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--- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--- All rights reserved.
---
--- Redistribution and use in source and binary forms, with or without
--- modification, are permitted provided that the following conditions are
--- met:
---
---     - Redistributions of source code must retain the above copyright
---       notice, this list of conditions and the following disclaimer.
---
---     - Redistributions in binary form must reproduce the above copyright
---       notice, this list of conditions and the following disclaimer in
---       the documentation and/or other materials provided with the
---       distribution.
---
---     - Neither the name of The Numerical ALgorithms Group Ltd. nor the
---       names of its contributors may be used to endorse or promote products
---       derived from this software without specific prior written permission.
---
--- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--- IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--- TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--- PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--- OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--- EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--- PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--- LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-
-
---% Mode and Type Resolution Rule Data and Ruleset Creation
-
---% resolveTT Rules
-
--- These rules are applied only once at the outermost position of a term
--- some things can't be done by term rewriting conveniently (e.g. set
--- difference), so a form is created which is interpreted by
--- resolveTTRed later. The meanings of these forms are:
--- Incl(x,y): y if x is a member of y, failed otherwise
--- SetEqual(x,y): x if y is a permutation of x, failed otherwise
--- SetComp(x,y): x-y, if y is a subset of x, failed otherwise
--- SetInter(x,y): intersection of x and y, if nonempty, failed otherwise
--- SetDiff(x,y): x-y, if x and y have a nonempty intersection, failed ...
-
--- These first rules will be expanded for each of MP, DMP and NDMP
-
-SETANDFILEQ($mpolyTTRules,'( _
-  ((Resolve (RN) (mpoly1 x t1)) . (mpoly1 x (Resolve (RN) t1))) _
-  ((Resolve (UP x t1) (mpoly1 y t2)) . _
-    (Resolve t1 (mpoly1 (Incl x y) t2))) _
-  ((Resolve (mpoly1 x t1) (G t2)) . _
-    (mpoly1 x (G (VarEqual t1 t2)))) _
-  ((Resolve (VARIABLE x) (mpoly1 y t2)) . _
-    (mpoly1 (Incl x y) t2)) _
-  ((Resolve (mpoly1 x t1) (mpoly1 y t2)) . _
-    (mpoly1 (SetEqual x y) (Resolve t1 t2))) _
-  ((Resolve (mpoly1 x t1) (mpoly1 y t2)) . _
-    (mpoly1 x (Resolve t1 (mpoly1 (SetComp y x) t2)))) _
-  ((Resolve (mpoly1 x t1) (mpoly1 y t2)) . _
-    (mpoly1 y (Resolve (mpoly1 (SetComp x y) t1) t2))) _
-  ((Resolve (mpoly1 x t1) (mpoly1 y t2)) . _
-    (mpoly1 (SetInter x y) (Resolve _
-      (mpoly1 (SetDiff x y) t1) (mpoly1 (SetDiff y x) t2)))) _
-  ))
-
--- These are the general rules, excluding those above.
