diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 14 | ||||
| -rw-r--r-- | src/algebra/strap/CLAGG-.lsp | 201 | ||||
| -rw-r--r-- | src/algebra/strap/EUCDOM-.lsp | 124 | ||||
| -rw-r--r-- | src/algebra/strap/FFIELDC-.lsp | 59 | ||||
| -rw-r--r-- | src/algebra/strap/HOAGG-.lsp | 233 | ||||
| -rw-r--r-- | src/algebra/strap/ISTRING.lsp | 45 | ||||
| -rw-r--r-- | src/algebra/strap/POLYCAT-.lsp | 296 | ||||
| -rw-r--r-- | src/algebra/strap/UFD-.lsp | 52 | ||||
| -rw-r--r-- | src/interp/compiler.boot | 70 | ||||
| -rw-r--r-- | src/interp/define.boot | 2 | ||||
| -rw-r--r-- | src/interp/g-opt.boot | 6 | ||||
| -rw-r--r-- | src/interp/g-util.boot | 12 | ||||
| -rw-r--r-- | src/interp/i-map.boot | 4 | ||||
| -rw-r--r-- | src/interp/i-spec1.boot | 4 | ||||
| -rw-r--r-- | src/interp/nruncomp.boot | 2 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1398 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1326 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9030 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31566 |
20 files changed, 22460 insertions, 22620 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index a8326673..2f1f304e 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,17 @@ +2010-06-09 Gabriel Dos Reis <gdr@cse.tamu.edu> + + * interp/compiler.boot (canReturn): Handle %when and %bind. + (compMatchAlternative): Generate %bind form. + (compMatch): Likewise. + (compReduce1): Rewrite. + (getIdentity): Tidy. + * interp/g-opt.boot (changeThrowToExit): HAndle %reduce. + (varIsAssigned): %store is side-effectful. + * interp/g-util.boot (expandReduce): New. Expand %reduce forms. + * interp/i-map.boot (getUserIdentifiersIn): Handle %reduce. + (findLocalVars1): Likewise. + * interp/i-spec1.boot (checkForFreeVariables): Likewise. + 2010-06-09 Gabriel Dos Reis <gdr@cs.tamu.edu> * interp/g-opt.boot (removeNeedlessThrow): Tidy. diff --git a/src/algebra/strap/CLAGG-.lsp b/src/algebra/strap/CLAGG-.lsp index 6d50e7cb..eb404d15 100644 --- a/src/algebra/strap/CLAGG-.lsp +++ b/src/algebra/strap/CLAGG-.lsp @@ -45,123 +45,90 @@ (LENGTH (SPADCALL |c| (|getShellEntry| $ 9)))) (DEFUN |CLAGG-;count;MANni;2| (|f| |c| $) - (PROG (|x| #0=#:G1429 #1=#:G1403 #2=#:G1401 #3=#:G1402) - (RETURN - (SEQ (PROGN - (LETT #3# NIL |CLAGG-;count;MANni;2|) - (SEQ (LETT |x| NIL |CLAGG-;count;MANni;2|) - (LETT #0# (SPADCALL |c| (|getShellEntry| $ 9)) - |CLAGG-;count;MANni;2|) - G190 - (COND - ((OR (ATOM #0#) (PROGN (SETQ |x| (CAR #0#)) NIL)) - (GO G191))) - (COND - ((SPADCALL |x| |f|) - (PROGN - (LETT #1# 1 |CLAGG-;count;MANni;2|) - (COND - (#3# (LETT #2# (+ #2# #1#) - |CLAGG-;count;MANni;2|)) - ('T - (PROGN - (LETT #2# #1# |CLAGG-;count;MANni;2|) - (LETT #3# 'T |CLAGG-;count;MANni;2|))))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T 0))))))) + (LET ((#0=#:G1402 NIL) (#1=#:G1403 T) + (#2=#:G1429 (SPADCALL |c| (|getShellEntry| $ 9)))) + (LOOP + (COND + ((ATOM #2#) (RETURN (COND (#1# 0) (T #0#)))) + (T (LET ((|x| (CAR #2#))) + (AND (SPADCALL |x| |f|) + (LET ((#3=#:G1401 1)) + (COND + (#1# (SETQ #0# #3#)) + (T (SETQ #0# (+ #0# #3#)))) + (SETQ #1# NIL)))))) + (SETQ #2# (CDR #2#))))) (DEFUN |CLAGG-;any?;MAB;3| (|f| |c| $) - (PROG (|x| #0=#:G1430 #1=#:G1408 #2=#:G1406 #3=#:G1407) - (RETURN - (SEQ (PROGN - (LETT #3# NIL |CLAGG-;any?;MAB;3|) - (SEQ (LETT |x| NIL |CLAGG-;any?;MAB;3|) - (LETT #0# (SPADCALL |c| (|getShellEntry| $ 9)) - |CLAGG-;any?;MAB;3|) - G190 - (COND - ((OR (ATOM #0#) (PROGN (SETQ |x| (CAR #0#)) NIL)) - (GO G191))) - (PROGN - (LETT #1# (SPADCALL |x| |f|) |CLAGG-;any?;MAB;3|) - (COND - (#3# (LETT #2# (COND (#2# T) ('T #1#)) - |CLAGG-;any?;MAB;3|)) - ('T - (PROGN - (LETT #2# #1# |CLAGG-;any?;MAB;3|) - (LETT #3# 'T |CLAGG-;any?;MAB;3|))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T NIL))))))) + (LET ((#0=#:G1407 NIL) (#1=#:G1408 T) + (#2=#:G1430 (SPADCALL |c| (|getShellEntry| $ 9)))) + (LOOP + (COND + ((ATOM #2#) (RETURN (COND (#1# NIL) (T #0#)))) + (T (LET ((|x| (CAR #2#))) + (LET ((#3=#:G1406 (SPADCALL |x| |f|))) + (COND (#1# (SETQ #0# #3#)) (T (SETQ #0# (OR #0# #3#)))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#))))) (DEFUN |CLAGG-;every?;MAB;4| (|f| |c| $) - (PROG (|x| #0=#:G1431 #1=#:G1412 #2=#:G1410 #3=#:G1411) - (RETURN - (SEQ (PROGN - (LETT #3# NIL |CLAGG-;every?;MAB;4|) - (SEQ (LETT |x| NIL |CLAGG-;every?;MAB;4|) - (LETT #0# (SPADCALL |c| (|getShellEntry| $ 9)) - |CLAGG-;every?;MAB;4|) - G190 - (COND - ((OR (ATOM #0#) (PROGN (SETQ |x| (CAR #0#)) NIL)) - (GO G191))) - (PROGN - (LETT #1# (SPADCALL |x| |f|) |CLAGG-;every?;MAB;4|) - (COND - (#3# (LETT #2# (COND (#2# #1#) ('T NIL)) - |CLAGG-;every?;MAB;4|)) - ('T - (PROGN - (LETT #2# #1# |CLAGG-;every?;MAB;4|) - (LETT #3# 'T |CLAGG-;every?;MAB;4|))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T T))))))) + (LET ((#0=#:G1411 NIL) (#1=#:G1412 T) + (#2=#:G1431 (SPADCALL |c| (|getShellEntry| $ 9)))) + (LOOP + (COND + ((ATOM #2#) (RETURN (COND (#1# T) (T #0#)))) + (T (LET ((|x| (CAR #2#))) + (LET ((#3=#:G1410 (SPADCALL |x| |f|))) + (COND + (#1# (SETQ #0# #3#)) + (T (SETQ #0# (AND #0# #3#)))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#))))) (DEFUN |CLAGG-;find;MAU;5| (|f| |c| $) (SPADCALL |f| (SPADCALL |c| (|getShellEntry| $ 9)) - (|getShellEntry| $ 24))) + (|getShellEntry| $ 26))) (DEFUN |CLAGG-;reduce;MAS;6| (|f| |x| $) (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 27))) + (|getShellEntry| $ 29))) (DEFUN |CLAGG-;reduce;MA2S;7| (|f| |x| |s| $) (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) |s| - (|getShellEntry| $ 29))) + (|getShellEntry| $ 31))) (DEFUN |CLAGG-;remove;M2A;8| (|f| |x| $) (SPADCALL (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 31)) - (|getShellEntry| $ 32))) + (|getShellEntry| $ 33)) + (|getShellEntry| $ 34))) (DEFUN |CLAGG-;select;M2A;9| (|f| |x| $) (SPADCALL (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 34)) - (|getShellEntry| $ 32))) + (|getShellEntry| $ 36)) + (|getShellEntry| $ 34))) (DEFUN |CLAGG-;remove;S2A;10| (|s| |x| $) (SPADCALL (CONS #'|CLAGG-;remove;S2A;10!0| (VECTOR $ |s|)) |x| - (|getShellEntry| $ 37))) + (|getShellEntry| $ 39))) (DEFUN |CLAGG-;remove;S2A;10!0| (|#1| $$) (SPADCALL |#1| (|getShellEntry| $$ 1) - (|getShellEntry| (|getShellEntry| $$ 0) 36))) + (|getShellEntry| (|getShellEntry| $$ 0) 38))) (DEFUN |CLAGG-;reduce;MA3S;11| (|f| |x| |s1| |s2| $) (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) |s1| |s2| - (|getShellEntry| $ 39))) + (|getShellEntry| $ 41))) (DEFUN |CLAGG-;removeDuplicates;2A;12| (|x| $) (SPADCALL (SPADCALL (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 41)) - (|getShellEntry| $ 32))) + (|getShellEntry| $ 43)) + (|getShellEntry| $ 34))) (DEFUN |Collection&| (|#1| |#2|) (LET* ((|dv$1| (|devaluate| |#1|)) (|dv$2| (|devaluate| |#2|)) (|dv$| (LIST '|Collection&| |dv$1| |dv$2|)) - ($ (|newShell| 43)) + ($ (|newShell| 45)) (|pv$| (|buildPredVector| 0 0 (LIST (|HasCategory| |#2| (LIST '|ConvertibleTo| '(|InputForm|))) @@ -181,26 +148,26 @@ (CONS (|dispatchFunction| |CLAGG-;count;MANni;2|) $)) (|setShellEntry| $ 21 (CONS (|dispatchFunction| |CLAGG-;any?;MAB;3|) $)) - (|setShellEntry| $ 22 + (|setShellEntry| $ 24 (CONS (|dispatchFunction| |CLAGG-;every?;MAB;4|) $)) - (|setShellEntry| $ 25 + (|setShellEntry| $ 27 (CONS (|dispatchFunction| |CLAGG-;find;MAU;5|) $)) - (|setShellEntry| $ 28 - (CONS (|dispatchFunction| |CLAGG-;reduce;MAS;6|) $)) (|setShellEntry| $ 30 + (CONS (|dispatchFunction| |CLAGG-;reduce;MAS;6|) $)) + (|setShellEntry| $ 32 (CONS (|dispatchFunction| |CLAGG-;reduce;MA2S;7|) $)) - (|setShellEntry| $ 33 - (CONS (|dispatchFunction| |CLAGG-;remove;M2A;8|) $)) (|setShellEntry| $ 35 + (CONS (|dispatchFunction| |CLAGG-;remove;M2A;8|) $)) + (|setShellEntry| $ 37 (CONS (|dispatchFunction| |CLAGG-;select;M2A;9|) $)) (COND ((|testBitVector| |pv$| 2) (PROGN - (|setShellEntry| $ 38 - (CONS (|dispatchFunction| |CLAGG-;remove;S2A;10|) $)) (|setShellEntry| $ 40 - (CONS (|dispatchFunction| |CLAGG-;reduce;MA3S;11|) $)) + (CONS (|dispatchFunction| |CLAGG-;remove;S2A;10|) $)) (|setShellEntry| $ 42 + (CONS (|dispatchFunction| |CLAGG-;reduce;MA3S;11|) $)) + (|setShellEntry| $ 44 (CONS (|dispatchFunction| |CLAGG-;removeDuplicates;2A;12|) $)))))))) @@ -210,37 +177,37 @@ (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|List| 7) (0 . |parts|) (|NonNegativeInteger|) (5 . |#|) (10 . |#|) (15 . |One|) (19 . +) (25 . |Zero|) (|Boolean|) - (|Mapping| 16 7) (29 . |count|) (35 . |true|) - (39 . |false|) (43 . |any?|) (49 . |every?|) - (|Union| 7 '"failed") (55 . |find|) (61 . |find|) - (|Mapping| 7 7 7) (67 . |reduce|) (73 . |reduce|) - (79 . |reduce|) (86 . |reduce|) (93 . |remove|) - (99 . |construct|) (104 . |remove|) (110 . |select|) - (116 . |select|) (122 . =) (128 . |remove|) - (134 . |remove|) (140 . |reduce|) (148 . |reduce|) - (156 . |removeDuplicates|) (161 . |removeDuplicates|)) - '#(|select| 166 |removeDuplicates| 172 |remove| 177 |reduce| - 189 |find| 210 |every?| 216 |count| 222 |any?| 228 |#| - 234) + (|Mapping| 16 7) (29 . |count|) (35 . |or|) (41 . |false|) + (45 . |any?|) (51 . |and|) (57 . |true|) (61 . |every?|) + (|Union| 7 '"failed") (67 . |find|) (73 . |find|) + (|Mapping| 7 7 7) (79 . |reduce|) (85 . |reduce|) + (91 . |reduce|) (98 . |reduce|) (105 . |remove|) + (111 . |construct|) (116 . |remove|) (122 . |select|) + (128 . |select|) (134 . =) (140 . |remove|) + (146 . |remove|) (152 . |reduce|) (160 . |reduce|) + (168 . |removeDuplicates|) (173 . |removeDuplicates|)) + '#(|select| 178 |removeDuplicates| 184 |remove| 189 |reduce| + 201 |find| 222 |every?| 228 |count| 234 |any?| 240 |#| + 246) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 42 + (|makeByteWordVec2| 44 '(1 6 8 0 9 1 8 10 0 11 1 0 10 0 12 0 10 0 13 2 10 0 0 0 14 0 10 0 15 2 0 - 10 17 0 18 0 16 0 19 0 16 0 20 2 0 16 - 17 0 21 2 0 16 17 0 22 2 8 23 17 0 24 - 2 0 23 17 0 25 2 8 7 26 0 27 2 0 7 26 - 0 28 3 8 7 26 0 7 29 3 0 7 26 0 7 30 - 2 8 0 17 0 31 1 6 0 8 32 2 0 0 17 0 - 33 2 8 0 17 0 34 2 0 0 17 0 35 2 7 16 - 0 0 36 2 6 0 17 0 37 2 0 0 7 0 38 4 8 - 7 26 0 7 7 39 4 0 7 26 0 7 7 40 1 8 0 - 0 41 1 0 0 0 42 2 0 0 17 0 35 1 0 0 0 - 42 2 0 0 7 0 38 2 0 0 17 0 33 4 0 7 - 26 0 7 7 40 3 0 7 26 0 7 30 2 0 7 26 - 0 28 2 0 23 17 0 25 2 0 16 17 0 22 2 - 0 10 17 0 18 2 0 16 17 0 21 1 0 10 0 - 12))))) + 10 17 0 18 2 16 0 0 0 19 0 16 0 20 2 + 0 16 17 0 21 2 16 0 0 0 22 0 16 0 23 + 2 0 16 17 0 24 2 8 25 17 0 26 2 0 25 + 17 0 27 2 8 7 28 0 29 2 0 7 28 0 30 3 + 8 7 28 0 7 31 3 0 7 28 0 7 32 2 8 0 + 17 0 33 1 6 0 8 34 2 0 0 17 0 35 2 8 + 0 17 0 36 2 0 0 17 0 37 2 7 16 0 0 38 + 2 6 0 17 0 39 2 0 0 7 0 40 4 8 7 28 0 + 7 7 41 4 0 7 28 0 7 7 42 1 8 0 0 43 1 + 0 0 0 44 2 0 0 17 0 37 1 0 0 0 44 2 0 + 0 7 0 40 2 0 0 17 0 35 4 0 7 28 0 7 7 + 42 3 0 7 28 0 7 32 2 0 7 28 0 30 2 0 + 25 17 0 27 2 0 16 17 0 24 2 0 10 17 0 + 18 2 0 16 17 0 21 1 0 10 0 12))))) '|lookupComplete|)) diff --git a/src/algebra/strap/EUCDOM-.lsp b/src/algebra/strap/EUCDOM-.lsp index 00c35bba..6af1eb73 100644 --- a/src/algebra/strap/EUCDOM-.lsp +++ b/src/algebra/strap/EUCDOM-.lsp @@ -311,9 +311,7 @@ (SETQ #2# (CDR #2#))))))))))))))) (DEFUN |EUCDOM-;multiEuclidean;LSU;11| (|l| |z| $) - (PROG (|n| |l1| |l2| #0=#:G1397 #1=#:G1524 #2=#:G1505 #3=#:G1503 - #4=#:G1504 #5=#:G1398 #6=#:G1525 #7=#:G1508 #8=#:G1506 - #9=#:G1507 |u| |v1| |v2|) + (PROG (|n| |l1| |l2| |u| |v1| |v2|) (RETURN (SEQ (LETT |n| (LENGTH |l|) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND @@ -330,80 +328,52 @@ |EUCDOM-;multiEuclidean;LSU;11|) (LETT |u| (SPADCALL - (PROGN - (LETT #4# NIL - |EUCDOM-;multiEuclidean;LSU;11|) - (SEQ - (LETT #0# NIL - |EUCDOM-;multiEuclidean;LSU;11|) - (LETT #1# |l1| - |EUCDOM-;multiEuclidean;LSU;11|) - G190 - (COND - ((OR (ATOM #1#) - (PROGN - (SETQ #0# (CAR #1#)) - NIL)) - (GO G191))) - (SEQ - (EXIT - (PROGN - (LETT #2# #0# - |EUCDOM-;multiEuclidean;LSU;11|) - (COND - (#4# - (LETT #3# - (SPADCALL #3# #2# - (|getShellEntry| $ 29)) - |EUCDOM-;multiEuclidean;LSU;11|)) - ('T - (PROGN - (LETT #3# #2# - |EUCDOM-;multiEuclidean;LSU;11|) - (LETT #4# 'T - |EUCDOM-;multiEuclidean;LSU;11|))))))) - (SETQ #1# (CDR #1#)) (GO G190) - G191 (EXIT NIL)) - (COND - (#4# #3#) - ('T (|spadConstant| $ 30)))) - (PROGN - (LETT #9# NIL - |EUCDOM-;multiEuclidean;LSU;11|) - (SEQ - (LETT #5# NIL - |EUCDOM-;multiEuclidean;LSU;11|) - (LETT #6# |l2| - |EUCDOM-;multiEuclidean;LSU;11|) - G190 - (COND - ((OR (ATOM #6#) - (PROGN - (SETQ #5# (CAR #6#)) - NIL)) - (GO G191))) - (SEQ - (EXIT - (PROGN - (LETT #7# #5# - |EUCDOM-;multiEuclidean;LSU;11|) - (COND - (#9# - (LETT #8# - (SPADCALL #8# #7# - (|getShellEntry| $ 29)) - |EUCDOM-;multiEuclidean;LSU;11|)) - ('T - (PROGN - (LETT #8# #7# - |EUCDOM-;multiEuclidean;LSU;11|) - (LETT #9# 'T - |EUCDOM-;multiEuclidean;LSU;11|))))))) - (SETQ #6# (CDR #6#)) (GO G190) - G191 (EXIT NIL)) - (COND - (#9# #8#) - ('T (|spadConstant| $ 30)))) + (LET + ((#0=#:G1504 NIL) (#1=#:G1505 T) + (#2=#:G1524 |l1|)) + (LOOP + (COND + ((ATOM #2#) + (RETURN + (COND + (#1# + (|spadConstant| $ 30)) + (T #0#)))) + (T + (LET ((#3=#:G1397 (CAR #2#))) + (LET ((#4=#:G1503 #3#)) + (COND + (#1# (SETQ #0# #4#)) + (T + (SETQ #0# + (SPADCALL #0# #4# + (|getShellEntry| $ + 29))))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#)))) + (LET + ((#5=#:G1507 NIL) (#6=#:G1508 T) + (#7=#:G1525 |l2|)) + (LOOP + (COND + ((ATOM #7#) + (RETURN + (COND + (#6# + (|spadConstant| $ 30)) + (T #5#)))) + (T + (LET ((#8=#:G1398 (CAR #7#))) + (LET ((#9=#:G1506 #8#)) + (COND + (#6# (SETQ #5# #9#)) + (T + (SETQ #5# + (SPADCALL #5# #9# + (|getShellEntry| $ + 29))))) + (SETQ #6# NIL))))) + (SETQ #7# (CDR #7#)))) |z| (|getShellEntry| $ 62)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND diff --git a/src/algebra/strap/FFIELDC-.lsp b/src/algebra/strap/FFIELDC-.lsp index ca71780b..2f429a7e 100644 --- a/src/algebra/strap/FFIELDC-.lsp +++ b/src/algebra/strap/FFIELDC-.lsp @@ -473,7 +473,7 @@ (SPADCALL |f| (|getShellEntry| $ 98))) (DEFUN |FFIELDC-;factorSquareFreePolynomial| (|f| $) - (PROG (|flist| |u| #0=#:G1520 #1=#:G1509 #2=#:G1507 #3=#:G1508) + (PROG (|flist|) (RETURN (SEQ (COND ((SPADCALL |f| (|spadConstant| $ 99) @@ -486,42 +486,29 @@ (EXIT (SPADCALL (SPADCALL (CAR |flist|) (|getShellEntry| $ 106)) - (PROGN - (LETT #3# NIL - |FFIELDC-;factorSquareFreePolynomial|) - (SEQ (LETT |u| NIL - |FFIELDC-;factorSquareFreePolynomial|) - (LETT #0# (CDR |flist|) - |FFIELDC-;factorSquareFreePolynomial|) - G190 - (COND - ((OR (ATOM #0#) - (PROGN - (SETQ |u| (CAR #0#)) - NIL)) - (GO G191))) - (PROGN - (LETT #1# - (SPADCALL (CAR |u|) (CDR |u|) - (|getShellEntry| $ 107)) - |FFIELDC-;factorSquareFreePolynomial|) + (LET ((#0=#:G1508 NIL) (#1=#:G1509 T) + (#2=#:G1520 (CDR |flist|))) + (LOOP + (COND + ((ATOM #2#) + (RETURN (COND - (#3# - (LETT #2# - (SPADCALL #2# #1# - (|getShellEntry| $ 108)) - |FFIELDC-;factorSquareFreePolynomial|)) - ('T - (PROGN - (LETT #2# #1# - |FFIELDC-;factorSquareFreePolynomial|) - (LETT #3# 'T - |FFIELDC-;factorSquareFreePolynomial|))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 - (EXIT NIL)) - (COND - (#3# #2#) - ('T (|spadConstant| $ 109)))) + (#1# (|spadConstant| $ 109)) + (T #0#)))) + (T + (LET ((|u| (CAR #2#))) + (LET + ((#3=#:G1507 + (SPADCALL (CAR |u|) (CDR |u|) + (|getShellEntry| $ 107)))) + (COND + (#1# (SETQ #0# #3#)) + (T + (SETQ #0# + (SPADCALL #0# #3# + (|getShellEntry| $ 108))))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#)))) (|getShellEntry| $ 110)))))))))) (DEFUN |FFIELDC-;gcdPolynomial;3Sup;16| (|f| |g| $) diff --git a/src/algebra/strap/HOAGG-.lsp b/src/algebra/strap/HOAGG-.lsp index a3159838..22fc5a79 100644 --- a/src/algebra/strap/HOAGG-.lsp +++ b/src/algebra/strap/HOAGG-.lsp @@ -45,134 +45,85 @@ (LENGTH (SPADCALL |c| (|getShellEntry| $ 15)))) (DEFUN |HOAGG-;any?;MAB;3| (|f| |c| $) - (PROG (|x| #0=#:G1428 #1=#:G1406 #2=#:G1404 #3=#:G1405) - (RETURN - (SEQ (PROGN - (LETT #3# NIL |HOAGG-;any?;MAB;3|) - (SEQ (LETT |x| NIL |HOAGG-;any?;MAB;3|) - (LETT #0# (SPADCALL |c| (|getShellEntry| $ 15)) - |HOAGG-;any?;MAB;3|) - G190 - (COND - ((OR (ATOM #0#) (PROGN (SETQ |x| (CAR #0#)) NIL)) - (GO G191))) - (PROGN - (LETT #1# (SPADCALL |x| |f|) |HOAGG-;any?;MAB;3|) - (COND - (#3# (LETT #2# (COND (#2# T) ('T #1#)) - |HOAGG-;any?;MAB;3|)) - ('T - (PROGN - (LETT #2# #1# |HOAGG-;any?;MAB;3|) - (LETT #3# 'T |HOAGG-;any?;MAB;3|))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T NIL))))))) + (LET ((#0=#:G1405 NIL) (#1=#:G1406 T) + (#2=#:G1428 (SPADCALL |c| (|getShellEntry| $ 15)))) + (LOOP + (COND + ((ATOM #2#) (RETURN (COND (#1# NIL) (T #0#)))) + (T (LET ((|x| (CAR #2#))) + (LET ((#3=#:G1404 (SPADCALL |x| |f|))) + (COND (#1# (SETQ #0# #3#)) (T (SETQ #0# (OR #0# #3#)))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#))))) (DEFUN |HOAGG-;every?;MAB;4| (|f| |c| $) - (PROG (|x| #0=#:G1429 #1=#:G1411 #2=#:G1409 #3=#:G1410) - (RETURN - (SEQ (PROGN - (LETT #3# NIL |HOAGG-;every?;MAB;4|) - (SEQ (LETT |x| NIL |HOAGG-;every?;MAB;4|) - (LETT #0# (SPADCALL |c| (|getShellEntry| $ 15)) - |HOAGG-;every?;MAB;4|) - G190 - (COND - ((OR (ATOM #0#) (PROGN (SETQ |x| (CAR #0#)) NIL)) - (GO G191))) - (PROGN - (LETT #1# (SPADCALL |x| |f|) |HOAGG-;every?;MAB;4|) - (COND - (#3# (LETT #2# (COND (#2# #1#) ('T NIL)) - |HOAGG-;every?;MAB;4|)) - ('T - (PROGN - (LETT #2# #1# |HOAGG-;every?;MAB;4|) - (LETT #3# 'T |HOAGG-;every?;MAB;4|))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T T))))))) + (LET ((#0=#:G1410 NIL) (#1=#:G1411 T) + (#2=#:G1429 (SPADCALL |c| (|getShellEntry| $ 15)))) + (LOOP + (COND + ((ATOM #2#) (RETURN (COND (#1# T) (T #0#)))) + (T (LET ((|x| (CAR #2#))) + (LET ((#3=#:G1409 (SPADCALL |x| |f|))) + (COND + (#1# (SETQ #0# #3#)) + (T (SETQ #0# (AND #0# #3#)))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#))))) (DEFUN |HOAGG-;count;MANni;5| (|f| |c| $) - (PROG (|x| #0=#:G1430 #1=#:G1415 #2=#:G1413 #3=#:G1414) - (RETURN - (SEQ (PROGN - (LETT #3# NIL |HOAGG-;count;MANni;5|) - (SEQ (LETT |x| NIL |HOAGG-;count;MANni;5|) - (LETT #0# (SPADCALL |c| (|getShellEntry| $ 15)) - |HOAGG-;count;MANni;5|) - G190 - (COND - ((OR (ATOM #0#) (PROGN (SETQ |x| (CAR #0#)) NIL)) - (GO G191))) - (COND - ((SPADCALL |x| |f|) - (PROGN - (LETT #1# 1 |HOAGG-;count;MANni;5|) - (COND - (#3# (LETT #2# (+ #2# #1#) - |HOAGG-;count;MANni;5|)) - ('T - (PROGN - (LETT #2# #1# |HOAGG-;count;MANni;5|) - (LETT #3# 'T |HOAGG-;count;MANni;5|))))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T 0))))))) + (LET ((#0=#:G1414 NIL) (#1=#:G1415 T) + (#2=#:G1430 (SPADCALL |c| (|getShellEntry| $ 15)))) + (LOOP + (COND + ((ATOM #2#) (RETURN (COND (#1# 0) (T #0#)))) + (T (LET ((|x| (CAR #2#))) + (AND (SPADCALL |x| |f|) + (LET ((#3=#:G1413 1)) + (COND + (#1# (SETQ #0# #3#)) + (T (SETQ #0# (+ #0# #3#)))) + (SETQ #1# NIL)))))) + (SETQ #2# (CDR #2#))))) (DEFUN |HOAGG-;members;AL;6| (|x| $) (SPADCALL |x| (|getShellEntry| $ 15))) (DEFUN |HOAGG-;count;SANni;7| (|s| |x| $) (SPADCALL (CONS #'|HOAGG-;count;SANni;7!0| (VECTOR $ |s|)) |x| - (|getShellEntry| $ 31))) + (|getShellEntry| $ 33))) (DEFUN |HOAGG-;count;SANni;7!0| (|#1| $$) (SPADCALL (|getShellEntry| $$ 1) |#1| - (|getShellEntry| (|getShellEntry| $$ 0) 30))) + (|getShellEntry| (|getShellEntry| $$ 0) 32))) (DEFUN |HOAGG-;member?;SAB;8| (|e| |c| $) (SPADCALL (CONS #'|HOAGG-;member?;SAB;8!0| (VECTOR $ |e|)) |c| - (|getShellEntry| $ 33))) + (|getShellEntry| $ 35))) (DEFUN |HOAGG-;member?;SAB;8!0| (|#1| $$) (SPADCALL (|getShellEntry| $$ 1) |#1| - (|getShellEntry| (|getShellEntry| $$ 0) 30))) + (|getShellEntry| (|getShellEntry| $$ 0) 32))) (DEFUN |HOAGG-;=;2AB;9| (|x| |y| $) - (PROG (|b| #0=#:G1432 |a| #1=#:G1431 #2=#:G1422 #3=#:G1420 - #4=#:G1421) - (RETURN - (SEQ (COND - ((SPADCALL |x| (SPADCALL |y| (|getShellEntry| $ 35)) - (|getShellEntry| $ 36)) - (PROGN - (LETT #4# NIL |HOAGG-;=;2AB;9|) - (SEQ (LETT |b| NIL |HOAGG-;=;2AB;9|) - (LETT #0# (SPADCALL |y| (|getShellEntry| $ 15)) - |HOAGG-;=;2AB;9|) - (LETT |a| NIL |HOAGG-;=;2AB;9|) - (LETT #1# (SPADCALL |x| (|getShellEntry| $ 15)) - |HOAGG-;=;2AB;9|) - G190 - (COND - ((OR (ATOM #1#) (PROGN (SETQ |a| (CAR #1#)) NIL) - (ATOM #0#) - (PROGN (SETQ |b| (CAR #0#)) NIL)) - (GO G191))) - (PROGN - (LETT #2# - (SPADCALL |a| |b| (|getShellEntry| $ 30)) - |HOAGG-;=;2AB;9|) - (COND - (#4# (LETT #3# (COND (#3# #2#) ('T NIL)) - |HOAGG-;=;2AB;9|)) - ('T - (PROGN - (LETT #3# #2# |HOAGG-;=;2AB;9|) - (LETT #4# 'T |HOAGG-;=;2AB;9|))))) - (SETQ #1# (PROG1 (CDR #1#) (SETQ #0# (CDR #0#)))) - (GO G190) G191 (EXIT NIL)) - (COND (#4# #3#) ('T T)))) - ('T NIL)))))) + (COND + ((SPADCALL |x| (SPADCALL |y| (|getShellEntry| $ 37)) + (|getShellEntry| $ 38)) + (LET ((#0=#:G1421 NIL) (#1=#:G1422 T) + (#2=#:G1431 (SPADCALL |x| (|getShellEntry| $ 15))) + (#3=#:G1432 (SPADCALL |y| (|getShellEntry| $ 15)))) + (LOOP + (COND + ((OR (ATOM #2#) (ATOM #3#)) (RETURN (COND (#1# T) (T #0#)))) + (T (LET ((|a| (CAR #2#)) (|b| (CAR #3#))) + (LET ((#4=#:G1420 + (SPADCALL |a| |b| (|getShellEntry| $ 32)))) + (COND + (#1# (SETQ #0# #4#)) + (T (SETQ #0# (AND #0# #4#)))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#)) + (SETQ #3# (CDR #3#))))) + ('T NIL))) (DEFUN |HOAGG-;coerce;AOf;10| (|x| $) (SPADCALL @@ -184,16 +135,16 @@ ((ATOM #0#) (RETURN (NREVERSE #1#))) (T (LET ((|a| (CAR #0#))) (SETQ #1# - (CONS (SPADCALL |a| (|getShellEntry| $ 39)) + (CONS (SPADCALL |a| (|getShellEntry| $ 41)) #1#))))) (SETQ #0# (CDR #0#)))) - (|getShellEntry| $ 41)) - (|getShellEntry| $ 42))) + (|getShellEntry| $ 43)) + (|getShellEntry| $ 44))) (DEFUN |HomogeneousAggregate&| (|#1| |#2|) (LET* ((|dv$1| (|devaluate| |#1|)) (|dv$2| (|devaluate| |#2|)) (|dv$| (LIST '|HomogeneousAggregate&| |dv$1| |dv$2|)) - ($ (|newShell| 44)) + ($ (|newShell| 46)) (|pv$| (|buildPredVector| 0 0 (LIST (|HasAttribute| |#1| '|finiteAggregate|) (|HasAttribute| |#1| '|shallowlyMutable|) @@ -218,24 +169,24 @@ (CONS (|dispatchFunction| |HOAGG-;#;ANni;2|) $)) (|setShellEntry| $ 23 (CONS (|dispatchFunction| |HOAGG-;any?;MAB;3|) $)) - (|setShellEntry| $ 24 + (|setShellEntry| $ 26 (CONS (|dispatchFunction| |HOAGG-;every?;MAB;4|) $)) - (|setShellEntry| $ 28 + (|setShellEntry| $ 30 (CONS (|dispatchFunction| |HOAGG-;count;MANni;5|) $)) - (|setShellEntry| $ 29 + (|setShellEntry| $ 31 (CONS (|dispatchFunction| |HOAGG-;members;AL;6|) $)) (COND ((|testBitVector| |pv$| 4) (PROGN - (|setShellEntry| $ 32 - (CONS (|dispatchFunction| |HOAGG-;count;SANni;7|) $)) (|setShellEntry| $ 34 + (CONS (|dispatchFunction| |HOAGG-;count;SANni;7|) $)) + (|setShellEntry| $ 36 (CONS (|dispatchFunction| |HOAGG-;member?;SAB;8|) $)) - (|setShellEntry| $ 37 + (|setShellEntry| $ 39 (CONS (|dispatchFunction| |HOAGG-;=;2AB;9|) $))))) (COND ((|testBitVector| |pv$| 5) - (|setShellEntry| $ 43 + (|setShellEntry| $ 45 (CONS (|dispatchFunction| |HOAGG-;coerce;AOf;10|) $))))))) $)) @@ -244,33 +195,33 @@ (|Equation| 7) (|List| 8) (0 . |eval|) (|Mapping| 7 7) (6 . |map|) (12 . |eval|) (|List| 7) (18 . |parts|) (|NonNegativeInteger|) (23 . |#|) (28 . |#|) (|Boolean|) - (33 . |true|) (37 . |false|) (|Mapping| 19 7) - (41 . |any?|) (47 . |every?|) (53 . |One|) (57 . +) - (63 . |Zero|) (67 . |count|) (73 . |members|) (78 . =) - (84 . |count|) (90 . |count|) (96 . |any?|) - (102 . |member?|) (108 . |#|) (113 . |size?|) (119 . =) - (|OutputForm|) (125 . |coerce|) (|List| $) - (130 . |commaSeparate|) (135 . |bracket|) - (140 . |coerce|)) - '#(|members| 145 |member?| 150 |every?| 156 |eval| 162 - |count| 168 |coerce| 180 |any?| 185 = 191 |#| 197) + (33 . |or|) (39 . |false|) (|Mapping| 19 7) (43 . |any?|) + (49 . |and|) (55 . |true|) (59 . |every?|) (65 . |One|) + (69 . +) (75 . |Zero|) (79 . |count|) (85 . |members|) + (90 . =) (96 . |count|) (102 . |count|) (108 . |any?|) + (114 . |member?|) (120 . |#|) (125 . |size?|) (131 . =) + (|OutputForm|) (137 . |coerce|) (|List| $) + (142 . |commaSeparate|) (147 . |bracket|) + (152 . |coerce|)) + '#(|members| 157 |member?| 162 |every?| 168 |eval| 174 + |count| 180 |coerce| 192 |any?| 197 = 203 |#| 209) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 43 + (|makeByteWordVec2| 45 '(2 7 0 0 9 10 2 6 0 11 0 12 2 0 0 0 9 13 1 6 14 0 15 1 14 16 0 17 1 0 16 0 - 18 0 19 0 20 0 19 0 21 2 0 19 22 0 23 - 2 0 19 22 0 24 0 16 0 25 2 16 0 0 0 - 26 0 16 0 27 2 0 16 22 0 28 1 0 14 0 - 29 2 7 19 0 0 30 2 6 16 22 0 31 2 0 - 16 7 0 32 2 6 19 22 0 33 2 0 19 7 0 - 34 1 6 16 0 35 2 6 19 0 16 36 2 0 19 - 0 0 37 1 7 38 0 39 1 38 0 40 41 1 38 - 0 0 42 1 0 38 0 43 1 0 14 0 29 2 0 19 - 7 0 34 2 0 19 22 0 24 2 0 0 0 9 13 2 - 0 16 7 0 32 2 0 16 22 0 28 1 0 38 0 - 43 2 0 19 22 0 23 2 0 19 0 0 37 1 0 - 16 0 18))))) + 18 2 19 0 0 0 20 0 19 0 21 2 0 19 22 + 0 23 2 19 0 0 0 24 0 19 0 25 2 0 19 + 22 0 26 0 16 0 27 2 16 0 0 0 28 0 16 + 0 29 2 0 16 22 0 30 1 0 14 0 31 2 7 + 19 0 0 32 2 6 16 22 0 33 2 0 16 7 0 + 34 2 6 19 22 0 35 2 0 19 7 0 36 1 6 + 16 0 37 2 6 19 0 16 38 2 0 19 0 0 39 + 1 7 40 0 41 1 40 0 42 43 1 40 0 0 44 + 1 0 40 0 45 1 0 14 0 31 2 0 19 7 0 36 + 2 0 19 22 0 26 2 0 0 0 9 13 2 0 16 7 + 0 34 2 0 16 22 0 30 1 0 40 0 45 2 0 + 19 22 0 23 2 0 19 0 0 39 1 0 16 0 18))))) '|lookupComplete|)) diff --git a/src/algebra/strap/ISTRING.lsp b/src/algebra/strap/ISTRING.lsp index 4cd0567f..23b54d95 100644 --- a/src/algebra/strap/ISTRING.lsp +++ b/src/algebra/strap/ISTRING.lsp @@ -544,47 +544,34 @@ $)))))) (DEFUN |ISTRING;concat;L$;28| (|l| $) - (PROG (#0=#:G1540 #1=#:G1495 #2=#:G1493 #3=#:G1494 |t| |s| #4=#:G1541 - |i|) + (PROG (|t| |s| #0=#:G1541 |i|) (RETURN (SEQ (LETT |t| (MAKE-FULL-CVEC - (PROGN - (LETT #3# NIL |ISTRING;concat;L$;28|) - (SEQ (LETT |s| NIL |ISTRING;concat;L$;28|) - (LETT #0# |l| |ISTRING;concat;L$;28|) G190 - (COND - ((OR (ATOM #0#) - (PROGN (SETQ |s| (CAR #0#)) NIL)) - (GO G191))) - (SEQ (EXIT (PROGN - (LETT #1# (QCSIZE |s|) - |ISTRING;concat;L$;28|) - (COND - (#3# - (LETT #2# (+ #2# #1#) - |ISTRING;concat;L$;28|)) - ('T - (PROGN - (LETT #2# #1# - |ISTRING;concat;L$;28|) - (LETT #3# 'T - |ISTRING;concat;L$;28|))))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 - (EXIT NIL)) - (COND (#3# #2#) ('T 0))) + (LET ((#1=#:G1494 NIL) (#2=#:G1495 T) + (#3=#:G1540 |l|)) + (LOOP + (COND + ((ATOM #3#) (RETURN (COND (#2# 0) (T #1#)))) + (T (LET ((|s| (CAR #3#))) + (LET ((#4=#:G1493 (QCSIZE |s|))) + (COND + (#2# (SETQ #1# #4#)) + (T (SETQ #1# (+ #1# #4#)))) + (SETQ #2# NIL))))) + (SETQ #3# (CDR #3#)))) (|spadConstant| $ 53)) |ISTRING;concat;L$;28|) (LETT |i| (|getShellEntry| $ 6) |ISTRING;concat;L$;28|) (SEQ (LETT |s| NIL |ISTRING;concat;L$;28|) - (LETT #4# |l| |ISTRING;concat;L$;28|) G190 + (LETT #0# |l| |ISTRING;concat;L$;28|) G190 (COND - ((OR (ATOM #4#) (PROGN (SETQ |s| (CAR #4#)) NIL)) + ((OR (ATOM #0#) (PROGN (SETQ |s| (CAR #0#)) NIL)) (GO G191))) (SEQ (|ISTRING;copyInto!;2$I$;29| |t| |s| |i| $) (EXIT (LETT |i| (+ |i| (QCSIZE |s|)) |ISTRING;concat;L$;28|))) - (SETQ #4# (CDR #4#)) (GO G190) G191 (EXIT NIL)) + (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) (EXIT |t|))))) (DEFUN |ISTRING;copyInto!;2$I$;29| (|y| |x| |s| $) diff --git a/src/algebra/strap/POLYCAT-.lsp b/src/algebra/strap/POLYCAT-.lsp index a5482945..5bc36a75 100644 --- a/src/algebra/strap/POLYCAT-.lsp +++ b/src/algebra/strap/POLYCAT-.lsp @@ -732,78 +732,64 @@ (|getShellEntry| $ 159))))))))))) (DEFUN |POLYCAT-;conditionP;MU;27| (|mat| $) - (PROG (#0=#:G1610 #1=#:G1730 #2=#:G1731 #3=#:G1605 #4=#:G1603 - #5=#:G1604 |nd| |ll| |ch| |l| #6=#:G1722 |u| #7=#:G1723 - #8=#:G1583 #9=#:G1581 #10=#:G1582 |mons| |m| #11=#:G1724 - |vars| |degs| |deg1| |redmons| |llR| |monslist| |ans| |i|) + (PROG (#0=#:G1610 #1=#:G1730 |nd| |ll| |ch| |l| #2=#:G1722 |mons| |m| + #3=#:G1724 |vars| |degs| |deg1| |redmons| |llR| |monslist| + |ans| |i|) (RETURN (SEQ (LETT |ll| (SPADCALL (SPADCALL |mat| (|getShellEntry| $ 166)) (|getShellEntry| $ 114)) |POLYCAT-;conditionP;MU;27|) (LETT |llR| - (LET ((#12=#:G1721 (|SPADfirst| |ll|)) - (#13=#:G1720 NIL)) + (LET ((#4=#:G1721 (|SPADfirst| |ll|)) + (#5=#:G1720 NIL)) (LOOP (COND - ((ATOM #12#) (RETURN (NREVERSE #13#))) - (T (LET ((|z| (CAR #12#))) - (SETQ #13# (CONS NIL #13#))))) - (SETQ #12# (CDR #12#)))) + ((ATOM #4#) (RETURN (NREVERSE #5#))) + (T (LET ((|z| (CAR #4#))) + (SETQ #5# (CONS NIL #5#))))) + (SETQ #4# (CDR #4#)))) |POLYCAT-;conditionP;MU;27|) (LETT |monslist| NIL |POLYCAT-;conditionP;MU;27|) (LETT |ch| (|spadConstant| $ 169) |POLYCAT-;conditionP;MU;27|) (SEQ (LETT |l| NIL |POLYCAT-;conditionP;MU;27|) - (LETT #6# |ll| |POLYCAT-;conditionP;MU;27|) G190 + (LETT #2# |ll| |POLYCAT-;conditionP;MU;27|) G190 (COND - ((OR (ATOM #6#) (PROGN (SETQ |l| (CAR #6#)) NIL)) + ((OR (ATOM #2#) (PROGN (SETQ |l| (CAR #2#)) NIL)) (GO G191))) (SEQ (LETT |mons| - (PROGN - (LETT #10# NIL - |POLYCAT-;conditionP;MU;27|) - (SEQ (LETT |u| NIL - |POLYCAT-;conditionP;MU;27|) - (LETT #7# |l| - |POLYCAT-;conditionP;MU;27|) - G190 - (COND - ((OR (ATOM #7#) - (PROGN (SETQ |u| (CAR #7#)) NIL)) - (GO G191))) - (SEQ (EXIT - (PROGN - (LETT #8# - (SPADCALL |u| - (|getShellEntry| $ 98)) - |POLYCAT-;conditionP;MU;27|) - (COND - (#10# - (LETT #9# - (SPADCALL #9# #8# - (|getShellEntry| $ 170)) - |POLYCAT-;conditionP;MU;27|)) - ('T - (PROGN - (LETT #9# #8# - |POLYCAT-;conditionP;MU;27|) - (LETT #10# 'T - |POLYCAT-;conditionP;MU;27|))))))) - (SETQ #7# (CDR #7#)) (GO G190) G191 - (EXIT NIL)) - (COND - (#10# #9#) - ('T (|IdentityError| '|setUnion|)))) + (LET ((#6=#:G1582 NIL) (#7=#:G1583 T) + (#8=#:G1723 |l|)) + (LOOP + (COND + ((ATOM #8#) + (RETURN + (COND + (#7# + (|IdentityError| '|setUnion|)) + (T #6#)))) + (T (LET ((|u| (CAR #8#))) + (LET + ((#9=#:G1581 + (SPADCALL |u| + (|getShellEntry| $ 98)))) + (COND + (#7# (SETQ #6# #9#)) + (T + (SETQ #6# + (SPADCALL #6# #9# + (|getShellEntry| $ 170))))) + (SETQ #7# NIL))))) + (SETQ #8# (CDR #8#)))) |POLYCAT-;conditionP;MU;27|) (LETT |redmons| NIL |POLYCAT-;conditionP;MU;27|) (SEQ (LETT |m| NIL |POLYCAT-;conditionP;MU;27|) - (LETT #11# |mons| - |POLYCAT-;conditionP;MU;27|) + (LETT #3# |mons| |POLYCAT-;conditionP;MU;27|) G190 (COND - ((OR (ATOM #11#) - (PROGN (SETQ |m| (CAR #11#)) NIL)) + ((OR (ATOM #3#) + (PROGN (SETQ |m| (CAR #3#)) NIL)) (GO G191))) (SEQ (LETT |vars| (SPADCALL |m| @@ -815,15 +801,15 @@ |POLYCAT-;conditionP;MU;27|) (LETT |deg1| (LET - ((#14=#:G1726 |degs|) - (#15=#:G1725 NIL)) + ((#10=#:G1726 |degs|) + (#11=#:G1725 NIL)) (LOOP (COND - ((ATOM #14#) - (RETURN (NREVERSE #15#))) + ((ATOM #10#) + (RETURN (NREVERSE #11#))) (T - (LET ((|d| (CAR #14#))) - (SETQ #15# + (LET ((|d| (CAR #10#))) + (SETQ #11# (CONS (SEQ (LETT |nd| @@ -840,14 +826,14 @@ "failed"))) ('T (LET - ((#16=#:G1612 + ((#12=#:G1612 (CDR |nd|))) (|check-subtype| - (>= #16# 0) + (>= #12# 0) '(|NonNegativeInteger|) - #16#)))))) - #15#))))) - (SETQ #14# (CDR #14#)))) + #12#)))))) + #11#))))) + (SETQ #10# (CDR #10#)))) |POLYCAT-;conditionP;MU;27|) (LETT |redmons| (CONS @@ -858,19 +844,19 @@ |POLYCAT-;conditionP;MU;27|) (EXIT (LETT |llR| (LET - ((#17=#:G1728 |l|) - (#18=#:G1729 |llR|) - (#19=#:G1727 NIL)) + ((#13=#:G1728 |l|) + (#14=#:G1729 |llR|) + (#15=#:G1727 NIL)) (LOOP (COND - ((OR (ATOM #17#) - (ATOM #18#)) - (RETURN (NREVERSE #19#))) + ((OR (ATOM #13#) + (ATOM #14#)) + (RETURN (NREVERSE #15#))) (T (LET - ((|u| (CAR #17#)) - (|v| (CAR #18#))) - (SETQ #19# + ((|u| (CAR #13#)) + (|v| (CAR #14#))) + (SETQ #15# (CONS (CONS (SPADCALL @@ -881,15 +867,15 @@ (|getShellEntry| $ 175)) |v|) - #19#))))) - (SETQ #17# (CDR #17#)) - (SETQ #18# (CDR #18#)))) + #15#))))) + (SETQ #13# (CDR #13#)) + (SETQ #14# (CDR #14#)))) |POLYCAT-;conditionP;MU;27|))) - (SETQ #11# (CDR #11#)) (GO G190) G191 + (SETQ #3# (CDR #3#)) (GO G190) G191 (EXIT NIL)) (EXIT (LETT |monslist| (CONS |redmons| |monslist|) |POLYCAT-;conditionP;MU;27|))) - (SETQ #6# (CDR #6#)) (GO G190) G191 (EXIT NIL)) + (SETQ #2# (CDR #2#)) (GO G190) G191 (EXIT NIL)) (LETT |ans| (SPADCALL (SPADCALL (SPADCALL |llR| (|getShellEntry| $ 111)) @@ -902,7 +888,7 @@ (SEQ (LETT |i| 0 |POLYCAT-;conditionP;MU;27|) (EXIT (CONS 0 (LET - ((#20=#:G1611 + ((#16=#:G1611 (|makeSimpleArray| (|getVMType| (|getShellEntry| $ 6)) @@ -923,67 +909,56 @@ (GO G191))) (SEQ (EXIT - (|setSimpleArrayEntry| #20# + (|setSimpleArrayEntry| #16# #0# - (PROGN - (LETT #5# NIL - |POLYCAT-;conditionP;MU;27|) - (SEQ - (LETT |m| NIL - |POLYCAT-;conditionP;MU;27|) - (LETT #2# |mons| - |POLYCAT-;conditionP;MU;27|) - G190 - (COND - ((OR (ATOM #2#) - (PROGN - (SETQ |m| - (CAR #2#)) - NIL)) - (GO G191))) - (SEQ - (EXIT - (PROGN - (LETT #3# - (SPADCALL |m| - (SPADCALL - (SPADCALL - (CDR |ans|) - (LETT |i| - (+ |i| 1) - |POLYCAT-;conditionP;MU;27|) - (|getShellEntry| - $ 181)) - (|getShellEntry| $ - 51)) - (|getShellEntry| $ - 182)) - |POLYCAT-;conditionP;MU;27|) - (COND - (#5# - (LETT #4# - (SPADCALL #4# #3# - (|getShellEntry| - $ 183)) - |POLYCAT-;conditionP;MU;27|)) - ('T - (PROGN - (LETT #4# #3# - |POLYCAT-;conditionP;MU;27|) - (LETT #5# 'T - |POLYCAT-;conditionP;MU;27|))))))) - (SETQ #2# (CDR #2#)) - (GO G190) G191 - (EXIT NIL)) - (COND - (#5# #4#) - ('T - (|spadConstant| $ 27))))))) + (LET + ((#17=#:G1604 NIL) + (#18=#:G1605 T) + (#19=#:G1731 |mons|)) + (LOOP + (COND + ((ATOM #19#) + (RETURN + (COND + (#18# + (|spadConstant| + $ 27)) + (T #17#)))) + (T + (LET + ((|m| (CAR #19#))) + (LET + ((#20=#:G1603 + (SPADCALL |m| + (SPADCALL + (SPADCALL + (CDR |ans|) + (LETT |i| + (+ |i| 1) + |POLYCAT-;conditionP;MU;27|) + (|getShellEntry| + $ 181)) + (|getShellEntry| + $ 51)) + (|getShellEntry| + $ 182)))) + (COND + (#18# + (SETQ #17# + #20#)) + (T + (SETQ #17# + (SPADCALL + #17# #20# + (|getShellEntry| + $ 183))))) + (SETQ #18# NIL))))) + (SETQ #19# (CDR #19#))))))) (SETQ #1# (PROG1 (CDR #1#) (SETQ #0# (QSADD1 #0#)))) (GO G190) G191 (EXIT NIL)) - #20#))))))))))) + #16#))))))))))) (DEFUN |POLYCAT-;charthRoot;SU;28| (|p| $) (PROG (|vars| |ans| |ch|) @@ -1126,40 +1101,29 @@ (SPADCALL |p| (|getShellEntry| $ 197))) (DEFUN |POLYCAT-;squareFreePart;2S;34| (|p| $) - (PROG (|s| |f| #0=#:G1732 #1=#:G1654 #2=#:G1652 #3=#:G1653) + (PROG (|s|) (RETURN - (SEQ (SPADCALL - (SPADCALL - (LETT |s| (SPADCALL |p| (|getShellEntry| $ 198)) - |POLYCAT-;squareFreePart;2S;34|) - (|getShellEntry| $ 199)) - (PROGN - (LETT #3# NIL |POLYCAT-;squareFreePart;2S;34|) - (SEQ (LETT |f| NIL |POLYCAT-;squareFreePart;2S;34|) - (LETT #0# (SPADCALL |s| (|getShellEntry| $ 202)) - |POLYCAT-;squareFreePart;2S;34|) - G190 - (COND - ((OR (ATOM #0#) - (PROGN (SETQ |f| (CAR #0#)) NIL)) - (GO G191))) - (PROGN - (LETT #1# (CAR |f|) - |POLYCAT-;squareFreePart;2S;34|) - (COND - (#3# (LETT #2# - (SPADCALL #2# #1# - (|getShellEntry| $ 182)) - |POLYCAT-;squareFreePart;2S;34|)) - ('T - (PROGN - (LETT #2# #1# - |POLYCAT-;squareFreePart;2S;34|) - (LETT #3# 'T - |POLYCAT-;squareFreePart;2S;34|))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T (|spadConstant| $ 43)))) - (|getShellEntry| $ 182)))))) + (SPADCALL + (SPADCALL + (LETT |s| (SPADCALL |p| (|getShellEntry| $ 198)) + |POLYCAT-;squareFreePart;2S;34|) + (|getShellEntry| $ 199)) + (LET ((#0=#:G1653 NIL) (#1=#:G1654 T) + (#2=#:G1732 (SPADCALL |s| (|getShellEntry| $ 202)))) + (LOOP + (COND + ((ATOM #2#) + (RETURN (COND (#1# (|spadConstant| $ 43)) (T #0#)))) + (T (LET ((|f| (CAR #2#))) + (LET ((#3=#:G1652 (CAR |f|))) + (COND + (#1# (SETQ #0# #3#)) + (T (SETQ #0# + (SPADCALL #0# #3# + (|getShellEntry| $ 182))))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#)))) + (|getShellEntry| $ 182))))) (DEFUN |POLYCAT-;content;SVarSetS;35| (|p| |v| $) (SPADCALL (SPADCALL |p| |v| (|getShellEntry| $ 59)) diff --git a/src/algebra/strap/UFD-.lsp b/src/algebra/strap/UFD-.lsp index 02114011..741e93a8 100644 --- a/src/algebra/strap/UFD-.lsp +++ b/src/algebra/strap/UFD-.lsp @@ -8,37 +8,29 @@ |UFD-;prime?;SB;2|)) (DEFUN |UFD-;squareFreePart;2S;1| (|x| $) - (PROG (|s| |f| #0=#:G1419 #1=#:G1406 #2=#:G1404 #3=#:G1405) + (PROG (|s|) (RETURN - (SEQ (SPADCALL - (SPADCALL - (LETT |s| (SPADCALL |x| (|getShellEntry| $ 8)) - |UFD-;squareFreePart;2S;1|) - (|getShellEntry| $ 10)) - (PROGN - (LETT #3# NIL |UFD-;squareFreePart;2S;1|) - (SEQ (LETT |f| NIL |UFD-;squareFreePart;2S;1|) - (LETT #0# (SPADCALL |s| (|getShellEntry| $ 14)) - |UFD-;squareFreePart;2S;1|) - G190 - (COND - ((OR (ATOM #0#) - (PROGN (SETQ |f| (CAR #0#)) NIL)) - (GO G191))) - (PROGN - (LETT #1# (CAR |f|) |UFD-;squareFreePart;2S;1|) - (COND - (#3# (LETT #2# - (SPADCALL #2# #1# - (|getShellEntry| $ 15)) - |UFD-;squareFreePart;2S;1|)) - ('T - (PROGN - (LETT #2# #1# |UFD-;squareFreePart;2S;1|) - (LETT #3# 'T |UFD-;squareFreePart;2S;1|))))) - (SETQ #0# (CDR #0#)) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T (|spadConstant| $ 16)))) - (|getShellEntry| $ 15)))))) + (SPADCALL + (SPADCALL + (LETT |s| (SPADCALL |x| (|getShellEntry| $ 8)) + |UFD-;squareFreePart;2S;1|) + (|getShellEntry| $ 10)) + (LET ((#0=#:G1405 NIL) (#1=#:G1406 T) + (#2=#:G1419 (SPADCALL |s| (|getShellEntry| $ 14)))) + (LOOP + (COND + ((ATOM #2#) + (RETURN (COND (#1# (|spadConstant| $ 16)) (T #0#)))) + (T (LET ((|f| (CAR #2#))) + (LET ((#3=#:G1404 (CAR |f|))) + (COND + (#1# (SETQ #0# #3#)) + (T (SETQ #0# + (SPADCALL #0# #3# + (|getShellEntry| $ 15))))) + (SETQ #1# NIL))))) + (SETQ #2# (CDR #2#)))) + (|getShellEntry| $ 15))))) (DEFUN |UFD-;prime?;SB;2| (|x| $) (EQL (LENGTH (SPADCALL (SPADCALL |x| (|getShellEntry| $ 18)) diff --git a/src/interp/compiler.boot b/src/interp/compiler.boot index 6323bf51..7ac0ce3e 100644 --- a/src/interp/compiler.boot +++ b/src/interp/compiler.boot @@ -1229,7 +1229,7 @@ canReturn(expr,level,exitCount,ValueFlag) == --SPAD: exit and friends or/[findThrow(gs,u,level+1,exitCount,ValueFlag) for u in l] or/[findThrow(gs,u,level,exitCount,ValueFlag) for u in rest expr] canReturn(data,level,exitCount,ValueFlag) - op = "COND" => + op = "COND" or op = '%when => level = exitCount => or/[canReturn(last u,level,exitCount,ValueFlag) for u in rest expr] or/[or/[canReturn(u,level,exitCount,ValueFlag) for u in v] @@ -1241,7 +1241,7 @@ canReturn(expr,level,exitCount,ValueFlag) == --SPAD: exit and friends pp expr canReturn(a,level,exitCount,nil) or canReturn(b,level,exitCount,ValueFlag) or canReturn(c,level,exitCount,ValueFlag) - op = "LET" or op = "LET*" => + op in '(LET LET_* %bind) => or/[canReturn(init,level,exitCount,false) for [.,init] in second expr] or canReturn(third expr,level,exitCount,ValueFlag) --now we have an ordinary form @@ -2145,7 +2145,7 @@ compMatchAlternative(sn,sm,pat,stmt,m,e) == body := null inits => stmtT.expr atom sn => ["LET",inits,stmtT.expr] - ["LET*",inits,stmtT.expr] + ["%bind",inits,stmtT.expr] [[guard,body],stmtT.mode,stmtT.env,eF] ++ Analyze and generate code for `is case'-pattern where the @@ -2171,7 +2171,7 @@ compMatch(["%Match",subject,altBlock],m,env) == stackAndThrow('"missing %b otherwise %d alternative in case pattern",nil) code := atom sn => ["LET",[[sn,se]],["COND",:nreverse altsCode]] - ["LET*",[[n,e] for n in sn for e in rest se], + ["%bind",[[n,e] for n in sn for e in rest se], ["COND",:nreverse altsCode]] [code,m,savedEnv] @@ -2205,46 +2205,48 @@ compReduce(form,m,e) == compReduce1(form,m,e,$formalArgList) compReduce1(form is ["REDUCE",op,.,collectForm],m,e,$formalArgList) == - [collectOp,:itl,body]:= collectForm - if string? op then op:= INTERN op + [collectOp,:itl,body] := collectForm + if string? op then op := INTERN op collectOp ~= "COLLECT" => systemError ['"illegal reduction form:",form] - $sideEffectsList: local := nil $until: local := nil - $initList: local := nil - $endTestList: local := nil oldEnv := e - $e:= e - itl:= [([.,$e]:= compIterator(x,$e) or return "failed").0 for x in itl] + itl := [([.,e]:= compIterator(x,e) or return "failed").0 for x in itl] itl="failed" => return nil - e:= $e - acc:= gensym() - afterFirst:= gensym() - bodyVal:= gensym() - [part1,m,e]:= comp(["%LET",bodyVal,body],m,e) or return nil - [part2,.,e]:= comp(["%LET",acc,bodyVal],m,e) or return nil - [part3,.,e]:= comp(["%LET",acc,parseTran [op,acc,bodyVal]],m,e) or return nil - identityCode:= - id:= getIdentity(op,e) => u.expr where u() == comp(id,m,e) or return nil + b := gensym() -- holds value of the body + [bval,bmode,e] := comp(['%LET,b,body],$EmptyMode,e) or return nil + accu := gensym() -- holds value of the accumulator + [move,.,e] := comp(['%LET,accu,b],$EmptyMode,e) or return nil + move.op := '%store -- in reality, we are not defining a new variable + [update,mode,e] := comp(['%LET,accu,[op,accu,b]],m,e) or return nil + update.op := '%store -- just update the accumulation variable. + nval := + id := getIdentity(op,e) => u.expr where + u() == comp(id,mode,e) or return nil ["IdentityError",MKQ op] - finalCode:= - ["PROGN", - ["%LET",afterFirst,nil], - ["REPEAT",:itl, - ["PROGN",part1, - ["IF", afterFirst,part3, - ["PROGN",part2,["%LET",afterFirst,MKQ true]]]]], - ["IF",afterFirst,acc,identityCode]] if $until then - [untilCode,.,e]:= comp($until,$Boolean,e) - finalCode:= substitute(["UNTIL",untilCode],'$until,finalCode) - [finalCode,m,oldEnv] + [untilCode,.,e]:= comp($until,$Boolean,e) or return nil + itl := substitute(["UNTIL",untilCode],'$until,itl) + firstTime := gensym() + finalCode := ['%reduce, + ['%init,accu,'%nil],['%init,firstTime,'%true],:itl, + ['%when,[firstTime,nval],['%otherwise,accu]], + ['%bind,[[b,third bval]], + ['%when,[firstTime,move],['%otherwise,update]], + ['%store,firstTime,'%false]]] + T := coerce([finalCode,mode,e],m) or return nil + [T.expr,T.mode,oldEnv] ++ returns the identity element of the `reduction' operation `x' ++ over a list -- a monoid homomorphism. getIdentity(x,e) == - -- The empty list should be indicated by name, not by its - -- object representation. - GETL(x,"THETA") is [y] => (y => y; "nil") + GETL(x,"THETA") is [y] => + y = 0 => $Zero + y = 1 => $One + -- The empty list should be indicated by name, not by its + -- object representation. + y => y + "nil" + nil numberize x == x=$Zero => 0 diff --git a/src/interp/define.boot b/src/interp/define.boot index cc247270..d40033e0 100644 --- a/src/interp/define.boot +++ b/src/interp/define.boot @@ -501,7 +501,7 @@ compDefineCategory2(form,signature,specialCases,body,m,e, ['sublisV,['PAIR,['QUOTE,sargl],['LIST,: [['devaluate,u] for u in sargl]]],body] body:= - ["%Bind",[[g:= gensym(),body]], + ["%bind",[[g:= gensym(),body]], ["setShellEntry",g,0,mkConstructor $form],g] fun:= compile [op',["LAM",sargl,body]] diff --git a/src/interp/g-opt.boot b/src/interp/g-opt.boot index 3557f554..dae16cde 100644 --- a/src/interp/g-opt.boot +++ b/src/interp/g-opt.boot @@ -124,7 +124,7 @@ subrname u == nil changeThrowToExit(s,g) == - atom s or first s in '(QUOTE SEQ REPEAT COLLECT %collect %repeat) => nil + atom s or first s in '(QUOTE SEQ REPEAT COLLECT %collect %repeat %reduce) => nil s is ["THROW", =g,:u] => (s.first := "EXIT"; s.rest := u) changeThrowToExit(first s,g) changeThrowToExit(rest s,g) @@ -480,7 +480,7 @@ findVMFreeVars form == ++ in `form'. varIsAssigned(var,form) == isAtomicForm form => false - form is [op,=var,:.] and op in '(%LET LETT SETQ) => true + form is [op,=var,:.] and op in '(%LET LETT SETQ %store) => true or/[varIsAssigned(var,f) for f in form] ++ Subroutine of optLET. Return true if the variable `var' locally @@ -621,7 +621,7 @@ for x in '( (%Call optCall) _ (SEQ optSEQ)_ (LET optLET)_ (LET_* optLET_*)_ - (%Bind optBind)_ + (%bind optBind)_ (LIST optLIST)_ (MINUS optMINUS)_ (QSMINUS optQSMINUS)_ diff --git a/src/interp/g-util.boot b/src/interp/g-util.boot index ac31d47e..e6926643 100644 --- a/src/interp/g-util.boot +++ b/src/interp/g-util.boot @@ -200,7 +200,7 @@ expandLoop(iters,body,ret) == if bodyInits ~= nil then body := ["LET",bodyInits,body] exits := ["COND", - [mkpf(exits,"OR"),["RETURN",ret]], + [mkpf(exits,"OR"),["RETURN",expandToVMForm ret]], [true,body]] body := ["LOOP",exits,:cont] -- Finally, set up loop-wide initializations. @@ -221,6 +221,9 @@ expandCollect ["%collect",:iters,body] == expandRepeat ["%repeat",:iters,body] == expandLoop(iters,body,["voidValue"]) +expandReduce ['%reduce,:iters,val,body] == + expandLoop(iters,body,val) + expandReturn(x is ['%return,.,y]) == $FUNNAME = nil => systemErrorHere ['expandReturn,x] ['RETURN_-FROM,$FUNNAME,expandToVMForm y] @@ -334,14 +337,17 @@ for x in [ ['%string?, :'STRINGP], -- general utility - ['%hash,:'SXHASH], - ['%lam, :'LAMBDA] + ['%hash, :'SXHASH], + ['%lam, :'LAMBDA], + ['%otherwise,:'T], + ['%when, :'COND] ] repeat property(first x,'%Rename) := rest x ++ Table of opcode-expander pairs. for x in [ ["%collect",:function expandCollect], ["%repeat",:function expandRepeat], + ['%reduce, :function expandReduce], ['%return, :function expandReturn], ["%eq",:function expandEq], diff --git a/src/interp/i-map.boot b/src/interp/i-map.boot index 90db927f..a0ed9d15 100644 --- a/src/interp/i-map.boot +++ b/src/interp/i-map.boot @@ -226,7 +226,7 @@ getUserIdentifiersIn body == body = $ClearBodyToken => nil [body] body is ["WRAPPED",:.] => nil - body is [op,:itl,body1] and op in '(COLLECT REPEAT %collect) => + body is [op,:itl,body1] and op in '(COLLECT REPEAT %repeat %collect %reduce) => userIds := S_+(getUserIdentifiersInIterators itl,getUserIdentifiersIn body1) S_-(userIds,getIteratorIds itl) @@ -1026,7 +1026,7 @@ findLocalVars1(op,form) == form is ['is,l,pattern] => findLocalVars1(op,l) for var in listOfVariables rest pattern repeat mkLocalVar(op,var) - form is [oper,:itrl,body] and oper in '(REPEAT COLLECT %collect %repeat) => + form is [oper,:itrl,body] and oper in '(REPEAT COLLECT %collect %repeat %reduce) => findLocalsInLoop(op,itrl,body) form is [y,:argl] => y is "Record" or (y is "Union" and argl is [[":",.,.],:.]) => diff --git a/src/interp/i-spec1.boot b/src/interp/i-spec1.boot index f6d51ed9..c297582e 100644 --- a/src/interp/i-spec1.boot +++ b/src/interp/i-spec1.boot @@ -815,7 +815,7 @@ checkForFreeVariables(v,locals) == op in '(LAMBDA QUOTE getValueFromEnvironment) => v op = "LETT" => -- Expands to a SETQ. ["SETF",:[checkForFreeVariables(a,locals) for a in args]] - op in '(COLLECT REPEAT %collect %repeat) => + op in '(COLLECT REPEAT %collect %repeat %reduce) => first(args) is ["STEP",var,:.] => $boundVariables := [var,:$boundVariables] r := [op,:[checkForFreeVariables(a,locals) for a in args]] @@ -834,7 +834,7 @@ checkForFreeVariables(v,locals) == ["getSimpleArrayEntry","envArg",positionInVec(0,#($freeVariables))] ["SETF",newvar,checkForFreeVariables(form,locals)] error "Non-simple variable bindings are not currently supported" - op in '(LET LET_* %Bind) => + op in '(LET LET_* %bind) => vars := [first init for init in first args] inits := [checkInit(init,locals) for init in first args] where checkInit([var,init],locals) == diff --git a/src/interp/nruncomp.boot b/src/interp/nruncomp.boot index 7d24c275..71cd6a21 100644 --- a/src/interp/nruncomp.boot +++ b/src/interp/nruncomp.boot @@ -516,7 +516,7 @@ buildFunctor($definition is [name,:args],sig,code,$locals,$e) == name='Integer => nil $ConstantAssignments epilogue:= $epilogue - ans := ["%Bind",bindings, + ans := ["%bind",bindings, :washFunctorBody optFunctorBody [:codePart1,:codePart2,:codePart3],"$"] $getDomainCode:= nil diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 6842726e..d2f1df71 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2266417 . 3481665220) +(2266417 . 3485084669) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1653) +(-32 R -1385) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -1653 UP UPUP -1936) +(-40 -1385 UP UPUP -3808) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2854 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2854 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2854 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2854 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) -(-41 R -1653) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2811 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2811 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2811 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2811 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) +(-41 R -1385) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -436) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4452 . T) (-4453 . T)) -((-2854 (-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|))))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|))))))) +((-2811 (-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|))))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1653) +(-54 |Base| R -1385) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-61 -3635) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +(-61 -2058) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3635) +(-62 -2058) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -3635) +(-63 -2058) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3635) +(-64 -2058) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3635) +(-65 -2058) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3635) +(-66 -2058) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -3635) +(-67 -2058) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -3635) +(-68 -2058) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3635) +(-69 -2058) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -3635) +(-70 -2058) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -3635) +(-71 -2058) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -3635) +(-72 -2058) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -3635) +(-73 -2058) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -3635) +(-74 -2058) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -3635) +(-77 -2058) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -3635) +(-78 -2058) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3635) +(-79 -2058) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3635) +(-80 -2058) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3635) +(-81 -2058) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -3635) +(-82 -2058) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3635) +(-83 -2058) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3635) +(-84 -2058) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3635) +(-85 -2058) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3635) +(-86 -2058) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3635) +(-87 -2058) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -3635) +(-88 -2058) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -3635) +(-89 -2058) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2854 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2811 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -392,7 +392,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1653 UP) +(-116 -1385 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -403,7 +403,7 @@ NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2854 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2811 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -419,7 +419,7 @@ NIL (-122 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -439,15 +439,15 @@ NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2854 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) +((-2811 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2811 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -472,11 +472,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4454 "*") . T)) NIL -(-136 |minix| -2474 S T$) +(-136 |minix| -2183 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2474 R) +(-137 |minix| -2183 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -499,7 +499,7 @@ NIL (-142) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4452 . T) (-4442 . T) (-4453 . T)) -((-2854 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-2811 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-143 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -524,7 +524,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4449 . T)) NIL -(-149 -1653 UP UPUP) +(-149 -1385 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -564,7 +564,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-159 R -1653) +(-159 R -1385) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -598,7 +598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4448)) (|HasAttribute| |#2| (QUOTE -4451)) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4445 -2854 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3171 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-4445 -2811 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3545 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-168 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4445 -2854 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3171 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . 