms -------";
|
neuper@38036
|
109 |
"-------- check make_polynomial with simple terms -------";
|
neuper@38036
|
110 |
"----- check 1 ---";
|
neuper@38036
|
111 |
val t = str2term "2*3*a";
|
neuper@38036
|
112 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
neuper@38036
|
113 |
if term2str t = "6 * a" then () else error "check make_polynomial 1";
|
neuper@38036
|
114 |
|
neuper@38036
|
115 |
"----- check 2 ---";
|
neuper@38036
|
116 |
val t = str2term "2*a + 3*a";
|
neuper@38036
|
117 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
neuper@38036
|
118 |
if term2str t = "5 * a" then () else error "check make_polynomial 2";
|
neuper@38036
|
119 |
|
neuper@38036
|
120 |
"----- check 3 ---";
|
neuper@38036
|
121 |
val t = str2term "2*a + 3*a + 3*a";
|
neuper@38036
|
122 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
neuper@38036
|
123 |
if term2str t = "8 * a" then () else error "check make_polynomial 3";
|
neuper@38036
|
124 |
|
neuper@38036
|
125 |
"----- check 4 ---";
|
neuper@38036
|
126 |
val t = str2term "3*a - 2*a";
|
neuper@38036
|
127 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
neuper@38036
|
128 |
if term2str t = "a" then () else error "check make_polynomial 4";
|
neuper@38036
|
129 |
|
neuper@38036
|
130 |
"----- check 5 ---";
|
neuper@38036
|
131 |
val t = str2term "4*(3*a - 2*a)";
|
neuper@38036
|
132 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
neuper@38036
|
133 |
if term2str t = "4 * a" then () else error "check make_polynomial 5";
|
neuper@38036
|
134 |
|
neuper@38036
|
135 |
"----- check 6 ---";
|
neuper@38036
|
136 |
val t = str2term "4*(3*a^^^2 - 2*a^^^2)";
|
neuper@38036
|
137 |
val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
|
neuper@38036
|
138 |
if term2str t = "4 * a ^^^ 2" then () else error "check make_polynomial 6";
|
neuper@38036
|
139 |
|
neuper@38036
|
140 |
"-------- fun is_multUnordered --------------------------";
|
neuper@38036
|
141 |
"-------- fun is_multUnordered --------------------------";
|
neuper@38036
|
142 |
"-------- fun is_multUnordered --------------------------";
|
neuper@41929
|
143 |
val thy = @{theory "Isac"};
|
neuper@38040
|
144 |
"===== works for a simple example, see rewrite.sml -- fun app_rev ===";
|
neuper@38040
|
145 |
val t = str2term "x^^^2 * x";
|
neuper@38040
|
146 |
val SOME (t', _) = rewrite_set_ thy true order_mult_ t;
|
neuper@38040
|
147 |
if term2str t' = "x * x ^^^ 2" then ()
|
neuper@38040
|
148 |
else error "poly.sml Poly.is'_multUnordered doesn't work";
|
neuper@38040
|
149 |
|
neuper@38040
|
150 |
(* 100928 trace_rewrite shows the first occurring difference in 267b:
|
neuper@38036
|
151 |
### rls: order_mult_ on: 5 * x ^^^ 2 * (2 * x ^^^ 7) + 5 * x ^^^ 2 * 3 + (6 * x ^^^ 7 + 9) + (-1 * (3 * x ^^^ 5 * (6 * x ^^^ 4)) + -1 * (3 * x ^^^ 5 * -1) +
|
neuper@38036
|
152 |
(-48 * x ^^^ 4 + 8))
|
neuper@38036
|
153 |
###### rls: e_rls-is_multUnordered on: p is_multUnordered
|
neuper@38036
|
154 |
####### try calc: Poly.is'_multUnordered'
|
neuper@38036
|
155 |
======= calc. to: False !!!!!!!!!!!!! INSTEAD OF TRUE in 2002 !!!!!!!!!!!!!
