aboutsummaryrefslogtreecommitdiff
path: root/src/algebra
diff options
context:
space:
mode:
Diffstat (limited to 'src/algebra')
-rw-r--r--src/algebra/Makefile.am7
-rw-r--r--src/algebra/Makefile.in6
-rw-r--r--src/algebra/indexedp.spad.pamphlet114
3 files changed, 55 insertions, 72 deletions
diff --git a/src/algebra/Makefile.am b/src/algebra/Makefile.am
index 181dedba..fbc86795 100644
--- a/src/algebra/Makefile.am
+++ b/src/algebra/Makefile.am
@@ -1639,6 +1639,7 @@ oa_algebra_layer_4_objects = \
$(OUT)/KERNEL.$(FASLEXT): $(OUT)/KERNEL2.$(FASLEXT)
$(OUT)/DVARCAT.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
$(OUT)/PDRING.$(FASLEXT): $(OUT)/PDSPC.$(FASLEXT)
+$(OUT)/IDPAM.$(FASLEXT): $(OUT)/IDPO.$(FASLEXT)
oa_algebra_layer_5 = \
CHARNZ DVARCAT DVARCAT- ELEMFUN \
@@ -1677,7 +1678,10 @@ oa_algebra_layer_6_nrlibs = \
oa_algebra_layer_6_objects = \
$(addprefix $(OUT)/, \
$(addsuffix .$(FASLEXT),$(oa_algebra_layer_6)))
+
$(OUT)/IFAMON.$(FASLEXT): $(OUT)/LMOPS.$(FASLEXT)
+$(OUT)/IDPOAM.$(FASLEXT): $(OUT)/IDPAM.$(FASLEXT)
+
oa_algebra_layer_7 = \
BTCAT BTCAT- LMOPS FMCAT IDPOAM \
IFAMON GRALG GRALG- \
@@ -1707,7 +1711,10 @@ oa_algebra_layer_8_nrlibs = \
oa_algebra_layer_8_objects = \
$(addprefix $(OUT)/, \
$(addsuffix .$(FASLEXT),$(oa_algebra_layer_8)))
+
$(OUT)/FT.$(FASLEXT): $(OUT)/FST.$(FASLEXT) $(OUT)/POLY.$(FASLEXT)
+$(OUT)/IDPOAMS.$(FASLEXT): $(OUT)/IDPOAM.$(FASLEXT)
+$(OUT)/IDPAG.$(FASLEXT): $(OUT)/IDPAM.$(FASLEXT)
oa_algebra_layer_9 = \
AMR AMR- DEGRED DLP EAB \
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index c66d563b..4f9cc577 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -2877,6 +2877,7 @@ $(OUT)/PALETTE.$(FASLEXT): $(OUT)/COLOR.$(FASLEXT)
$(OUT)/KERNEL.$(FASLEXT): $(OUT)/KERNEL2.$(FASLEXT)
$(OUT)/DVARCAT.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
$(OUT)/PDRING.$(FASLEXT): $(OUT)/PDSPC.$(FASLEXT)
+$(OUT)/IDPAM.$(FASLEXT): $(OUT)/IDPO.$(FASLEXT)
$(OUT)/CHARPOL.$(FASLEXT): $(OUT)/SETCAT-.$(FASLEXT)
$(OUT)/PROPFRML.$(FASLEXT): $(OUT)/KERNEL.$(FASLEXT)
@@ -2886,12 +2887,17 @@ $(OUT)/PROPFUN2.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT)
$(OUT)/DIFEXT.$(FASLEXT): $(OUT)/DSEXT.$(FASLEXT)
$(OUT)/BYTE.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT)
$(OUT)/SYSNNI.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) $(OUT)/ORDFIN.$(FASLEXT)
+
$(OUT)/IFAMON.$(FASLEXT): $(OUT)/LMOPS.$(FASLEXT)
+$(OUT)/IDPOAM.$(FASLEXT): $(OUT)/IDPAM.$(FASLEXT)
$(OUT)/BSTREE.$(FASLEXT): $(OUT)/BTREE.$(FASLEXT)
$(OUT)/ITAYLOR.$(FASLEXT): $(OUT)/STREAM.$(FASLEXT)
$(OUT)/BTREE.$(FASLEXT): $(OUT)/TREE.$(FASLEXT)
+
$(OUT)/FT.$(FASLEXT): $(OUT)/FST.$(FASLEXT) $(OUT)/POLY.$(FASLEXT)
+$(OUT)/IDPOAMS.$(FASLEXT): $(OUT)/IDPOAM.$(FASLEXT)
+$(OUT)/IDPAG.$(FASLEXT): $(OUT)/IDPAM.$(FASLEXT)
$(OUT)/ANY.$(FASLEXT): $(OUT)/SEX.$(FASLEXT)
$(OUT)/SEX.$(FASLEXT): $(OUT)/SEXOF.$(FASLEXT)
diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet
index dab47a6a..bbb78cd0 100644
--- a/src/algebra/indexedp.spad.pamphlet
+++ b/src/algebra/indexedp.spad.pamphlet
@@ -26,7 +26,7 @@
++ respect to an ordered indexing set.
