1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/test/Tools/isac/Knowledge/rational-2.sml Fri Jul 16 06:57:34 2021 +0200
1.3 @@ -0,0 +1,1791 @@
1.4 +(* Title: tests for rationals
1.5 + Author: Walther Neuper
1.6 + Use is subject to license terms.
1.7 +*)
1.8 +
1.9 +"-----------------------------------------------------------------------------";
1.10 +"-----------------------------------------------------------------------------";
1.11 +"table of contents -----------------------------------------------------------";
1.12 +"-----------------------------------------------------------------------------";
1.13 +"-------- integration lev.1 fun factout_p_ -----------------------------------";
1.14 +"-------- integration lev.1 fun cancel_p_ ------------------------------------";
1.15 +"-------- integration lev.1 fun common_nominator_p_ --------------------------";
1.16 +"-------- integration lev.1 fun add_fraction_p_ ------------------------------";
1.17 +"Rfuns-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";
1.18 +"Rfuns-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";
1.19 +"-------- rls norm_Rational downto fun gcd_poly ------------------------------";
1.20 +"Rfuns-------- rls norm_Rational downto fun add_fraction_p_ -----------------------";
1.21 +"----------- rewrite_set_ Partial_Fractions norm_Rational --------------------------------------";
1.22 +"----------- fun check_frac_sum with Free A and Const AA ---------------------------------------";
1.23 +"----------- fun cancel_p with Const AA --------------------------------------------------------";
1.24 +"-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";
1.25 +"-------- rewrite_set_ add_fractions_p from: Mathematik 1 Schalk -------------";
1.26 +"-------- integration lev.1 -- lev.5: cancel_p_ & add_fractions_p_ -----------";
1.27 +"Rfuns-------- reverse rewrite ----------------------------------------------------";
1.28 +"Rfuns-------- 'reverse-ruleset' cancel_p -----------------------------------------";
1.29 +"-------- investigate rls norm_Rational --------------------------------------";
1.30 +"-------- examples: rls norm_Rational ----------------------------------------";
1.31 +"-------- rational numerals --------------------------------------------------";
1.32 +"-------- examples cancellation from: Mathematik 1 Schalk --------------------";
1.33 +"-------- examples common denominator from: Mathematik 1 Schalk --------------";
1.34 +"-------- examples multiply and cancel from: Mathematik 1 Schalk -------------";
1.35 +"-------- examples common denominator and multiplication from: Schalk --------";
1.36 +"-------- examples double fractions from: Mathematik 1 Schalk ----------------";
1.37 +"-------- me Schalk I No.186 -------------------------------------------------";
1.38 +"-------- interSteps ..Simp_Rat_Double_No-1.xml ------------------------------";
1.39 +"-------- interSteps ..Simp_Rat_Cancel_No-1.xml ------------------------------";
1.40 +"-------- investigate rulesets for cancel_p ----------------------------------";
1.41 +"-------- fun eval_get_denominator -------------------------------------------";
1.42 +"-------- several errpats in complicated term --------------------------------";
1.43 +"-------- WN1309xx non-terminating rls norm_Rational -------------------------";
1.44 +"-----------------------------------------------------------------------------";
1.45 +"-----------------------------------------------------------------------------";
1.46 +
1.47 +
1.48 +"-------- integration lev.1 fun factout_p_ -----------------------------------";
1.49 +"-------- integration lev.1 fun factout_p_ -----------------------------------";
1.50 +"-------- integration lev.1 fun factout_p_ -----------------------------------";
1.51 +val t = TermC.str2term "(x \<up> 2 + -1*y \<up> 2) / (x \<up> 2 + -1*x*y)"
1.52 +val SOME (t', asm) = factout_p_ thy t;
1.53 +if UnparseC.term t' = "(x + y) * (x + - 1 * y) / (x * (x + - 1 * y))"
1.54 +then () else error ("factout_p_ term 1 changed: " ^ UnparseC.term t')
1.55 +;
1.56 +if UnparseC.terms asm = "[\"x \<noteq> 0\", \"x + - 1 * y \<noteq> 0\"]"
1.57 +then () else error "factout_p_ asm 1 changed"
1.58 +;
1.59 +val t = TermC.str2term "nothing + to_cancel ::real";
1.60 +if NONE = factout_p_ thy t then () else error "factout_p_ doesn't report non-applicable";
1.61 +;
1.62 +val t = TermC.str2term "((3 * x \<up> 2 + 6 *x + 3) / (2*x + 2))";
1.63 +val SOME (t', asm) = factout_p_ thy t;
1.64 +if UnparseC.term t' = "(3 + 3 * x) * (1 + x) / (2 * (1 + x))" andalso
1.65 + UnparseC.terms asm = "[\"1 + x \<noteq> 0\"]"
1.66 +then () else error "factout_p_ 1 changed";
1.67 +
1.68 +"-------- integration lev.1 fun cancel_p_ ------------------------------------";
1.69 +"-------- integration lev.1 fun cancel_p_ ------------------------------------";
1.70 +"-------- integration lev.1 fun cancel_p_ ------------------------------------";
1.71 +val t = TermC.str2term "(x \<up> 2 + -1*y \<up> 2) / (x \<up> 2 + -1*x*y)"
1.72 +val SOME (t', asm) = cancel_p_ thy t;
1.73 +if (UnparseC.term t', UnparseC.terms asm) = ("(x + y) / x", "[\"x \<noteq> 0\"]")
1.74 +then () else error ("cancel_p_ (t', asm) 1 changed: " ^ UnparseC.term t')
1.75 +;
1.76 +val t = TermC.str2term "nothing + to_cancel ::real";
1.77 +if NONE = cancel_p_ thy t then () else error "cancel_p_ doesn't report non-applicable";
1.78 +;
1.79 +val t = TermC.str2term "((3 * x \<up> 2 + 6 *x + 3) / (2*x + 2))";
1.80 +val SOME (t', asm) = cancel_p_ thy t;
1.81 +if UnparseC.term t' = "(3 + 3 * x) / 2" andalso UnparseC.terms asm = "[]"
1.82 +then () else error "cancel_p_ 1 changed";
1.83 +
1.84 +"-------- integration lev.1 fun common_nominator_p_ --------------------------";
1.85 +"-------- integration lev.1 fun common_nominator_p_ --------------------------";
1.86 +"-------- integration lev.1 fun common_nominator_p_ --------------------------";
1.87 +val t = TermC.str2term ("y / (a*x + b*x + c*x) " ^
1.88 + (* n1 d1 *)
1.89 + "+ a / (x*y)");
1.90 + (* n2 d2 *)
1.91 +val SOME (t', asm) = common_nominator_p_ thy t;
1.92 +if UnparseC.term t' =
1.93 + ("y * y / (x * ((a + b + c) * y)) " ^
1.94 + (* n1 *d2'/ (c'* ( d1' *d2')) *)
1.95 + "+ a * (a + b + c) / (x * ((a + b + c) * y))")
1.96 + (* n2 * d1' / (c'* ( d1' *d2')) *)
1.97 +then () else error "common_nominator_p_ term 1 changed";
1.98 +if UnparseC.terms asm = "[\"a + b + c \<noteq> 0\", \"y \<noteq> 0\", \"x \<noteq> 0\"]"
1.99 +then () else error "common_nominator_p_ asm 1 changed"
1.100 +
1.101 +"-------- example in mail Nipkow";
1.102 +val t = TermC.str2term "x/(x \<up> 2 + -1*y \<up> 2) + y/(x \<up> 2 + -1*x*y)";
1.103 +val SOME (t', asm) = common_nominator_p_ thy t;
1.104 +if UnparseC.term t' =
1.105 + "x * x / ((x + - 1 * y) * ((x + y) * x)) +\ny * (x + y) / ((x + - 1 * y) * ((x + y) * x))"
1.106 +then () else error "common_nominator_p_ term 2 changed"
1.107 +;
1.108 +if UnparseC.terms asm = "[\"x + y \<noteq> 0\", \"x \<noteq> 0\", \"x + - 1 * y \<noteq> 0\"]"
1.109 +then () else error "common_nominator_p_ asm 2 changed"
1.110 +
1.111 +"-------- example: applicable tested by SML code";
1.112 +val t = TermC.str2term "nothing / to_add";
1.113 +if NONE = common_nominator_p_ thy t then () else error "common_nominator_p_ term 3 changed";
1.114 +;
1.115 +val t = TermC.str2term "((x + (-1)) / (x + 1)) + ((x + 1) / (x + (-1)))";
1.116 +val SOME (t', asm) = common_nominator_p_ thy t;
1.117 +if UnparseC.term t' =
1.118 + "(x + - 1) * (- 1 + x) / ((1 + x) * (- 1 + x)) +\n(x + 1) * (1 + x) / ((1 + x) * (- 1 + x))"
1.119 + andalso UnparseC.terms asm = "[\"1 + x \<noteq> 0\", \"- 1 + x \<noteq> 0\"]"
1.120 +then () else error "common_nominator_p_ 3 changed";
1.121 +
1.122 +"-------- integration lev.1 fun add_fraction_p_ ------------------------------";
1.123 +"-------- integration lev.1 fun add_fraction_p_ ------------------------------";
1.124 +"-------- integration lev.1 fun add_fraction_p_ ------------------------------";
1.125 +val t = TermC.str2term "((x + (-1)) / (x + 1)) + ((x + 1) / (x + (-1)))";
1.126 +val SOME (t', asm) = add_fraction_p_ thy t;
1.127 +if UnparseC.term t' = "(2 + 2 * x \<up> 2) / (- 1 + x \<up> 2)"
1.128 +then () else error "add_fraction_p_ 3 changed";
1.129 +;
1.130 +if UnparseC.terms asm = "[\"- 1 + x \<up> 2 \<noteq> 0\"]"
1.131 +then () else error "add_fraction_p_ 3 changed";
1.132 +;
1.133 +val t = TermC.str2term "nothing / to_add";
1.134 +if NONE = add_fraction_p_ thy t then () else error "add_fraction_p_ term 3 changed";
1.135 +;
1.136 +val t = TermC.str2term "((x + (-1)) / (x + 1)) + ((x + 1) / (x + (-1)))";
1.137 +val SOME (t', asm) = add_fraction_p_ thy t;
1.138 +if UnparseC.term t' = "(2 + 2 * x \<up> 2) / (- 1 + x \<up> 2)" andalso
1.139 + UnparseC.terms asm = "[\"- 1 + x \<up> 2 \<noteq> 0\"]"
1.140 +then () else error "add_fraction_p_ 3 changed";
1.141 +
1.142 +"-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";
1.143 +"-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";
1.144 +"-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";
1.145 +(* trace down until prepats are evaluated
1.146 + (which does not to work, because substitution is not done -- compare rew_sub!);
1.147 + keep this sequence for the case, factout_p, cancel_p, common_nominator_p, add_fraction_p
1.148 + (again) get prepat = [] changed to <>[]. *)
1.149 +val t = TermC.str2term "(x \<up> 2 + -1*y \<up> 2) / (x \<up> 2 + -1*x*y)";
1.150 +
1.151 +(*rewrite_set_ @{theory Isac_Knowledge} true cancel t = NONE; !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
1.152 +"~~~~~ fun rewrite_set_, args:"; val (thy, bool, rls, term) = (thy, false, cancel_p, t);
1.153 +"~~~~~ fun rewrite__set_, args:"; val (thy, i, _, _, (rrls as Rrls _), t) =
1.154 + (thy, 1, bool, [], rls, term);
1.155 +(*val (t', asm, rew) = app_rev thy (i+1) rrls t; rew = false!!!!!!!!!!!!!!!!!!!!!*)
1.156 +"~~~~~ and app_rev, args:"; val (thy, i, rrls, t) = (thy, (i+1), rrls, t);
1.157 + fun chk_prepat thy erls [] t = true
1.158 + | chk_prepat thy erls prepat t =
1.159 + let
1.160 + fun chk (pres, pat) =
1.161 + (let
1.162 + val subst: Type.tyenv * Envir.tenv =
1.163 + Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
1.164 + in
1.165 + snd (eval__true thy (i + 1) (map (Envir.subst_term subst) pres) [] erls)
1.166 + end) handle Pattern.MATCH => false
1.167 + fun scan_ f [] = false (*scan_ NEVER called by []*)
1.168 + | scan_ f (pp::pps) =
1.169 + if f pp then true else scan_ f pps;
1.170 + in scan_ chk prepat end;
1.171 + (* apply the normal_form of a rev-set *)
1.172 + fun app_rev' thy (Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}) t =
1.173 + if chk_prepat thy erls prepat t
1.174 + then ((*tracing("### app_rev': t = "^UnparseC.term t);*) normal_form t)
1.175 + else NONE;
1.176 +(* val opt = app_rev' thy rrls t ..NONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
1.177 +"~~~~~ and app_rev', args:"; val (thy, (Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}), t) =
1.178 + (thy, rrls, t);
1.179 +(* chk_prepat thy erls prepat t = false!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
1.180 +(* app_sub thy i rrls t = false!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
1.181 +"~~~~~ fun chk_prepat, args:"; val (thy, erls, prepat, t) = (thy, erls, prepat, t);
1.182 + fun chk (pres, pat) =
1.183 + (let
1.184 + val subst: Type.tyenv * Envir.tenv =
1.185 + Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
1.186 + in
1.187 + snd (eval__true thy (i + 1) (map (Envir.subst_term subst) pres) [] erls)
1.188 + end) handle Pattern.MATCH => false
1.189 + fun scan_ f [] = false (*scan_ NEVER called by []*)
1.190 + | scan_ f (pp::pps) =
1.191 + if f pp then true else scan_ f pps;
1.192 +
1.193 +(*========== inhibit exn WN130823: prepat is empty ====================================
1.194 +(* scan_ chk prepat = false!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
1.195 +"~~~~~ fun , args:"; val (f, (pp::pps)) = (chk, prepat);
1.196 +f;
1.197 +val ([t1, t2], t) = pp;
1.198 +UnparseC.term t1 = "?r is_expanded";
1.199 +UnparseC.term t2 = "?s is_expanded";
1.200 +UnparseC.term t = "?r / ?s";
1.201 +(* f pp = false!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
1.202 +"~~~~~ fun chk, args:"; val (pres, pat) = (pp);
1.203 + val subst: Type.tyenv * Envir.tenv =
1.204 + Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
1.205 +(*subst =
1.206 + ({}, {(("r", 0), ("real", Var (("r", 0), "real"))),
1.207 + (("s", 0), ("real", Var (("s", 0), "real")))}*)
1.208 +;
1.209 + snd (eval__true thy (i + 1) (map (Envir.subst_term subst) pres) [] erls)
1.210 +"~~~~~ fun eval__true, args:"; val (thy, i, asms, bdv, rls) =
1.211 + (thy, (i + 1), (map (Envir.subst_term subst) pres), [], erls);
1.212 +UnparseC.terms asms; (* = "[\"?r is_expanded\",\"?s is_expanded\"]"*)
1.213 +asms = [@{term True}] orelse asms = []; (* = false*)
1.214 +asms = [@{term False}] ; (* = false*)
1.215 +"~~~~~ fun chk, args:"; val (indets, (a::asms)) = ([], asms);
1.216 +bdv (*= []: _a list*);
1.217 +val bdv : (term * term) list = [];
1.218 +rewrite__set_ thy (i+1) false;
1.219 +UnparseC.term a = "?r is_expanded"; (*hier m"usste doch der Numerator eingesetzt sein ??????????????*)
1.220 +val SOME (Const ("HOL.False", _), []) = rewrite__set_ thy (i+1) false bdv rls a
1.221 +============ inhibit exn WN130823: prepat is empty ===================================*)
1.222 +
1.223 +"-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";
1.224 +"-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";
1.225 +"-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";
1.226 +val t = TermC.str2term "(12 * x * y) / (8 * y \<up> 2 )";
1.227 +(* "-------- example 187a": exception Div raised...
1.228 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)
1.229 +val t = TermC.str2term "(8 * x \<up> 2 * y * z ) / (18 * x * y \<up> 2 * z )";
1.230 +(* "-------- example 187b": doesn't terminate...
1.231 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)
1.232 +val t = TermC.str2term "(9 * x \<up> 5 * y \<up> 2 * z \<up> 4) / (15 * x \<up> 6 * y \<up> 3 * z )";
1.233 +(* "-------- example 187c": doesn't terminate...
1.234 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)
1.235 +"~~~~~ fun rewrite_set_, args:"; val (thy, bool, rls, term) = (@{theory Isac_Knowledge}, false, cancel_p, t);
1.236 +(* WN130827: exception Div raised...
1.237 +rewrite__set_ thy 1 bool [] rls term
1.238 +*)
1.239 +"~~~~~ and rewrite__set_, args:"; val (thy, i, _, _, (rrls as Rrls _), t) =
1.240 + (thy, 1, bool, [], rls, term);
1.241 +(* WN130827: exception Div raised...