|
neuper@38036
|
156 |
*)
|
neuper@38036
|
157 |
val t = str2term "5 * x ^^^ 2 * (2 * x ^^^ 7) + 5 * x ^^^ 2 * 3 + (6 * x ^^^ 7 + 9) + (-1 * (3 * x ^^^ 5 * (6 * x ^^^ 4)) + -1 * (3 * x ^^^ 5 * -1) + (-48 * x ^^^ 4 + 8))";
|
neuper@38036
|
158 |
|
neuper@38036
|
159 |
"----- is_multUnordered ---";
|
neuper@38036
|
160 |
val tsort = sort_variables t;
|
neuper@38036
|
161 |
term2str tsort = "2 * (5 * (x ^^^ 2 * x ^^^ 7)) + 3 * (5 * x ^^^ 2) + 6 * x ^^^ 7 + 9 +\n-1 * (3 * (6 * (x ^^^ 4 * x ^^^ 5))) +\n-1 * (-1 * (3 * x ^^^ 5)) +\n-48 * x ^^^ 4 +\n8";
|
neuper@38036
|
162 |
is_polyexp t;
|
neuper@38036
|
163 |
tsort = t;
|
neuper@38036
|
164 |
is_polyexp t andalso not (t = sort_variables t);
|
neuper@38036
|
165 |
if is_multUnordered t then () else error "poly.sml diff. is_multUnordered 1";
|
neuper@38036
|
166 |
|
neuper@38036
|
167 |
"----- eval_is_multUnordered ---";
|
neuper@38036
|
168 |
val tm = str2term "(5 * x ^^^ 2 * (2 * x ^^^ 7) + 5 * x ^^^ 2 * 3 + (6 * x ^^^ 7 + 9) + (-1 * (3 * x ^^^ 5 * (6 * x ^^^ 4)) + -1 * (3 * x ^^^ 5 * -1) + (-48 * x ^^^ 4 + 8))) is_multUnordered";
|
neuper@38036
|
169 |
case eval_is_multUnordered "testid" "" tm thy of
|
neuper@41924
|
170 |
SOME (_, Const ("HOL.Trueprop", _) $
|
neuper@41922
|
171 |
(Const ("HOL.eq", _) $
|
neuper@38036
|
172 |
(Const ("Poly.is'_multUnordered", _) $ _) $
|
neuper@41928
|
173 |
Const ("HOL.True", _))) => ()
|
neuper@38036
|
174 |
| _ => error "poly.sml diff. eval_is_multUnordered";
|
neuper@38036
|
175 |
|
neuper@38040
|
176 |
"----- rewrite_set_ STILL DIDN'T WORK";
|
neuper@38040
|
177 |
val SOME (t, _) = rewrite_set_ thy true order_mult_ t;
|
neuper@38040
|
178 |
term2str t;
|
neuper@38036
|
179 |
|
neuper@38036
|
180 |
"-------- examples from textbook Schalk I ---------------";
|
neuper@38036
|
181 |
"-------- examples from textbook Schalk I ---------------";
|
neuper@38036
|
182 |
"-------- examples from textbook Schalk I ---------------";
|
neuper@38036
|
183 |
"-----SPB Schalk I p.63 No.267b ---";
|
neuper@42395
|
184 |
val t = str2term "(5*x^^^2 + 3) * (2*x^^^7 + 3) - (3*x^^^5 + 8) * (6*x^^^4 - 1)";
|
neuper@37926
|
185 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@42395
|
186 |
if (term2str t) = "17 + 15 * x ^^^ 2 + -48 * x ^^^ 4 + 3 * x ^^^ 5 + 6 * x ^^^ 7 + -8 * x ^^^ 9"
|
neuper@42395
|
187 |
then () else error "poly.sml: diff.behav. in make_polynomial 1";
|
neuper@37906
|
188 |
|
neuper@38036
|
189 |
"-----SPB Schalk I p.63 No.275b ---";
|
neuper@42395
|
190 |
val t = str2term "(3*x^^^2 - 2*x*y + y^^^2) * (x^^^2 - 2*y^^^2)";
|
neuper@42395
|
191 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@42395
|
192 |
if (term2str t) = ("3 * x ^^^ 4 + -2 * x ^^^ 3 * y + -5 * x ^^^ 2 * y ^^^ 2 + " ^
|
neuper@42395
|
193 |
"4 * x * y ^^^ 3 +\n-2 * y ^^^ 4")
|
neuper@42395
|
194 |
then () else error "poly.sml: diff.behav. in make_polynomial 2";
|
neuper@37906
|
195 |
|
neuper@38036
|
196 |
"-----SPB Schalk I p.63 No.279b ---";
|
neuper@42395
|
197 |
val t = str2term "(x-a)*(x-b)*(x-c)*(x-d)";
|
neuper@42395
|
