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[Axiom-developer] 20080821.01.tpd.patch (add MappingPackage4)
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20080821.01.tpd.patch (add MappingPackage4) |
|
Date: |
Thu, 21 Aug 2008 23:13:06 -0500 |
Modify mappkg.spad to add MappingPackage4, including algebra test
file and )help documentation. Fix corresponding operation count
message in test.input regression.
===================================================================
diff --git a/changelog b/changelog
index 377aa85..3ba51a4 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,12 @@
+20080821 tpd src/algebra/Makefile add MappingPackage4
+20080821 tpd src/algebra/exposed.lsp add MappingPackage4
+20080821 tpd src/algebra/mappkg.spad add MAPPKG4
+20080821 tpd src/input/test.input repair regressions
+20080820 tpd src/input/test.input fix typos
+20080819 tpd src/input/Makefile overload.input added
+20080819 dxc src/input/overload.input added
+20080819 tpd src/input/Makefile overload.input added
+20080819 dxc src/input/overload.input added
20080818 tpd src/input/Makefile biquat.input added
20080818 dxc src/input/biquat.input added
20080818 dxc "David Cyganski" (no known email)
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index d140609..7ea5dea 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -244,7 +244,6 @@ LAYER3=\
annacat.spad.pamphlet (NIPROB ODEPROB PDEPROB OPTPROB NUMINT ODECAT PDECAT
OPTCAT)
color.spad.pamphlet (COLOR PALETTE)
-mappkg.spad.pamphlet (MAPHACK1 MAPHACK2 MAPHACK3 MAPPKG1 MAPPKG2 MAPPKG3)
paramete.spad.pamphlet (PARPCURV PARPC2 PARSCURV PARSC2 PARSURF PARSU2
suchthat.spad.pamphlet (SUCH)
ystream.spad.pamphlet (YSTREAM)
@@ -388,6 +387,8 @@ drawpak.spad.pamphlet (DRAWCX)
free.spad.pamphlet (LMOPS FMONOID FGROUP FAMONC IFAMON FAMONOID FAGROUP)
fourier.spad.pamphlet (FCOMP FSERIES)
functions.spad.pamphlet (BFUNCT)
+mappkg.spad.pamphlet (MAPHACK1 MAPHACK2 MAPHACK3 MAPHACK4
+ MAPPKG1 MAPPKG2 MAPPKG3 MAPPKG4)
mesh.spad.pamphlet (MESH)
moebius.spad.pamphlet (MOEBIUS)
mring.spad.pamphlet (MRING MRF2)
@@ -414,6 +415,7 @@ LAYER10=\
${OUT}/IPADIC.o ${OUT}/IROOT.o ${OUT}/IR2.o ${OUT}/LEXP.o \
${OUT}/LIECAT.o ${OUT}/LIECAT-.o ${OUT}/LIST2.o ${OUT}/LIST2MAP.o \
${OUT}/LMOPS.o ${OUT}/LZSTAGG.o ${OUT}/LZSTAGG-.o ${OUT}/MAGMA.o \
+ ${OUT}/MAPPKG4.o \
${OUT}/MESH.o ${OUT}/MOEBIUS.o ${OUT}/MODFIELD.o ${OUT}/MODOP.o \
${OUT}/MRING.o ${OUT}/MTHING.o ${OUT}/NCNTFRAC.o ${OUT}/NCODIV.o \
${OUT}/NUMTUBE.o ${OUT}/ODR.o ${OUT}/OFMONOID.o ${OUT}/ONECOMP.o \
@@ -3130,7 +3132,6 @@ check:
document: ${DOCFILES}
<<genericRules>>
-
<<spadhelp>>
<<ps (DOC from SRC)>>
<<libdb.text (OUT from IN)>>
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index ed6155a..9701e7f 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -208,6 +208,7 @@