1.242 + val (t', asm, rew) = app_rev thy (i+1) rrls t
1.243 +*)
1.244 +"~~~~~ fun app_rev, args:"; val (thy, i, rrls, t) = (thy, (i+1), rrls, t);
1.245 +(* WN130827: exception Div raised...
1.246 + val opt = app_rev' thy rrls t
1.247 +*)
1.248 +"~~~~~ fun app_rev', args:"; val (thy, (Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}), t) =
1.249 + (thy, rrls, t);
1.250 +chk_prepat thy erls prepat t = true;
1.251 +(* WN130827: exception Div raised...
1.252 +normal_form t
1.253 +*)
1.254 +(* lookup Rational.thy, cancel_p: normal_form = cancel_p_ thy*)
1.255 +"~~~~~ fun cancel_p_, args:"; val (t) = (t);
1.256 +val opt = check_fraction t;
1.257 +val SOME (numerator, denominator) = opt
1.258 + val vs = TermC.vars_of t
1.259 + val baseT = type_of numerator
1.260 + val expT = HOLogic.realT
1.261 +val (SOME a, SOME b) = (poly_of_term vs numerator, poly_of_term vs denominator);
1.262 +(*"-------- example 187a": exception Div raised...
1.263 +val a = [(12, [1, 1])]: poly
1.264 +val b = [(8, [0, 2])]: poly
1.265 + val ((a', b'), c) = gcd_poly a b
1.266 +*)
1.267 +(* "-------- example 187b": doesn't terminate...
1.268 +val a = [(8, [2, 1, 1])]: poly
1.269 +val b = [(18, [1, 2, 1])]: poly
1.270 + val ((a', b'), c) = gcd_poly a b
1.271 +*)
1.272 +(* "-------- example 187c": doesn't terminate...
1.273 +val a = [(9, [5, 2, 4])]: poly
1.274 +val b = [(15, [6, 3, 1])]: poly
1.275 + val ((a', b'), c) = gcd_poly a b
1.276 +*)
1.277 +
1.278 +"-------- rls norm_Rational downto fun gcd_poly ------------------------------";
1.279 +"-------- rls norm_Rational downto fun gcd_poly ------------------------------";
1.280 +"-------- rls norm_Rational downto fun gcd_poly ------------------------------";
1.281 +val t = TermC.str2term "(x \<up> 2 - 4)*(3 - y) / ((y \<up> 2 - 9)*(2+x))";
1.282 +Rewrite.trace_on := false (*true false*);
1.283 +(* trace stops with ...: (and then jEdit hangs)..
1.284 +rewrite_set_ thy false norm_Rational t;
1.285 +:
1.286 +### rls: cancel_p on: (-12 + 4 * y + 3 * x \<up> 2 + -1 * (x \<up> 2 * y)) /
1.287 +(-18 + -9 * x + 2 * y \<up> 2 + x * y \<up> 2)
1.288 +*)
1.289 +val t = TermC.str2term (*copy from above: "::real" is not required due to " \<up> "*)
1.290 + ("(-12 + 4 * y + 3 * x \<up> 2 + -1 * (x \<up> 2 * y)) /" ^
1.291 + "(-18 + -9 * x + 2 * y \<up> 2 + x * y \<up> 2)");
1.292 +(*cancel_p_ thy t;
1.293 +exception Div raised*)
1.294 +
1.295 +"~~~~~ fun cancel_p_, args:"; val (t) = (t);
1.296 +val opt = check_fraction t;
1.297 +val SOME (numerator, denominator) = opt
1.298 + val vs = TermC.vars_of t
1.299 + val baseT = type_of numerator
1.300 + val expT = HOLogic.realT;
1.301 +(*default_print_depth 3; 999*)
1.302 +val (SOME a, SOME b) = (poly_of_term vs numerator, poly_of_term vs denominator);
1.303 +(*default_print_depth 3; 999*)
1.304 +(* does not terminate instead of returning ?:
1.305 + val ((a', b'), c) = gcd_poly a b
1.306 +val a = [(~12, [0, 0]), (3, [2, 0]), (4, [0, 1]), (~1, [2, 1])]: poly
1.307 +val b = [(~18, [0, 0]), (~9, [1, 0]), (2, [0, 2]), (1, [1, 2])]: poly
1.308 +*)
1.309 +
1.310 +"-------- rls norm_Rational downto fun add_fraction_p_ -----------------------";
1.311 +"-------- rls norm_Rational downto fun add_fraction_p_ -----------------------";
1.312 +"-------- rls norm_Rational downto fun add_fraction_p_ -----------------------";
1.313 +val thy = @{theory Isac_Knowledge};
1.314 +"----- SK060904-2a non-termination of add_fraction_p_";
1.315 +val t = TermC.str2term (" (a + b * x) / (a + -1 * (b * x)) + " ^
1.316 + " (-1 * a + b * x) / (a + b * x) ");
1.317 +(* rewrite_set_ thy false norm_Rational t
1.318 +exception Div raised*)
1.319 +(* rewrite_set_ thy false add_fractions_p t;
1.320 +exception Div raised*)
1.321 +"~~~~~ fun rewrite_set_, args:"; val (thy, bool, rls, term) =
1.322 + (@{theory Isac_Knowledge}, false, add_fractions_p, t);
1.323 +"~~~~~ and rewrite__set_, args:"; val (thy, i, _, _, (rrls as Rrls _), t) =
1.324 + (thy, 1, bool, [], rls, term);
1.325 +(* app_rev thy (i+1) rrls t;
1.326 +exception Div raised*)
1.327 +"~~~~~ and app_rev, args:"; val (thy, i, rrls, t) = (thy, (i+1), rrls, t);
1.328 + fun chk_prepat thy erls [] t = true
1.329 + | chk_prepat thy erls prepat t =
1.330 + let
1.331 + fun chk (pres, pat) =
1.332 + (let
1.333 + val subst: Type.tyenv * Envir.tenv =
1.334 + Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
1.335 + in
1.336 + snd (eval__true thy (i + 1) (map (Envir.subst_term subst) pres) [] erls)
1.337 + end) handle Pattern.MATCH => false
1.338 + fun scan_ f [] = false (*scan_ NEVER called by []*)
1.339 + | scan_ f (pp::pps) =
1.340 + if f pp then true else scan_ f pps;
1.341 + in scan_ chk prepat end;
1.342 + (* apply the normal_form of a rev-set *)
1.343 + fun app_rev' thy (Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}) t =
1.344 + if chk_prepat thy erls prepat t
1.345 + then ((*tracing("### app_rev': t = "^UnparseC.term t);*) normal_form t)
1.346 + else NONE;
1.347 +(* val opt = app_rev' thy rrls t;
1.348 +exception Div raised*)
1.349 +(* val opt = app_rev' thy rrls t;
1.350 +exception Div raised*)
1.351 +"~~~~~ and app_rev', args:"; val (thy, (Rrls{erls,prepat,scr=Rfuns{normal_form,...},...}), t) =
1.352 + (thy, rrls, t);
1.353 +chk_prepat thy erls prepat t = true = true;
1.354 +(*normal_form t
1.355 +exception Div raised*)
1.356 +(* lookup Rational.thy, val add_fractions_p: normal_form = add_fraction_p_ thy*)
1.357 +(*add_fraction_p_ thy t
1.358 +exception Div raised*)
1.359 +"~~~~~ fun add_fraction_p_, args:"; val ((_: theory), t) = (thy, t);
1.360 +val SOME ((n1, d1), (n2, d2)) = check_frac_sum t;
1.361 +UnparseC.term n1; UnparseC.term d1; UnparseC.term n2; UnparseC.term d2;
1.362 + val vs = TermC.vars_of t;
1.363 +(*default_print_depth 3; 999*)
1.364 +val (SOME _, SOME a, SOME _, SOME b) =
1.365 + (poly_of_term vs n1, poly_of_term vs d1, poly_of_term vs n2, poly_of_term vs d2);
1.366 +(*default_print_depth 3; 999*)
1.367 +(*
1.368 +val a = [(1, [1, 0, 0]), (~1, [0, 1, 1])]: poly
1.369 +val b = [(1, [1, 0, 0]), (1, [0, 1, 1])]: poly
1.370 + val ((a', b'), c) = gcd_poly a b
1.371 +*)
1.372 +
1.373 +"----------- fun check_frac_sum with Free A and Const AA ---------------------------------------";
1.374 +"----------- fun check_frac_sum with Free A and Const AA ---------------------------------------";
1.375 +"----------- fun check_frac_sum with Free A and Const AA ---------------------------------------";
1.376 +val thy = @{theory Isac_Knowledge(*Partial_Fractions*)}
1.377 +val ctxt = Proof_Context.init_global thy;
1.378 +
1.379 +(*---------- (1) with Free A, B ----------------------------------------------------------------*)
1.380 +val t = (the o (parseNEW ctxt)) "3 = A / 2 + A / 4 + (B / 2 + -1 * B / (2::real))";
1.381 + (* required for applying thms in rewriting \<up> ^*)
1.382 +(* we get details from here..*)
1.383 +
1.384 +Rewrite.trace_on := false;
1.385 +val SOME (t', _) = Rewrite.rewrite_set_ thy true add_fractions_p t;
1.386 +Rewrite.trace_on := false;
1.387 +(* Rewrite.trace_on:
1.388 +add_fractions_p on: 3 = A / 2 + A / 4 + (B / 2 + -1 * B / 2) --> 3 = A / 2 + A / 4 + 0 / 2 *)
1.389 + (* |||||||||||||||||||||||||||||||||||| *)
1.390 +
1.391 +val t = (the o (parseNEW ctxt))(* ||||||||||||||||||||||||| GUESS 1 GUESS 1 GUESS 1 GUESS 1 *)
1.392 + "A / 2 + A / 4 + (B / 2 + -1 * B / (2::real))";
1.393 +"~~~~~ fun add_fraction_p_ , ad-hoc args:"; val (t) = (t);
1.394 +val NONE = (*case*) check_frac_sum t (*of*)
1.395 +
1.396 +(* Rewrite.trace_on:
1.397 +add_fractions_p on: 3 = A / 2 + A / 4 + (B / 2 + -1 * B / 2) --> 3 = A / 2 + A / 4 + 0 / 2 *)
1.398 + (* |||||||||||||||||||||||||||| *)
1.399 +val t = (the o (parseNEW ctxt))(* ||||||||||||||||||||||||| GUESS 2 GUESS 2 GUESS 2 GUESS 2 *)
1.400 + "A / 4 + (B / 2 + -1 * B / (2::real))";
1.401 +"~~~~~ fun add_fraction_p_ , ad-hoc args:"; val (t) = (t);
1.402 +val SOME ((n1, d1), (n2, d2)) = (*case*) check_frac_sum t (*of*);
1.403 +(*+*)if (UnparseC.term n1, UnparseC.term d1) = ("A" , "4") andalso
1.404 +(*+*) (UnparseC.term n2, UnparseC.term d2) = ("B / 2 + - 1 * B / 2", "1")
1.405 +(*+*)then () else error "check_frac_sum (A / 4 + (B / 2 + -1 * B / (2::real))) changed";
1.406 +
1.407 + val vs = TermC.vars_of t;
1.408 +val (SOME [(1, [1, 0])], SOME [(4, [0, 0])], NONE, SOME [(1, [0, 0])]) =
1.409 + (*case*) (poly_of_term vs n1, poly_of_term vs d1, poly_of_term vs n2, poly_of_term vs d2) (*of*);
1.410 +
1.411 +"~~~~~ fun poly_of_term , args:"; val (vs, t) = (vs, n1);
1.412 +val SOME [(1, [xxx, 0])] = SOME [monom_of_term vs (1, replicate (length vs) 0) t];
1.413 +(*+*)if xxx = 1 then () else error "monom_of_term changed"
1.414 +
1.415 +"~~~~~ fun monom_of_term , args:"; val (vs, (c, es), (Free (id, _))) =
1.416 + (vs, (1, replicate (length vs) 0), t);
1.417 +case vs of [Free ("A", _), Free ("B", _)] =>
1.418 + if c = 1 andalso id = "A"
1.419 + then () else error "monom_of_term Free changed 1"
1.420 +| _ => error "monom_of_term Free changed 2";
1.421 +
1.422 +(*---------- (2) with Const AA, BB --------------------------------------------------------------*)
1.423 +val t = (the o (parseNEW ctxt)) "3 = AA / 2 + AA / 4 + (BB / 2 + -1 * BB / 2)";
1.424 + (*AA :: real*)
1.425 +(* we get details from here..*)
1.426 +
1.427 +Rewrite.trace_on := false;
1.428 +val SOME (t', _) = Rewrite.rewrite_set_ thy true add_fractions_p t;
1.429 +Rewrite.trace_on := false;
1.430 +(* Rewrite.trace_on:
1.431 +add_fractions_p on: 3 = A / 2 + A / 4 + (B / 2 + -1 * B / 2) --> 3 = A / 2 + A / 4 + 0 / 2 *)
1.432 + (* |||||||||||||||||||||||||||||||||||| *)
1.433 +val t = (the o (parseNEW ctxt))(* ||||||||||||||||||||||||| *)
1.434 + "AA / 2 + AA / 4 + (BB / 2 + -1 * BB / 2)";
1.435 +"~~~~~ fun add_fraction_p_ , ad-hoc args:"; val (t) = (t);
1.436 +val NONE = (*case*) check_frac_sum t (*of*)
1.437 +
1.438 +(* Rewrite.trace_on:
1.439 +add_fractions_p on: 3 = A / 2 + A / 4 + (B / 2 + -1 * B / 2) --> 3 = A / 2 + A / 4 + 0 / 2 *)
1.440 + (* |||||||||||||||||||||||||||| *)
1.441 +val t = (the o (parseNEW ctxt))(* ||||||||||||||||||||||||| *)
1.442 + "AA / 4 + (BB / 2 + -1 * BB / 2)";
1.443 +"~~~~~ fun add_fraction_p_ , ad-hoc args:"; val (t) = (t);
1.444 +val SOME ((n1, d1), (n2, d2)) = (*case*) check_frac_sum t (*of*);
1.445 +(*+*)if (UnparseC.term n1, UnparseC.term d1) = ("AA" , "4") andalso
1.446 +(*+*) (UnparseC.term n2, UnparseC.term d2) = ("BB / 2 + - 1 * BB / 2", "1")
1.447 +(*+*)then () else error "check_frac_sum (AA / 4 + (BB / 2 + -1 * BB / 2)) changed";
1.448 +
1.449 + val vs = TermC.vars_of t;
1.450 +val (SOME [(1, [1, 0])], SOME [(4, [0, 0])], NONE, SOME [(1, [0, 0])]) =
1.451 + (*case*) (poly_of_term vs n1, poly_of_term vs d1, poly_of_term vs n2, poly_of_term vs d2) (*of*);
1.452 +
1.453 +"~~~~~ fun poly_of_term , args:"; val (vs, t) = (vs, n1);
1.454 +val SOME [(1, [xxx, 0])] = SOME [monom_of_term vs (1, replicate (length vs) 0) t];
1.455 +(*+*)if xxx = 1 then () else error "monom_of_term changed"
1.456 +
1.457 +"~~~~~ fun monom_of_term , args:"; val (vs, (c, es), (Const (id, _))) =
1.458 + (vs, (1, replicate (length vs) 0), t);
1.459 +case vs of [Const ("Partial_Fractions.AA", _), Const ("Partial_Fractions.BB", _)] =>
1.460 + if c = 1 andalso id = "Partial_Fractions.AA"
1.461 + then () else error "monom_of_term Const changed 1"
1.462 +| _ => error "monom_of_term Const changed 2";
1.463 +
1.464 +"----------- fun cancel_p with Const AA --------------------------------------------------------";
1.465 +"----------- fun cancel_p with Const AA --------------------------------------------------------";
1.466 +"----------- fun cancel_p with Const AA --------------------------------------------------------";
1.467 +val thy = @{theory Partial_Fractions};
1.468 +val ctxt = Proof_Context.init_global @{theory}
1.469 +val SOME t = TermC.parseNEW ctxt "2 * AA / 2"; (* Const ("Free ("AA", "real") *)
1.470 +
1.471 +val SOME (t', _) = rewrite_set_ thy true cancel_p t;
1.472 +case t' of
1.473 + Const ("Rings.divide_class.divide", _) $ Const ("Partial_Fractions.AA", _) $
