Merge remote-tracking branch 'michalt/fibon' into HEAD

fibon/Hackage/Agum/ChangeLog

-2010-06-21  John D. Ramsdell  <ramsdell@mitre.org>
-
-	* agum.cabal (Version): Released as version 2.3.
-
-	* agum.cabal (Build-Depends): changes dependency to
-	base >= 3 && <5, containers
-
-2009-09-17  John D. Ramsdell  <ramsdell@mitre.org>
-
-	* agum.cabal (Version): Released as version 2.2.
-
-2009-09-14  John D. Ramsdell  <ramsdell@.mitre.org>
-
-	* src/Algebra/AbelianGroup/IntLinEq.hs: Integer solutions to
-	linear equation solver was placed in its own module.
-
-2009-09-13  John D. Ramsdell  <ramsdell@mitre.org>
-
-	* src/Algebra/AbelianGroup/UnificationMatching.hs (unify): Changed
-	the result to be a substitution since unification always succeeds.
-
-2009-09-05  John D. Ramsdell  <ramsdell@mitre.org>
-
-	* src/Algebra/AbelianGroup/UnificationMatching.hs:  Added
-	reference to Andrew Kennedy's Ph.D. thesis as it contains a proof
-	of correctness of the implemented matching algorithm.
-
-	* agum.cabal (Version): Released as version 2.1.
-
-2009-08-29  John D. Ramsdell  <ramsdell@mitre.org>
-
-	* src/Algebra/AbelianGroup/UnificationMatching.hs (Substitution,
-	apply): Hid the representation of a substitution and supplied a
-	function for applying a substitution to a term.
-
-	* agum.cabal (Version): Released as version 2.0.

fibon/Hackage/Agum/Makefile

-TOP = ../../..
-include $(TOP)/mk/boilerplate.mk
-SRCS = src/Algebra/AbelianGroup/IntLinEq.hs \
-       src/Algebra/AbelianGroup/UnificationMatching.hs \
-       src/Algebra/AbelianGroup/Main.hs
-STDIN_FILE = eqn.txt
-HC_OPTS += -isrc -package base -package containers
-include $(TOP)/mk/target.mk

fibon/Hackage/Agum/readme.txt

-This package contains a library for unification and matching in
-an Abelian group and a program that exercises the library.
-
-$ agum
-Abelian group unification and matching -- :? for help
-agum> 2x+y=3z
-Problem:   2x + y = 3z
-Unifier:   [x : g0,y : -2g0 + 3g2,z : g2]
-Matcher:   [x : g0,y : -2g0 + 3z]
-
-agum> 2x=x+y
-Problem:   2x = x + y
-Unifier:   [x : g1,y : g1]
-Matcher:   no solution
-
-agum> 64x-41y=a
-Problem:   64x - 41y = a
-Unifier:   [a : 64g1 - 41g2,x : g1,y : g2]
-Matcher:   [x : -16a - 41g6,y : -25a - 64g6]
-
-agum> :quit