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T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#1| (QUOTE -4451)) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-354))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1653) +(-190 R -1385) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1653 UP UPUP R) +(-217 -1385 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-218 -1653 FP) +(-218 -1385 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-219) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2854 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2811 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1653) +(-221 R -1385) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-225 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4449 . T)) NIL -(-226 R -1653) +(-226 R -1385) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-227) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3161 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3535 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -847,7 +847,7 @@ NIL (-229 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-230 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -884,22 +884,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-239 S -2474 R) +(-239 S -2183 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) -(-240 -2474 R) +(-240 -2183 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) NIL -(-241 -2474 A B) +(-241 -2183 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-242 -2474 R) +(-242 -2183 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -919,7 +919,7 @@ NIL (-247 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-248 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -927,7 +927,7 @@ NIL (-249 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2811 (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-732))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2811 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (-2811 (|HasAttribute| |#3| (QUOTE -4449)) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-255 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -999,7 +999,7 @@ NIL (-267 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-268 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1044,11 +1044,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-279 R -1653) +(-279 R -1385) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-280 R -1653) +(-280 R -1385) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1100,7 +1100,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-293 S R |Mod| -1313 -2946 |exactQuo|) +(-293 S R |Mod| -1576 -2523 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL @@ -1122,21 +1122,21 @@ NIL NIL (-298 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-300) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-301 -1653 S) +(-301 -1385 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-302 E -1653) +(-302 E -1385) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1184,7 +1184,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-314 -1653) +(-314 -1385) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1199,7 +1199,7 @@ NIL (-317 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2854 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2854 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) +((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2811 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2811 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) (-318 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1210,9 +1210,9 @@ NIL NIL (-320 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4449 -2854 (-1754 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2854 (-1754 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 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(-1121)))) (-2811 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2811 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) +(-321 R -1385) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1223,7 +1223,7 @@ NIL (-323 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-324 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1255,12 +1255,12 @@ NIL (-331 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) -(-332 S -1653) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +(-332 S -1385) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-373)))) -(-333 -1653) +(-333 -1385) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL @@ -1284,15 +1284,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-339 S -1653 UP UPUP R) +(-339 S -1385 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-340 -1653 UP UPUP R) +(-340 -1385 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-341 -1653 UP UPUP R) +(-341 -1385 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1312,26 +1312,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-346 S -1653 UP UPUP) +(-346 S -1385 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-368)))) -(-347 -1653 UP UPUP) +(-347 -1385 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-348 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-2811 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-349 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-350 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-351 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1348,31 +1348,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-355 R UP -1653) +(-355 R UP -1385) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-356 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-2811 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-357 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-358 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-359 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-2811 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-360 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) -(-361 -1653 GF) +((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +(-361 -1385 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1380,14 +1380,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-363 -1653 FP FPP) +(-363 -1385 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-364 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1466,7 +1466,7 @@ NIL NIL (-384) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4435 . T) (-4443 . T) (-3161 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-4435 . T) (-4443 . T) (-3535 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-385 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1520,7 +1520,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-398 -1653 UP UPUP R) +(-398 -1385 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1544,11 +1544,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-404 -3635 |returnType| -4400 |symbols|) +(-404 -2058 |returnType| -4038 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-405 -1653 UP) +(-405 -1385 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1570,7 +1570,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4435)) (|HasAttribute| |#1| (QUOTE -4443))) (-410) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3161 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3535 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-411 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1583,7 +1583,7 @@ NIL (-413 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4439 -12 (|has| |#1| (-6 -4450)) (|has| |#1| (-458)) (|has| |#1| (-6 -4439))) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2854 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2811 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-414 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1604,11 +1604,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-419 R -1653 UP A) +(-419 R -1385 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) ((-4449 . T)) NIL -(-420 R -1653 UP A |ibasis|) +(-420 R -1385 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1047) (|devaluate| |#2|)))) @@ -1627,7 +1627,7 @@ NIL (-424 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) +((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) (-425 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1656,7 +1656,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4452 . T) (-4442 . T) (-4453 . T)) NIL -(-432 R -1653) +(-432 R -1385) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1664,7 +1664,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4439 -12 (|has| |#1| (-6 -4439)) (|has| |#2| (-6 -4439))) (-4446 . T) (-4447 . T) (-4449 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4439)) (|HasAttribute| |#2| (QUOTE -4439)))) -(-434 R -1653) +(-434 R -1385) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL @@ -1674,17 +1674,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-436 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4449 -2854 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) +((-4449 -2811 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) NIL -(-437 R -1653) +(-437 R -1385) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-438 R -1653) +(-438 R -1385) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-439 R -1653) +(-439 R -1385) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1692,7 +1692,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-441 R -1653 UP) +(-441 R -1385 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-48))))) @@ -1724,7 +1724,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-449 R UP -1653) +(-449 R UP -1385) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1771,7 +1771,7 @@ NIL (-460 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-461 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-477 |lv| -1653 R) +(-477 |lv| -1385 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1851,11 +1851,11 @@ NIL (-480 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . 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T)) -((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109)))) (-482 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4453 . T) (-4452 . T)) @@ -1871,7 +1871,7 @@ NIL (-485 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-486) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1879,11 +1879,11 @@ NIL (-487 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2811 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) (-489) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1891,8 +1891,8 @@ NIL (-490 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-491 -1653 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +(-491 -1385 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1903,7 +1903,7 @@ NIL (-493) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2854 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2811 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-494 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1928,7 +1928,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-500 -1653 UP |AlExt| |AlPol|) +(-500 -1385 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1939,16 +1939,16 @@ NIL (-502 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-503 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-504 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-505 R UP -1653) +(-505 R UP -1385) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1968,7 +1968,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-510 -1653 |Expon| |VarSet| |DPoly|) +(-510 -1385 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-1186))))) @@ -2019,7 +2019,7 @@ NIL (-522 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-523) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2027,15 +2027,15 @@ NIL (-524 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((-2854 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) +((-2811 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) (-525 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-526 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-527 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2047,7 +2047,7 @@ NIL (-529 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-530) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2080,7 +2080,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-538 K -1653 |Par|) +(-538 K -1385 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2104,7 +2104,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-544 K -1653 |Par|) +(-544 K -1385 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2155,12 +2155,12 @@ NIL (-556 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) -(-557 R -1653) +((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +(-557 R -1385) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-558 R0 -1653 UP UPUP R) +(-558 R0 -1385 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2170,7 +2170,7 @@ NIL NIL (-560 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3161 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3535 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-561 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2180,7 +2180,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-563 R -1653) +(-563 R -1385) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2192,7 +2192,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-566 R -1653 L) +(-566 R -1385 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -662) (|devaluate| |#2|)))) @@ -2200,11 +2200,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-568 -1653 UP UPUP R) +(-568 -1385 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-569 -1653 UP) +(-569 -1385 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL @@ -2216,15 +2216,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-572 R -1653 L) +(-572 R -1385 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -662) (|devaluate| |#2|)))) -(-573 R -1653) +(-573 R -1385) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1148)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-635))))) -(-574 -1653 UP) +(-574 -1385 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2232,27 +2232,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-576 -1653) +(-576 -1385) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-577 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-3161 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3535 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-578) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-579 R -1653) +(-579 R -1385) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-288))) (|HasCategory| |#2| (QUOTE (-635))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-288)))) (|HasCategory| |#1| (QUOTE (-562)))) -(-580 -1653 UP) +(-580 -1385 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-581 R -1653) +(-581 R -1385) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2284,11 +2284,11 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-589 R -1653) +(-589 R -1385) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-590 E -1653) +(-590 E -1385) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) NIL NIL @@ -2296,7 +2296,7 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-592 -1653) +(-592 -1385) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186))))) @@ -2327,7 +2327,7 @@ NIL (-599 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2854 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-2811 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2811 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-600 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2335,7 +2335,7 @@ NIL (-601 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) (-602 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) (((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -2352,7 +2352,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-606 R -1653 FG) +(-606 R -1385 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2363,7 +2363,7 @@ NIL (-608 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-609 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2382,12 +2382,12 @@ NIL NIL (-613 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4449 -2854 (-1754 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) -((-2854 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) +((-4449 -2811 (-2115 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-2811 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-614 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-615 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2412,7 +2412,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-621 -1653 UP) +(-621 -1385 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2440,7 +2440,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-854)))) -(-628 R -1653) +(-628 R -1385) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL @@ -2472,18 +2472,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-636 R -1653) +(-636 R -1385) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-637 |lv| -1653) +(-637 |lv| -1385) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-638) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2254) (QUOTE (-52))))))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -1409) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (QUOTE (-1109)))) (-639 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2494,8 +2494,8 @@ NIL NIL (-641 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4449 -2854 (-1754 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) -((-2854 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) +((-4449 -2811 (-2115 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-2811 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-642 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2507,7 +2507,7 @@ NIL (-644 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1741 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) +((-2104 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) (-645 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4449 . T)) @@ -2531,7 +2531,7 @@ NIL (-650 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-651 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2543,7 +2543,7 @@ NIL (-653 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-654 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2560,7 +2560,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-658 R -1653 L) +(-658 R -1385 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL @@ -2580,11 +2580,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-663 -1653 UP) +(-663 -1385 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-664 A -3906) +(-664 A -3757) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) @@ -2620,11 +2620,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4453 . T) (-4452 . T)) NIL -(-673 -1653) +(-673 -1385) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-674 -1653 |Row| |Col| M) +(-674 -1385 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2635,7 +2635,7 @@ NIL (-676 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4449 . T) (-4452 . T) (-4446 . T) (-4447 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2854 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2811 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-677) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2655,7 +2655,7 @@ NIL (-681 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-682) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2711,7 +2711,7 @@ NIL (-695 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4452 . T) (-4453 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-696 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2720,7 +2720,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-698 S -1653 FLAF FLAS) +(-698 S -1385 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2730,8 +2730,8 @@ NIL NIL (-700) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3171 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2854 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2854 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2854 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2854 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2854 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2854 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2854 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) +((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3545 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2811 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2811 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2811 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2811 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2811 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2811 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2811 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) (-701 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4453 . T)) @@ -2744,13 +2744,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-704 OV E -1653 PG) +(-704 OV E -1385 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-705) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3161 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3535 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-706 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2776,7 +2776,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-712 S -2910 I) +(-712 S -3651 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2796,14 +2796,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-717 R |Mod| -1313 -2946 |exactQuo|) +(-717 R |Mod| -1576 -2523 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-718 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-719 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2812,7 +2812,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-721 R |Mod| -1313 -2946 |exactQuo|) +(-721 R |Mod| -1576 -2523 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4449 . T)) NIL @@ -2824,7 +2824,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4447 . T) (-4446 . T)) NIL -(-724 -1653) +(-724 -1385) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) ((-4449 . T)) NIL @@ -2860,7 +2860,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-733 -1653 UP) +(-733 -1385 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2879,7 +2879,7 @@ NIL (-737 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-738 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -3012,11 +3012,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-771 -1653) +(-771 -1385) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-772 P -1653) +(-772 P -1385) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3024,7 +3024,7 @@ NIL NIL NIL NIL -(-774 UP -1653) +(-774 UP -1385) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3040,7 +3040,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4454 "*") . T)) NIL -(-778 R -1653) +(-778 R -1385) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3060,7 +3060,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-783 -1653 |ExtF| |SUEx| |ExtP| |n|) +(-783 -1385 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3075,7 +3075,7 @@ NIL (-786 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(-570))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-2104 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-2104 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-2104 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-787 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3083,7 +3083,7 @@ NIL (-788 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3144,23 +3144,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-804 -2854 R OS S) +(-804 -2811 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-805 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2854 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2811 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-806) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-807 R -1653 L) +(-807 R -1385 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-808 R -1653) +(-808 R -1385) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3168,7 +3168,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-810 R -1653) +(-810 R -1385) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3176,11 +3176,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-812 -1653 UP UPUP R) +(-812 -1385 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-813 -1653 UP L LQ) +(-813 -1385 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3188,38 +3188,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-815 -1653 UP L LQ) +(-815 -1385 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-816 -1653 UP) +(-816 -1385 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-817 -1653 L UP A LO) +(-817 -1385 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-818 -1653 UP) +(-818 -1385 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-819 -1653 LO) +(-819 -1385 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") 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The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-823 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4454 "*") |has| |#2| (-368)) (-4445 |has| |#2| (-368)) (-4450 |has| |#2| (-368)) (-4444 |has| |#2| (-368)) (-4449 . T) (-4447 . T) (-4446 . T)) @@ -3287,7 +3287,7 @@ NIL (-839 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4449 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2854 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-840 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3327,12 +3327,12 @@ NIL (-849 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4449 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2854 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-850) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-851 -2474 S) +(-851 -2183 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3368,11 +3368,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) -(-860 R |sigma| -2783) +(-860 R |sigma| -2227) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p, x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) -(-861 |x| R |sigma| -2783) +(-861 |x| R |sigma| -2227) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-368)))) @@ -3439,15 +3439,15 @@ NIL (-877 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2854 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) +((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2811 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) (-878 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2854 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2811 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-879 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-880) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3507,7 +3507,7 @@ NIL (-894 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-1741 (|HasCategory| |#2| (QUOTE (-1058)))) (-1741 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1741 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) +((-12 (-2104 (|HasCategory| |#2| (QUOTE (-1058)))) (-2104 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-2104 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-895 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3516,7 +3516,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-897 R -2910) +(-897 R -3651) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3540,7 +3540,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-903 UP -1653) +(-903 UP -1385) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3563,7 +3563,7 @@ NIL (-908 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-909 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3579,7 +3579,7 @@ NIL (-912 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4449 . T)) -((-2854 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) +((-2811 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (-913 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3600,7 +3600,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) -(-918 R0 -1653 UP UPUP R) +(-918 R0 -1385 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-925 -1653) +(-925 -1385) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3644,11 +3644,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4454 "*") . T)) NIL -(-929 -1653 P) +(-929 -1385 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-930 |xx| -1653) +(-930 |xx| -1385) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) NIL NIL @@ -3672,7 +3672,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-936 R -1653) +(-936 R -1385) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3684,7 +3684,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-939 S R -1653) +(-939 S R -1385) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3704,11 +3704,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -893) (|devaluate| |#1|)))) -(-944 R -1653 -2910) +(-944 R -1385 -3651) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-945 -2910) +(-945 -3651) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3731,7 +3731,7 @@ NIL (-950 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-951 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3756,7 +3756,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-957 E V R P -1653) +(-957 E V R P -1385) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3767,8 +3767,8 @@ NIL (-959 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-960 E V R P -1653) +((|HasCategory| |#1| (QUOTE (-916))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-960 E V R P -1385) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-458)))) @@ -3791,12 +3791,12 @@ NIL (-965 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-966) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-967 -1653) +(-967 -1385) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3811,11 +3811,11 @@ NIL (-970 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) (-971 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) ((-4449 -12 (|has| |#2| (-479)) (|has| |#1| (-479)))) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-972) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3904,7 +3904,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-994 K R UP -1653) +(-994 K R UP -1385) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -3963,11 +3963,11 @@ NIL (-1008 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4445 |has| |#1| (-294)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) (-1009 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1010 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3976,14 +3976,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1012 -1653 UP UPUP |radicnd| |n|) +(-1012 -1385 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2854 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2854 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2854 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2854 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2811 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2811 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2811 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2811 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) (-1013 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2854 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2811 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-1014) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -4016,19 +4016,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) NIL -(-1022 R -1653) +(-1022 R -1385) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1023 R -1653) +(-1023 R -1385) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1024 -1653 UP) +(-1024 -1385 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1025 -1653 UP) +(-1025 -1385 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4063,8 +4063,8 @@ NIL (-1033 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) -((-2854 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) -(-1034 -1653 L) +((-2811 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) +(-1034 -1385 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4100,14 +4100,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1043 -1653 |Expon| |VarSet| |FPol| |LFPol|) +(-1043 -1385 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1044) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2254) (QUOTE (-52))))))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -1409) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1045) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4164,7 +4164,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4449 . T)) NIL -(-1059 |xx| -1653) +(-1059 |xx| -1385) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4183,7 +4183,7 @@ NIL (-1063 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4452 . T) (-4447 . T) (-4446 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2854 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) +((|HasCategory| |#3| (QUOTE (-174))) (-2811 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) (-1064 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4219,7 +4219,7 @@ NIL (-1072) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2254) (QUOTE (-52))))))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -1409) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1073 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4268,11 +4268,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1085 |Base| R -1653) +(-1085 |Base| R -1385) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1086 |Base| R -1653) +(-1086 |Base| R -1385) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) NIL NIL @@ -4287,7 +4287,7 @@ NIL (-1089 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4445 |has| |#1| (-368)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) (-1090 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4315,7 +4315,7 @@ NIL (-1096 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1097 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4375,7 +4375,7 @@ NIL (-1111 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) ((-4452 . T) (-4442 . T) (-4453 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1112 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) 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(QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2811 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-1123 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4428,7 +4428,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1125 R -1653) +(-1125 R -1385) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4467,16 +4467,16 @@ NIL (-1134 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1135 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1136 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4453 . T) (-4452 . T)) NIL -(-1137 UP -1653) +(-1137 UP -1385) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4531,11 +4531,11 @@ NIL (-1150 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2854 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2811 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) (-1151 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4449 . T) (-4441 |has| |#2| (-6 (-4454 "*"))) (-4452 . T) (-4446 . T) (-4447 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2854 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2811 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1152 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4555,7 +4555,7 @@ NIL (-1156 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1157 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4567,7 +4567,7 @@ NIL (-1159 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109)))) (-1160) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4595,7 +4595,7 @@ NIL (-1166 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4453 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1167) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4453 . T) (-4452 . T)) @@ -4603,11 +4603,11 @@ NIL (-1168) NIL ((-4453 . T) (-4452 . 