(|MappingPackage1| . MAPPKG1)
(|MappingPackage2| . MAPPKG2)
(|MappingPackage3| . MAPPKG3)
+ (|MappingPackage4| . MAPPKG4)
(|MathMLFormat| . MMLFORM)
(|Matrix| . MATRIX)
(|MatrixCategoryFunctions2| . MATCAT2)
diff --git a/src/algebra/mappkg.spad.pamphlet b/src/algebra/mappkg.spad.pamphlet
index 5ec4358..ca1dc5f 100644
--- a/src/algebra/mappkg.spad.pamphlet
+++ b/src/algebra/mappkg.spad.pamphlet
@@ -2,7 +2,7 @@
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra mappkg.spad}
-\author{Stephen M. Watt, William Burge}
+\author{Stephen M. Watt, William Burge, Timothy Daly}
\maketitle
\begin{abstract}
\end{abstract}
@@ -83,7 +83,8 @@ MappingPackageInternalHacks3(A: SetCategory, B: SetCategory,
C: SetCategory):_
)set message test on
)set message auto off
)clear all
---S 1
+
+--S 1 of 26
power(q: FRAC INT, n: INT): FRAC INT == q**n
--R
--R Function declaration power : (Fraction Integer,Integer) -> Fraction
@@ -91,7 +92,7 @@ power(q: FRAC INT, n: INT): FRAC INT == q**n
--R Type:
Void
--E 1
---S 2
+--S 2 of 26
power(2,3)
--R
--R Compiling function power with type (Fraction Integer,Integer) ->
@@ -101,15 +102,15 @@ power(2,3)
--R Type: Fraction
Integer
--E 2
---S 3
+--S 3 of 26
rewop := twist power
--R
--R
---R (3) theMap(MAPPKG3;twist;MM;5!0)
+--I (3) theMap(MAPPKG3;twist;MM;5!0)
--R Type: ((Integer,Fraction Integer) -> Fraction
Integer)
--E 3
---S 4
+--S 4 of 26
rewop(3, 2)
--R
--R
@@ -117,21 +118,21 @@ rewop(3, 2)
--R Type: Fraction
Integer
--E 4
---S 5
+--S 5 of 26
square: FRAC INT -> FRAC INT
--R
--R Type:
Void
--E 5
---S 6
+--S 6 of 26
square:= curryRight(power, 2)
--R
--R
---R (6) theMap(MAPPKG3;curryRight;MBM;1!0,0)
+--I (6) theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R Type: (Fraction Integer -> Fraction
Integer)
--E 6
---S 7
+--S 7 of 26
square 4
--R
--R
@@ -139,15 +140,15 @@ square 4
--R Type: Fraction
Integer
--E 7
---S 8
+--S 8 of 26
squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT)
--R
--R
---R (8) theMap(MAPPKG3;constantRight;MM;3!0)
+--I (8) theMap(MAPPKG3;constantRight;MM;3!0)
--R Type: ((Fraction Integer,Fraction Integer) -> Fraction
Integer)
--E 8
---S 9
+--S 9 of 26
squirrel(1/2, 1/3)
--R
--R
@@ -157,15 +158,15 @@ squirrel(1/2, 1/3)
--R Type: Fraction
Integer
--E 9
---S 10
+--S 10 of 26
sixteen := curry(square, 4/1)
--R
--R
---R (10) theMap(MAPPKG2;curry;MAM;2!0,0)
+--I (10) theMap(MAPPKG2;curry;MAM;2!0,0)
--R Type: (() -> Fraction
Integer)
--E 10
---S 11
+--S 11 of 26
sixteen()
--R
--R
@@ -173,15 +174,15 @@ sixteen()
--R Type: Fraction
Integer
--E 11
---S 12
+--S 12 of 26
square2:=square*square
--R
--R
---R (12) theMap(MAPPKG3;*;MMM;6!0,0)
+--I (12) theMap(MAPPKG3;*;MMM;6!0,0)
--R Type: (Fraction Integer -> Fraction