1.474 + Const ("Groups.one_class.one", _) => ()
1.475 +| _ => error "WRONG rewrite_set_ cancel_p (2 * AA / 2) \<longrightarrow> AA changed";
1.476 +
1.477 +"~~~~~ fun cancel_p , args:"; val (t) = (t);
1.478 +val opt = check_fraction t
1.479 +val SOME (numerator, denominator) = (*case*) opt (*of*);
1.480 +
1.481 +if UnparseC.term numerator = "2 * AA" andalso UnparseC.term denominator = "2"
1.482 +then () else error "check_fraction (2 * AA / 2) changed";
1.483 + val vs = TermC.vars_of t;
1.484 +case vs of
1.485 + [Const ("Partial_Fractions.AA", _)] => ()
1.486 +| _ => error "rewrite_set_ cancel_p (2 * AA / 2) \<longrightarrow> AA/1 changed";
1.487 +
1.488 +
1.489 +"-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";
1.490 +"-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";
1.491 +"-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";
1.492 +val thy = @{theory "Rational"};
1.493 +"-------- WN";
1.494 +val t = TermC.str2term "(2 + -3 * x) / 9";
1.495 +if NONE = rewrite_set_ thy false cancel_p t then ()
1.496 +else error "rewrite_set_ cancel_p must return NONE, if the term cannot be cancelled";
1.497 +
1.498 +"-------- example 186a";
1.499 +val t = TermC.str2term "(14 * x * y) / (x * y)";
1.500 + is_expanded (TermC.str2term "14 * x * y");
1.501 + is_expanded (TermC.str2term "x * y");
1.502 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.503 +if (UnparseC.term t', UnparseC.terms asm) = ("14 / 1", "[]")
1.504 +then () else error "rational.sml cancel Schalk 186a";
1.505 +
1.506 +"-------- example 186b";
1.507 +val t = TermC.str2term "(60 * a * b) / ( 15 * a * b )";
1.508 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.509 +if (UnparseC.term t', UnparseC.terms asm) = ("4 / 1", "[]")
1.510 +then () else error "rational.sml cancel Schalk 186b";
1.511 +
1.512 +"-------- example 186c";
1.513 +val t = TermC.str2term "(144 * a \<up> 2 * b * c) / (12 * a * b * c)";
1.514 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.515 +if (UnparseC.term t', UnparseC.terms asm) = ("12 * a / 1", "[]")
1.516 +then () else error "rational.sml cancel Schalk 186c";
1.517 +
1.518 +(* !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! exception Div raised !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1.519 + see --- fun rewrite_set_ downto fun gcd_poly ---
1.520 +"-------- example 187a";
1.521 +val t = TermC.str2term "(12 * x * y) / (8 * y \<up> 2 )";
1.522 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.523 +if (UnparseC.term t', UnparseC.terms asm) = ("3 * x / (2 * y)", "[\"4 * y ~= 0\"]")
1.524 +then () else error "rational.sml cancel Schalk 187a";
1.525 +*)
1.526 +
1.527 +(* doesn't terminate !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1.528 + see --- fun rewrite_set_ downto fun gcd_poly ---
1.529 +"-------- example 187b";
1.530 +val t = TermC.str2term "(8 * x \<up> 2 * y * z ) / (18 * x * y \<up> 2 * z )";
1.531 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.532 +if (UnparseC.term t', UnparseC.terms asm) = ("4 * x / (9 * y)", "[\"2 * (z * (y * x)) ~= 0\"]")
1.533 +then () else error "rational.sml cancel Schalk 187b";
1.534 +*)
1.535 +
1.536 +(* doesn't terminate !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1.537 + see --- fun rewrite_set_ downto fun gcd_poly ---
1.538 +"-------- example 187c";
1.539 +val t = TermC.str2term "(9 * x \<up> 5 * y \<up> 2 * z \<up> 4) / (15 * x \<up> 6 * y \<up> 3 * z )";
1.540 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.541 +if (UnparseC.term t', UnparseC.terms asm) =
1.542 + ("3 * z \<up> 3 / (5 * (y * x))", "[\"3 * (z * (y \<up> 2 * x \<up> 5)) ~= 0\"]")
1.543 +then () else error "rational.sml cancel Schalk 187c";
1.544 +*)
1.545 +
1.546 +"-------- example 188a";
1.547 +val t = TermC.str2term "(-8 + 8 * x) / (-9 + 9 * x)";
1.548 + is_expanded (TermC.str2term "8 * x + -8");
1.549 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.550 +if (UnparseC.term t', UnparseC.terms asm) = ("8 / 9", "[]")
1.551 +then () else error "rational.sml cancel Schalk 188a";
1.552 +
1.553 +val t = TermC.str2term "(8*((-1) + x))/(9*((-1) + x))";
1.554 +val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
1.555 +if (UnparseC.term t', UnparseC.terms asm) = ("8 / 9", "[]")
1.556 +then () else error "rational.sml cancel Schalk make_polynomial 1";
1.557 +
1.558 +"-------- example 188b";
1.559 +val t = TermC.str2term "(-15 + 5 * x) / (-18 + 6 * x)";
1.560 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.561 +if (UnparseC.term t', UnparseC.terms asm) = ("5 / 6", "[]")
1.562 +then () else error "rational.sml cancel Schalk 188b";
1.563 +
1.564 +"-------- example 188c";
1.565 +val t = TermC.str2term "(a + -1 * b) / (b + -1 * a)";
1.566 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.567 +if (UnparseC.term t', UnparseC.terms asm) = ("- 1 / 1", "[]")
1.568 +then () else error "rational.sml cancel Schalk 188c";
1.569 +
1.570 +is_expanded (TermC.str2term "a + -1 * b") = true;
1.571 +val t = TermC.str2term "((- 1)*(b + (-1) * a))/(1*(b + (- 1) * a))";
1.572 +val SOME (t', asm) = rewrite_set_ thy false make_polynomial t;
1.573 +if (UnparseC.term t', UnparseC.terms asm) = ("(a + - 1 * b) / (- 1 * a + b)", "[]")
1.574 +then () else error "rational.sml cancel Schalk make_polynomial 2";
1.575 +
1.576 +"-------- example 190a";
1.577 +val t = TermC.str2term "( 27 * a \<up> 3 + 9 * a \<up> 2 + 3 * a + 1 ) / ( 27 * a \<up> 3 + 18 * a \<up> 2 + 3 * a )";
1.578 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.579 +if (UnparseC.term t', UnparseC.terms asm) =
1.580 + ("(1 + 9 * a \<up> 2) / (3 * a + 9 * a \<up> 2)", "[\"3 * a + 9 * a \<up> 2 \<noteq> 0\"]")
1.581 +then () else error "rational.sml cancel Schalk 190a";
1.582 +
1.583 +"-------- example 190c";
1.584 +val t = TermC.str2term "((1 + 9 * a \<up> 2)*(1 + 3 * a))/((3 * a + 9 * a \<up> 2)*(1 + 3 * a))";
1.585 +val SOME (t', asm) = rewrite_set_ thy false make_polynomial t;
1.586 +if (UnparseC.term t', UnparseC.terms asm) =
1.587 + ("(1 + 3 * a + 9 * a \<up> 2 + 27 * a \<up> 3) /\n(3 * a + 18 * a \<up> 2 + 27 * a \<up> 3)", "[]")
1.588 +then () else error "rational.sml make_polynomial Schalk 190c";
1.589 +
1.590 +"-------- example 191a";
1.591 +val t = TermC.str2term "( x \<up> 2 + -1 * y \<up> 2 ) / ( x + y )";
1.592 + is_expanded (TermC.str2term "x \<up> 2 + - 1 * y \<up> 2") = false; (*!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
1.593 + is_expanded (TermC.str2term "x + y") = true;
1.594 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.595 +if (UnparseC.term t', UnparseC.terms asm) = ("(x + - 1 * y) / 1", "[]")
1.596 +then () else error "rational.sml make_polynomial Schalk 191a";
1.597 +
1.598 +"-------- example 191b";
1.599 +val t = TermC.str2term "((x + (- 1) * y)*(x + y))/((1)*(x + y))";
1.600 +val SOME (t', asm) = rewrite_set_ thy false make_polynomial t;
1.601 +if (UnparseC.term t', UnparseC.terms asm) = ("(x \<up> 2 + - 1 * y \<up> 2) / (x + y)", "[]")
1.602 +then () else error "rational.sml make_polynomial Schalk 191b";
1.603 +
1.604 +"-------- example 191c";
1.605 +val t = TermC.str2term "( 9 * x \<up> 2 + -30 * x + 25 ) / ( 9 * x \<up> 2 + -25 )";
1.606 + is_expanded (TermC.str2term "9 * x \<up> 2 + -30 * x + 25") = true;
1.607 + is_expanded (TermC.str2term "25 + -30*x + 9*x \<up> 2") = true;
1.608 + is_expanded (TermC.str2term "-25 + 9*x \<up> 2") = true;
1.609 +
1.610 +val t = TermC.str2term "(((-5) + 3 * x)*((-5) + 3 * x))/((5 + 3 * x)*((-5) + 3 * x))";
1.611 +val SOME (t', asm) = rewrite_set_ thy false make_polynomial t;
1.612 +if (UnparseC.term t', UnparseC.terms asm) = ("(25 + - 30 * x + 9 * x \<up> 2) / (- 25 + 9 * x \<up> 2)", "[]")
1.613 +then () else error "rational.sml make_polynomial Schalk 191c";
1.614 +
1.615 +"-------- example 192b";
1.616 +val t = TermC.str2term "( 7 * x \<up> 3 + - 1 * x \<up> 2 * y ) / ( 7 * x * y \<up> 2 + - 1 * y \<up> 3 )";
1.617 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.618 +if (UnparseC.term t', UnparseC.terms asm) = ("x \<up> 2 / y \<up> 2", "[\"y \<up> 2 \<noteq> 0\"]")
1.619 +then () else error "rational.sml cancel_p Schalk 192b";
1.620 +
1.621 +val t = TermC.str2term "((x \<up> 2)*(7 * x + (-1) * y))/((y \<up> 2)*(7 * x + (-1) * y))";
1.622 +val SOME (t', asm) = rewrite_set_ thy false make_polynomial t;
1.623 +if (UnparseC.term t', UnparseC.terms asm) =
1.624 + ("(7 * x \<up> 3 + - 1 * x \<up> 2 * y) /\n(7 * x * y \<up> 2 + - 1 * y \<up> 3)", "[]")
1.625 +then () else error "rational.sml make_polynomial Schalk 192b";
1.626 +
1.627 +val t = TermC.str2term "((x \<up> 2)*(7 * x + (-1) * y))/((y \<up> 2)*(7 * x + (-1) * y))";
1.628 +val SOME (t', asm) = rewrite_set_ thy false make_polynomial t;
1.629 +if (UnparseC.term t', UnparseC.terms asm) =
1.630 + ("(7 * x \<up> 3 + - 1 * x \<up> 2 * y) /\n(7 * x * y \<up> 2 + - 1 * y \<up> 3)", "[]")
1.631 +then () else error "rational.sml make_polynomial Schalk WN050929 not working";
1.632 +
1.633 +"-------- example 193a";
1.634 +val t = TermC.str2term "( x \<up> 2 + -6 * x + 9 ) / ( x \<up> 2 + -9 )";
1.635 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.636 +if (UnparseC.term t', UnparseC.terms asm) = ("(- 3 + x) / (3 + x)", "[\"3 + x \<noteq> 0\"]")
1.637 +then () else error "rational.sml cancel_p Schalk 193a";
1.638 +
1.639 +"-------- example 193b";
1.640 +val t = TermC.str2term "( x \<up> 2 + -8 * x + 16 ) / ( 2 * x \<up> 2 + -32 )";
1.641 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.642 +if (UnparseC.term t', UnparseC.terms asm) = ("(- 4 + x) / (8 + 2 * x)", "[\"8 + 2 * x \<noteq> 0\"]")
1.643 +then () else error "rational.sml cancel_p Schalk 193b";
1.644 +
1.645 +"-------- example 193c";
1.646 +val t = TermC.str2term "( 2 * x + -50 * x \<up> 3 ) / ( 25 * x \<up> 2 + -10 * x + 1 )";
1.647 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.648 +if (UnparseC.term t', UnparseC.terms asm) =
1.649 + ("(2 * x + 10 * x \<up> 2) / (1 + - 5 * x)", "[\"1 + - 5 * x \<noteq> 0\"]")
1.650 +then () else error "rational.sml cancel_p Schalk 193c";
1.651 +
1.652 +(*WN: improved with new numerals*)
1.653 +val t = TermC.str2term "(-25 + 9*x \<up> 2)/(5 + 3*x)";
1.654 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.655 +if (UnparseC.term t', UnparseC.terms asm) = ("(- 5 + 3 * x) / 1", "[]")
1.656 +then () else error "rational.sml cancel WN 1";
1.657 +
1.658 +"-------- example heuberger";
1.659 +val t = TermC.str2term ("(x \<up> 4 + x * y + x \<up> 3 * y + y \<up> 2) / " ^
1.660 + "(x + 5 * x \<up> 2 + y + 5 * x * y + x \<up> 2 * y \<up> 3 + x * y \<up> 4)");
1.661 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.662 +if (UnparseC.term t', UnparseC.terms asm) =
1.663 + ("(x \<up> 3 + y) / (1 + 5 * x + x * y \<up> 3)", "[\"1 + 5 * x + x * y \<up> 3 \<noteq> 0\"]")
1.664 +then () else error "rational.sml cancel_p heuberger";
1.665 +
1.666 +"-------- rewrite_set_ add_fractions_p from: Mathematik 1 Schalk -------------";
1.667 +"-------- rewrite_set_ add_fractions_p from: Mathematik 1 Schalk -------------";
1.668 +"-------- rewrite_set_ add_fractions_p from: Mathematik 1 Schalk -------------";
1.669 +(*deleted example 204 ... 236b at update Isabelle2012-->2013*)
1.670 +
1.671 +"-------- integration lev.1 -- lev.5: cancel_p_ & add_fractions_p_ -----------";
1.672 +"-------- integration lev.1 -- lev.5: cancel_p_ & add_fractions_p_ -----------";
1.673 +"-------- integration lev.1 -- lev.5: cancel_p_ & add_fractions_p_ -----------";
1.674 +val t = TermC.str2term ("123 = (a*x)/(b*x) + (c*x)/(d*x) + (e*x)/(f*x::real)");
1.675 +"-------- gcd_poly integration level 1: works on exact term";
1.676 +if NONE = cancel_p_ thy t then () else error "cancel_p_ works on exact fraction";
1.677 +if NONE = add_fraction_p_ thy t then () else error "add_fraction_p_ works on exact fraction";
1.678 +
1.679 +"-------- gcd_poly integration level 2: picks out ONE appropriate subterm";
1.680 +val SOME (t', asm) = rewrite_set_ thy false cancel_p t;
1.681 +if UnparseC.term t' = "123 = a * x / (b * x) + c * x / (d * x) + e / f"