-
-SETANDFILEQ($generalTTRules, '( _
-  ((Resolve (L (L t1)) (M t2)) . (M (Resolve t1 t2))) _
-  ((Resolve (EQ t1) (B)) . (B)) _
-  ((Resolve (SY) t1) . (Resolve (P (I)) t1)) _
-  ((Resolve (M t1) (SM x t2)) . (M (Resolve t1 t2))) _
-  ((Resolve (M t1) (RM x y t2)) . (M (Resolve t1 t2))) _
-  ((Resolve (SM x t1) (RM y y t2)) . _
-    (SM (VarEqual x y) (Resolve t1 t2))) _
-  ((Resolve (V t1) (L t2)) . (V (Resolve t1 t2))) _
-  ((Resolve (FF t1) (FR t2)) . (FR (Resolve t1 t2))) _
-  ((Resolve (F) (RN)) . (F) ) _
- _
-  ((Resolve (OV x) (OV y)) . (OV (SetUnion x y))) _
-  ((Resolve (P t1) (UP y t2)) . (Resolve (P t1) t2)) _
- _
-  ((Resolve (UP y t1) (G t2)) . (UP y (G (VarEqual t1 t2)))) _
-  ((Resolve (P t1) (P t2)) . (P (Resolve t1 t2))) _
-  ((Resolve (G t1) (G t2)) . (G (Resolve t1 t2))) _
-  ((Resolve (G t1) (P t2)) . (P (G (VarEqual t1 t2)))) _
- _
-  ((Resolve (AF t1) (EF t2)) . (EF (Resolve t1 t2))) _
-  ((Resolve (AF t1) (LF t2)) . (LF (Resolve t1 t2))) _
-  ((Resolve (AF t1) (FE t2)) . (FE (Resolve t1 t2))) _
-  ((Resolve (EF t1) (LF t2)) . (LF (Resolve t1 t2))) _
-  ((Resolve (EF t1) (FE t2)) . (FE (Resolve t1 t2))) _
-  ((Resolve (LF t1) (FE t2)) . (FE (Resolve t1 t2))) _
- _
-  ((Resolve (RN) (P t1)) . (P (Resolve (RN) t1))) _
-  ((Resolve (RN) (UP x t1)) . (UP x (Resolve (RN) t1))) _
-  ((Resolve (RN) (UPS x t1)) . (UPS x (Resolve (RN) t1))) _
-  ((Resolve (RN) (CFPS x t1)) . (CFPS x (Resolve (RN) t1))) _
- _
-  ((Resolve (RR) (EF t1)) . (EF (Resolve (RR) t1))) _
-  ((Resolve (P t1) (AF t2)) . (AF (Resolve t1 t2 ))) _
-  ((Resolve (P t1) (EF t2)) . (EF (Resolve t1 t2 ))) _
-  ((Resolve (P t1) (LF t2)) . (LF (Resolve t1 t2 ))) _
- _
-  ((Resolve (MP x t1) (DMP y t2)) . _
-    (MP (SetEqual x y) (Resolve t1 t2))) _
-  ((Resolve (MP x t1) (DMP y t2)) . _
-    (MP x (Resolve t1 (DMP (SetComp y x) t2)))) _
-  ((Resolve (MP x t1) (DMP y t2)) . _
-    (MP y (Resolve (MP (SetComp x y) t1) t2))) _
-  ((Resolve (MP x t1) (DMP y t2)) . _
-    (MP (SetInter x y) (Resolve _
-      (MP (SetDiff x y) t1) (DMP (SetDiff y x) t2)))) _
- _
-  ((Resolve (MP x t1) (NDMP y t2)) . _
-    (MP (SetEqual x y) (Resolve t1 t2))) _
-  ((Resolve (MP x t1) (NDMP y t2)) . _
-    (MP x (Resolve t1 (NDMP (SetComp y x) t2)))) _
-  ((Resolve (MP x t1) (NDMP y t2)) . _
-    (MP y (Resolve (MP (SetComp x y) t1) t2))) _
-  ((Resolve (MP x t1) (NDMP y t2)) . _
-    (MP (SetInter x y) (Resolve _
-      (MP (SetDiff x y) t1) (NDMP (SetDiff y x) t2)))) _
- _
-  ((Resolve (DMP x t1) (NDMP y t2)) . _
-    (DMP (SetEqual x y) (Resolve t1 t2))) _
-  ((Resolve (DMP x t1) (NDMP y t2)) . _
-    (DMP x (Resolve t1 (NDMP (SetComp y x) t2)))) _
-  ((Resolve (DMP x t1) (NDMP y t2)) . _
-    (DMP y (Resolve (DMP (SetComp x y) t1) t2))) _
-  ((Resolve (DMP x t1) (NDMP y t2)) . _
-    (DMP (SetInter x y) (Resolve _
-      (DMP (SetDiff x y) t1) (NDMP (SetDiff y x) t2)))) _
-  ))
-
--- The following creates the ruleset