Integer)
--E 12
---S 13
+--S 13 of 26
square2 3
--R
--R
@@ -189,7 +190,7 @@ square2 3
--R Type: Fraction
Integer
--E 13
---S 14
+--S 14 of 26
sc(x: FRAC INT): FRAC INT == x + 1
--R
--R Function declaration sc : Fraction Integer -> Fraction Integer has
@@ -197,23 +198,23 @@ sc(x: FRAC INT): FRAC INT == x + 1
--R Type:
Void
--E 14
---S 15
+--S 15 of 26
incfns := [sc**i for i in 0..10]
--R
--R Compiling function sc with type Fraction Integer -> Fraction Integer
--R
--R
--R (15)
---R [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0)]
+--I [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0)]
--R Type: List (Fraction Integer -> Fraction
Integer)
--E 15
---S 16
+--S 16 of 26
[f 4 for f in incfns]
--R
--R
@@ -221,7 +222,7 @@ incfns := [sc**i for i in 0..10]
--R Type: List Fraction
Integer
--E 16
---S 17
+--S 17 of 26
times(n:NNI, i:INT):INT == n*i
--R
--R Function declaration times : (NonNegativeInteger,Integer) -> Integer
@@ -229,25 +230,25 @@ times(n:NNI, i:INT):INT == n*i
--R Type:
Void
--E 17
---S 18
+--S 18 of 26
r := recur(times)
--R
--R Compiling function times with type (NonNegativeInteger,Integer) ->
--R Integer
--R
---R (18) theMap(MAPPKG1;recur;2M;7!0,0)
+--I (18) theMap(MAPPKG1;recur;2M;7!0,0)
--R Type: ((NonNegativeInteger,Integer) ->
Integer)
--E 18
---S 19
+--S 19 of 26
fact := curryRight(r, 1)
--R
--R
---R (19) theMap(MAPPKG3;curryRight;MBM;1!0,0)
+--I (19) theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R Type: (NonNegativeInteger ->
Integer)
--E 19
---S 20
+--S 20 of 26
fact 4
--R
--R
@@ -255,7 +256,7 @@ fact 4
--R Type:
PositiveInteger
--E 20
---S 21
+--S 21 of 26
mto2ton(m, n) ==
raiser := square^n
raiser m
@@ -263,7 +264,7 @@ mto2ton(m, n) ==
--R Type:
Void
--E 21
---S 22
+--S 22 of 26
mto2ton(3, 3)
--R
--R Compiling function mto2ton with type (PositiveInteger,
@@ -273,7 +274,7 @@ mto2ton(3, 3)
--R Type: Fraction
Integer
--E 22
---S 23
+--S 23 of 26
shiftfib(r: List INT) : INT ==
t := r.1
r.1 := r.2
@@ -285,7 +286,7 @@ shiftfib(r: List INT) : INT ==
--R Type:
Void
--E 23
---S 24
+--S 24 of 26
fibinit: List INT := [0, 1]
--R
--R
@@ -293,16 +294,16 @@ fibinit: List INT := [0, 1]
--R Type: List
Integer
--E 24
---S 25
+--S 25 of 26
fibs := curry(shiftfib, fibinit)
--R
--R Compiling function shiftfib with type List Integer -> Integer
--R
---R (25) theMap(MAPPKG2;curry;MAM;2!0,0)
+--I (25) theMap(MAPPKG2;curry;MAM;2!0,0)
--R Type: (() ->
Integer)
--E 25
---S 26
+--S 26 of 26
[fibs() for i in 0..30]
--R
--R
@@ -312,6 +313,16 @@ fibs := curry(shiftfib, fibinit)
--R 317811, 514229, 832040]
--R Type: List
Integer
--E 26
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
)spool
)lisp (bye)
@
@@ -486,9 +497,10 @@ By currying over the argument we get a function with
private state.