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4638,9 +4638,9 @@ NIL NIL (-1177 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4454 "*") -2854 (-1754 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-1754 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4445 -2854 (-1754 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-1754 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . 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-899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1183 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1184 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1185) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4683,7 +4683,7 @@ NIL (-1188 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . 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(|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4727,7 +4727,7 @@ NIL (-1199 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2046) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2254) (|devaluate| |#2|)))))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2854 (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3679) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1409) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2811 (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1200 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4783,7 +4783,7 @@ NIL (-1213 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4453 . T) (-4452 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1214 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4792,7 +4792,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1216 R -1653) +(-1216 R -1385) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4800,7 +4800,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1218 R -1653) +(-1218 R -1385) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -893) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -893) (|devaluate| |#1|))))) @@ -4815,7 +4815,7 @@ NIL (-1221 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1222 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) 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(|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4828,7 +4828,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-1225 -1653) +(-1225 -1385) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) 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(LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1242 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4931,7 +4931,7 @@ NIL (-1250 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4448 |has| |#2| (-368)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2854 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2854 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2854 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-1251 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4947,7 +4947,7 @@ NIL (-1254 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3838) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2940) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) (-1255 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -4975,15 +4975,15 @@ NIL (-1261 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-1262 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2854 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1263 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4454 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4445 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2854 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) +((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2811 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) (-1264 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4999,7 +4999,7 @@ NIL (-1267 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3894) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3655) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-1268 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) @@ -5007,12 +5007,12 @@ NIL (-1269 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2854 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2854 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3894) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1727) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3655) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -2421) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1270 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1271 -1653 UP L UTS) +(-1271 -1385 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-562)))) @@ -5039,7 +5039,7 @@ NIL (-1277 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4453 . T) (-4452 . T)) -((-2854 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2854 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2854 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2811 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1278) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5072,7 +5072,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1286 K R UP -1653) +(-1286 K R UP -1385) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5108,11 +5108,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-1295 S -1653) +(-1295 S -1385) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1296 -1653) +(-1296 -1385) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 1e00e24e..c5b0ea19 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(189883 . 3481665227) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) #0#) |has| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (-313 (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))))) -((((-570)) . T) (($) -2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) +(189883 . 3485084675) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) #0#) |has| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (-313 (-2 (|:| -3679 |#1|) (|:| -1409 |#2|))))) +((((-570)) . T) (($) -2811 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-570)) . T)) -((($ $) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) +((($ $) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T)) -((($) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) +((($) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) (|has| |#1| (-916)) ((((-868)) . T)) ((((-868)) . T)) @@ -24,19 +24,19 @@ ((((-227)) . T) (((-868)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T)) -(-2854 (|has| |#1| (-21)) (|has| |#1| (-854))) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -(-2854 (|has| |#1| (-826)) (|has| |#1| (-856))) +(-2811 (|has| |#1| (-21)) (|has| |#1| (-854))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +(-2811 (|has| |#1| (-826)) (|has| |#1| (-856))) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . T)) ((((-868)) . 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T) (($) -2811 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2811 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -250,10 +250,10 @@ ((((-171 (-227))) |has| |#1| (-1031)) (((-171 (-384))) |has| |#1| (-1031)) (((-542)) |has| |#1| (-620 (-542))) (((-1182 |#1|)) . T) (((-899 (-570))) |has| |#1| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384))))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . 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T)) (-12 (|has| |#4| (-235)) (|has| |#4| (-1058))) (-12 (|has| |#3| (-235)) (|has| |#3| (-1058))) -(-2854 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2854 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2811 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2811 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) @@ -271,14 +271,14 @@ (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(((|#2|) . T) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) (|has| |#1| (-562)) -((((-570)) -2854 (|has| |#4| (-174)) (|has| |#4| (-854)) (-12 (|has| |#4| (-1047 (-570))) (|has| |#4| (-1109))) (|has| |#4| (-1058))) ((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-1109))) (((-413 (-570))) -12 (|has| |#4| (-1047 (-413 (-570)))) (|has| |#4| (-1109)))) -((((-570)) -2854 (|has| |#3| (-174)) (|has| |#3| (-854)) (-12 (|has| |#3| (-1047 (-570))) (|has| |#3| (-1109))) (|has| |#3| (-1058))) ((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-1109))) (((-413 (-570))) -12 (|has| |#3| (-1047 (-413 (-570)))) (|has| |#3| (-1109)))) +((((-570)) -2811 (|has| |#4| (-174)) (|has| |#4| (-854)) (-12 (|has| |#4| (-1047 (-570))) (|has| |#4| (-1109))) (|has| |#4| (-1058))) ((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-1109))) (((-413 (-570))) -12 (|has| |#4| (-1047 (-413 (-570)))) (|has| |#4| (-1109)))) +((((-570)) -2811 (|has| |#3| (-174)) (|has| |#3| (-854)) (-12 (|has| |#3| (-1047 (-570))) (|has| |#3| (-1109))) (|has| |#3| (-1058))) ((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-1109))) (((-413 (-570))) -12 (|has| |#3| (-1047 (-413 (-570)))) (|has| |#3| (-1109)))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-562)) -(-2854 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2811 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#1|) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) @@ -291,21 +291,21 @@ ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))) ((($) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (($) . 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T)) ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570))))) -(((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) -((((-2 (|:| -2190 |#1|) (|:| -3229 |#2|))) . T)) +(((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +((((-2 (|:| -2594 |#1|) (|:| -1459 |#2|))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) @@ -313,14 +313,14 @@ (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-413 $) (-413 $)) |has| |#2| (-562)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))) . T)) +((((-2 (|:| -3679 (-1168)) (|:| -1409 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-916)) ((((-1168) (-52)) . T)) ((((-570)) |has| #0=(-413 |#2|) (-645 (-570))) ((#0#) . T)) ((((-542)) . T) (((-227)) . T) (((-384)) . T) (((-899 (-384))) . T)) ((((-868)) . T)) -(-2854 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2811 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) |has| |#1| (-174))) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) ((((-868)) . T)) @@ -334,15 +334,15 @@ (|has| |#1| (-1109)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . 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T)) (((|#1| (-980)) . T)) ((((-570)) . T) ((|#2|) . T)) @@ -352,7 +352,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1161)) -((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) +((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -364,27 +364,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) -((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . 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T)) +(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) #0#) |has| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (-313 (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))))) ((((-868)) . T)) ((((-570) |#1|) . T)) ((((-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#2| (-620 (-542)))) (((-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#2| (-620 (-899 (-384))))) (((-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#2| (-620 (-899 (-570)))))) ((($) . T)) ((((-868)) . T)) -((($ $) -2854 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2811 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -2854 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2811 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((((-868)) . T)) (|has| (-1262 |#2| |#3| |#4|) (-148)) @@ -395,16 +395,16 @@ ((((-868)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2854 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2811 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) . T)) ((((-570) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) -(-2854 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2811 (|has| |#1| (-21)) (|has| |#1| (-854))) ((((-868)) |has| |#1| (-1109))) -(-2854 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-917 |#1|)) . T)) ((((-413 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-570) |#1|))) @@ -415,7 +415,7 @@ ((((-868)) . 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T)) (((#0=(-705) (-1182 #0#)) . T)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) @@ -452,18 +452,18 @@ ((((-868)) . T) (((-1277 |#3|)) . T)) ((((-587 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) ((($) . T) (((-413 (-570))) . T)) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2854 (|has| |#1| (-174)) (|has| |#1| (-562)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2811 (|has| |#1| (-174)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) . T)) ((((-868)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((($) . T)) -((($ $) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((#1=(-1269 |#1| |#2| |#3|) #1#) |has| |#1| (-368)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . 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T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2811 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) (|has| (-1103 |#1|) (-1109)) (((|#2| (-825 |#1|)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) @@ -471,20 +471,20 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2|) . T) ((|#6|) . T)) (|has| |#1| (-368)) ((((-570)) . T) ((|#2|) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . 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T)) (|has| (-413 |#2|) (-148)) (|has| (-413 |#2|) (-146)) @@ -856,15 +856,15 @@ (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) +((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-394) (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) +((((-394) (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#2| (-1161)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) @@ -882,7 +882,7 @@ ((((-394) (-1168)) . T)) (|has| |#1| (-562)) ((((-1244 (-570)) $) . T) (((-570) |#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#2| (-854)) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) -(-2854 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-2811 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-174)) ((|#4|) . T) (((-570)) . T)) (((|#2|) |has| |#2| (-174))) @@ -1010,7 +1010,7 @@ (((|#1|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-413 (-570))) . T)) -((($) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) (|has| |#1| (-834)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (|has| |#1| (-1109)) @@ -1021,13 +1021,13 @@ (((|#4|) |has| |#4| (-1109))) (((|#3|) |has| |#3| (-1109))) (|has| |#3| (-373)) -((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2854 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) +((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) ((((-868)) . T)) ((((-868)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2854 (|has| |#1| (-368)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#1| |#1|) |has| |#1| (-174))) (|has| |#2| (-368)) @@ -1035,19 +1035,19 @@ (((|#1|) |has| |#1| (-174))) ((((-413 (-570))) . T) (((-570)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) -((($ $) -2854 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2811 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) ((($) . T) (((-570)) . 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T)) -(-2854 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +(-2811 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) (((|#1|) |has| |#1| (-174))) (|has| $ (-148)) (|has| $ (-148)) @@ -1057,15 +1057,15 @@ ((((-868)) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2854 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) ((($ $) |has| |#1| (-290 $ $)) ((|#1| $) |has| |#1| (-290 |#1| |#1|))) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-1186)) . T)) (|has| |#1| (-562)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) @@ -1077,7 +1077,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#4| (-854)) -(((|#2| (-242 (-2473 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-242 (-2865 |#1|) (-777)) (-870 |#1|)) . T)) (|has| |#3| (-854)) (((|#1| (-537 |#3|) |#3|) . T)) (|has| |#1| (-148)) @@ -1091,21 +1091,21 @@ (|has| |#1| (-148)) ((((-413 (-570))) |has| |#2| (-368)) (($) . 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T)) -(-2854 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-562)) (((|#1|) . T)) (((|#1|) . T)) @@ -1129,11 +1129,11 @@ (((|#1| (-413 (-570))) . T)) (((|#3|) . T) (((-618 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) -((((-570)) -2854 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-570)) -2811 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1141,8 +1141,8 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) |has| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (-313 (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))))) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) |has| (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|)) (-313 (-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) |has| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (-313 (-2 (|:| -3679 |#1|) (|:| -1409 |#2|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) |has| (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|)) (-313 (-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))))) ((((-868)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1156,10 +1156,10 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) ((((-570)) . T) (($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (|has| (-1103 |#1|) (-1109)) -(((|#2| |#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) -(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)))) -((((-570) (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2| |#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) +(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)))) +((((-570) (-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((((-570)) . T)) ((((-1191)) . T)) ((((-777)) . T)) @@ -1177,39 +1177,39 @@ ((((-117 |#1|)) . T)) (((|#1|) . T)) ((((-413 (-570))) . T) (($) . 