IndexedDirectProductCategory(A:BasicType,S:OrderedType): Category ==
- BasicType with
+ Join(BasicType,ConvertibleFrom List IndexedProductTerm(A,S)) with
if A has SetCategory and S has SetCategory then SetCategory
map: (A -> A, %) -> %
++ map(f,z) returns the new element created by applying the
@@ -47,7 +47,7 @@ IndexedDirectProductCategory(A:BasicType,S:OrderedType): Category ==
++ reductum(z) returns a new element created by removing the
++ leading coefficient/support pair from the element z.
++ Error: if z has no support.
- terms: % -> List Pair(S,A)
+ terms: % -> List IndexedProductTerm(A,S)
++ \spad{terms x} returns the list of terms in \spad{x}.
++ Each term is a pair of a support (the first component)
++ and the corresponding value (the second component).
@@ -94,46 +94,25 @@ IndexedDirectProductObject(A,S): Public == Private where
A: BasicType
S: OrderedType
Public == IndexedDirectProductCategory(A,S)
- Private == add
- Term == Pair(S,A)
- Rep == List Term
- -- Return the index of a term
- termIndex(t: Term): S == first t
- -- Return the value of a term
- termValue(t: Term): A == second t
-
- x = y ==
- x' := rep x
- y' := rep y
- while not null x' and not null y' repeat
- termIndex first x' ~= termIndex first y' => return false
- termValue first x' ~= termValue first y' => return false
- x' := rest x'
- y' := rest y'
- null x' and null y'
-
+ Private == List IndexedProductTerm(A,S) add
if A has CoercibleTo OutputForm and S has CoercibleTo OutputForm then
coerce(x:%):OutputForm ==
- bracket [rarrow(termIndex(t)::OutputForm, termValue(t)::OutputForm)
+ bracket [rarrow(index(t)::OutputForm, coefficient(t)::OutputForm)
for t in rep x]
- -- sample():% == [[sample()$S,sample()$A]$Term]$Rep
-
- monomial(r,s) == per [[s,r]]
- map(f,x) == per [[termIndex tm,f termValue tm] for tm in rep x]
-
- reductum x ==
- per rest rep x
+ monomial(r,s) == per [term(s,r)]
+ map(f,x) == per [term(index tm,f coefficient tm) for tm in rep x]
+ reductum x == per rest rep x
leadingCoefficient x ==
null rep x =>
error "Can't take leadingCoefficient of empty product element"
- termValue first rep x
+ coefficient first rep x
leadingSupport x ==
null rep x =>
error "Can't take leadingCoefficient of empty product element"
- termIndex first rep x
-
+ index first rep x
terms x == rep x
+ convert l == per l
@
\section{domain IDPAM IndexedDirectProductAbelianMonoid}
@@ -145,18 +124,14 @@ IndexedDirectProductObject(A,S): Public == Private where
IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedType):
Join(AbelianMonoid,IndexedDirectProductCategory(A,S))
== IndexedDirectProductObject(A,S) add
- --representations
- Term == Pair(S,A)
+ Term == IndexedProductTerm(A,S)
import Term
- import List Term
- termIndex(t: Term): S == first t
- termValue(t: Term): A == second t
r: A
n: NonNegativeInteger
f: A -> A
s: S
- 0 == nil$List(Term) pretend %
+ 0 == convert nil$List(Term)
zero? x == null terms x
import %tail: List Term -> List Term from Foreign Builtin
@@ -178,17 +153,17 @@ IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedType):
res: List Term := nil
while not empty? x' and not empty? y' repeat
newcell: List Term := nil
- if termIndex x'.first = termIndex y'.first then
- r := termValue x'.first + termValue y'.first
+ if index x'.first = index y'.first then
+ r := coefficient x'.first + coefficient y'.first
if not zero? r then