Type: List Integer
See Also:
+o )show MappingPackage1
o )help MappingPackage2
o )help MappingPackage3
-o )show MappingPackage1
+o )help MappingPackage4
o $AXIOM/doc/src/algebra/mappkg.spad.dvi
@
@@ -595,7 +607,7 @@ power(2,3)
rewop := twist power
--R
--R
---R (3) theMap(MAPPKG3;twist;MM;5!0)
+--I (3) theMap(MAPPKG3;twist;MM;5!0)
--R Type: ((Integer,Fraction Integer) -> Fraction
Integer)
--E 3
@@ -617,7 +629,7 @@ square: FRAC INT -> FRAC INT
square:= curryRight(power, 2)
--R
--R
---R (6) theMap(MAPPKG3;curryRight;MBM;1!0,0)
+--I (6) theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R Type: (Fraction Integer -> Fraction
Integer)
--E 6
@@ -633,7 +645,7 @@ square 4
squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT)
--R
--R
---R (8) theMap(MAPPKG3;constantRight;MM;3!0)
+--I (8) theMap(MAPPKG3;constantRight;MM;3!0)
--R Type: ((Fraction Integer,Fraction Integer) -> Fraction
Integer)
--E 8
@@ -651,7 +663,7 @@ squirrel(1/2, 1/3)
sixteen := curry(square, 4/1)
--R
--R
---R (10) theMap(MAPPKG2;curry;MAM;2!0,0)
+--I (10) theMap(MAPPKG2;curry;MAM;2!0,0)
--R Type: (() -> Fraction
Integer)
--E 10
@@ -667,7 +679,7 @@ sixteen()
square2:=square*square
--R
--R
---R (12) theMap(MAPPKG3;*;MMM;6!0,0)
+--I (12) theMap(MAPPKG3;*;MMM;6!0,0)
--R Type: (Fraction Integer -> Fraction
Integer)
--E 12
@@ -694,12 +706,12 @@ incfns := [sc**i for i in 0..10]
--R
--R
--R (15)
---R [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0)]
+--I [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0)]
--R Type: List (Fraction Integer -> Fraction
Integer)
--E 15
@@ -725,7 +737,7 @@ r := recur(times)
--R Compiling function times with type (NonNegativeInteger,Integer) ->
--R Integer
--R
---R (18) theMap(MAPPKG1;recur;2M;7!0,0)
+--I (18) theMap(MAPPKG1;recur;2M;7!0,0)
--R Type: ((NonNegativeInteger,Integer) ->
Integer)
--E 18
@@ -733,7 +745,7 @@ r := recur(times)
fact := curryRight(r, 1)
--R
--R
---R (19) theMap(MAPPKG3;curryRight;MBM;1!0,0)
+--I (19) theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R Type: (NonNegativeInteger ->
Integer)
--E 19
@@ -788,7 +800,7 @@ fibs := curry(shiftfib, fibinit)
--R
--R Compiling function shiftfib with type List Integer -> Integer
--R
---R (25) theMap(MAPPKG2;curry;MAM;2!0,0)
+--I (25) theMap(MAPPKG2;curry;MAM;2!0,0)
--R Type: (() ->
Integer)
--E 25
@@ -977,8 +989,9 @@ By currying over the argument we get a function with
private state.
See Also:
o )help MappingPackage1
-o )help MappingPackage3
o )show MappingPackage2
+o )help MappingPackage3
+o )help MappingPackage4
o $AXIOM/doc/src/algebra/mappkg.spad.dvi
@
@@ -1052,7 +1065,7 @@ power(2,3)
rewop := twist power
--R
--R
---R (3) theMap(MAPPKG3;twist;MM;5!0)
+--I (3) theMap(MAPPKG3;twist;MM;5!0)
--R Type: ((Integer,Fraction Integer) -> Fraction
Integer)
--E 3
@@ -1074,7 +1087,7 @@ square: FRAC INT -> FRAC INT
square:= curryRight(power, 2)
--R
--R
---R (6) theMap(MAPPKG3;curryRight;MBM;1!0,0)
+--I (6) theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R Type: (Fraction Integer -> Fraction
Integer)
--E 6
@@ -1090,7 +1103,7 @@ square 4
squirrel:= constantRight(square)$MAPPKG3(FRAC INT,FRAC INT,FRAC INT)
--R
--R