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T)) (((|#1|) |has| |#1| (-313 |#1|))) @@ -1261,11 +1261,11 @@ (|has| |#1| (-373)) ((((-1186) $) |has| |#1| (-520 (-1186) $)) (($ $) |has| |#1| (-313 $)) ((|#1| |#1|) |has| |#1| (-313 |#1|)) (((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|))) ((((-1186)) |has| |#1| (-907 (-1186)))) -(-2854 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) +(-2811 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-394) |#1|) . T)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-1109)) (((|#2|) . T) (((-868)) . T)) ((((-868)) . T)) @@ -1273,8 +1273,8 @@ ((((-917 |#1|)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1283,16 +1283,16 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (((|#1| |#1|) . T)) (((#0=(-876 |#1|)) |has| #0# (-313 #0#))) -((((-570)) . 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T)) (|has| |#1| (-1212)) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) @@ -1304,8 +1304,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (|has| |#1| (-368)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -1320,29 +1320,29 @@ (((|#1| |#2|) . T)) (|has| |#1| (-854)) (|has| |#1| (-854)) -((($) . T) (((-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) -(-2854 (|has| |#1| (-174)) (|has| |#1| (-562))) +((($) . T) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((((-413 (-570))) . T) (((-413 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1182 |#1|)) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1542,8 +1542,8 @@ (((|#1|) . T) (((-570)) . T) (($) . T)) (((|#2|) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#2|) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) @@ -1556,7 +1556,7 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) #0#) |has| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (-313 (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) #0#) |has| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (-313 (-2 (|:| -3679 |#1|) (|:| -1409 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1109)) (|has| |#2| (-368)) @@ -1566,16 +1566,16 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (((|#1|) |has| |#1| (-174))) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) -((($) -2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T)) (((|#1|) . T)) ((((-1168) (-52)) . T)) (((|#1|) . T)) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . 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T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) |has| |#2| (-174))) -((($) -2854 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((-570)) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) +((($) -2811 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((-570)) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058)))) ((((-570) |#3|) . T)) ((((-570) (-145)) . T)) ((((-145)) . T)) @@ -1601,19 +1601,19 @@ (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#2|) . T)) ((((-1244 (-570)) $) . T) (((-570) (-145)) . 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T)) -(-2854 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) -(-2854 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) +(-2811 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) +(-2811 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) (((|#4|) . T)) (|has| |#1| (-146)) ((((-1168) |#1|) . T)) @@ -1627,24 +1627,24 @@ (((|#3|) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) . T)) +((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-368)))) -(((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)))) +(((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-368)))) +(((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)))) (|has| |#2| (-368)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +(((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) (((|#2|) |has| |#2| (-1058))) ((((-1168) |#1|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) @@ -1653,8 +1653,8 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-394) (-1168)) . 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T)) (|has| |#1| (-1109)) -(((|#2| (-488 (-2473 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-488 (-2865 |#1|) (-777)) (-870 |#1|)) . T)) ((((-413 (-570))) . #0=(|has| |#2| (-368))) (($) . #0#)) (((|#1| (-537 (-1186)) (-1186)) . T)) (((|#1|) . T)) @@ -1706,17 +1706,17 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) +((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((((-1186) (-52)) . T)) ((((-413 (-570)) |#1|) . T) (($ $) . T)) (((|#1| (-570)) . T)) ((((-917 |#1|)) . T)) -(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2854 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2811 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) (|has| |#1| (-856)) (|has| |#1| (-856)) @@ -1736,13 +1736,13 @@ (((|#1|) |has| |#1| (-174))) (|has| |#1| (-290 |#1| |#1|)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) -(((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)))) -((($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -(-2854 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-916))) -((($) -2854 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +(((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)))) +((($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +(-2811 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-916))) +((($) -2811 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-570) |#2|) . T)) -(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)))) (|has| |#1| (-354)) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) (((|#2|) . T) (((-570)) . T)) @@ -1751,7 +1751,7 @@ (|has| |#1| (-826)) (|has| |#1| (-826)) (((|#1|) . T)) -(-2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-854)) (|has| |#1| (-854)) (|has| |#1| (-854)) @@ -1760,14 +1760,14 @@ ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . T)) (|has| |#1| (-854)) -(((#0=(-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) #0#) |has| (-2 (|:| -2046 (-1168)) (|:| -2254 (-52))) (-313 (-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))))) +(((#0=(-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) #0#) |has| (-2 (|:| -3679 (-1168)) (|:| -1409 (-52))) (-313 (-2 (|:| -3679 (-1168)) (|:| -1409 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#1| (-1109)) ((((-868)) . T) (((-1191)) . T)) @@ -1791,11 +1791,11 @@ (((|#1| (-777) (-1091)) . T)) (((|#3|) . T)) ((((-145)) . T)) -((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) -2854 (|has| |#1| (-854)) (|has| |#1| (-1047 (-570)))) ((|#1|) . T)) +((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) -2811 (|has| |#1| (-854)) (|has| |#1| (-1047 (-570)))) ((|#1|) . T)) (((|#1|) . T)) ((((-145)) . 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T)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-1058))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) |has| (-2 (|:| -2046 |#1|) (|:| -2254 |#2|)) (-313 (-2 (|:| -2046 |#1|) (|:| -2254 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) |has| (-2 (|:| -3679 |#1|) (|:| -1409 |#2|)) (-313 (-2 (|:| -3679 |#1|) (|:| -1409 |#2|))))) (|has| |#1| (-368)) (((|#1|) |has| |#1| (-174))) (((|#1| |#1|) . T)) @@ -2150,7 +2150,7 @@ (((|#1|) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-650 $)) . T) (((-1168)) . T) (((-1186)) . T) (((-570)) . T) (((-227)) . T) (((-868)) . 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T)) +((((-2 (|:| -3679 (-1168)) (|:| -1409 (-52)))) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -2203,17 +2203,17 @@ ((((-705)) . T) (((-413 (-570))) . T) (((-570)) . T)) (((|#1| |#1|) |has| |#1| (-174))) (((|#2|) . T)) -((($) . T) (((-570)) . T) (((-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-570)) . T) (((-413 (-570))) -2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570) |#1|) . 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T)) ((((-570) |#1|) . T)) ((((-1186)) |has| (-413 |#2|) (-907 (-1186)))) -(((|#1|) . T) (($) -2854 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) +(((|#1|) . T) (($) -2811 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) ((((-542)) |has| |#2| (-620 (-542)))) ((((-695 |#2|)) . T) (((-868)) . T)) (((|#1|) . T)) @@ -2363,22 +2363,22 @@ (((|#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-876 |#1|)) . T)) (((|#1|) |has| |#1| (-174))) -(-2854 (|has| |#4| (-799)) (|has| |#4| (-854))) -(-2854 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2811 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-2811 (|has| |#3| (-799)) (|has| |#3| (-854))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . 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T)) @@ -2489,10 +2489,10 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) @@ -2502,10 +2502,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-368))) -((($) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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T)) ((((-413 (-570))) |has| |#2| (-1047 (-413 (-570)))) (((-570)) |has| |#2| (-1047 (-570))) ((|#2|) . T) (((-870 |#1|)) . T)) ((($) . T) (((-117 |#1|)) . T) (((-413 (-570))) . T)) ((((-1134 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) @@ -2563,22 +2563,22 @@ (((|#1| |#2|) . T)) ((((-1186) |#1|) . T)) (((|#4|) . T)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1186) (-52)) . T)) ((((-1262 |#2| |#3| |#4|) (-323 |#2| |#3| |#4|)) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . 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T)) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) ((((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-562)) (($) |has| |#1| (-562))) -((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) +((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) (|has| |#1| (-368)) -((($) |has| |#1| (-854)) (((-570)) -2854 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) |has| |#1| (-854)) (((-570)) -2811 (|has| |#1| (-21)) (|has| |#1| (-854)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-148)) @@ -2591,17 +2591,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2| |#3|) . T)) -(-2854 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2811 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1| (-537 |#2|)) . T)) (((|#1| (-777)) . T)) (((|#1| (-537 (-1097 (-1186)))) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (|has| |#2| (-916)) -(-2854 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2811 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-868)) . T)) -(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)))) -(((|#2|) -2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((($ $) . T) ((#0=(-1262 |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) |has| #0# (-38 (-413 (-570))))) ((((-917 |#1|)) . T)) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) @@ -2609,14 +2609,14 @@ ((((-868)) . T)) ((($) . T)) ((($) . T)) -(-2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-368)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(-2854 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2854 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2811 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) ((((-570)) |has| |#1| (-645 (-570))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-868)) . T)) @@ -2661,28 +2661,28 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#2|) . T)) -(((|#2|) -2854 (|has| |#2| (-6 (-4454 "*"))) (|has| |#2| (-174)))) -(-2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(((|#2|) -2811 (|has| |#2| (-6 (-4454 "*"))) (|has| |#2| (-174)))) +(-2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#2| (-916)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-174))) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) -((((-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))) . T)) +((((-2 (|:| -3679 (-1168)) (|:| -1409 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) -(-2854 (|has| |#1| (-294)) (|has| |#1| (-368))) +(-2811 (|has| |#1| (-294)) (|has| |#1| (-368))) ((((-145)) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (|has| |#1| (-854)) @@ -2698,7 +2698,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-189)) . T) (((-868)) . T)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -2711,7 +2711,7 @@ ((((-868)) . T)) ((((-1168)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) +((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) (|has| |#1| (-856)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) @@ -2723,16 +2723,16 @@ (((|#2|) . T)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T) (((-618 $)) . T)) -(-2854 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2854 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2811 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2811 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-1186) (-52)) . T)) -(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2854 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-916)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (|has| |#1| (-916)) @@ -2749,12 +2749,12 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#1| (-826)) (((#0=(-917 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((((-413 |#2|)) . T)) (|has| |#1| (-854)) -((((-1213 |#1|)) . T) (((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-1213 |#1|)) . T) (((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) . T) ((#1=(-570) #1#) . T) (($ $) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-1058)) (((-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) @@ -2770,29 +2770,29 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) -((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) +((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) ((((-570) |#3|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2046 (-1186)) (|:| -2254 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3679 (-1186)) (|:| -1409 #0#))) . T)) (|has| |#1| (-354)) ((((-570)) . T)) ((((-868)) . T)) (((|#1|) . T)) (((#0=(-1263 |#1| |#2| |#3| |#4|) $) |has| #0# (-290 #0# #0#))) (|has| |#1| (-368)) -(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2854 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2854 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2811 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2811 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((#0=(-1091) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) (((#0=(-413 (-570)) #0#) . T) ((#1=(-705) #1#) . T) (($ $) . T)) ((((-320 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) ((((-868)) . T)) (|has| |#1| (-1109)) (((|#1|) . T)) -(((|#1|) -2854 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) -(((|#1|) -2854 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -2811 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -2811 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) ((((-585)) . T)) @@ -2817,7 +2817,7 @@ (((|#1|) . T)) ((((-570)) . T)) (((|#2|) . T) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (($) . T) (((-570)) . T)) -(-2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2861,7 +2861,7 @@ (|has| |#2| (-1031)) ((($) . T)) (|has| |#1| (-916)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2870,10 +2870,10 @@ (|has| |#1| (-368)) ((((-917 |#1|)) . T)) ((($) . T) (((-570)) . T) ((|#1|) . T) (((-413 (-570))) . T)) -((($) -2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) |has| |#1| (-854)) (((-570)) -2854 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) -2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) |has| |#1| (-854)) (((-570)) -2811 (|has| |#1| (-21)) (|has| |#1| (-854)))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) -(-2854 (|has| |#1| (-373)) (|has| |#1| (-856))) +(-2811 (|has| |#1| (-373)) (|has| |#1| (-856))) (((|#1|) . T)) ((((-777)) . T)) ((((-868)) . T)) @@ -2884,17 +2884,17 @@ ((((-570)) . T) (($) . T)) ((((-570)) . T) (($) . T)) ((((-777) |#1|) . T)) -(((|#2| (-242 (-2473 |#1|) (-777))) . T)) +(((|#2| (-242 (-2865 |#1|) (-777))) . T)) (((|#1| (-537 |#3|)) . T)) ((((-413 (-570))) . T)) -(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-1168)) . T) (((-868)) . T)) -(((#0=(-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) #0#) |has| (-2 (|:| -2046 (-1186)) (|:| -2254 (-52))) (-313 (-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))))) +(((#0=(-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) #0#) |has| (-2 (|:| -3679 (-1186)) (|:| -1409 (-52))) (-313 (-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))))) ((((-1168)) . T)) (|has| |#1| (-916)) (|has| |#2| (-368)) (((|#1|) . T) (($) . T) (((-570)) . T)) -(-2854 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) (((|#1|) . T)) @@ -2911,11 +2911,11 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (-12 (|has| |#1| (-551)) (|has| |#1| (-834))) ((((-868)) . T)) -((((-1186)) -2854 