1.682 +then () else error "level 2, rewrite_set_ cancel_p: changed";
1.683 +val SOME (t', asm) = rewrite_set_ thy false add_fractions_p t;
1.684 +if UnparseC.term t' = "123 = (b * c * x + a * d * x) / (b * d * x) + e * x / (f * x)"
1.685 +then () else error "level 2, rewrite_set_ add_fractions_p: changed";
1.686 +
1.687 +"-------- gcd_poly integration level 3: rewrites all appropriate subterms";
1.688 +val SOME (t', asm) = rewrite_set_ thy false cancel_p_rls t;
1.689 +if UnparseC.term t' = "123 = a / b + c / d + e / f"
1.690 +then () else error "level 3, rewrite_set_ cancel_p_rls: changed";
1.691 +val SOME (t', asm) = rewrite_set_ thy false add_fractions_p_rls t; (*CREATE add_fractions_p_rls*)
1.692 +if UnparseC.term t' = "123 = (b * d * e * x + b * c * f * x + a * d * f * x) / (b * d * f * x)"
1.693 +then () else error "level 3, rewrite_set_ add_fractions_p_rls: changed";
1.694 +
1.695 +"-------- gcd_poly integration level 4: iteration cancel_p -- add_fraction_p";
1.696 +(* simpler variant *)
1.697 +val testrls = Rule_Set.append_rules "testrls" Rule_Set.empty [Rls_ cancel_p, Rls_ add_fractions_p]
1.698 +val SOME (t', asm) = rewrite_set_ thy false testrls t;
1.699 +(*Rewrite.trace_on := false;
1.700 +# rls: testrls on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
1.701 +## rls: cancel_p on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
1.702 +## rls: add_fractions_p on: 123 = a * x / (b * x) + c * x / (d * x) + e / f
1.703 +## rls: cancel_p on: 123 = (b * c * x + a * d * x) / (b * d * x) + e / f
1.704 +## rls: add_fractions_p on: 123 = (b * c + a * d) / (b * d) + e / f
1.705 +## rls: cancel_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
1.706 +## rls: add_fractions_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f) *)
1.707 +if UnparseC.term t' = "123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)"
1.708 +then () else error "level 4, rewrite_set_ *_p: changed";
1.709 +
1.710 +(* complicated variant *)
1.711 +val testrls_rls = Rule_Set.append_rules "testrls_rls" Rule_Set.empty [Rls_ cancel_p_rls, Rls_ add_fractions_p_rls];
1.712 +val SOME (t', asm) = rewrite_set_ thy false testrls_rls t;
1.713 +(*# rls: testrls_rls on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
1.714 +## rls: cancel_p_rls on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
1.715 +### rls: cancel_p on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
1.716 +### rls: cancel_p on: 123 = a * x / (b * x) + c * x / (d * x) + e / f
1.717 +### rls: cancel_p on: 123 = a * x / (b * x) + c / d + e / f
1.718 +### rls: cancel_p on: 123 = a / b + c / d + e / f
1.719 +## rls: add_fractions_p_rls on: 123 = a / b + c / d + e / f
1.720 +### rls: add_fractions_p on: 123 = a / b + c / d + e / f
1.721 +### rls: add_fractions_p on: 123 = (b * c + a * d) / (b * d) + e / f
1.722 +### rls: add_fractions_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
1.723 +## rls: cancel_p_rls on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
1.724 +### rls: cancel_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
1.725 +## rls: add_fractions_p_rls on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
1.726 +### rls: add_fractions_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f) *)
1.727 +if UnparseC.term t' = "123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)"
1.728 +then () else error "level 4, rewrite_set_ *_p_rls: changed"
1.729 +
1.730 +"-------- gcd_poly integration level 5: cancel_p & add_fraction_p within norm_Rational";
1.731 +val SOME (t', asm) = rewrite_set_ thy false norm_Rational t;
1.732 +if UnparseC.term t' = "123 = (a * d * f + b * c * f + b * d * e) / (b * d * f)"
1.733 +then () else error "level 5, rewrite_set_ norm_Rational: changed"
1.734 +
1.735 +"-------- reverse rewrite ----------------------------------------------------";
1.736 +"-------- reverse rewrite ----------------------------------------------------";
1.737 +"-------- reverse rewrite ----------------------------------------------------";
1.738 +(** the term for which reverse rewriting is demonstrated **)
1.739 +val t = TermC.str2term "(9 + -1 * x \<up> 2) / (9 + 6 * x + x \<up> 2)";
1.740 +val Rrls {scr = Rfuns {init_state = ini, locate_rule = loc,
1.741 + next_rule = nex, normal_form = nor, ...},...} = cancel_p;
1.742 +
1.743 +(** normal_form produces the result in ONE step **)
1.744 + val SOME (t', _) = nor t;
1.745 +if UnparseC.term t' = "(3 + - 1 * x) / (3 + x)" then ()
1.746 +else error "rational.sml normal_form (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2)";
1.747 +
1.748 +(** initialize the interpreter state used by the 'me' **)
1.749 + val (t, _, revsets, _) = ini t;
1.750 +
1.751 +if length (hd revsets) = 11 then () else error "length of revset changed";
1.752 +(*//----------------------------------TOODOO (*Rfuns revsets \<longrightarrow> broken*)
1.753 +if (revsets |> nth 1 |> nth 1 |> id_of_thm) =
1.754 + (@{thm realpow_twoI} |> Thm.get_name_hint |> ThmC.cut_id)
1.755 +then () else error "first element of revset changed";
1.756 +if
1.757 +(revsets |> nth 1 |> nth 1 |> Rule.to_string) = "Thm (\"realpow_twoI\",?r1 \<up> 2 = ?r1 * ?r1)" andalso
1.758 +(revsets |> nth 1 |> nth 2 |> Rule.to_string) = "Thm (\"#: 9 = 3 \<up> 2\",9 = 3 \<up> 2)" andalso
1.759 +(revsets |> nth 1 |> nth 3 |> Rule.to_string) = "Thm (\"#: 6 * x = 2 * (3 * x)\",6 * x = 2 * (3 * x))"
1.760 +andalso
1.761 +(revsets |> nth 1 |> nth 4 |> Rule.to_string) = "Thm (\"#: -3 * x = -1 * (3 * x)\",-3 * x = -1 * (3 * x))"
1.762 +andalso
1.763 +(revsets |> nth 1 |> nth 5 |> Rule.to_string) = "Thm (\"#: 9 = 3 * 3\",9 = 3 * 3)" andalso
1.764 +(revsets |> nth 1 |> nth 6 |> Rule.to_string) = "Rls_ (\"sym_order_mult_rls_\")" andalso
1.765 +(revsets |> nth 1 |> nth 7 |> Rule.to_string) =
1.766 + "Thm (\"sym_mult.assoc\",?a * (?b * ?c) = ?a * ?b * ?c)"
1.767 +then () else error "first 7 elements in revset changed"
1.768 + \\----------------------------------TOODOO (*Rfuns revsets \<longrightarrow> broken*)*)
1.769 +
1.770 +(** find the rule 'r' to apply to term 't' **)
1.771 +(*/------- WN1309: since cancel_ (accepted "-" between monomials) has been replaced by cancel_p_
1.772 + for Isabelle2013, we don't get a working revset, but non-termination:
1.773 +
1.774 + val SOME (r as (Thm (str, thm))) = nex revsets t;
1.775 + :
1.776 +((3 * 3 + -1 * x * x) / (3 * 3 + 2 * 3 * x + x * x),
1.777 + Rls_ ("sym_order_mult_rls_"), ((3 * 3 + -1 * (x * x)) / (3 * 3 + 2 * (3 * x) + x * x), []))", "
1.778 +((3 * 3 + -1 * (x * x)) / (3 * 3 + 2 * (3 * x) + x * x),
1.779 + Thm ("sym_mult.assoc", ""), ((3 * 3 + -1 * (x * x)) / (3 * 3 + 2 * 3 * x + x * x), []))", "
1.780 +((3 * 3 + -1 * (x * x)) / (3 * 3 + 2 * 3 * x + x * x),
1.781 + Thm ("sym_mult.assoc", ""), ((3 * 3 + -1 * x * x) / (3 * 3 + 2 * 3 * x + x * x), []))", "
1.782 +((3 * 3 + -1 * x * x) / (3 * 3 + 2 * 3 * x + x * x), Rls_ ("sym_order_mult_rls_"), ((3 * 3 + -1 * (x * x)) / (3 * 3 + 2 * (3 * x) + x * x), []))", "
1.783 + :
1.784 +### Isabelle2002:
1.785 + Thm ("sym_#mult_2_3", "6 = 2 * 3")
1.786 +### Isabelle2009-2 for cancel_ (not cancel_p_):
1.787 +if str = "sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))"
1.788 + andalso ThmC.string_of_thm thm =
1.789 + (string_of_thm (Thm.make_thm @{theory "Isac_Knowledge"}
1.790 + (Trueprop $ (Thm.term_of o the o (TermC.parse thy)) "9 = 3 \<up> 2"))) then ()
1.791 +else error "rational.sml next_rule (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2)";
1.792 +\---------------------------------------------------------------------------------------/*)
1.793 +
1.794 +(** check, if the rule 'r' applied by the user to 't' belongs to the ruleset;
1.795 + if the rule is OK, the term resulting from applying the rule is returned,too;
1.796 + there might be several rule applications inbetween,
1.797 + which are listed after the head in reverse order **)
1.798 +(*/-------------------------------------------- Isabelle2013: this gives "error id_of_thm";
1.799 + we don't repair this, because interaction within "reverse rewriting" never worked properly:
1.800 +
1.801 + val (r, (t, asm))::_ = loc revsets t r;
1.802 +if UnparseC.term t = "(9 - x \<up> 2) / (3 \<up> 2 + 6 * x + x \<up> 2)" andalso asm = []
1.803 +then () else error "rational.sml locate_rule (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2)";
1.804 +
1.805 +(* find the next rule to apply *)
1.806 + val SOME (r as (Thm (str, thm))) = nex revsets t;
1.807 +if str = "sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))" andalso
1.808 + ThmC.string_of_thm thm = (string_of_thm (ThmC_Def.make_thm @{theory "Isac_Knowledge"}
1.809 + (Trueprop $ (Thm.term_of o the o (TermC.parse thy)) "9 = 3 \<up> 2"))) then ()
1.810 +else error "rational.sml next_rule (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2)";
1.811 +
1.812 +(*check the next rule*)
1.813 + val (r, (t, asm)) :: _ = loc revsets t r;
1.814 +if UnparseC.term t = "(3 \<up> 2 - x \<up> 2) / (3 \<up> 2 + 6 * x + x \<up> 2)" then ()
1.815 +else error "rational.sml locate_rule (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2) II";
1.816 +
1.817 +(*find and check the next rules, rewrite*)
1.818 + val SOME r = nex revsets t;
1.819 + val (r,(t,asm))::_ = loc revsets t r;
1.820 +if UnparseC.term t = "(3 \<up> 2 - x \<up> 2) / (3 \<up> 2 + 2 * 3 * x + x \<up> 2)" then ()
1.821 +else error "rational.sml locate_rule II";
1.822 +
1.823 + val SOME r = nex revsets t;
1.824 + val (r,(t,asm))::_ = loc revsets t r;
1.825 +if UnparseC.term t = "(3 - x) * (3 + x) / (3 \<up> 2 + 2 * 3 * x + x \<up> 2)" then ()
1.826 +else error "rational.sml next_rule II";
1.827 +
1.828 + val SOME r = nex revsets t;
1.829 + val (r,(t,asm))::_ = loc revsets t r;
1.830 +if UnparseC.term t = "(3 - x) * (3 + x) / ((3 + x) * (3 + x))" then ()
1.831 +else error "rational.sml next_rule III";
1.832 +
1.833 + val SOME r = nex revsets t;
1.834 + val (r, (t, asm)) :: _ = loc revsets t r;
1.835 + val ss = UnparseC.term t;
1.836 +if ss = "(3 - x) / (3 + x)" andalso UnparseC.terms asm = "[\"3 + x ~= 0\"]" then ()
1.837 +else error "rational.sml: new behav. in rev-set cancel";
1.838 +\--------------------------------------------------------------------------------------/*)
1.839 +
1.840 +"-------- 'reverse-ruleset' cancel_p -----------------------------------------";
1.841 +"-------- 'reverse-ruleset' cancel_p -----------------------------------------";
1.842 +"-------- 'reverse-ruleset' cancel_p -----------------------------------------";
1.843 +(*WN130909: the example below shows, why "reverse rewriting" only worked for
1.844 + special cases.*)
1.845 +
1.846 +(*the term for which reverse rewriting is demonstrated*)
1.847 +val t = TermC.str2term "(9 + (-1)*x \<up> 2) / (9 + ((-6)*x + x \<up> 2))";
1.848 +val Rrls {scr=Rfuns {init_state=ini,locate_rule=loc,
1.849 + next_rule=nex,normal_form=nor,...},...} = cancel_p;
1.850 +
1.851 +(*normal_form produces the result in ONE step*)
1.852 +val SOME (t', _) = nor t;
1.853 +if UnparseC.term t' = "(3 + x) / (3 + - 1 * x)"
1.854 +then () else error "cancel_p normal_form CHANGED";;
1.855 +
1.856 +(*initialize the interpreter state used by the 'me'*)
1.857 +val SOME (t', asm) = cancel_p_ thy t;
1.858 +if (UnparseC.term t', UnparseC.terms asm) = ("(3 + x) / (3 + - 1 * x)", "[\"3 + - 1 * x \<noteq> 0\"]")
1.859 +then () else error "cancel_p CHANGED";;
1.860 +
1.861 +val (t,_,revsets,_) = ini t;
1.862 +
1.863 +(* WN.10.10.02: dieser Fall terminiert nicht
1.864 + (make_polynomial enth"alt zu viele rules)
1.865 +WN060823 'init_state' requires rewriting on specified location in the term
1.866 +default_print_depth 99; Rfuns; default_print_depth 3;
1.867 +WN060831 cycling "sym_order_mult_rls_" "sym_mult.assoc"
1.868 + as was with make_polynomial before ?!?* )
1.869 +
1.870 +val SOME r = nex revsets t;
1.871 +eq_Thm (r, Thm ("sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))",
1.872 + mk_thm thy "9 = 3 \<up> 2"));
1.873 +( *WN060831 *** id_of_thm
1.874 + Exception- ERROR raised ...