fibon/Hackage/Agum/src/Algebra/AbelianGroup/IntLinEq.hs

--- Integer Solutions of Linear Inhomogeneous Equations
---
--- Copyright (C) 2009 John D. Ramsdell
---
--- This program is free software: you can redistribute it and/or modify
--- it under the terms of the GNU General Public License as published by
--- the Free Software Foundation, either version 3 of the License, or
--- (at your option) any later version.
-
--- This program is distributed in the hope that it will be useful,
--- but WITHOUT ANY WARRANTY; without even the implied warranty of
--- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
--- GNU General Public License for more details.
-
--- You should have received a copy of the GNU General Public License
--- along with this program.  If not, see <http://www.gnu.org/licenses/>.
-
--- |
--- Module      : Algebra.AbelianGroup.IntLinEq
--- Copyright   : (C) 2009 John D. Ramsdell
--- License     : GPL
---
--- Integer Solutions of Linear Inhomogeneous Equations
---
--- A linear equation with integer coefficients is represented as a
--- pair of lists of non-zero integers, the coefficients and the
--- constants.  If there are no constants, the linear equation
--- represented by (c, []) is the homogeneous equation:
---
--- >     c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1] = 0
---
--- where n is the length of c.  Otherwise, (c, d) represents the
--- inhomogeneous equation:
---
--- >     c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1] = g
---
--- where g = gcd(d[0], d[1], ..., d[m-1]), and m is the length of d.
--- Thus g is the greatest common denominator of the elements of d.
---
--- A solution is a partial map from variables to terms, and a term is
--- a pair of lists of integers, the variable part of the term followed
--- by the constant part.  The variable part may specify variables not
--- in the input.  In other words, the length of the coefficents in the
--- answer may exceed the length of the coefficients in the input.  For
--- example, the solution of
---
--- >     64x - 41y = 1
---
--- is x = -41z - 16 and y = -64z - 25.  The computed solution is read
--- off the list returned as an answer.
---
--- >     intLinEq [64,-41] [1] =
--- >         [(0,([0,0,0,0,0,0,-41],[-16])),
--- >         (1,([0,0,0,0,0,0,-64],[-25]))]
---
--- The algorithm used to find solutions is described in Vol. 2 of The
--- Art of Computer Programming \/ Seminumerical Alorithms, 2nd Ed.,
--- 1981, by Donald E. Knuth, pg. 327.  To show sums, we write
---
--- >     sum[i] c[i]*x[i] for c[0]*x[0] + c[1]*x[1] + ... + c[n-1]*x[n-1].
---
--- The algorithm's initial values are the linear equation (c,d) and an
--- empty substitution s.
---
--- 1.  Let c[i] be the smallest non-zero coefficient in absolute value.
---
--- 2.  If c[i] < 0, multiply c and d by -1 and goto step 1.
---
--- 3.  If c[i] = 1, a general solution of the following form has been
--- found:
---
--- >     x[i] = sum[j] -c'[j]*x[j] + d[k] for all k
---
---  where c' is c with c'[i] = 0.  Use the equation to eliminate x[i]
---  from the range of the current substitution s.  If variable x[i] is
---  in the original equation, add the mapping to substitution s.
---
--- 4.  If c[i] divides every coefficient in c,
---
---     * if c[i] divides every constant in d, divide c and d by c[i]
---       and goto step 3,
---
---     * otherwise fail because there is no solution.
---
--- 5.  Otherwise, eliminate x[i] as above in favor of freshly created
--- variable x[n], where n is the length of c.
---
--- >    x[n] = sum[j] (c[j] div c[i] * x[j])
---
--- Goto step 1 and solve the equation:
---
--- >    c[i]*x[n] + sum[j] (c[j] mod c[i])*x[j] = d[k] for all k
-
-module Algebra.AbelianGroup.IntLinEq
-    (LinEq, Subst, intLinEq) where
-
--- | A linear equation with integer coefficients is represented as a
--- pair of lists of non-zero integers, the coefficients and the
--- constants.
-type LinEq = ([Int], [Int])
-
--- | A solution to a linear equation is a partial map from variables
--- to terms, and a term is a pair of lists of integers, the variable
--- part of the term followed by the constant part.  The variable part
--- may specify variables not in the input.  In other words, the length
--- of the coefficents in the answer may exceed the length of the
--- coefficients in the input.
-type Subst = [(Int, LinEq)]
-
--- | Find integer solutions to a linear equation or fail when there
--- are no solutions.
-intLinEq :: Monad m => LinEq -> m Subst
-intLinEq (coefficients, constants) =
-    intLinEqLoop (length coefficients) (coefficients, constants) []
-
--- The algorithm used to find solutions is described in Vol. 2 of The
--- Art of Computer Programming / Seminumerical Alorithms, 2nd Ed.,
--- 1981, by Donald E. Knuth, pg. 327.
-
--- On input, n is the number of variables in the original problem, c
--- is the coefficients, d is the constants, and subst is a list of