-
-createResolveTTRules() ==
-  -- expand multivariate polynomial rules
-  mps := '(MP DMP NDMP)
-  mpRules := "append"/[SUBST(mp,'mpoly1,$mpolyTTRules) for mp in mps]
-  $Res := CONS('(t1 t2 x y),
-    EQSUBSTLIST($nameList,$abList,append($generalTTRules,mpRules)))
-  true
-
---% resolveTM Rules
-
--- Same rules as for resolveTT, with two exceptions:
--- Diff(x,y): removes y from x, if possible, failed otherwise
--- SetIncl(x,y): y if x is a subset of y, failed otherwise
-
--- These first rules will be expanded for each of MP, DMP and NDMP
-
-SETANDFILEQ($mpolyTMRules,'( _
-  ((Resolve (mpoly1 x t1) (P t2)) . (Resolve t1 (P t2))) _
-  ((Resolve (mpoly1 (x) t1) (UP x t2)) . (UP x (Resolve t1 t2))) _
-  ((Resolve (mpoly1 x t1) (UP y t2)) . _
-    (UP y (Resolve (mpoly1 (Diff x y) t1) t2))) _
-  ((Resolve (UP x t1) (mpoly1 y t2)) . _
-    (Resolve t1 (mpoly1 (Incl x y) t2))) _
-  ((Resolve (VARIABLE x) (mpoly1 y t2)) . _
-    (mpoly1 (Incl x y) (Resolve (I) t2))) _
-  ((Resolve (mpoly1 x t1) (mpoly2 y t2)) . _
-    (Resolve t1 (mpoly2 (SetIncl x y) t2))) _
-  ((Resolve (mpoly1 x t1) (mpoly2 y t2)) . _
-    (mpoly2 y (Resolve (mpoly1 (SetComp x y) t1) t2))) _
-  ((Resolve (mpoly1 x t1) (mpoly2 y t2)) . _
-    (Resolve (mpoly1 (SetDiff x y) t1) (mpoly2 y t2))) _
- ))
-
--- These are the general rules, excluding those above.
-
-SETANDFILEQ($generalTMRules,'( _
-  ((Resolve (VARIABLE x) (P t1)) . (P (Resolve (I) t1))) _
-  ((Resolve (VARIABLE x) (UP y t1)) . _
-    (UP (VarEqual x y) (Resolve (I) t1))) _
-  ((Resolve (VARIABLE x) (UPS y t1)) . _
-    (UPS (VarEqual x y) (Resolve (I) t1))) _
-  ((Resolve (VARIABLE x) (CFPS y t1)) . _
-    (CFPS (VarEqual x y) (Resolve (RN) t1))) _
-  ((Resolve (VARIABLE x) (ELFPS y t1)) . _
-    (ELFPS (VarEqual x y) (Resolve (RN) t1))) _
-  ((Resolve (VARIABLE x) (EF t1)) . (EF t1)) _
-  ((Resolve (L (L (SY))) (M _*_*)) . (M (P (I)))) _
-  ((Resolve (L (L (SY))) (SM x _*_*)) . (SM x (P (I)))) _
-  ((Resolve (L (L t1)) (M t2)) . (M (Resolve t1 t2))) _
-  ((Resolve (L (L t1)) (SM x t2)) . (SM x (Resolve t1 t2))) _
-  ((Resolve (L (L t1)) (RM x y t2)) . (RM x y (Resolve t1 t2))) _
-  ((Resolve (SY) t1) . (Resolve (P (I)) t1)) _
-  ((Resolve (VARIABLE x) t1) . (Resolve (P (I)) t1)) _
-  ((Resolve (SM x t1) (M t2)) . (M (Resolve t1 t2))) _
-  ((Resolve (RM x y t1) (M t2)) . (M (Resolve t1 t2))) _
- _
-  ((Resolve (M t1) (L _*_*)) . (L (L t1))) _
-  ((Resolve (SM x t1) (L _*_*)) . (L (L t1))) _
-  ((Resolve (RM x y t1) (L _*_*)) . (L (L t1))) _
-  ((Resolve (M t1) (L t2)) . (L (Resolve (L t1) t2))) _
-  ((Resolve (SM x t1) (L t2)) . (L (Resolve (L t1) t2))) _
-  ((Resolve (RM x y t1) (L t2)) . (L (Resolve (L t1) t2))) _
- _
-  ((Resolve (M t1) (V _*_*)) . (V (V t1))) _
-  ((Resolve (SM x t1) (V _*_*)) . (V (V t1))) _
-  ((Resolve (RM x y t1) (V _*_*)) . (V (V t1))) _
-  ((Resolve (M t1) (V t2)) . (V (Resolve (V t1) t2))) _