1.875 +val (r,(t,asm))::_ = loc revsets t r;
1.876 +UnparseC.term t;
1.877 +
1.878 + val SOME r = nex revsets t;
1.879 + val (r,(t,asm))::_ = loc revsets t r;
1.880 + UnparseC.term t;
1.881 +*)
1.882 +
1.883 +"-------- examples: rls norm_Rational ----------------------------------------";
1.884 +"-------- examples: rls norm_Rational ----------------------------------------";
1.885 +"-------- examples: rls norm_Rational ----------------------------------------";
1.886 +(*Rewrite.trace_on:=true;*)
1.887 +val t = TermC.str2term "Not (6*x is_atom)";
1.888 +val SOME (t',_) = rewrite_set_ thy false powers_erls t; UnparseC.term t';
1.889 +"HOL.True";
1.890 +val t = TermC.str2term "1 < 2";
1.891 +val SOME (t',_) = rewrite_set_ thy false powers_erls t; UnparseC.term t';
1.892 +"HOL.True";
1.893 +
1.894 +val t = TermC.str2term "(6*x) \<up> 2";
1.895 +val SOME (t',_) = rewrite_ thy dummy_ord powers_erls false
1.896 + (ThmC.numerals_to_Free @{thm realpow_def_atom}) t;
1.897 +if UnparseC.term t' = "6 * x * (6 * x) \<up> (2 + - 1)" then ()
1.898 +else error "rational.sml powers_erls (6*x) \<up> 2";
1.899 +
1.900 +val t = TermC.str2term "-1 * (-2 * (5 / 2 * (13 * x / 2)))";
1.901 +val SOME (t',_) = rewrite_set_ thy false norm_Rational t; UnparseC.term t';
1.902 +if UnparseC.term t' = "65 * x / 2" then () else error "rational.sml 4";
1.903 +
1.904 +val t = TermC.str2term "1 - ((13*x)/2 - 5/2) \<up> 2";
1.905 +val SOME (t',_) = rewrite_set_ thy false norm_Rational t; UnparseC.term t';
1.906 +if UnparseC.term t' = "(- 21 + 130 * x + - 169 * x \<up> 2) / 4" then ()
1.907 +else error "rational.sml 5";
1.908 +
1.909 +(*SRAM Schalk I, p.92 Nr. 609a*)
1.910 +val t = TermC.str2term "2*(3 - x/5)/3 - 4*(1 - x/3) - x/3 - 2*(x/2 - 1/4)/27 +5/54";
1.911 +val SOME (t',_) = rewrite_set_ thy false norm_Rational t; UnparseC.term t';
1.912 +if UnparseC.term t' = "(- 255 + 112 * x) / 135" then ()
1.913 +else error "rational.sml 6";
1.914 +
1.915 +(*SRAM Schalk I, p.92 Nr. 610c*)
1.916 +val t = TermC.str2term "((x- 1)/(x+1) + 1) / ((x- 1)/(x+1) - (x+1)/(x- 1)) - 2";
1.917 +val SOME (t',_) = rewrite_set_ thy false norm_Rational t; UnparseC.term t';
1.918 +if UnparseC.term t' = "(3 + x) / - 2" then () else error "rational.sml 7";
1.919 +
1.920 +(*SRAM Schalk I, p.92 Nr. 476a*)
1.921 +val t = TermC.str2term "(x \<up> 2/(1 - x \<up> 2) + 1)/(x/(1 - x) + 1) * (1 + x)";
1.922 +(*. a/b : c/d translated to a/b * d/c .*)
1.923 +val SOME (t',_) = rewrite_set_ thy false norm_Rational t; UnparseC.term t';
1.924 +if UnparseC.term t' = "1" then () else error "rational.sml 8";
1.925 +
1.926 +(*Schalk I, p.92 Nr. 472a*)
1.927 +val t = TermC.str2term "((8*x \<up> 2 - 32*y \<up> 2)/(2*x + 4*y))/((4*x - 8*y)/(x + y))";
1.928 +val SOME (t',_) = rewrite_set_ thy false norm_Rational t; UnparseC.term t';
1.929 +if UnparseC.term t' = "x + y" then () else error "rational.sml p.92 Nr. 472a";
1.930 +
1.931 +(*Schalk I, p.70 Nr. 480b: SEE rational.sml --- nonterminating rls norm_Rational ---*)
1.932 +
1.933 +(*WN130910 add_fractions_p exception Div raised + history:
1.934 +### WN.2.6.03 from rlang.sml 56a
1.935 +val t = TermC.str2term "(a + b * x) / (a + -1 * (b * x)) + (-1 * a + b * x) / (a + b * x) = 4 * (a * b) / (a \<up> 2 + -1 * b \<up> 2)";
1.936 +val NONE = rewrite_set_ thy false add_fractions_p t;
1.937 +
1.938 +THE ERROR ALREADY OCCURS IN THIS PART:
1.939 +val t = TermC.str2term "(a + b * x) / (a + -1 * (b * x)) + (-1 * a + b * x) / (a + b * x)";
1.940 +val NONE = add_fraction_p_ thy t;
1.941 +
1.942 +SEE Test_Some.thy: section {* add_fractions_p downto exception Div raised ===
1.943 +*)
1.944 +
1.945 +"-------- rational numerals --------------------------------------------------";
1.946 +"-------- rational numerals --------------------------------------------------";
1.947 +"-------- rational numerals --------------------------------------------------";
1.948 +(*SRA Schalk I, p.40 Nr. 164b *)
1.949 +val t = TermC.str2term "(47/6 - 76/9 + 13/4)/(35/12)";
1.950 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.951 +if UnparseC.term t = "19 / 21" then ()
1.952 +else error "rational.sml: diff.behav. in norm_Rational_mg 1";
1.953 +
1.954 +(*SRA Schalk I, p.40 Nr. 166a *)
1.955 +val t = TermC.str2term "((5/4)/(4+22/7) + 37/20)*(110/3 - 110/9 * 23/11)";
1.956 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.957 +if UnparseC.term t = "45 / 2" then ()
1.958 +else error "rational.sml: diff.behav. in norm_Rational_mg 2";
1.959 +
1.960 +"-------- examples cancellation from: Mathematik 1 Schalk --------------------";
1.961 +"-------- examples cancellation from: Mathematik 1 Schalk --------------------";
1.962 +"-------- examples cancellation from: Mathematik 1 Schalk --------------------";
1.963 +(* e190c Stefan K.*)
1.964 +val t = TermC.str2term "((1 + 9*a \<up> 2) * (1 + 3*a)) / ((3*a + 9*a \<up> 2) * (1 + 3*a))";
1.965 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.966 +if UnparseC.term t = "(1 + 9 * a \<up> 2) / (3 * a + 9 * a \<up> 2)"
1.967 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 3";
1.968 +
1.969 +(* e192b Stefan K.*)
1.970 +val t = TermC.str2term "(x \<up> 2 * (7*x + (-1)*y)) / (y \<up> 2 * (7*x + (-1)*y))";
1.971 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.972 +if UnparseC.term t = "x \<up> 2 / y \<up> 2"
1.973 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 4";
1.974 +
1.975 +(*SRC Schalk I, p.66 Nr. 379c *)
1.976 +val t = TermC.str2term "(a - b)/(b - a)";
1.977 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.978 +if UnparseC.term t = "- 1"
1.979 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 5";
1.980 +
1.981 +(*SRC Schalk I, p.66 Nr. 380b *)
1.982 +val t = TermC.str2term "15*(3*x + 3) * (4*x + 9) / (12*(2*x + 7) * (5*x + 5))";
1.983 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.984 +if UnparseC.term t = "(27 + 12 * x) / (28 + 8 * x)"
1.985 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 6";
1.986 +
1.987 +(* e190c Stefan K.*)
1.988 +val t = TermC.str2term "((1 + 9*a \<up> 2) * (1 + 3*a)) / ((3*a + 9*a \<up> 2) * (1 + 3 * a))";
1.989 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.990 +if UnparseC.term t = "(1 + 9 * a \<up> 2) / (3 * a + 9 * a \<up> 2)"
1.991 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 3";
1.992 +
1.993 +(* e192b Stefan K.*)
1.994 +val t = TermC.str2term "(x \<up> 2 * (7*x + (-1)*y)) / (y \<up> 2 * (7*x + (-1)*y))";
1.995 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.996 +if UnparseC.term t = "x \<up> 2 / y \<up> 2"
1.997 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 4";
1.998 +
1.999 +(*SRC Schalk I, p.66 Nr. 379c *)
1.1000 +val t = TermC.str2term "(a - b) / (b - a)";
1.1001 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1002 +if UnparseC.term t = "- 1"
1.1003 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 5";
1.1004 +
1.1005 +(*SRC Schalk I, p.66 Nr. 380b *)
1.1006 +val t = TermC.str2term "15*(3*x + 3) * (4*x + 9) / (12*(2*x + 7) * (5*x + 5))";
1.1007 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1008 +if UnparseC.term t = "(27 + 12 * x) / (28 + 8 * x)"
1.1009 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 6";
1.1010 +
1.1011 +(* extreme example from somewhere *)
1.1012 +val t = TermC.str2term
1.1013 + ("(a \<up> 4 * x + -1*a \<up> 4 * y + 4*a \<up> 3 * b * x + -4*a \<up> 3 * b * y + " ^
1.1014 + "6*a \<up> 2 * b \<up> 2 * x + -6*a \<up> 2 * b \<up> 2 * y + 4*a * b \<up> 3 * x + -4*a * b \<up> 3 * y + " ^
1.1015 + "b \<up> 4 * x + -1*b \<up> 4 * y) " ^
1.1016 + " / (a \<up> 2 * x \<up> 3 + -3*a \<up> 2 * x \<up> 2 * y + 3*a \<up> 2 * x * y \<up> 2 + -1*a \<up> 2 * y \<up> 3 + " ^
1.1017 + "2*a * b * x \<up> 3 + -6*a * b * x \<up> 2 * y + 6*a * b * x * y \<up> 2 + -2*a * b * y \<up> 3 + " ^
1.1018 + "b \<up> 2 * x \<up> 3 + -3*b \<up> 2 * x \<up> 2 * y + 3*b \<up> 2 * x * y \<up> 2 + -1*b \<up> 2 * y \<up> 3)")
1.1019 +val SOME (t, _) = rewrite_set_ thy false cancel_p t;
1.1020 +if UnparseC.term t = "(a \<up> 2 + 2 * a * b + b \<up> 2) / (x \<up> 2 + - 2 * x * y + y \<up> 2)"
1.1021 +then () else error "with Isabelle2002: NONE -- now SOME changed";
1.1022 +
1.1023 +(*Schalk I, p.66 Nr. 381a *)
1.1024 +(* ATTENTION: here the rls is very slow. In Isabelle2002 this required 2 min *)
1.1025 +val t = TermC.str2term "18*(a + b) \<up> 3 * (a - b) \<up> 2 / (72*(a - b) \<up> 3 * (a + b) \<up> 2)";
1.1026 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1027 +if UnparseC.term t = "(a + b) / (4 * a + - 4 * b)"
1.1028 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 8";
1.1029 +
1.1030 +(*SRC Schalk I, p.66 Nr. 381b *)
1.1031 +val t = TermC.str2term "(4*x \<up> 2 - 20*x + 25) / (2*x - 5) \<up> 3";
1.1032 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1033 +if UnparseC.term t = "1 / (- 5 + 2 * x)"
1.1034 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 9";
1.1035 +
1.1036 +(*SRC Schalk I, p.66 Nr. 381c *)
1.1037 +val t = TermC.str2term "(27*a \<up> 3 + 9*a \<up> 2+3*a+1) / (27*a \<up> 3 + 18*a \<up> 2+3*a)";
1.1038 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1039 +if UnparseC.term t = "(1 + 9 * a \<up> 2) / (3 * a + 9 * a \<up> 2)"
1.1040 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 10";
1.1041 +
1.1042 +(*SRC Schalk I, p.66 Nr. 383a *)
1.1043 +val t = TermC.str2term "(5*a \<up> 2 - 5*a*b) / (a - b) \<up> 2";
1.1044 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1045 +if UnparseC.term t = "- 5 * a / (- 1 * a + b)"
1.1046 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 11";
1.1047 +
1.1048 +"----- NOT TERMINATING ?: worked before 0707xx";
1.1049 +val t = TermC.str2term "(a \<up> 2 - 1)*(b + 1) / ((b \<up> 2 - 1)*(a+1))";
1.1050 +(* WN130911 "exception Div raised" by
1.1051 + cancel_p_ thy (TermC.str2term ("(-1 + -1 * b + a \<up> 2 + a \<up> 2 * b) /" ^
1.1052 + "(-1 + -1 * a + b \<up> 2 + a * b \<up> 2)"))
1.1053 +
1.1054 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1055 +if UnparseC.term t = "(1 + -1 * a) / (1 + -1 * b)" then ()
1.1056 +else error "rational.sml MG tests 3e";
1.1057 +*)
1.1058 +
1.1059 +"-------- examples common denominator from: Mathematik 1 Schalk --------------";
1.1060 +"-------- examples common denominator from: Mathematik 1 Schalk --------------";
1.1061 +"-------- examples common denominator from: Mathematik 1 Schalk --------------";
1.1062 +(*SRA Schalk I, p.67 Nr. 403a *)
1.1063 +val t = TermC.str2term "4/x - 3/y - 1";
1.1064 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1065 +if UnparseC.term t = "(- 3 * x + 4 * y + - 1 * x * y) / (x * y)"
1.1066 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 12";
1.1067 +
1.1068 +val t = TermC.str2term "(2*a+3*b)/(b*c) + (3*c+a)/(a*c) - (2*a \<up> 2+3*b*c)/(a*b*c)";
1.1069 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1070 +if UnparseC.term t = "4 / c"
1.1071 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 13";
1.1072 +
1.1073 +(*SRA Schalk I, p.67 Nr. 410b *)
1.1074 +val t = TermC.str2term "1/(x+1) + 1/(x+2) - 2/(x+3)";
1.1075 +(* WN130911 non-termination due to non-termination of
1.1076 + cancel_p_ thy (TermC.str2term "(5 + 3 * x) / (6 + 11 * x + 6 * x \<up> 2 + x \<up> 3)")
1.1077 +
1.1078 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1079 +if UnparseC.term t = "(5 + 3 * x) / (6 + 11 * x + 6 * x \<up> 2 + x \<up> 3)"
1.1080 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 14";
1.1081 +*)
1.1082 +
1.1083 +(*SRA Schalk I, p.67 Nr. 413b *)
1.1084 +val t = TermC.str2term "(1 + x)/(1 - x) - (1 - x)/(1 + x) + 2*x/(1 - x \<up> 2)";
1.1085 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1086 +if UnparseC.term t = "6 * x / (1 + - 1 * x \<up> 2)"
1.1087 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 15";
1.1088 +
1.1089 +(*SRA Schalk I, p.68 Nr. 414a *)
1.1090 +val t = TermC.str2term "(x + 2)/(x - 1) + (x - 3)/(x - 2) - (x + 1)/((x - 1)*(x - 2))";
1.1091 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1092 +if UnparseC.term t ="(- 2 + - 5 * x + 2 * x \<up> 2) / (2 + - 3 * x + x \<up> 2)"
1.1093 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 16";
1.1094 +
1.1095 +(*SRA Schalk I, p.68 Nr. 428b *)
1.1096 +val t = TermC.str2term
1.1097 + "1/(a - b) \<up> 2 + 1/(a + b) \<up> 2 - 2/(a \<up> 2 - b \<up> 2) - 4*(b \<up> 2 - 1)/(a \<up> 2 - b \<up> 2) \<up> 2";
1.1098 +(* WN130911 non-termination due to non-termination of
1.1099 + cancel_p_ thy (TermC.str2term "(4 + -4 * b \<up> 2) / (a \<up> 4 + -2 * (a \<up> 2 * b \<up> 2) + b \<up> 4)")
1.1100 +
1.1101 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1102 +if UnparseC.term t = "4 / (a \<up> 4 + -2 * a \<up> 2 * b \<up> 2 + b \<up> 4)"
1.1103 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 18";
1.1104 +*)
1.1105 +
1.1106 +(*SRA Schalk I, p.68 Nr. 430b *)
1.1107 +val t = TermC.str2term
1.1108 + "a \<up> 2/(a - 3*b) - 108*a*b \<up> 3/((a+3*b)*(a \<up> 2 - 9*b \<up> 2)) - 9*b \<up> 2*(a - 3*b)/(a+3*b) \<up> 2";
1.1109 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1110 +if UnparseC.term t = "a + 3 * b"
1.1111 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 19";
1.1112 +
1.1113 +(*SRA Schalk I, p.68 Nr. 432 *)
1.1114 +val t = TermC.str2term
1.1115 + ("(a \<up> 2 + a*b) / (a \<up> 2 - b \<up> 2) - (b \<up> 2 - a*b) / (b \<up> 2 - a \<up> 2) + " ^
1.1116 + "a \<up> 2*(a - b) / (a \<up> 3 - a \<up> 2*b) - 2*a*(a \<up> 2 - b \<up> 2) / (a \<up> 3 - a*b \<up> 2) - " ^
1.1117 + "2*b \<up> 2 / (a \<up> 2 - b \<up> 2)");
1.1118 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1119 +if UnparseC.term t = (*"0" ..isabisac15 | Isabelle2017..*) "0 / (a \<up> 2 + - 1 * b \<up> 2)"
1.1120 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 20";
1.1121 +
1.1122 +(* some example *)
1.1123 +val t = TermC.str2term "3*a / (a*b) + x/y";
1.1124 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1125 +if UnparseC.term t = "(3 * y + b * x) / (b * y)"
1.1126 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 21";
1.1127 +
1.1128 +
1.1129 +"-------- examples multiply and cancel from: Mathematik 1 Schalk -------------";
1.1130 +"-------- examples multiply and cancel from: Mathematik 1 Schalk -------------";
1.1131 +"-------- examples multiply and cancel from: Mathematik 1 Schalk -------------";