---R (8) theMap(MAPPKG3;constantRight;MM;3!0)
+--I (8) theMap(MAPPKG3;constantRight;MM;3!0)
--R Type: ((Fraction Integer,Fraction Integer) -> Fraction
Integer)
--E 8
@@ -1108,7 +1121,7 @@ squirrel(1/2, 1/3)
sixteen := curry(square, 4/1)
--R
--R
---R (10) theMap(MAPPKG2;curry;MAM;2!0,0)
+--I (10) theMap(MAPPKG2;curry;MAM;2!0,0)
--R Type: (() -> Fraction
Integer)
--E 10
@@ -1124,7 +1137,7 @@ sixteen()
square2:=square*square
--R
--R
---R (12) theMap(MAPPKG3;*;MMM;6!0,0)
+--I (12) theMap(MAPPKG3;*;MMM;6!0,0)
--R Type: (Fraction Integer -> Fraction
Integer)
--E 12
@@ -1151,12 +1164,12 @@ incfns := [sc**i for i in 0..10]
--R
--R
--R (15)
---R [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
---R theMap(MAPPKG1;**;MNniM;6!0,0)]
+--I [theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0), theMap(MAPPKG1;**;MNniM;6!0,0),
+--I theMap(MAPPKG1;**;MNniM;6!0,0)]
--R Type: List (Fraction Integer -> Fraction
Integer)
--E 15
@@ -1182,7 +1195,7 @@ r := recur(times)
--R Compiling function times with type (NonNegativeInteger,Integer) ->
--R Integer
--R
---R (18) theMap(MAPPKG1;recur;2M;7!0,0)
+--I (18) theMap(MAPPKG1;recur;2M;7!0,0)
--R Type: ((NonNegativeInteger,Integer) ->
Integer)
--E 18
@@ -1190,7 +1203,7 @@ r := recur(times)
fact := curryRight(r, 1)
--R
--R
---R (19) theMap(MAPPKG3;curryRight;MBM;1!0,0)
+--I (19) theMap(MAPPKG3;curryRight;MBM;1!0,0)
--R Type: (NonNegativeInteger ->
Integer)
--E 19
@@ -1245,7 +1258,7 @@ fibs := curry(shiftfib, fibinit)
--R
--R Compiling function shiftfib with type List Integer -> Integer
--R
---R (25) theMap(MAPPKG2;curry;MAM;2!0,0)
+--I (25) theMap(MAPPKG2;curry;MAM;2!0,0)
--R Type: (() ->
Integer)
--E 25
@@ -1436,6 +1449,7 @@ See Also:
o )help MappingPackage1
o )help MappingPackage2
o )show MappingPackage3
+o )help MappingPackage4
o $AXIOM/doc/src/algebra/mappkg.spad.dvi
@
@@ -1499,6 +1513,320 @@ MappingPackage3(A:SetCategory, B:SetCategory,
C:SetCategory):_
fbc*fab == comp(fbc,fab,#1)
@
+\section{package MAPPKG4 MappingPackage4}
+<<MappingPackage4.input>>=
+-- mappkg.spad.pamphlet MappingPackage4.input
+)spool MappingPackage4.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 21
+p:=(x:EXPR(INT)):EXPR(INT)+->3*x
+--R
+--R
+--R (1) theMap(Closure)
+--R Type: (Expression Integer -> Expression
Integer)
+--E 1
+
+--S 2 of 21
+q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3
+--R
+--R
+--R (2) theMap(Closure)
+--R Type: (Expression Integer -> Expression
Integer)
+--E 2
+
+--S 3 of 21
+(p+q)(4)-(p(4)+q(4))
+--R
+--R
+--R (3) 0
+--R Type: Expression
Integer
+--E 3
+
+--S 4 of 21
+(p+q)(x)-(p(x)+q(x))
+--R
+--R
+--R (4) 0
+--R Type: Expression
Integer
+--E 4
+
+--S 5 of 21
+(p-q)(4)-(p(4)-q(4))
+--R
+--R
+--R (5) 0
+--R Type: Expression
Integer
+--E 5
+
+--S 6 of 21
+(p-q)(x)-(p(x)-q(x))
+--R
+--R
+--R (6) 0
+--R Type: Expression
Integer
+--E 6
+
+--S 7 of 21
+(p*q)(4)-(p(4)*q(4))
+--R
+--R
+--R (7) 0
+--R Type: Expression
Integer
+--E 7
+
+--S 8 of 21
+(p*q)(x)-(p(x)*q(x))
+--R
+--R
+--R (8) 0
+--R Type: Expression
Integer
+--E 8
+
+--S 9 of 21
+(p/q)(4)-(p(4)/q(4))
+--R
+--R
+--R (9) 0
+--R Type: Expression
Integer
+--E 9
+
+--S 10 of 21
+(p/q)(x)-(p(x)/q(x))
+--R
+--R