198 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@37906
|
199 |
if (term2str t) =
|
neuper@42395
|
200 |
("a * b * c * d + -1 * a * b * c * x + -1 * a * b * d * x + a * b * x ^^^ 2 +\n" ^
|
neuper@42395
|
201 |
"-1 * a * c * d * x +\na * c * x ^^^ 2 +\na * d * x ^^^ 2 +\n-1 * a * x ^^^ 3 +\n" ^
|
neuper@42395
|
202 |
"-1 * b * c * d * x +\nb * c * x ^^^ 2 +\nb * d * x ^^^ 2 +\n-1 * b * x ^^^ 3 +\n" ^
|
neuper@42395
|
203 |
"c * d * x ^^^ 2 +\n-1 * c * x ^^^ 3 +\n-1 * d * x ^^^ 3 +\nx ^^^ 4")
|
neuper@42395
|
204 |
then () else error "poly.sml: diff.behav. in make_polynomial 3";
|
neuper@37906
|
205 |
|
neuper@38036
|
206 |
"-----SPB Schalk I p.63 No.291 ---";
|
neuper@42395
|
207 |
val t = str2term "(5+96*x^^^3+8*x*(-4+(7- 3*x)*4*x))*(5*(2- 3*x)- (-15*x*(-8*x- 5)))";
|
neuper@42395
|
208 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@42395
|
209 |
if (term2str t) = "50 + -770 * x + 4520 * x ^^^ 2 + -16320 * x ^^^ 3 + -26880 * x ^^^ 4"
|
neuper@42395
|
210 |
then () else error "poly.sml: diff.behav. in make_polynomial 4";
|
neuper@37906
|
211 |
|
neuper@38036
|
212 |
"-----SPB Schalk I p.64 No.295c ---";
|
neuper@42395
|
213 |
val t = str2term "(13*a^^^4*b^^^9*c - 12*a^^^3*b^^^6*c^^^9)^^^2";
|
neuper@42395
|
214 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@42395
|
215 |
if (term2str t) = ("169 * a ^^^ 8 * b ^^^ 18 * c ^^^ 2 + -312 * a ^^^ 7 * b ^^^ 15 * c ^^^ 10" ^
|
neuper@42395
|
216 |
" +\n144 * a ^^^ 6 * b ^^^ 12 * c ^^^ 18")
|
neuper@42395
|
217 |
then ()else error "poly.sml: diff.behav. in make_polynomial 5";
|
neuper@37906
|
218 |
|
neuper@38036
|
219 |
"-----SPB Schalk I p.64 No.299a ---";
|
neuper@42395
|
220 |
val t = str2term "(x - y)*(x + y)";
|
neuper@42395
|
221 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@42395
|
222 |
if (term2str t) = "x ^^^ 2 + -1 * y ^^^ 2"
|
neuper@42395
|
223 |
then () else error "poly.sml: diff.behav. in make_polynomial 6";
|
neuper@37906
|
224 |
|
neuper@38036
|
225 |
"-----SPB Schalk I p.64 No.300c ---";
|
neuper@42395
|
226 |
val t = str2term "(3*x^^^2*y - 1)*(3*x^^^2*y + 1)";
|
neuper@42395
|
227 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@42395
|
228 |
if (term2str t) = "-1 + 9 * x ^^^ 4 * y ^^^ 2"
|
neuper@42395
|
229 |
then () else error "poly.sml: diff.behav. in make_polynomial 7";
|
neuper@37906
|
230 |
|
neuper@38036
|
231 |
"-----SPB Schalk I p.64 No.302 ---";
|
neuper@37906
|
232 |
val t = str2term
|
neuper@42395
|
233 |
"(13*x^^^2 + 5)*(13*x^^^2 - 5) - (5*x^^^2 + 3)*(5*x^^^2 - 3) - (12*x^^^2 + 4)*(12*x^^^2 - 4)";
|
neuper@42395
|
234 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@42395
|
235 |
if term2str t = "0"
|
neuper@42395
|
236 |
then () else error "poly.sml: diff.behav. in make_polynomial 8";
|
neuper@42395
|
237 |
(* RL?MG?: Bei Berechnung sollte 3 mal real_plus_minus_binom1_p aus expand_poly verwendet werden *)
|
neuper@37906
|
238 |
|
neuper@38036
|
239 |
"-----SPB Schalk I p.64 No.306a ---";
|
neuper@37906
|
240 |
val t = str2term "((x^^^2 + 1)*(x^^^2 - 1))^^^2";
|
neuper@37926
|
241 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