1.1132 +(*------- SRM Schalk I, p.68 Nr. 436a *)
1.1133 +val t = TermC.str2term "3*(x+y) / (15*(x - y)) * 25*(x - y) \<up> 2 / (18*(x + y) \<up> 2)";
1.1134 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1135 +if UnparseC.term t = "(- 5 * x + 5 * y) / (- 18 * x + - 18 * y)"
1.1136 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 22";
1.1137 +
1.1138 +(*------- SRM.test Schalk I, p.68 Nr. 436b *)
1.1139 +val t = TermC.str2term "5*a*(a - b) \<up> 2*(a + b) \<up> 3/(7*b*(a - b) \<up> 3) * 7*b/(a + b) \<up> 3";
1.1140 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1141 +if UnparseC.term t = "5 * a / (a + - 1 * b)"
1.1142 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 23";
1.1143 +
1.1144 +(*------- Schalk I, p.68 Nr. 437a *)
1.1145 +val t = TermC.str2term "(3*a - 4*b) / (4*c+3*e) * (3*a+4*b)/(9*a \<up> 2 - 16*b \<up> 2)";
1.1146 +(* raises an exception for unclear reasons:
1.1147 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1148 +:
1.1149 +### rls: cancel_p on: (9 * a \<up> 2 + -16 * b \<up> 2) / (4 * c + 3 * e) /
1.1150 +(9 * a \<up> 2 + -16 * b \<up> 2)
1.1151 +exception Div raised
1.1152 +
1.1153 +BUT
1.1154 +val t = TermC.str2term
1.1155 + ("(9 * a \<up> 2 + -16 * b \<up> 2) / (4 * c + 3 * e) /" ^
1.1156 + "(9 * a \<up> 2 + -16 * b \<up> 2)");
1.1157 +NONE = cancel_p_ thy t;
1.1158 +
1.1159 +if UnparseC.term t = "1 / (4 * c + 3 * e)" then ()
1.1160 +else error "rational.sml: diff.behav. in norm_Rational_mg 24";
1.1161 +*)
1.1162 +
1.1163 +"----- S.K. corrected non-termination 060904";
1.1164 +val t = TermC.str2term "(3*a - 4*b) * (3*a+4*b)/((4*c+3*e)*(9*a \<up> 2 - 16*b \<up> 2))";
1.1165 +val SOME (t, _) = rewrite_set_ thy false make_polynomial t;
1.1166 +if UnparseC.term t =
1.1167 + "(9 * a \<up> 2 + - 16 * b \<up> 2) /\n(36 * a \<up> 2 * c + 27 * a \<up> 2 * e + - 64 * b \<up> 2 * c +\n - 48 * b \<up> 2 * e)"
1.1168 +then () else error "rational.sml: S.K.8..corrected 060904-6";
1.1169 +
1.1170 +"----- S.K. corrected non-termination of cancel_p_";
1.1171 +val t'' = TermC.str2term ("(9 * a \<up> 2 + -16 * b \<up> 2) /" ^
1.1172 + "(36 * a \<up> 2 * c + (27 * a \<up> 2 * e + (-64 * b \<up> 2 * c + -48 * b \<up> 2 * e)))");
1.1173 +(* /--- DOES NOT TERMINATE AT TRANSITION isabisac15 --> Isabelle2017 --------------------------\
1.1174 +val SOME (t',_) = rewrite_set_ thy false cancel_p t'';
1.1175 +if UnparseC.term t' = "1 / (4 * c + 3 * e)"
1.1176 +then () else error "rational.sml: diff.behav. in cancel_p S.K.8";
1.1177 + \--- DOES NOT TERMINATE AT TRANSITION isabisac15 --> Isabelle2017 --------------------------/*)
1.1178 +
1.1179 +(*------- Schalk I, p.68 Nr. 437b*)
1.1180 +val t = TermC.str2term "(a + b)/(x \<up> 2 - y \<up> 2) * ((x - y) \<up> 2/(a \<up> 2 - b \<up> 2))";
1.1181 +(*val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1182 +:
1.1183 +#### rls: cancel_p on: (a * x \<up> 2 + -2 * (a * (x * y)) + a * y \<up> 2 + b * x \<up> 2 +
1.1184 + -2 * (b * (x * y)) +
1.1185 + b * y \<up> 2) /
1.1186 +(a \<up> 2 * x \<up> 2 + -1 * (a \<up> 2 * y \<up> 2) + -1 * (b \<up> 2 * x \<up> 2) +
1.1187 + b \<up> 2 * y \<up> 2)
1.1188 +exception Div raised
1.1189 +*)
1.1190 +
1.1191 +(*------- SRM Schalk I, p.68 Nr. 438a *)
1.1192 +val t = TermC.str2term "x*y / (x*y - y \<up> 2) * (x \<up> 2 - x*y)";
1.1193 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1194 +if UnparseC.term t = "x \<up> 2"
1.1195 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 24";
1.1196 +
1.1197 +(*------- SRM Schalk I, p.68 Nr. 439b *)
1.1198 +val t = TermC.str2term "(4*x \<up> 2 + 4*x + 1) * ((x \<up> 2 - 2*x \<up> 3) / (4*x \<up> 2 + 2*x))";
1.1199 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1200 +if UnparseC.term t = "(x + - 4 * x \<up> 3) / 2"
1.1201 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 25";
1.1202 +
1.1203 +(*------- SRM Schalk I, p.68 Nr. 440a *)
1.1204 +val t = TermC.str2term "(x \<up> 2 - 2*x) / (x \<up> 2 - 3*x) * (x - 3) \<up> 2 / (x \<up> 2 - 4)";
1.1205 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1206 +if UnparseC.term t = "(- 3 + x) / (2 + x)"
1.1207 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 26";
1.1208 +
1.1209 +"----- Schalk I, p.68 Nr. 440b SK11 works since 0707xx";
1.1210 +val t = TermC.str2term "(a \<up> 3 - 9*a) / (a \<up> 3*b - a*b \<up> 3) * (a \<up> 2*b + a*b \<up> 2) / (a+3)";
1.1211 +(* WN130911 non-termination for unclear reasons:
1.1212 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1213 +
1.1214 +... ENDS WITH THIS TRACE:
1.1215 +:
1.1216 +### rls: cancel_p on: (-9 * (a \<up> 3 * b) + -9 * (a \<up> 2 * b \<up> 2) + a \<up> 5 * b +
1.1217 + a \<up> 4 * b \<up> 2) /
1.1218 +(a \<up> 3 * b + -1 * (a * b \<up> 3)) /
1.1219 +(3 + a)
1.1220 +BUT THIS IS CORRECTLY RECOGNISED
1.1221 +val t = TermC.str2term
1.1222 + ("(-9 * (a \<up> 3 * b) + -9 * (a \<up> 2 * b \<up> 2) + a \<up> 5 * b + a \<up> 4 * b \<up> 2) /" ^
1.1223 + "(a \<up> 3 * b + -1 * (a * b \<up> 3)) / (3 + (a::real))");
1.1224 +AS
1.1225 +NONE = cancel_p_ thy t;
1.1226 +
1.1227 +if UnparseC.term t = "(-3 * a + a \<up> 2) / (a + -1 * b)" then ()
1.1228 +else error "rational.sml: diff.behav. in norm_Rational 27";
1.1229 +*)
1.1230 +
1.1231 +"----- SK12 works since 0707xx";
1.1232 +val t = TermC.str2term "(a \<up> 3 - 9*a) * (a \<up> 2*b+a*b \<up> 2) / ((a \<up> 3*b - a*b \<up> 3) * (a+3))";
1.1233 +(* WN130911 non-termination due to non-termination of
1.1234 + cancel_p_ thy (TermC.str2term "(4 + -4 * b \<up> 2) / (a \<up> 4 + -2 * (a \<up> 2 * b \<up> 2) + b \<up> 4)")
1.1235 +
1.1236 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1237 +if UnparseC.term t' = "(-3 * a + a \<up> 2) / (a + -1 * b)" then ()
1.1238 +else error "rational.sml: diff.behav. in norm_Rational 28";
1.1239 +*)
1.1240 +
1.1241 +"-------- examples common denominator and multiplication from: Schalk --------";
1.1242 +"-------- examples common denominator and multiplication from: Schalk --------";
1.1243 +"-------- examples common denominator and multiplication from: Schalk --------";
1.1244 +(*------- SRAM Schalk I, p.69 Nr. 441b *)
1.1245 +val t = TermC.str2term "(4*a/3 + 3*b \<up> 2/a \<up> 3 + b/(4*a))*(4*b/(3*a))";
1.1246 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1247 +if UnparseC.term t = "(36 * b \<up> 3 + 3 * a \<up> 2 * b \<up> 2 + 16 * a \<up> 4 * b) /\n(9 * a \<up> 4)"
1.1248 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 28";
1.1249 +
1.1250 +(*------- SRAM Schalk I, p.69 Nr. 442b *)
1.1251 +val t = TermC.str2term ("(15*a \<up> 2/x \<up> 3 - 5*b \<up> 4/x \<up> 2 + 25*c \<up> 2/x) * " ^
1.1252 + "(x \<up> 3/(5*a*b \<up> 3*c \<up> 3)) + 1/c \<up> 3 * (b*x/a - 3*a/b \<up> 3)");
1.1253 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1254 +if UnparseC.term t = "5 * x \<up> 2 / (a * b \<up> 3 * c)"
1.1255 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 29";
1.1256 +
1.1257 +(*------- SRAM Schalk I, p.69 Nr. 443b *)
1.1258 +val t = TermC.str2term "(a/2 + b/3) * (b/3 - a/2)";
1.1259 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1260 +if UnparseC.term t = "(- 9 * a \<up> 2 + 4 * b \<up> 2) / 36"
1.1261 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 30";
1.1262 +
1.1263 +(*------- SRAM Schalk I, p.69 Nr. 445b *)
1.1264 +val t = TermC.str2term "(a \<up> 2/9 + 2*a/(3*b) + 4/b \<up> 2)*(a/3 - 2/b) + 8/b \<up> 3";
1.1265 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1266 +if UnparseC.term t = "a \<up> 3 / 27"
1.1267 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 31";
1.1268 +
1.1269 +(*------- SRAM Schalk I, p.69 Nr. 446b *)
1.1270 +val t = TermC.str2term "(x/(5*x + 4*y) - y/(5*x - 4*y) + 1)*(25*x \<up> 2 - 16*y \<up> 2)";
1.1271 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1272 +if UnparseC.term t = (*"30 * x \<up> 2 + -9 * x * y + -20 * y \<up> 2" ..isabisac15 | Isabelle2017..*)
1.1273 + "(- 30 * x \<up> 2 + 9 * x * y + 20 * y \<up> 2) / - 1"
1.1274 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 32";
1.1275 +
1.1276 +(*------- SRAM Schalk I, p.69 Nr. 449a *)(*Achtung: rechnet ca 8 Sekunden*)
1.1277 +val t = TermC.str2term
1.1278 +"(2*x \<up> 2/(3*y)+x/y \<up> 2)*(4*x \<up> 4/(9*y \<up> 2)+x \<up> 2/y \<up> 4)*(2*x \<up> 2/(3*y) - x/y \<up> 2)";
1.1279 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1280 +if UnparseC.term t = "(- 81 * x \<up> 4 + 16 * x \<up> 8 * y \<up> 4) / (81 * y \<up> 8)"
1.1281 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 33";
1.1282 +
1.1283 +(*------- SRAM Schalk I, p.69 Nr. 450a *)
1.1284 +val t = TermC.str2term
1.1285 +"(4*x/(3*y)+2*y/(3*x)) \<up> 2 - (2*y/(3*x) - 2*x/y)*(2*y/(3*x)+2*x/y)";
1.1286 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1287 +if UnparseC.term t = "(52 * x \<up> 2 + 16 * y \<up> 2) / (9 * y \<up> 2)"
1.1288 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 34";
1.1289 +
1.1290 +(*------- SRAM Schalk I, p.69 Nr. 442b --- abgewandelt*)
1.1291 +val t = TermC.str2term
1.1292 + ("(15*a \<up> 4/(a*x \<up> 3) - 5*a*((b \<up> 4 - 5*c \<up> 2*x) / x \<up> 2)) * " ^
1.1293 + "(x \<up> 3/(5*a*b \<up> 3*c \<up> 3)) + a/c \<up> 3 * (x*(b/a) - 3*b*(a/b \<up> 4))");
1.1294 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1295 +if UnparseC.term t = "5 * x \<up> 2 / (b \<up> 3 * c)"
1.1296 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 53";
1.1297 +
1.1298 +
1.1299 +"-------- examples double fractions from: Mathematik 1 Schalk ----------------";
1.1300 +"-------- examples double fractions from: Mathematik 1 Schalk ----------------";
1.1301 +"-------- examples double fractions from: Mathematik 1 Schalk ----------------";
1.1302 +"----- SRD Schalk I, p.69 Nr. 454b";
1.1303 +val t = TermC.str2term "((2 - x)/(2*a)) / (2*a/(x - 2))";
1.1304 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1305 +if UnparseC.term t = "(- 4 + 4 * x + - 1 * x \<up> 2) / (4 * a \<up> 2)"
1.1306 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 35";
1.1307 +
1.1308 +"----- SRD Schalk I, p.69 Nr. 455a";
1.1309 +val t = TermC.str2term "(a \<up> 2 + 1)/(a \<up> 2 - 1) / ((a+1)/(a - 1))";
1.1310 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1311 +if UnparseC.term t = "(1 + a \<up> 2) / (1 + 2 * a + a \<up> 2)" then ()
1.1312 +else error "rational.sml: diff.behav. in norm_Rational_mg 36";
1.1313 +
1.1314 +"----- Schalk I, p.69 Nr. 455b";
1.1315 +val t = TermC.str2term "(x \<up> 2 - 4)/(y \<up> 2 - 9)/((2+x)/(3 - y))";
1.1316 +(* WN130911 non-termination due to non-termination of
1.1317 + cancel_p_ thy (TermC.str2term ("(-12 + 4 * y + 3 * x \<up> 2 + -1 * (x \<up> 2 * y)) /" ^
1.1318 + "(-18 + -9 * x + 2 * y \<up> 2 + x * y \<up> 2)"))
1.1319 +
1.1320 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1321 +if UnparseC.term t = "(2 + -1 * x) / (3 + y)" then ()
1.1322 +else error "rational.sml: diff.behav. in norm_Rational_mg 37";
1.1323 +*)
1.1324 +
1.1325 +"----- SK060904-1a non-termination of cancel_p_ ?: worked before 0707xx";
1.1326 +val t = TermC.str2term "(x \<up> 2 - 4)*(3 - y) / ((y \<up> 2 - 9)*(2+x))";
1.1327 +(* WN130911 non-termination due to non-termination of
1.1328 + cancel_p_ thy (TermC.str2term ("(-12 + 4 * y + 3 * x \<up> 2 + -1 * (x \<up> 2 * y)) /" ^
1.1329 + "(-18 + -9 * x + 2 * y \<up> 2 + x * y \<up> 2)"))
1.1330 +
1.1331 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1332 +if UnparseC.term t = "(2 + -1 * x) / (3 + y)" then ()
1.1333 +else error "rational.sml: diff.behav. in norm_Rational_mg 37b";
1.1334 +*)
1.1335 +
1.1336 +"----- ?: worked before 0707xx";
1.1337 +val t = TermC.str2term "(3 + -1 * y) / (-9 + y \<up> 2)";
1.1338 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1339 +if UnparseC.term t = "- 1 / (3 + y)"
1.1340 +then () else error "rational.sml: -1 / (3 + y) norm_Rational";
1.1341 +
1.1342 +"----- SRD Schalk I, p.69 Nr. 456b";
1.1343 +val t = TermC.str2term "(b \<up> 3 - b \<up> 2) / (b \<up> 2+b) / (b \<up> 2 - 1)";
1.1344 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1345 +if UnparseC.term t = "b / (1 + 2 * b + b \<up> 2)"
1.1346 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 38";
1.1347 +
1.1348 +"----- SRD Schalk I, p.69 Nr. 457b";
1.1349 +val t = TermC.str2term "(16*a \<up> 2 - 9*b \<up> 2)/(2*a+3*a*b) / ((4*a+3*b)/(4*a \<up> 2 - 9*a \<up> 2*b \<up> 2))";
1.1350 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1351 +if UnparseC.term t = "8 * a \<up> 2 + - 6 * a * b + - 12 * a \<up> 2 * b + 9 * a * b \<up> 2"
1.1352 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 39";
1.1353 +
1.1354 +"----- Schalk I, p.69 Nr. 458b works since 0707";
1.1355 +val t = TermC.str2term "(2*a \<up> 2*x - a \<up> 2) / (a*x - b*x) / (b \<up> 2*(2*x - 1) / (x*(a - b)))";
1.1356 +(*val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1357 +:
1.1358 +### rls: cancel_p on: (-1 * a \<up> 2 + 2 * (a \<up> 2 * x)) / (a * x + -1 * (b * x)) /
1.1359 +((-1 * b \<up> 2 + 2 * (b \<up> 2 * x)) / (a * x + -1 * (b * x)))
1.1360 +exception Div raised
1.1361 +
1.1362 +BUT
1.1363 +val t = TermC.str2term
1.1364 + ("(-1 * a \<up> 2 + 2 * (a \<up> 2 * x)) / (a * x + -1 * (b * x)) /" ^
1.1365 + "((-1 * b \<up> 2 + 2 * (b \<up> 2 * x)) / (a * x + -1 * (b * x)))");
1.1366 +NONE = cancel_p_ thy t;
1.1367 +
1.1368 +if UnparseC.term t = "a \<up> 2 / b \<up> 2" then ()
1.1369 +else error "rational.sml: diff.behav. in norm_Rational_mg 39b";
1.1370 +*)
1.1371 +
1.1372 +"----- SRD Schalk I, p.69 Nr. 459b";
1.1373 +val t = TermC.str2term "(a \<up> 2 - b \<up> 2)/(a*b) / (4*(a+b) \<up> 2/a)";
1.1374 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1375 +if UnparseC.term t = "(a + - 1 * b) / (4 * a * b + 4 * b \<up> 2)" then ()
1.1376 +else error "rational.sml: diff.behav. in norm_Rational_mg 41";
1.1377 +
1.1378 +"----- Schalk I, p.69 Nr. 460b nonterm.SK";
1.1379 +val t = TermC.str2term "(9*(x \<up> 2 - 8*x + 16) / (4*(y \<up> 2 - 2*y + 1))) / ((3*x - 12) / (16*y - 16))";
1.1380 +(*val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1381 +exception Div raised
1.1382 +
1.1383 +BUT
1.1384 +val t = TermC.str2term
1.1385 + ("(144 + -72 * x + 9 * x \<up> 2) / (4 + -8 * y + 4 * y \<up> 2) /" ^
1.1386 + "((-12 + 3 * x) / (-16 + 16 * y))");
1.1387 +NONE = cancel_p_ thy t;
1.1388 +
1.1389 +if UnparseC.term t = !!!!!!!!!!!!!!!!!!!!!!!!!