+--R (10) 0
+--R Type: Expression
Integer
+--E 10
+
+--S 11 of 21
+r:=(x:INT):INT+-> (x*x*x)
+--R
+--R
+--R (11) theMap(Closure)
+--R Type: (Integer ->
Integer)
+--E 11
+
+--S 12 of 21
+s:=(y:INT):INT+-> (y*y+3)
+--R
+--R
+--R (12) theMap(Closure)
+--R Type: (Integer ->
Integer)
+--E 12
+
+--S 13 of 21
+(r+s)(4)-(r(4)+s(4))
+--R
+--R
+--R (13) 0
+--R Type:
NonNegativeInteger
+--E 13
+
+--S 14 of 21
+(r-s)(4)-(r(4)-s(4))
+--R
+--R
+--R (14) 0
+--R Type:
NonNegativeInteger
+--E 14
+
+--S 15 of 21
+(r*s)(4)-(r(4)*s(4))
+--R
+--R
+--R (15) 0
+--R Type:
NonNegativeInteger
+--E 15
+
+--S 16 of 21
+t:=(x:INT):EXPR(INT)+-> (x*x*x)
+--R
+--R
+--R (16) theMap(Closure)
+--R Type: (Integer -> Expression
Integer)
+--E 16
+
+--S 17 of 21
+u:=(y:INT):EXPR(INT)+-> (y*y+3)
+--R
+--R
+--R (17) theMap(Closure)
+--R Type: (Integer -> Expression
Integer)
+--E 17
+
+--S 18 of 21
+(t/u)(4)-(t(4)/u(4))
+--R
+--R
+--R (18) 0
+--R Type: Expression
Integer
+--E 18
+
+--S 19 of 21
+h:=(x:EXPR(INT)):EXPR(INT)+->1
+--R
+--R (19) theMap(Closure)
+--R Type: (Expression Integer -> Expression
Integer)
+--E 19
+
+--S 20 of 21
+(p/h)(x)
+--R
+--R (20) 3x
+--R Type: Expression
Integer
+--E 20
+
+--S 21 of 21
+(q/h)(x)
+--R
+--R (21) 2x + 3
+--R Type: Expression
Integer
+--E 21
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
+)spool
+)lisp (bye)
+@
+<<MappingPackage4.help>>=
+====================================================================
+MappingPackage examples
+====================================================================
+
+We can construct some simple maps that take a variable x
+into an equation:
+
+ p:=(x:EXPR(INT)):EXPR(INT)+->3*x
+ q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3
+
+Now we can do the four arithmetic operations, +, -, *, / on these
+newly constructed mappings. Since the maps are from the domain
+Expression Integer to the same domain we can also use symbolic
+values for the argument. All of the following will return 0,
+showing that function composition is equivalent to the result
+of doing the operations individually.
+
+ (p+q)(4)-(p(4)+q(4))
+ (p+q)(x)-(p(x)+q(x))
+
+ (p-q)(4)-(p(4)-q(4))
+ (p-q)(x)-(p(x)-q(x))
+
+ (p*q)(4)-(p(4)*q(4))
+ (p*q)(x)-(p(x)*q(x))
+
+ (p/q)(4)-(p(4)/q(4))
+ (p/q)(x)-(p(x)/q(x))
+
+We can construct simple maps from Integer to Integer but this
+limits our ability to do division.
+
+ r:=(x:INT):INT+-> (x*x*x)
+ s:=(y:INT):INT+-> (y*y+3)
+
+Again, all of these will return 0:
+
+ (r+s)(4)-(r(4)+s(4))
+ (r-s)(4)-(r(4)-s(4))
+ (r*s)(4)-(r(4)*s(4))
+
+If we want to do division with Integer inputs we create the
+appropriate map:
+
+ t:=(x:INT):EXPR(INT)+-> (x*x*x)
+ u:=(y:INT):EXPR(INT)+-> (y*y+3)
+
+ (t/u)(4)-(t(4)/u(4))
+
+We can even recover the original functions if we make a map
+that always returns the constant 1:
+
+ h:=(x:EXPR(INT)):EXPR(INT)+->1
+
+ theMap(Closure)
+ Type: (Expression Integer -> Expression Integer)
+
+ (p/h)(x)
+
+ 3x
+ Type: Expression Integer
+ (q/h)(x)
+
+ 2x + 3
+ Type: Expression Integer
+
+See Also:
+o )show MappingPackage1
+o )help MappingPackage2
+o )help MappingPackage3
+o )help MappingPackage4
+o $AXIOM/doc/src/algebra/mappkg.spad.dvi