242 |
if (term2str t) = "1 + 2 * x ^^^ 4 + 2 * -2 * x ^^^ 4 + x ^^^ 8" then ()
|
neuper@42395
|
243 |
else error "poly.sml: diff.behav. in 2 * x ^^^ 4 + 2 * -2 * x ^^^ 4 = -2 * x ^^^ 4";
|
neuper@37906
|
244 |
|
neuper@37906
|
245 |
(*WN071729 when reducing "rls reduce_012_" for Schaerding,
|
neuper@37906
|
246 |
the above resulted in the term below ... but reduces from then correctly*)
|
neuper@37906
|
247 |
val t = str2term "1 + 2 * x ^^^ 4 + 2 * -2 * x ^^^ 4 + x ^^^ 8";
|
neuper@37926
|
248 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@42395
|
249 |
if (term2str t) = "1 + -2 * x ^^^ 4 + x ^^^ 8"
|
neuper@42395
|
250 |
then () else error "poly.sml: diff.behav. in make_polynomial 9b";
|
neuper@37906
|
251 |
|
neuper@38036
|
252 |
"-----SPB Schalk I p.64 No.296a ---";
|
neuper@37906
|
253 |
val t = str2term "(x - a)^^^3";
|
neuper@37926
|
254 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
255 |
if (term2str t) = "-1 * a ^^^ 3 + 3 * a ^^^ 2 * x + -3 * a * x ^^^ 2 + x ^^^ 3"
|
neuper@38031
|
256 |
then () else error "poly.sml: diff.behav. in make_polynomial 10";
|
neuper@37906
|
257 |
|
neuper@38036
|
258 |
"-----SPB Schalk I p.64 No.296c ---";
|
neuper@37906
|
259 |
val t = str2term "(-3*x - 4*y)^^^3";
|
neuper@37926
|
260 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@42395
|
261 |
if (term2str t) = "-27 * x ^^^ 3 + -108 * x ^^^ 2 * y + -144 * x * y ^^^ 2 + -64 * y ^^^ 3"
|
neuper@38031
|
262 |
then () else error "poly.sml: diff.behav. in make_polynomial 11";
|
neuper@37906
|
263 |
|
neuper@38036
|
264 |
"-----SPB Schalk I p.62 No.242c ---";
|
neuper@37906
|
265 |
val t = str2term "x^^^(-4)*(x^^^(-4)*y^^^(-2))^^^(-1)*y^^^(-2)";
|
neuper@37926
|
266 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@42395
|
267 |
if (term2str t) = "1"
|
neuper@42395
|
268 |
then () else error "poly.sml: diff.behav. in make_polynomial 12";
|
neuper@37906
|
269 |
|
neuper@38036
|
270 |
"-----SPB Schalk I p.60 No.209a ---";
|
neuper@37906
|
271 |
val t = str2term "a^^^(7-x) * a^^^x";
|
neuper@37926
|
272 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@42395
|
273 |
if term2str t = "a ^^^ 7"
|
neuper@42395
|
274 |
then () else error "poly.sml: diff.behav. in make_polynomial 13";
|
neuper@37906
|
275 |
|
neuper@38036
|
276 |
"-----SPB Schalk I p.60 No.209d ---";
|
neuper@37906
|
277 |
val t = str2term "d^^^x * d^^^(x+1) * d^^^(2 - 2*x)";
|
neuper@37926
|
278 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@42395
|
279 |
if term2str t = "d ^^^ 3"
|
neuper@42395
|
280 |
then () else error "poly.sml: diff.behav. in make_polynomial 14";
|
neuper@37906
|
281 |
|
neuper@37906
|
282 |
(*---------------------------------------------------------------------*)
|
neuper@42395
|
283 |
(*---------------- ?RL?Bsple bei denen es Probleme gibt----------------*)
|
neuper@37906
|
284 |
(*---------------------------------------------------------------------*)
|
neuper@38036
|
285 |
"-----Schalk I p.64 No.303 ---";
|
neuper@37906
|
286 |
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)";