1.1390 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 42";
1.1391 +*)
1.1392 +
1.1393 +"----- some variant of the above; was non-terminating before";
1.1394 +val t = TermC.str2term "9*(x \<up> 2 - 8*x+16)*(16*y - 16)/(4*(y \<up> 2 - 2*y+1)*(3*x - 12))";
1.1395 +val SOME (t , _) = rewrite_set_ thy false norm_Rational t;
1.1396 +if UnparseC.term t = "(48 + - 12 * x) / (1 + - 1 * y)"
1.1397 +then () else error "some variant of the above; was non-terminating before";
1.1398 +
1.1399 +"----- SRD Schalk I, p.70 Nr. 472a";
1.1400 +val t = TermC.str2term ("((8*x \<up> 2 - 32*y \<up> 2) / (2*x + 4*y)) / ((4*x - 8*y) / (x + y))");
1.1401 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1402 +if UnparseC.term t = "x + y"
1.1403 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 43";
1.1404 +
1.1405 +"----- Schalk I, p.70 Nr. 478b ----- Rechenzeit: 5 sec";
1.1406 +val t = TermC.str2term ("(a - (a*b + b \<up> 2)/(a+b))/(b+(a - b)/(1+(a+b)/(a - b))) / " ^
1.1407 + "((a - a \<up> 2/(a+b))/(a+(a*b)/(a - b)))");
1.1408 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1409 +if UnparseC.term t = "(2 * a \<up> 3 + 2 * a \<up> 2 * b) / (a \<up> 2 * b + b \<up> 3)"
1.1410 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 51";
1.1411 +
1.1412 +(*SRD Schalk I, p.69 Nr. 461a *)
1.1413 +val t = TermC.str2term "(2/(x+3) + 2/(x - 3)) / (8*x/(x \<up> 2 - 9))";
1.1414 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1415 +if UnparseC.term t = "1 / 2"
1.1416 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 44";
1.1417 +
1.1418 +(*SRD Schalk I, p.69 Nr. 464b *)
1.1419 +val t = TermC.str2term "(a - a/(a - 2)) / (a + a/(a - 2))";
1.1420 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1421 +if UnparseC.term t = "(- 3 + a) / (- 1 + a)"
1.1422 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 45";
1.1423 +
1.1424 +(*SRD Schalk I, p.69 Nr. 465b *)
1.1425 +val t = TermC.str2term "((x+3*y)/9 + (4*y \<up> 2 - 9*z \<up> 2)/(16*x)) / (x/9 + y/6 + z/4)";
1.1426 +(* WN130911 non-termination due to non-termination of
1.1427 + cancel_p_ thy (TermC.str2term
1.1428 + ("("(576 * x \<up> 2 + 1728 * (x * y) + 1296 * y \<up> 2 + -2916 * z \<up> 2) /" ^
1.1429 + "(576 * x \<up> 2 + 864 * (x * y) + 1296 * (x * z))"))
1.1430 +
1.1431 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1432 +if UnparseC.term t = "(4 * x + 6 * y + -9 * z) / (4 * x)"
1.1433 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 46";
1.1434 +*)
1.1435 +
1.1436 +(*SRD Schalk I, p.69 Nr. 466b *)
1.1437 +val t = TermC.str2term "((1 - 7*(x - 2)/(x \<up> 2 - 4)) / (6/(x+2))) / (3/(x+5)+30/(x \<up> 2 - 25))";
1.1438 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1439 +if UnparseC.term t = "(25 + - 10 * x + x \<up> 2) / 18"
1.1440 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 47";
1.1441 +
1.1442 +(*SRD Schalk I, p.70 Nr. 469 *)
1.1443 +val t = TermC.str2term ("3*b \<up> 2 / (4*a \<up> 2 - 8*a*b + 4*b \<up> 2) / " ^
1.1444 + "(a / (a \<up> 2*b - b \<up> 3) + (a - b) / (4*a*b \<up> 2 + 4*b \<up> 3) - 1 / (4*b \<up> 2))");
1.1445 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1446 +if UnparseC.term t = "- 3 * b \<up> 3 / (- 2 * a + 2 * b)"
1.1447 +then () else error "rational.sml: diff.behav. in norm_Rational_mg 48";
1.1448 +
1.1449 +(*//----------------------------------TOODOO (*Rfuns revsets \<longrightarrow> broken*)
1.1450 +"-------- me Schalk I No.186 -------------------------------------------------";
1.1451 +"-------- me Schalk I No.186 -------------------------------------------------";
1.1452 +"-------- me Schalk I No.186 -------------------------------------------------";
1.1453 +val fmz = ["Term ((14 * x * y) / ( x * y ))", "normalform N"];
1.1454 +val (dI',pI',mI') =
1.1455 + ("Rational",["rational", "simplification"],
1.1456 + ["simplification", "of_rationals"]);
1.1457 +val p = e_pos'; val c = [];
1.1458 +val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1.1459 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.1460 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.1461 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.1462 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.1463 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.1464 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.1465 +val (p,_,f,nxt,_,pt) = me nxt p c pt;
1.1466 +val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
1.1467 +val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
1.1468 +val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;(*++ for explicit script*)
1.1469 +val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;(*++ for explicit script*)
1.1470 +case (f2str f, nxt) of
1.1471 + ("14", ("End_Proof'", _)) => ()
1.1472 + | _ => error "rational.sml diff.behav. in me Schalk I No.186";
1.1473 + \\----------------------------------TOODOO (*Rfuns revsets \<longrightarrow> broken*)*)
1.1474 +
1.1475 +(*//----------------------------------TOODOO (*Rfuns revsets \<longrightarrow> broken*)
1.1476 +"-------- interSteps ..Simp_Rat_Double_No-1.xml ------------------------------";
1.1477 +"-------- interSteps ..Simp_Rat_Double_No-1.xml ------------------------------";
1.1478 +"-------- interSteps ..Simp_Rat_Double_No-1.xml ------------------------------";
1.1479 +reset_states ();
1.1480 +CalcTree [(["Term (((2 - x)/(2*a)) / (2*a/(x - 2)))", "normalform N"],
1.1481 + ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
1.1482 +Iterator 1;
1.1483 +moveActiveRoot 1;
1.1484 +autoCalculate 1 CompleteCalc;
1.1485 +val ((pt, p), _) = get_calc 1;
1.1486 +(*
1.1487 +Test_Tool.show_pt pt;
1.1488 +[
1.1489 +(([], Frm), Simplify ((2 - x) / (2 * a) / (2 * a / (x - 2)))),
1.1490 +(([1], Frm), (2 - x) / (2 * a) / (2 * a / (x - 2))),
1.1491 +(([1], Res), (2 + -1 * x) / (2 * a) / (2 * a / (x + -1 * 2))),
1.1492 +(([2], Res), (2 + -1 * x) / (2 * a) / (2 * a / (-2 + x))),
1.1493 +(([3], Res), (2 + -1 * x) * (-2 + x) / (2 * a * (2 * a))),
1.1494 +(([4], Res), (-4 + 4 * x + -1 * x \<up> 2) / (4 * a \<up> 2)),
1.1495 +(([], Res), (-4 + 4 * x + -1 * x \<up> 2) / (4 * a \<up> 2))]
1.1496 +*)
1.1497 +interSteps 1 ([1], Res);
1.1498 +val ((pt, p), _) = get_calc 1;
1.1499 +(*Test_Tool.show_pt pt;
1.1500 +[
1.1501 +(([], Frm), Simplify ((2 - x) / (2 * a) / (2 * a / (x - 2)))),
1.1502 +(([1], Frm), (2 - x) / (2 * a) / (2 * a / (x - 2))),
1.1503 +(([1,1], Frm), (2 - x) / (2 * a) / (2 * a / (x - 2))),
1.1504 +(([1,1], Res), (2 - x) / (2 * a) / (2 * a / (x + -1 * 2))),
1.1505 +(([1,2], Res), (2 + -1 * x) / (2 * a) / (2 * a / (x + -1 * 2))),
1.1506 +(([1], Res), (2 + -1 * x) / (2 * a) / (2 * a / (x + -1 * 2))),
1.1507 +(([2], Res), (2 + -1 * x) / (2 * a) / (2 * a / (-2 + x))),
1.1508 +(([3], Res), (2 + -1 * x) * (-2 + x) / (2 * a * (2 * a))),
1.1509 +(([4], Res), (-4 + 4 * x + -1 * x \<up> 2) / (4 * a \<up> 2)),
1.1510 +(([], Res), (-4 + 4 * x + -1 * x \<up> 2) / (4 * a \<up> 2))]
1.1511 +*)
1.1512 +val (t, asm) = get_obj g_result pt [1, 1];
1.1513 +if UnparseC.term t = "(2 - x) / (2 * a) / (2 * a / (x + -1 * 2))" andalso UnparseC.terms asm = "[]"
1.1514 +then () else error "2nd interSteps ..Simp_Rat_Double_No-1 changed on [1, 1]";
1.1515 +val (t, asm) = get_obj g_result pt [1, 2];
1.1516 +if UnparseC.term t = "(2 + -1 * x) / (2 * a) / (2 * a / (x + -1 * 2))" andalso UnparseC.terms asm = "[]"
1.1517 +then () else error "3rd interSteps ..Simp_Rat_Double_No-1 changed on [1, 2]";
1.1518 + \\----------------------------------TOODOO (*Rfuns revsets \<longrightarrow> broken*)*)
1.1519 +
1.1520 +
1.1521 +(*//----------------------------------TOODOO (*Rfuns revsets \<longrightarrow> broken*)
1.1522 +"-------- interSteps ..Simp_Rat_Cancel_No-1.xml ------------------------------";
1.1523 +"-------- interSteps ..Simp_Rat_Cancel_No-1.xml ------------------------------";
1.1524 +"-------- interSteps ..Simp_Rat_Cancel_No-1.xml ------------------------------";
1.1525 +reset_states ();
1.1526 +CalcTree [(["Term ((a^2 + -1*b^2) / (a^2 + -2*a*b + b^2))", "normalform N"],
1.1527 + ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
1.1528 +Iterator 1;
1.1529 +moveActiveRoot 1;
1.1530 +autoCalculate 1 CompleteCalc;
1.1531 +val ((pt, p), _) = get_calc 1;
1.1532 +(*Test_Tool.show_pt pt;
1.1533 +[
1.1534 +(([], Frm), Simplify ((a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * a * b + b \<up> 2))),
1.1535 +(([1], Frm), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * a * b + b \<up> 2)),
1.1536 +(([1], Res), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * (a * b) + b \<up> 2)),
1.1537 +(([2], Res), (a + b) / (a + -1 * b)),
1.1538 +(([], Res), (a + b) / (a + -1 * b))]
1.1539 +*)
1.1540 +interSteps 1 ([2], Res);
1.1541 +val ((pt, p), _) = get_calc 1;
1.1542 +(*Test_Tool.show_pt pt;
1.1543 +[
1.1544 +(([], Frm), Simplify ((a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * a * b + b \<up> 2))),
1.1545 +(([1], Frm), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * a * b + b \<up> 2)),
1.1546 +(([1], Res), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * (a * b) + b \<up> 2)),
1.1547 +(([2,1], Frm), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * (a * b) + b \<up> 2)),
1.1548 +(([2,1], Res), (a + b) / (a + -1 * b)),
1.1549 +(([2], Res), (a + b) / (a + -1 * b)),
1.1550 +(([], Res), (a + b) / (a + -1 * b))]
1.1551 +*)
1.1552 +interSteps 1 ([2,1],Res);
1.1553 +val ((pt, p), _) = get_calc 1;
1.1554 +(*Test_Tool.show_pt pt;
1.1555 +[
1.1556 +(([], Frm), Simplify ((a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * a * b + b \<up> 2))),
1.1557 +(([1], Frm), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * a * b + b \<up> 2)),
1.1558 +(([1], Res), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * (a * b) + b \<up> 2)),
1.1559 +(([2,1], Frm), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * (a * b) + b \<up> 2)),
1.1560 +(([2,1,1], Frm), (a \<up> 2 + -1 * b \<up> 2) / (a \<up> 2 + -2 * (a * b) + b \<up> 2)),
1.1561 +(([2,1,1], Res), (a \<up> 2 + -1 * (a * b) + a * b + -1 * b \<up> 2) /
1.1562 +(a \<up> 2 + -2 * (a * b) + 1 * b \<up> 2)),
1.1563 +(([2,1,2], Res), (a \<up> 2 + -1 * (a * b) + a * b + -1 * b \<up> 2) /
1.1564 +(a \<up> 2 + -2 * (a * b) + -1 \<up> 2 * b \<up> 2)),
1.1565 +(([2,1,3], Res), (a \<up> 2 + -1 * (a * b) + a * b + -1 * b \<up> 2) /
1.1566 +(a \<up> 2 + -2 * (a * b) + (-1 * b) \<up> 2)),
1.1567 +(([2,1,4], Res), (a * a + -1 * (a * b) + a * b + -1 * b \<up> 2) /
1.1568 +(a \<up> 2 + -2 * (a * b) + (-1 * b) \<up> 2)),
1.1569 +(([2,1,5], Res), (a * a + -1 * (a * b) + a * b + -1 * (b * b)) /
1.1570 +(a \<up> 2 + -2 * (a * b) + (-1 * b) \<up> 2)),
1.1571 +(([2,1,6], Res), (a * a + -1 * (a * b) + a * b + -1 * (b * b)) /
1.1572 +(a \<up> 2 + -1 * (2 * (a * b)) + (-1 * b) \<up> 2)),
1.1573 +(([2,1,7], Res), (a * a + a * (-1 * b) + (b * a + b * (-1 * b))) /
1.1574 +(a \<up> 2 + 2 * (a * (-1 * b)) + (-1 * b) \<up> 2)),
1.1575 +(([2,1,8], Res), (a * a + a * (-1 * b) + (b * a + b * (-1 * b))) /
1.1576 +(a \<up> 2 + 2 * a * (-1 * b) + (-1 * b) \<up> 2)),
1.1577 +(([2,1,9], Res), (a * (a + -1 * b) + (b * a + b * (-1 * b))) /
1.1578 +(a \<up> 2 + 2 * a * (-1 * b) + (-1 * b) \<up> 2)),
1.1579 +(([2,1,10], Res), (a * (a + -1 * b) + b * (a + -1 * b)) /
1.1580 +(a \<up> 2 + 2 * a * (-1 * b) + (-1 * b) \<up> 2)),
1.1581 +(([2,1,11], Res), (a + b) * (a + -1 * b) / (a \<up> 2 + 2 * a * (-1 * b) + (-1 * b) \<up> 2)),
1.1582 +(([2,1,12], Res), (a + b) * (a + -1 * b) / ((a + -1 * b) * (a + -1 * b))),
1.1583 +(([2,1,13], Res), (a + b) / (a + -1 * b)),
1.1584 +(([2,1], Res), (a + b) / (a + -1 * b)),
1.1585 +(([2], Res), (a + b) / (a + -1 * b)),
1.1586 +(([], Res), (a + b) / (a + -1 * b))]
1.1587 +*)
1.1588 +val newnds = children (get_nd pt [2,1]) (*see "fun detailrls"*);
1.1589 +if length newnds = 13 then () else error "rational.sml: interSteps cancel_p rev_rew_p";
1.1590 +
1.1591 +val p = ([2,1,9],Res);
1.1592 +getTactic 1 p;
1.1593 +val (_, tac, _) = ME_Misc.pt_extract (pt, p);
1.1594 +case tac of SOME (Rewrite ("sym_distrib_left", _)) => ()
1.1595 +| _ => error "rational.sml: getTactic, sym_real_plus_binom_times1";
1.1596 + \\----------------------------------TOODOO (*Rfuns revsets \<longrightarrow> broken*)*)
1.1597 +
1.1598 +
1.1599 +"-------- investigate rulesets for cancel_p ----------------------------------";