- newcell := cons([termIndex x'.first, r], empty())
+ newcell := [term(index x'.first, r)]
x' := rest x'
y' := rest y'
- else if termIndex x'.first > termIndex y'.first then
- newcell := cons(x'.first, empty())
+ else if index x'.first > index y'.first then
+ newcell := [x'.first]
x' := rest x'
else
- newcell := cons(y'.first, empty())
+ newcell := [y'.first]
y' := rest y'
if not empty? newcell then
if not empty? endcell then
@@ -202,32 +177,29 @@ IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedType):
x'
if empty? res then res := end
else qsetrest!(endcell, end)
- res pretend %
+ convert res
n * x ==
- n = 0 => 0
- n = 1 => x
- [[termIndex u,a] for u in terms x
- | not zero?(a:=n * termValue u)] pretend %
+ zero? n => 0
+ one? n => x
+ convert [term(index u,a) for u in terms x
+ | not zero?(a:=n * coefficient u)]
monomial(r,s) ==
zero? r => 0
- [[s,r]] pretend %
+ convert [term(s,r)]
map(f,x) ==
- [[termIndex tm,a] for tm in terms x
- | not zero?(a:=f termValue tm)] pretend %
+ convert [term(index tm,a) for tm in terms x
+ | not zero?(a:=f coefficient tm)]
reductum x ==
null terms x => 0
- rest(terms x) pretend %
+ convert rest(terms x)
leadingCoefficient x ==
null terms x => 0
- termValue terms(x).first
-
- pair2Term(t: Pair(A,S)): Term ==
- [second t, first t]
+ coefficient terms(x).first
@
\section{domain IDPOAM IndexedDirectProductOrderedAbelianMonoid}
@@ -304,16 +276,14 @@ IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedType):
Join(AbelianGroup,IndexedDirectProductCategory(A,S))
== IndexedDirectProductAbelianMonoid(A,S) add
--representations
- Term == Pair(S,A)
- termIndex(t: Term): S == first t
- termValue(t: Term): A == second t
+ Term == IndexedProductTerm(A,S)
- -x == [[termIndex u,-termValue u] for u in terms x] pretend %
+ -x == convert [term(index u,-coefficient u) for u in terms x]
n:Integer * x:% ==
- n = 0 => 0
- n = 1 => x
- [[termIndex u,a] for u in terms x
- | not zero?(a := n * termValue u)] pretend %
+ zero? n => 0
+ one? n => x
+ convert [term(index u,a) for u in terms x
+ | not zero?(a := n * coefficient u)]
import %tail: List Term -> List Term from Foreign Builtin
@@ -330,17 +300,17 @@ IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedType):
res: List Term := nil
while not empty? x' and not empty? y' repeat
newcell: List Term := nil
- if termIndex x'.first = termIndex y'.first then
- r := termValue x'.first - termValue y'.first
+ if index x'.first = index y'.first then
+ r := coefficient x'.first - coefficient y'.first
if not zero? r then
- newcell := cons([termIndex x'.first, r], empty())
+ newcell := [term(index x'.first, r)]
x' := rest x'
y' := rest y'
- else if termIndex x'.first > termIndex y'.first then
- newcell := cons(x'.first, empty())
+ else if index x'.first > index y'.first then
+ newcell := [x'.first]
x' := rest x'
else
- newcell := cons([termIndex y'.first,-termValue y'.first], empty())
+ newcell := [term(index y'.first,-coefficient y'.first)]
y' := rest y'
if not empty? newcell then
if not empty? endcell then
@@ -350,11 +320,11 @@ IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedType):
res := newcell;
endcell := res
end :=
- empty? x' => terms(-(y' pretend %))
+ empty? x' => terms(-convert y')
x'
if empty? res then res := end
else qsetrest!(endcell, end)
- res pretend %
+ convert res
@
\section{License}
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-26 05:46:08 +0000