|
neuper@37926
|
287 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@42395
|
288 |
if term2str t = "1280 * b ^^^ 4"
|
neuper@42395
|
289 |
then () else error "poly.sml: diff.behav. in make_polynomial 14b";
|
neuper@37906
|
290 |
(* Richtig - aber Binomische Formel wurde nicht verwendet! *)
|
neuper@37906
|
291 |
|
neuper@37906
|
292 |
(*--------------------------------------------------------------------*)
|
neuper@37906
|
293 |
(*----------------------- Eigene Beispiele ---------------------------*)
|
neuper@37906
|
294 |
(*--------------------------------------------------------------------*)
|
neuper@38036
|
295 |
"-----SPO ---";
|
neuper@37906
|
296 |
val t = str2term "a^^^2*a^^^(-2)";
|
neuper@37926
|
297 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
298 |
if term2str t = "1" then ()
|
neuper@38031
|
299 |
else error "poly.sml: diff.behav. in make_polynomial 15";
|
neuper@38036
|
300 |
"-----SPO ---";
|
neuper@37906
|
301 |
val t = str2term "a + a + a";
|
neuper@37926
|
302 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
303 |
if term2str t = "3 * a" then ()
|
neuper@38031
|
304 |
else error "poly.sml: diff.behav. in make_polynomial 16";
|
neuper@38036
|
305 |
"-----SPO ---";
|
neuper@37906
|
306 |
val t = str2term "a + b + b + b";
|
neuper@37926
|
307 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
308 |
if term2str t = "a + 3 * b" then ()
|
neuper@38031
|
309 |
else error "poly.sml: diff.behav. in make_polynomial 17";
|
neuper@38036
|
310 |
"-----SPO ---";
|
neuper@37906
|
311 |
val t = str2term "a^^^2*b*b^^^(-1)";
|
neuper@37926
|
312 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
313 |
if term2str t = "a ^^^ 2" then ()
|
neuper@38031
|
314 |
else error "poly.sml: diff.behav. in make_polynomial 18";
|
neuper@38036
|
315 |
"-----SPO ---";
|
neuper@37906
|
316 |
val t = str2term "a^^^2*a^^^(-2)";
|
neuper@37926
|
317 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
318 |
if (term2str t) = "1" then ()
|
neuper@38031
|
319 |
else error "poly.sml: diff.behav. in make_polynomial 19";
|
neuper@38036
|
320 |
"-----SPO ---";
|
neuper@37906
|
321 |
val t = str2term "b + a - b";
|
neuper@37926
|
322 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
323 |
if (term2str t) = "a" then ()
|
neuper@38031
|
324 |
else error "poly.sml: diff.behav. in make_polynomial 20";
|
neuper@38036
|
325 |
"-----SPO ---";
|
neuper@37906
|
326 |
val t = str2term "b * a * a";
|
neuper@37926
|
327 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
328 |
if term2str t = "a ^^^ 2 * b" then ()
|
neuper@38031
|
329 |
else error "poly.sml: diff.behav. in make_polynomial 21";
|
neuper@38036
|
330 |
"-----SPO ---";
|
neuper@37906
|
331 |
val t = str2term "(a^^^2)^^^3";
|
neuper@37926
|
332 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
333 |
if term2str t = "a ^^^ 6" then ()
|
neuper@38031
|
334 |
else error "poly.sml: diff.behav. in make_polynomial 22";
|
neuper@38036
|
335 |
"-----SPO ---";
|
neuper@37906
|
336 |
val t = str2term "x^^^2 * y^^^2 + x * x^^^2 * y";
|