1.1600 +"-------- investigate rulesets for cancel_p ----------------------------------";
1.1601 +"-------- investigate rulesets for cancel_p ----------------------------------";
1.1602 +val thy = @{theory "Rational"};
1.1603 +val t = TermC.str2term "(a \<up> 2 + -1*b \<up> 2) / (a \<up> 2 + -2*a*b + b \<up> 2)";
1.1604 +val tt = TermC.str2term "(1 * a + 1 * b) * (1 * a + -1 * b)"(*numerator only*);
1.1605 +
1.1606 +"----- with rewrite_set_";
1.1607 +val SOME (tt',asm) = rewrite_set_ thy false make_polynomial tt;
1.1608 +if UnparseC.term tt'= "a \<up> 2 + - 1 * b \<up> 2" then () else error "rls chancel_p 1";
1.1609 +val tt = TermC.str2term "((1 * a + -1 * b) * (1 * a + -1 * b))"(*denominator only*);
1.1610 +val SOME (tt',asm) = rewrite_set_ thy false make_polynomial tt;
1.1611 +if UnparseC.term tt' = "a \<up> 2 + - 2 * a * b + b \<up> 2" then () else error "rls chancel_p 2";
1.1612 +
1.1613 +"----- with Derive.do_one; WN1130912 not investigated further, will be discontinued";
1.1614 +val SOME (tt, _) = factout_p_ thy t;
1.1615 +if UnparseC.term tt = "(a + b) * (a + - 1 * b) / ((a + - 1 * b) * (a + - 1 * b))"
1.1616 +then () else error "rls chancel_p 3";
1.1617 +
1.1618 +"--- with simpler ruleset";
1.1619 +val {rules, rew_ord= (_, ro), ...} = Rule_Set.rep (assoc_rls "rev_rew_p");
1.1620 +val der = Derive.do_one thy Atools_erls rules ro NONE tt;
1.1621 +if length der = 12 then () else error "WN1130912 rls chancel_p 4";
1.1622 +(*default_print_depth 99;*) writeln (Derive.deriv2str der); (*default_print_depth 3;*)
1.1623 +
1.1624 +(*default_print_depth 99;*) map (UnparseC.term o #1) der; (*default_print_depth 3;*)
1.1625 +"...,(-1 * b \<up> 2 + a \<up> 2) / (-2 * (a * b) + a \<up> 2 + (-1 * b) \<up> 2) ]";
1.1626 +(*default_print_depth 99;*) map (Rule.to_string o #2) der; (*default_print_depth 3;*)
1.1627 +(*default_print_depth 99;*) map (UnparseC.term o #1 o #3) der; (*default_print_depth 3;*)
1.1628 +
1.1629 +val der = Derive.do_one thy Atools_erls rules ro NONE
1.1630 + (TermC.str2term "(1 * a + 1 * b) * (1 * a + -1 * b)");
1.1631 +(*default_print_depth 99;*) writeln (Derive.deriv2str der); (*default_print_depth 3;*)
1.1632 +
1.1633 +val {rules, rew_ord=(_,ro),...} = Rule_Set.rep (assoc_rls "rev_rew_p");
1.1634 +val der = Derive.do_one thy Atools_erls rules ro NONE
1.1635 + (TermC.str2term "(1 * a + -1 * b) * (1 * a + -1 * b)");
1.1636 +(*default_print_depth 99;*) writeln (Derive.deriv2str der); (*default_print_depth 3;*)
1.1637 +(*default_print_depth 99;*) map (UnparseC.term o #1) der; (*default_print_depth 3;*)
1.1638 +(*WN060829 ...postponed*)
1.1639 +
1.1640 +
1.1641 +"-------- fun eval_get_denominator -------------------------------------------";
1.1642 +"-------- fun eval_get_denominator -------------------------------------------";
1.1643 +"-------- fun eval_get_denominator -------------------------------------------";
1.1644 +val thy = @{theory Isac_Knowledge};
1.1645 +val t = Thm.term_of (the (TermC.parse thy "get_denominator ((a +x)/b)"));
1.1646 +val SOME (_, t') = eval_get_denominator "" 0 t thy;
1.1647 +if UnparseC.term t' = "get_denominator ((a + x) / b) = b"
1.1648 +then () else error "get_denominator ((a + x) / b) = b"
1.1649 +
1.1650 +
1.1651 +"-------- several errpats in complicated term --------------------------------";
1.1652 +"-------- several errpats in complicated term --------------------------------";
1.1653 +"-------- several errpats in complicated term --------------------------------";
1.1654 +(*WN12xxxx TODO: instead of Gabriella's example here (27.Jul.12) find a simpler one
1.1655 + WN130912: kept this test, although not clear what for*)
1.1656 +reset_states ();
1.1657 +CalcTree [(["Term ((5*b + 25)/(a^2 - b^2) * (a - b)/(5*b))", "normalform N"],
1.1658 + ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
1.1659 +Iterator 1;
1.1660 +moveActiveRoot 1;
1.1661 +autoCalculate 1 CompleteCalc;
1.1662 +val ((pt, p), _) = get_calc 1;
1.1663 +(*Test_Tool.show_pt pt;
1.1664 +[
1.1665 +(([], Frm), Simplify ((5 * b + 25) / (a \<up> 2 - b \<up> 2) * (a - b) / (5 * b))),
1.1666 +(([1], Frm), (5 * b + 25) / (a \<up> 2 - b \<up> 2) * (a - b) / (5 * b)),
1.1667 +(([1], Res), (5 * b + 25) / (a \<up> 2 + -1 * b \<up> 2) * (a + -1 * b) / (5 * b)),
1.1668 +(([2], Res), (5 * b + 25) * (a + -1 * b) / (a \<up> 2 + -1 * b \<up> 2) / (5 * b)),
1.1669 +(([3], Res), (25 * a + -25 * b + 5 * (a * b) + -5 * b \<up> 2) / (a \<up> 2 + -1 * b \<up> 2) /
1.1670 +(5 * b)),
1.1671 +(([4], Res), (25 + 5 * b) / (a + b) / (5 * b)),
1.1672 +(([5], Res), (25 + 5 * b) / ((a + b) * (5 * b))),
1.1673 +(([6], Res), (25 + 5 * b) / (5 * (a * b) + 5 * b \<up> 2)),
1.1674 +(([7], Res), (5 + b) / (a * b + b \<up> 2)),
1.1675 +(([], Res), (5 + b) / (a * b + b \<up> 2))] *)
1.1676 +
1.1677 +
1.1678 +"-------- WN1309xx non-terminating rls norm_Rational -------------------------";
1.1679 +"-------- WN1309xx non-terminating rls norm_Rational -------------------------";
1.1680 +"-------- WN1309xx non-terminating rls norm_Rational -------------------------";
1.1681 +(*------- Schalk I, p.70 Nr. 480b; a/b : c/d translated to a/b * d/c*)
1.1682 +val t = TermC.str2term
1.1683 + ("((12*x*y / (9*x \<up> 2 - y \<up> 2)) / (1 / (3*x - y) \<up> 2 - 1 / (3*x + y) \<up> 2)) * " ^
1.1684 + "((1/(x - 5*y) \<up> 2 - 1/(x + 5*y) \<up> 2) / (20*x*y / (x \<up> 2 - 25*y \<up> 2)))");
1.1685 +
1.1686 +(*1st factor separately simplified *)
1.1687 +val t = TermC.str2term "((12*x*y / (9*x \<up> 2 - y \<up> 2)) / (1 / (3*x - y) \<up> 2 - 1 / (3*x + y) \<up> 2))";
1.1688 +val SOME (t', _) = rewrite_set_ thy false norm_Rational t;
1.1689 +if UnparseC.term t' = "(- 9 * x \<up> 2 + y \<up> 2) / - 1" then () else error "Nr. 480b lhs changed";
1.1690 +(*2nd factor separately simplified *)
1.1691 +val t = TermC.str2term "((1/(x - 5*y) \<up> 2 - 1/(x + 5*y) \<up> 2) / (20*x*y / (x \<up> 2 - 25*y \<up> 2)))";
1.1692 +val SOME (t',_) = rewrite_set_ thy false norm_Rational t; UnparseC.term t';
1.1693 +if UnparseC.term t' = "- 1 / (- 1 * x \<up> 2 + 25 * y \<up> 2)" then () else error "Nr. 480b rhs changed";
1.1694 +
1.1695 +"-------- Schalk I, p.70 Nr. 477a: terms are exploding ?!?";
1.1696 +val t = TermC.str2term ("b*y/(b - 2*y)/((b \<up> 2 - y \<up> 2)/(b+2*y)) /" ^
1.1697 + "(b \<up> 2*y + b*y \<up> 2) * (a+x) \<up> 2 / ((b \<up> 2 - 4*y \<up> 2) * (a+2*x) \<up> 2)");
1.1698 +(*val SOME (t',_) = rewrite_set_ thy false norm_Rational t;
1.1699 +:
1.1700 +### rls: cancel_p on: (a \<up> 2 * (b * y) + 2 * (a * (b * (x * y))) + b * (x \<up> 2 * y)) /
1.1701 +(b + -2 * y) /
1.1702 +((b \<up> 2 + -1 * y \<up> 2) / (b + 2 * y)) /
1.1703 +(b \<up> 2 * y + b * y \<up> 2) /
1.1704 +(a \<up> 2 * b \<up> 2 + -4 * (a \<up> 2 * y \<up> 2) + 4 * (a * (b \<up> 2 * x)) +
1.1705 + -16 * (a * (x * y \<up> 2)) +
1.1706 + 4 * (b \<up> 2 * x \<up> 2) +
1.1707 + -16 * (x \<up> 2 * y \<up> 2))
1.1708 +exception Div raised
1.1709 +
1.1710 +BUT
1.1711 +val t = TermC.str2term
1.1712 + ("(a \<up> 2 * (b * y) + 2 * (a * (b * (x * y))) + b * (x \<up> 2 * y)) /" ^
1.1713 + "(b + -2 * y) /" ^
1.1714 + "((b \<up> 2 + -1 * y \<up> 2) / (b + 2 * y)) /" ^
1.1715 + "(b \<up> 2 * y + b * y \<up> 2) /" ^
1.1716 + "(a \<up> 2 * b \<up> 2 + -4 * (a \<up> 2 * y \<up> 2) + 4 * (a * (b \<up> 2 * x)) +" ^
1.1717 + "-16 * (a * (x * y \<up> 2)) +" ^
1.1718 + "4 * (b \<up> 2 * x \<up> 2) +" ^
1.1719 + "-16 * (x \<up> 2 * y \<up> 2))");
1.1720 +NONE = cancel_p_ thy t;
1.1721 +*)
1.1722 +
1.1723 +(*------- Schalk I, p.70 Nr. 476b in 2003 this worked using 10 sec. *)
1.1724 +val t = TermC.str2term
1.1725 + ("((a \<up> 2 - b \<up> 2)/(2*a*b) + 2*a*b/(a \<up> 2 - b \<up> 2)) / ((a \<up> 2 + b \<up> 2)/(2*a*b) + 1) / " ^
1.1726 + "((a \<up> 2 + b \<up> 2) \<up> 2 / (a + b) \<up> 2)");
1.1727 +(* Rewrite.trace_on := true;
1.1728 +rewrite_set_ thy false norm_Rational t;
1.1729 +:
1.1730 +#### rls: cancel_p on: (2 * (a \<up> 7 * b) + 4 * (a \<up> 6 * b \<up> 2) + 6 * (a \<up> 5 * b \<up> 3) +
1.1731 + 8 * (a \<up> 4 * b \<up> 4) +
1.1732 + 6 * (a \<up> 3 * b \<up> 5) +
1.1733 + 4 * (a \<up> 2 * b \<up> 6) +
1.1734 + 2 * (a * b \<up> 7)) /
1.1735 +(2 * (a \<up> 9 * b) + 4 * (a \<up> 8 * b \<up> 2) +
1.1736 + 2 * (2 * (a \<up> 7 * b \<up> 3)) +
1.1737 + 4 * (a \<up> 6 * b \<up> 4) +
1.1738 + -4 * (a \<up> 4 * b \<up> 6) +
1.1739 + -4 * (a \<up> 3 * b \<up> 7) +
1.1740 + -4 * (a \<up> 2 * b \<up> 8) +
1.1741 + -2 * (a * b \<up> 9))
1.1742 +
1.1743 +if UnparseC.term t = "1 / (a \<up> 2 + -1 * b \<up> 2)" then ()
1.1744 +else error "rational.sml: diff.behav. in norm_Rational_mg 49";
1.1745 +*)
1.1746 +
1.1747 +"-------- Schalk I, p.70 Nr. 480a: terms are exploding ?!?";
1.1748 +val t = TermC.str2term ("(1/x + 1/y + 1/z) / (1/x - 1/y - 1/z) / " ^
1.1749 + "(2*x \<up> 2 / (x \<up> 2 - z \<up> 2) / (x / (x + z) + x / (x - z)))");
1.1750 +(* Rewrite.trace_on := true;
1.1751 +rewrite_set_ thy false norm_Rational t;
1.1752 +:
1.1753 +#### rls: cancel_p on: (2 * (x \<up> 6 * (y \<up> 2 * z)) + 2 * (x \<up> 6 * (y * z \<up> 2)) +
1.1754 + 2 * (x \<up> 5 * (y \<up> 2 * z \<up> 2)) +
1.1755 + -2 * (x \<up> 4 * (y \<up> 2 * z \<up> 3)) +
1.1756 + -2 * (x \<up> 4 * (y * z \<up> 4)) +
1.1757 + -2 * (x \<up> 3 * (y \<up> 2 * z \<up> 4))) /
1.1758 +(-2 * (x \<up> 6 * (y \<up> 2 * z)) + -2 * (x \<up> 6 * (y * z \<up> 2)) +
1.1759 + 2 * (x \<up> 5 * (y \<up> 2 * z \<up> 2)) +
1.1760 + 2 * (x \<up> 4 * (y \<up> 2 * z \<up> 3)) +
1.1761 + 2 * (x \<up> 4 * (y * z \<up> 4)) +
1.1762 + -2 * (x \<up> 3 * (y \<up> 2 * z \<up> 4)))
1.1763 +*)
1.1764 +
1.1765 +"-------- Schalk I, p.60 Nr. 215d: terms are exploding, internal loop does not terminate";
1.1766 +val t = TermC.str2term "(a-b) \<up> 3 * (x+y) \<up> 4 / ((x+y) \<up> 2 * (a-b) \<up> 5)";
1.1767 +(* Kein Wunder, denn Z???ler und Nenner extra als Polynom dargestellt ergibt:
1.1768 +
1.1769 +val t = TermC.str2term "(a-b) \<up> 3 * (x+y) \<up> 4";
1.1770 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1771 +UnparseC.term t;
1.1772 +"a \<up> 3 * x \<up> 4 + 4 * a \<up> 3 * x \<up> 3 * y +6 * a \<up> 3 * x \<up> 2 * y \<up> 2 +4 * a \<up> 3 * x * y \<up> 3 +a \<up> 3 * y \<up> 4 +-3 * a \<up> 2 * b * x \<up> 4 +-12 * a \<up> 2 * b * x \<up> 3 * y +-18 * a \<up> 2 * b * x \<up> 2 * y \<up> 2 +-12 * a \<up> 2 * b * x * y \<up> 3 +-3 * a \<up> 2 * b * y \<up> 4 +3 * a * b \<up> 2 * x \<up> 4 +12 * a * b \<up> 2 * x \<up> 3 * y +18 * a * b \<up> 2 * x \<up> 2 * y \<up> 2 +12 * a * b \<up> 2 * x * y \<up> 3 +3 * a * b \<up> 2 * y \<up> 4 +-1 * b \<up> 3 * x \<up> 4 +-4 * b \<up> 3 * x \<up> 3 * y +-6 * b \<up> 3 * x \<up> 2 * y \<up> 2 +-4 * b \<up> 3 * x * y \<up> 3 +-1 * b \<up> 3 * y \<up> 4";
1.1773 +val t = TermC.str2term "((x+y) \<up> 2 * (a-b) \<up> 5)";
1.1774 +val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1775 +UnparseC.term t;
1.1776 +"a \<up> 5 * x \<up> 2 + 2 * a \<up> 5 * x * y + a \<up> 5 * y \<up> 2 +-5 * a \<up> 4 * b * x \<up> 2 +-10 * a \<up> 4 * b * x * y +-5 * a \<up> 4 * b * y \<up> 2 +10 * a \<up> 3 * b \<up> 2 * x \<up> 2 +20 * a \<up> 3 * b \<up> 2 * x * y +10 * a \<up> 3 * b \<up> 2 * y \<up> 2 +-10 * a \<up> 2 * b \<up> 3 * x \<up> 2 +-20 * a \<up> 2 * b \<up> 3 * x * y +-10 * a \<up> 2 * b \<up> 3 * y \<up> 2 +5 * a * b \<up> 4 * x \<up> 2 +10 * a * b \<up> 4 * x * y +5 * a * b \<up> 4 * y \<up> 2 +-1 * b \<up> 5 * x \<up> 2 +-2 * b \<up> 5 * x * y +-1 * b \<up> 5 * y \<up> 2";
1.1777 +
1.1778 +anscheinend macht dem Rechner das Krzen diese Bruches keinen Spass mehr ...*)
1.1779 +
1.1780 +"-------- Schalk I, p.70 Nr. 480b: terms are exploding, Rewrite.trace_on stops at";
1.1781 +val t = TermC.str2term ("((12*x*y/(9*x \<up> 2 - y \<up> 2))/" ^
1.1782 + "(1/(3*x - y) \<up> 2 - 1/(3*x + y) \<up> 2)) *" ^
1.1783 + "(1/(x - 5*y) \<up> 2 - 1/(x + 5*y) \<up> 2)/" ^
1.1784 + "(20*x*y/(x \<up> 2 - 25*y \<up> 2))");
1.1785 +(*val SOME (t, _) = rewrite_set_ thy false norm_Rational t;
1.1786 +:
1.1787 +#### rls: cancel_p on: (19440 * (x \<up> 8 * y \<up> 2) + -490320 * (x \<up> 6 * y \<up> 4) +
1.1788 + 108240 * (x \<up> 4 * y \<up> 6) +
1.1789 + -6000 * (x \<up> 2 * y \<up> 8)) /
1.1790 +(2160 * (x \<up> 8 * y \<up> 2) + -108240 * (x \<up> 6 * y \<up> 4) +
1.1791 + 1362000 * (x \<up> 4 * y \<up> 6) +
1.1792 + -150000 * (x \<up> 2 * y \<up> 8))
1.1793 +*)
1.1794 +