-  ((Resolve (SM x t1) (V t2)) . (V (Resolve (V t1) t2))) _
-  ((Resolve (RM x y t1) (V t2)) . (V (Resolve (V t1) t2))) _
- _
-  ((Resolve (L t1) (V t2)) . (V (Resolve t1 t2))) _
-  ((Resolve (V t1) (L t2)) . (L (Resolve t1 t2))) _
-  ((Resolve (FF t1) (FR t2)) . (FR (Resolve t1 t2))) _
-  ((Resolve (UP x t1) (P t2)) . (Resolve t1 (P t2))) _
- ))
-
--- Private abbreviation table for resolve rules
-SETANDFILEQ($resolveAbbreviations, '( _
-    (P .  Polynomial) _
-    (G .  Gaussian) _
-    (L .  List) _
-    (M .  Matrix) _
-    (EQ . Equation) _
-    (B .  Boolean) _
-    (SY . Symbol) _
-    (I .  Integer) _
-    (SM . SquareMatrix) _
-    (RM . RectangularMatrix) _
-    (V .  Vector) _
-    (FF . FactoredForm) _
-    (FR . FactoredRing) _
-    (RN . RationalNumber) _
-    (F .  Float) _
-    (OV . OrderedVariableList) _
-    (UP . UnivariatePoly) _
-    (DMP . DistributedMultivariatePolynomial) _
-    (MP . MultivariatePolynomial) _
-    (HDMP . HomogeneousDistributedMultivariatePolynomial) _
-    (QF . QuotientField) _
-    (RF . RationalFunction) _
-    (RE . RadicalExtension) _
-    (RR . RationalRadicals) _
-    (UPS . UnivariatePowerSeries) _
-    (CFPS . ContinuedFractionPowerSeries) _
-    (ELFPS . EllipticFunctionPowerSeries) _
-    (EF . ElementaryFunction) _
-    (VARIABLE . Variable) _
- ))
-
-SETANDFILEQ($newResolveAbbreviations, '( _
-    (P .  Polynomial) _
-    (G .  Complex) _
-    (L .  List) _
-    (M .  Matrix) _
-    (EQ . Equation) _
-    (B .  Boolean) _
-    (SY . Symbol) _
-    (I .  Integer) _
-    (SM . SquareMatrix) _
-    (RM . RectangularMatrix) _
-    (V .  Vector) _
-    (FF . Factored) _
-    (FR . Factored) _
-    (F .  Float) _
-    (OV . OrderedVariableList) _
-    (UP . UnivariatePolynomial) _
-    (DMP . DistributedMultivariatePolynomial) _
-    (MP . MultivariatePolynomial) _
-    (HDMP . HomogeneousDistributedMultivariatePolynomial) _
-    (QF . Fraction) _
-    (UPS . UnivariatePowerSeries) _
-    (VARIABLE . Variable) _
- ))
-
--- The following creates the ruleset
-
-createResolveTMRules() ==
-  -- expand multivariate polynomial rules
-  mps := '(MP DMP NDMP)
-  mpRules0 := "append"/[SUBST(mp,'mpoly1,$mpolyTMRules) for mp in mps]
-  mpRules := "append"/[SUBST(mp,'mpoly2,mpRules0) for mp in mps]
-  $ResMode := CONS('(t1 t2 x y),
-    EQSUBSTLIST($nameList,$abList,append(mpRules,$generalTMRules)))
-  true
-
-createTypeEquivRules() ==
-  -- used by eqType, for example
-  $TypeEQ := CONS('(t1), EQSUBSTLIST($nameList,$abList,'(
-    ((QF (P t1)) . (RF t1))
-      ((QF (I)) . (RN))
-        ((RE (RN)) . (RR)) )))
-  $TypeEqui := CONS(CAR $TypeEQ, [[b,:a] for [a,:b] in CDR $TypeEQ])
-  true
-
-initializeRuleSets() ==
-  $abList: local :=
-    ASSOCLEFT $newResolveAbbreviations
-  $nameList: local :=
-    ASSOCRIGHT $newResolveAbbreviations
-  createResolveTTRules()
-  createResolveTMRules()
-  createTypeEquivRules()
-  $ruleSetsInitialized := true
-  true