neuper@37926
|
337 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
338 |
if term2str t = "x ^^^ 3 * y + x ^^^ 2 * y ^^^ 2" then ()
|
neuper@38031
|
339 |
else error "poly.sml: diff.behav. in make_polynomial 23";
|
neuper@38036
|
340 |
"-----SPO ---";
|
neuper@37906
|
341 |
val t = (term_of o the o (parse thy)) "a^^^2 * (-a)^^^2";
|
neuper@37926
|
342 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
343 |
if (term2str t) = "a ^^^ 4" then ()
|
neuper@38031
|
344 |
else error "poly.sml: diff.behav. in make_polynomial 24";
|
neuper@38036
|
345 |
"-----SPO ---";
|
neuper@37906
|
346 |
val t = str2term "a * b * b^^^(-1) + a";
|
neuper@37926
|
347 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
348 |
if (term2str t) = "2 * a" then ()
|
neuper@38031
|
349 |
else error "poly.sml: diff.behav. in make_polynomial 25";
|
neuper@38036
|
350 |
"-----SPO ---";
|
neuper@37906
|
351 |
val t = str2term "a*c*b^^^(2*n) + 3*a + 5*b^^^(2*n)*c*b";
|
neuper@37926
|
352 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t; term2str t;
|
neuper@37906
|
353 |
if (term2str t) = "3 * a + 5 * b ^^^ (1 + 2 * n) * c + a * b ^^^ (2 * n) * c"
|
neuper@38031
|
354 |
then () else error "poly.sml: diff.behav. in make_polynomial 26";
|
neuper@37906
|
355 |
|
neuper@42395
|
356 |
(*MG030627 -------------vvv-: Verschachtelte Terme -----------*)
|
neuper@38036
|
357 |
"-----SPO ---";
|
neuper@37906
|
358 |
val t = str2term "(1 + (x*y*a) + x)^^^(1 + (x*y*a) + x)";
|
neuper@42395
|
359 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@37906
|
360 |
if term2str t = "(1 + x + a * x * y) ^^^ (1 + x + a * x * y)"
|
neuper@42395
|
361 |
then () else error "poly.sml: diff.behav. in make_polynomial 27";(*SPO*)
|
neuper@42395
|
362 |
|
neuper@37906
|
363 |
val t = str2term "(1 + x*(y*z)*zz)^^^(1 + x*(y*z)*zz)";
|
neuper@42395
|
364 |
val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
|
neuper@37906
|
365 |
if term2str t = "(1 + x * y * z * zz) ^^^ (1 + x * y * z * zz)"
|
neuper@42395
|
366 |
then () else error "poly.sml: diff.behav. in make_polynomial 28";
|
neuper@37906
|
367 |
|
neuper@38036
|
368 |
"-------- check pbl 'polynomial simplification' --------";
|
neuper@38036
|
369 |
"-------- check pbl 'polynomial simplification' --------";
|
neuper@38036
|
370 |
"-------- check pbl 'polynomial simplification' --------";
|
neuper@42395
|
371 |
val fmz = ["Term ((5*x^^^2 + 3) * (2*x^^^7 + 3) - (3*x^^^5 + 8) * (6*x^^^4 - 1))", "normalform N"];
|
neuper@38036
|
372 |
"-----0 ---";
|
neuper@37906
|
373 |
case refine fmz ["polynomial","simplification"]of
|
neuper@37906
|
374 |
[Matches (["polynomial", "simplification"], _)] => ()
|
neuper@38031
|
375 |
| _ => error "poly.sml diff.behav. in check pbl, refine";
|
neuper@37906
|
376 |
(*...if there is an error, then ...*)
|
neuper@37906
|
377 |
|
neuper@38036
|
378 |
"-----1 ---";
|
wneuper@59111
|
379 |
default_print_depth 7;
|
neuper@37906
|
380 |
val pbt = get_pbt ["polynomial","simplification"];
|
wneuper@59111
|
381 |
default_print_depth 3;
|
neuper@37906
|
382 |
(*if there is ...