+
+@
+<<package MAPPKG4 MappingPackage4>>=
+)abbrev package MAPPKG4 MappingPackage4
+++ Author: Timothy Daly
+++ Description: Functional Composition
+++ Given functions f and g, returns the applicable closure
+MappingPackage4(A:SetCategory, B:Ring):
+ with
+ "+": (A->B, A->B) -> (A->B)
+ ++ \spad(+) does functional addition
+ ++
+ ++E f:=(x:INT):INT +-> 3*x
+ ++E g:=(x:INT):INT +-> 2*x+3
+ ++E (f+g)(4)
+ "-": (A->B, A->B) -> (A->B)
+ ++ \spad(+) does functional addition
+ ++
+ ++E f:=(x:INT):INT +-> 3*x
+ ++E g:=(x:INT):INT +-> 2*x+3
+ ++E (f-g)(4)
+ "*": (A->B, A->B) -> (A->B)
+ ++ \spad(+) does functional addition
+ ++
+ ++E f:=(x:INT):INT +-> 3*x
+ ++E g:=(x:INT):INT +-> 2*x+3
+ ++E (f*g)(4)
+ "/": (A->Expression(Integer), A->Expression(Integer)) ->
(A->Expression(Integer))
+ ++ \spad(+) does functional addition
+ ++
+ ++E p:=(x:EXPR(INT)):EXPR(INT)+->3*x
+ ++E q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3
+ ++E (p/q)(4)
+ ++E (p/q)(x)
+ == add
+ fab ==> (A -> B)
+ faei ==> (A -> Expression(Integer))
+
+ funcAdd(g:fab,h:fab,x:A):B == ((g x) + (h x))$B
+
+ (a:fab)+(b:fab) == funcAdd(a,b,#1)
+
+ funcSub(g:fab,h:fab,x:A):B == ((g x) - (h x))$B
+
+ (a:fab)-(b:fab) == funcSub(a,b,#1)
+
+ funcMul(g:fab,h:fab,x:A):B == ((g x) * (h x))$B
+
+ (a:fab)*(b:fab) == funcMul(a,b,#1)
+
+ funcDiv(g:faei,h:faei,x:A):Expression(Integer)
+ == ((g x) / (h x))$Expression(Integer)
+
+ (a:faei)/(b:faei) == funcDiv(a,b,#1)
+
+@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
@@ -1541,6 +1869,7 @@ MappingPackage3(A:SetCategory, B:SetCategory,
C:SetCategory):_
<<package MAPPKG1 MappingPackage1>>
<<package MAPPKG2 MappingPackage2>>
<<package MAPPKG3 MappingPackage3>>
+<<package MAPPKG4 MappingPackage4>>
@
\eject
\begin{thebibliography}{99}
diff --git a/src/input/test.input.pamphlet b/src/input/test.input.pamphlet
index ea9b453..7ffe5b8 100644
--- a/src/input/test.input.pamphlet
+++ b/src/input/test.input.pamphlet
@@ -484,7 +484,6 @@ Bracket parsing and empty-set types. Fixed by SCM, verified
on 10/30/90
<<*>>=
)clear all
-@
--S 35
{}$(List INT)
--R
@@ -827,7 +826,7 @@ m = [[1,2],[2,3]] -- Should return type EQ POLY
SQMATRIX(2, INT)
--S 64
1+"asd" -- These should both fail in the same way
--R
---R There are 11 exposed and 5 unexposed library operations named +
+--R There are 12 exposed and 5 unexposed library operations named +
--R having 2 argument(s) but none was determined to be applicable.
--R Use HyperDoc Browse, or issue
--R )display op +
@@ -847,7 +846,7 @@ m = [[1,2],[2,3]] -- Should return type EQ POLY
SQMATRIX(2, INT)
--S 65
1/"asd"
--R
---R There are 12 exposed and 12 unexposed library operations named /
+--R There are 13 exposed and 12 unexposed library operations named /
--R having 2 argument(s) but none was determined to be applicable.
--R Use HyperDoc Browse, or issue
--R )display op /
@@ -1608,7 +1607,7 @@ s - sin(a*x)
--E 121
@
-Complex & AlgebraicNumber coercions. fixed by SCM 6/91
+Complex \& AlgebraicNumber coercions. fixed by SCM 6/91
<<*>>=
)clear all
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- [Axiom-developer] 20080821.01.tpd.patch (add MappingPackage4),
daly <=