|
neuper@37906
|
383 |
> val NoMatch' {Given=gi, Where=wh, Find=fi,...} = match_pbl fmz pbt;
|
neuper@37906
|
384 |
... then trace_rewrite:*)
|
neuper@37906
|
385 |
|
neuper@38036
|
386 |
"-----2 ---";
|
neuper@52101
|
387 |
trace_rewrite := false;
|
neuper@37906
|
388 |
match_pbl fmz pbt;
|
neuper@42395
|
389 |
trace_rewrite := false;
|
neuper@37906
|
390 |
(*... if there is no rewrite, then there is something wrong with prls*)
|
neuper@52101
|
391 |
|
neuper@38036
|
392 |
"-----3 ---";
|
wneuper@59111
|
393 |
default_print_depth 7;
|
neuper@37906
|
394 |
val prls = (#prls o get_pbt) ["polynomial","simplification"];
|
wneuper@59111
|
395 |
default_print_depth 3;
|
neuper@42395
|
396 |
val t = str2term "((5*x^^^2 + 3) * (2*x^^^7 + 3) - (3*x^^^5 + 8) * (6*x^^^4 - 1)) is_polyexp";
|
neuper@37926
|
397 |
val SOME (t',_) = rewrite_set_ thy false prls t;
|
neuper@48760
|
398 |
if t' = @{term True} then ()
|
neuper@38031
|
399 |
else error "poly.sml: diff.behav. in check pbl 'polynomial..";
|
neuper@42395
|
400 |
(*... if this works, but --1-- does still NOT work, check types:*)
|
neuper@37906
|
401 |
|
neuper@38036
|
402 |
"-----4 ---";
|
neuper@42395
|
403 |
(*show_types:=true;*)
|
neuper@37906
|
404 |
(*
|
neuper@37906
|
405 |
> val NoMatch' {Given=gi, Where=wh, Find=fi,...} = match_pbl fmz pbt;
|
neuper@37906
|
406 |
val wh = [False "(t_::real => real) (is_polyexp::real)"]
|
neuper@37906
|
407 |
......................^^^^^^^^^^^^...............^^^^*)
|
neuper@37906
|
408 |
val Matches' _ = match_pbl fmz pbt;
|
neuper@42395
|
409 |
(*show_types:=false;*)
|
neuper@37906
|
410 |
|
neuper@38036
|
411 |
"-------- me 'poly. simpl.' Schalk I p.63 No.267b -------";
|
neuper@38036
|
412 |
"-------- me 'poly. simpl.' Schalk I p.63 No.267b -------";
|
neuper@38036
|
413 |
"-------- me 'poly. simpl.' Schalk I p.63 No.267b -------";
|
neuper@42395
|
414 |
val fmz = ["Term ((5*x^^^2 + 3) * (2*x^^^7 + 3) - (3*x^^^5 + 8) * (6*x^^^4 - 1))", "normalform N"];
|
neuper@37906
|
415 |
val (dI',pI',mI') =
|
neuper@37991
|
416 |
("Poly",["polynomial","simplification"],
|
neuper@37906
|
417 |
["simplification","for_polynomials"]);
|
neuper@37906
|
418 |
val p = e_pos'; val c = [];
|
neuper@37906
|
419 |
val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
|
neuper@37906
|
420 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
421 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37924
|
422 |
(writeln o (itms2str_ ctxt)) (get_obj g_pbl pt (fst p));
|
neuper@37906
|
423 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
424 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
425 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
426 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
427 |
val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
|
neuper@37906
|
428 |
val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
|
neuper@37906
|
429 |
val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
|
neuper@42395
|
430 |
if f2str f = "17 + 15 * x ^^^ 2 + -48 * x ^^^ 4 + 3 * x ^^^ 5 + 6 * x ^^^ 7 + -8 * x ^^^ 9"
|
neuper@38031
|
431 |
then () else error "poly.sml diff.behav. in me Schalk I p.63 No.267b";
|
neuper@37906
|
432 |
|
neuper@38036
|
433 |
"-------- interSteps for Schalk 299a --------------------";
|
neuper@38036
|
434 |
"-------- interSteps for Schalk 299a --------------------";
|
neuper@38036
|
435 |
"-------- interSteps for Schalk 299a --------------------";
|
s1210629013@55445
|
436 |
reset_states ();
|
neuper@37906
|
437 |
CalcTree
|
neuper@42395
|
438 |
[(["Term ((x - y)*(x + (y::real)))", "normalform N"],
|
neuper@37991
|
439 |
("Poly",["polynomial","simplification"],
|
neuper@37906
|
440 |
["simplification","for_polynomials"]))];
|
neuper@37906
|
441 |
Iterator 1;
|
neuper@37906
|
442 |
moveActiveRoot 1;
|
s1210629013@55446
|
443 |
autoCalculate' 1 CompleteCalc;
|
neuper@37906
|
444 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
445 |
|
neuper@37906
|
446 |
interSteps 1 ([1],Res)(*<ERROR> syserror in detailstep </ERROR>*);
|
neuper@37906
|
447 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
448 |
if existpt' ([1,1], Frm) pt then ()
|
neuper@38031
|
449 |
else error "poly.sml: interSteps doesnt work again 1";
|
neuper@37906
|
450 |
|
neuper@37906
|
451 |
interSteps 1 ([1,1],Res)(*<ERROR> syserror in detailstep </ERROR>*);
|
neuper@37906
|
452 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@42395
|
453 |
(*============ inhibit exn WN120316 ==============================================
|
neuper@37906
|
454 |
if existpt' ([1,1,1], Frm) pt then ()
|
neuper@38031
|
455 |
else error "poly.sml: interSteps doesnt work again 2";
|
neuper@42395
|
456 |
============ inhibit exn WN120316 ==============================================*)
|
neuper@37906
|
457 |
|
neuper@38036
|
458 |
"-------- norm_Poly NOT COMPLETE ------------------------";
|
neuper@38036
|
459 |
"-------- norm_Poly NOT COMPLETE ------------------------";
|
neuper@38036
|
460 |
"-------- norm_Poly NOT COMPLETE ------------------------";
|
neuper@37926
|
461 |
val SOME (f',_) = rewrite_set_ thy false norm_Poly
|
neuper@42395
|
462 |
(str2term "L = k - 2 * q + (k - 2 * q) + (k - 2 * q) + (k - 2 * q) + senkrecht + oben");
|
neuper@42395
|
463 |
if term2str f' = "L = 2 * 2 * k + oben + 2 * -4 * q + senkrecht"
|
neuper@42395
|
464 |
then ((*norm_Poly NOT COMPLETE -- TODO MG*))
|
neuper@42395
|
465 |
else error "norm_Poly changed behavior";
|
neuper@38036
|
466 |
|
neuper@38036
|
467 |
"-------- ord_make_polynomial ---------------------------";
|
neuper@38036
|
468 |
"-------- ord_make_polynomial ---------------------------";
|
neuper@38036
|
469 |
"-------- ord_make_polynomial ---------------------------";
|
neuper@37906
|
470 |
val t1 = str2term "2 * b + (3 * a + 3 * b)";
|
neuper@37906
|
471 |
val t2 = str2term "3 * a + 3 * b + 2 * b";
|
neuper@37906
|
472 |
|
neuper@42395
|
473 |
if ord_make_polynomial true thy [] (t1, t2) then ()
|
neuper@38031
|
474 |
else error "poly.sml: diff.behav. in ord_make_polynomial";
|
neuper@37906
|
475 |
|
neuper@37906
|
476 |
(*WN071202: ^^^ why then is there no rewriting ...*)
|
neuper@37906
|
477 |
val term = str2term "2*b + (3*a + 3*b)";
|
neuper@41929
|
478 |
val NONE = rewrite_set_ (@{theory "Isac"}) false order_add_mult term;
|
neuper@37906
|
479 |
|
neuper@37906
|
480 |
(*or why is there no rewriting this way...*)
|
neuper@37906
|
481 |
val t1 = str2term "2 * b + (3 * a + 3 * b)";
|
neuper@37906
|
482 |
val t2 = str2term "3 * a + (2 * b + 3 * b)";
|
neuper@37906
|
483 |
|