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) +((((-1186)) -2811 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) (|has| |#1| (-368)) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) (|has| |#1| (-368)) @@ -2927,7 +2927,7 @@ (((|#2|) |has| |#1| (-368))) (((|#2|) |has| |#1| (-368))) ((((-570)) . T) (($) . T)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2956,11 +2956,11 @@ (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#2|) |has| |#1| (-368))) ((((-384)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-384)))) (((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-570))))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . T)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (((|#3|) . T)) ((((-1168)) . T) (((-512)) . T) (((-227)) . T) (((-570)) . T)) (((|#1|) . T)) @@ -2968,23 +2968,23 @@ (|has| |#1| (-562)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) -(-2854 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#2|) . T)) (((|#2|) . T)) -(-2854 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) -((((-2 (|:| -2046 (-1168)) (|:| -2254 |#1|))) . T)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +(-2811 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -3679 (-1168)) (|:| -1409 |#1|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-413 (-570)))) -(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) ((((-1168) |#1|) . T)) (|has| |#1| (-148)) -(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) -(-2854 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) (|has| |#1| (-148)) ((((-587 |#1|)) . T)) @@ -2998,7 +2998,7 @@ ((((-413 (-570))) |has| |#2| (-1047 (-570))) (((-570)) |has| |#2| (-1047 (-570))) (((-1186)) |has| |#2| (-1047 (-1186))) ((|#2|) . T)) (((#0=(-413 |#2|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2854 (|has| |#1| (-146)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-354))) (|has| |#1| (-148)) ((((-868)) . T)) ((($) . T)) @@ -3024,7 +3024,7 @@ ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3046,7 +3046,7 @@ ((((-570)) . T)) ((((-868)) . T)) ((((-570)) . T)) -(-2854 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2811 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -3058,10 +3058,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) $) . T) (((-650 (-570)) $) . T)) -(-2854 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121)) (|has| |#1| (-1109))) +(-2811 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121)) (|has| |#1| (-1109))) (|has| |#1| (-1161)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) @@ -3078,9 +3078,9 @@ (((|#1|) |has| |#1| (-313 |#1|))) ((((-570) |#1|) . T) (((-1244 (-570)) $) . T)) ((((-1186) |#1|) . T)) -(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T)) -(((|#1|) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) +(((|#1|) -2811 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) ((((-570)) . T) (((-413 (-570))) . T)) (((|#1|) . T)) (|has| |#1| (-562)) @@ -3089,14 +3089,14 @@ ((((-384)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-562)) (|has| |#1| (-1109)) ((((-786 |#1| (-870 |#2|))) |has| (-786 |#1| (-870 |#2|)) (-313 (-786 |#1| (-870 |#2|))))) -(-2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3108,13 +3108,13 @@ (|has| |#2| (-368)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((((-2 (|:| -2046 (-1168)) (|:| -2254 (-52)))) . T)) +((((-2 (|:| -3679 (-1168)) (|:| -1409 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-570)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((((-868)) . T)) -(-2854 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2811 (|has| |#3| (-799)) (|has| |#3| (-854))) ((((-868)) . T)) ((((-1129)) . T) (((-868)) . T)) ((((-542)) . T) (((-868)) . T)) @@ -3125,12 +3125,12 @@ ((((-570)) . T)) (((|#3|) . T)) ((((-868)) . T)) -(-2854 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) -((((-570)) . T) (((-413 (-570))) -2854 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570))))) ((|#2|) . T) (($) -2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-870 |#1|)) . T)) -((((-1134 |#1| |#2|)) . T) ((|#2|) . T) (($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-1182 |#1|)) . T) (((-570)) . 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T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) +((((-1182 |#1|)) . T) (((-570)) . T) (($) -2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1091)) . T) ((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +(-2811 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-1097 (-1186))) . T) (($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) (((#0=(-587 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (((|#1|) |has| |#1| (-174))) @@ -3148,7 +3148,7 @@ (((|#1|) . T)) ((((-868)) . T)) ((((-298 |#3|)) . T)) -(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -2854 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -2811 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) @@ -3156,21 +3156,21 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) -2854 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) -((($ $) -2854 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . 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T)) (((|#1|) |has| |#1| (-174))) -(-2854 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) (((|#1|) . T)) -(-2854 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-542)) . T)) @@ -3211,14 +3211,14 @@ ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-1186)) |has| |#1| (-907 (-1186)))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) -((($) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) -(((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570)))) ((|#1| |#1|) . 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T)) (|has| |#2| (-826)) (|has| |#2| (-826)) -((((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2854 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -2811 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((((-570)) |has| |#1| (-893 (-570))) (((-384)) |has| |#1| (-893 (-384)))) @@ -3255,7 +3255,7 @@ (((|#1|) . 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T)) -(-2854 (|has| |#2| (-799)) (|has| |#2| (-854))) -(-2854 (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-856)) (|has| |#2| (-856)))) +(-2811 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2811 (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-856)) (|has| |#2| (-856)))) ((((-876 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-373)) @@ -3301,7 +3301,7 @@ (((|#1|) . T)) ((((-868)) . T)) (|has| |#2| (-916)) -((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) +((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570))))) ((((-868)) . T)) ((((-868)) . T)) @@ -3328,7 +3328,7 @@ ((((-1191)) . T)) ((((-650 |#1|)) . T)) ((($) . T) (((-570)) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . 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T)) -((($) -2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) (((-1186) $) . T)) (|has| |#2| (-916)) ((((-1269 |#1| |#2| |#3|)) . T)) @@ -3666,7 +3666,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-174))) ((((-705)) . T)) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-1191)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1191)) . T)) @@ -3683,13 +3683,13 @@ ((((-1191)) . T)) ((((-1191)) . T)) ((((-1191)) . T)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1191)) . T)) ((((-1191)) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) -(-2854 (|has| |#1| (-174)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-174)) (|has| |#1| (-562))) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1| (-777)) . T)) @@ -3704,16 +3704,16 @@ ((((-899 (-384))) . T) (((-899 (-570))) . T) (((-1186)) . T) (((-542)) . T)) (((|#1|) . T)) ((((-868)) . T)) -(-2854 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-2854 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) +(-2811 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799)))) ((((-570)) . T)) ((((-570)) . T)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2854 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2811 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) -(-2854 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-2811 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-368)) @@ -3744,7 +3744,7 @@ (((|#1| |#2|) . T)) ((((-570)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-570)) . T)) -(-2854 (|has| |#1| (-354)) (|has| |#1| (-373))) +(-2811 (|has| |#1| (-354)) (|has| |#1| (-373))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-413 (-570))) . T) (($) . T) (((-570)) . T)) @@ -3756,7 +3756,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-570) $) . T) (((-650 (-570)) $) . T)) ((($) . T) (((-413 (-570))) . T)) (|has| |#1| (-916)) @@ -3768,14 +3768,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-570)) . T)) ((((-1191)) . T)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2854 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2811 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#2|) . T)) -(-2854 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2811 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -2854 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) +((((-868)) -2811 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) ((((-413 |#2|) |#3|) . T)) ((((-413 (-570))) . T) (($) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -3789,19 +3789,19 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((#0=(-570) #0#) . T)) ((($) . T) (((-413 (-570))) . T)) -(-2854 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2854 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2811 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2811 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) (|has| |#4| (-799)) -(-2854 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-2811 (|has| |#4| (-799)) (|has| |#4| (-854))) (|has| |#4| (-854)) (|has| |#3| (-799)) ((((-1191)) . T)) -(-2854 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2811 (|has| |#3| (-799)) (|has| |#3| (-854))) (|has| |#3| (-854)) ((((-570)) . T)) (((|#2|) . T)) -((((-1186)) -2854 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) +((((-1186)) -2811 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-777) |#1|))) (|has| |#1| (-907 (-1186))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3816,11 +3816,11 @@ ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-1149 |#1| |#2|)) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2|) . T) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) -((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) +((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1031)) -(((|#2|) . T) (((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) ((((-868)) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-384)) . #0=(|has| |#2| (-1031))) (((-227)) . #0#)) ((((-298 |#3|)) . T)) @@ -3837,15 +3837,15 @@ ((((-1184 |#1| |#2| |#3|)) . T)) ((((-1184 |#1| |#2| |#3|)) . T) (((-1177 |#1| |#2| |#3|)) . T)) ((((-868)) . T)) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#1|) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-368)) -(((|#3|) . T) ((|#2|) . T) (($) -2854 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2854 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) -(((|#2|) . T) (($) -2854 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2854 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) +(((|#3|) . T) ((|#2|) . T) (($) -2811 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2811 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) +(((|#2|) . T) (($) -2811 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2811 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -3859,7 +3859,7 @@ ((((-189)) . T) (((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-130)) . T) (((-868)) . T)) ((((-570) |#1|) . T) (((-1244 (-570)) $) . T)) ((((-130)) . T)) @@ -3868,13 +3868,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-368)) (|has| |#2| (-290 |#2| |#2|))) (($ $) . T) (((-570) |#1|) . T)) ((($ $) . T) (((-413 (-570)) |#1|) . T)) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) -(-2854 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) +(-2811 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-537 |#2|)) . T)) -((((-2 (|:| -2046 (-1186)) (|:| -2254 (-52)))) . T)) +((((-2 (|:| -3679 (-1186)) (|:| -1409 (-52)))) . T)) ((((-570) (-130)) . T)) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) @@ -3889,8 +3889,8 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) -(-2854 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2854 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2811 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2811 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((($) . T)) (((|#2| (-537 (-870 |#1|))) . T)) ((((-1191)) . T)) @@ -3905,13 +3905,13 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-868)) -2854 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2811 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#2| (-777)) . T)) (((|#1| |#2|) . T)) ((((-1168) |#1|) . T)) ((((-413 |#2|)) . T)) -((((-2 (|:| -2046 |#1|) (|:| -2254 |#2|))) . T)) +((((-2 (|:| -3679 |#1|) (|:| -1409 |#2|))) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) ((($) . T) ((|#2|) . T)) @@ -3922,14 +3922,14 @@ ((((-570)) . T) (($) . T)) (((|#2| $) |has| |#2| (-290 |#2| |#2|))) (((|#1| (-650 |#1|)) |has| |#1| (-854))) -(-2854 (|has| |#1| (-235)) (|has| |#1| (-354))) -(-2854 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-235)) (|has| |#1| (-354))) +(-2811 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1273 |#1|)) . T) (((-570)) . T) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) (|has| |#1| (-1109)) (((|#1|) . T)) -((((-1273 |#1|)) . T) (((-570)) . T) (($) -2854 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2854 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) +((((-1273 |#1|)) . T) (((-570)) . T) (($) -2811 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2811 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) ((((-413 (-570))) . T) (($) . T)) -((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2854 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2854 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2811 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2811 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) @@ -3945,11 +3945,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1149 |#1| |#2|) #0#) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#1|) . 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185915) ((-608 . -290) 185867) ((-611 . -619) 185834) ((-394 . -102) T) ((-1129 . -144) T) ((-127 . -619) 185766) ((-880 . -1109) T) ((-664 . -417) 185750) ((-720 . -619) 185732) ((-251 . -619) 185699) ((-189 . -619) 185681) ((-163 . -619) 185663) ((-158 . -619) 185645) ((-1292 . -732) T) ((-1111 . -34) T) ((-877 . -801) NIL) ((-877 . -798) NIL) ((-864 . -856) T) ((-737 . -893) NIL) ((-1301 . -132) T) ((-386 . -132) T) ((-899 . -622) 185613) ((-911 . -102) T) ((-737 . -1047) 185489) ((-1184 . -1227) T) ((-537 . -132) T) ((-1183 . -1227) T) ((-1096 . -417) 185473) ((-1009 . -495) 185457) ((-118 . -406) 185434) ((-1177 . -1227) T) ((-788 . -417) 185418) ((-786 . -417) 185402) ((-950 . -34) T) ((-700 . -1161) NIL) ((-254 . -654) 185237) ((-253 . -654) 185059) ((-823 . -927) 185038) ((-460 . -417) 185022) ((-608 . -19) 185006) ((-1155 . -1220) 184975) ((-1177 . -893) NIL) ((-1177 . -891) 184927) ((-608 . -610) 184904) ((-1213 . -619) 184836) ((-1185 . -619) 184818) ((-62 . -401) T) ((-1183 . -1047) 184753) ((-1177 . -1047) 184719) ((-700 . -38) 184669) ((-40 . -652) 184599) ((-480 . -290) 184557) ((-1233 . -619) 184539) ((-737 . -382) 184523) ((-844 . -619) 184505) ((-664 . -1067) T) ((-1261 . -1011) 184471) ((-1240 . -1011) 184437) ((-252 . -1227) T) ((-1097 . -622) 184421) ((-1072 . -1203) 184396) ((-1085 . -622) 184373) ((-878 . -620) 184180) ((-878 . -619) 184162) ((-1199 . -495) 184099) ((-424 . -1031) 184077) ((-48 . -313) 184064) ((-1072 . -107) 184010) ((-485 . -495) 183947) ((-526 . -1227) T) ((-1177 . -343) 183899) ((-1150 . -495) 183870) ((-1177 . -382) 183822) ((-1096 . -1067) T) ((-443 . -102) T) ((-185 . -1109) T) ((-254 . -34) T) ((-253 . -34) T) ((-788 . -1067) T) ((-786 . -1067) T) ((-737 . -907) 183799) ((-460 . -1067) T) ((-59 . -495) 183783) ((-1043 . -1065) 183757) ((-525 . -495) 183741) ((-522 . -495) 183725) ((-503 . -495) 183709) ((-502 . -495) 183693) ((-247 . -520) 183626) ((-1043 . -111) 183593) ((-1184 . -907) 183506) ((-1183 . -907) 183412) 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182045) ((-523 . -622) 182026) ((-570 . -834) T) ((-242 . -1227) T) ((-1043 . -622) 181995) ((-842 . -111) 181960) ((-833 . -111) 181939) ((-1261 . -619) 181921) ((-1240 . -619) 181903) ((-1240 . -620) 181574) ((-1182 . -916) 181553) ((-1134 . -916) 181532) ((-48 . -38) 181497) ((-1299 . -1121) T) ((-542 . -290) 181453) ((-608 . -619) 181365) ((-608 . -620) 181326) ((-1297 . -1121) T) ((-366 . -622) 181310) ((-326 . -622) 181294) ((-242 . -1047) 181121) ((-1182 . -654) 181046) ((-1134 . -654) 180971) ((-860 . -654) 180945) ((-724 . -619) 180927) ((-552 . -373) T) ((-1299 . -23) T) ((-1297 . -23) T) ((-497 . -1109) T) ((-384 . -622) 180877) ((-384 . -624) 180859) ((-1043 . -1058) T) ((-871 . -102) T) ((-1199 . -290) 180838) ((-171 . -373) 180789) ((-1013 . -1227) T) ((-842 . -622) 180743) ((-833 . -622) 180698) ((-44 . -23) T) ((-485 . -290) 180677) ((-592 . -1109) T) ((-1155 . -1118) 180646) ((-1113 . -1112) 180598) ((-396 . -21) T) ((-396 . -25) T) ((-153 . -1121) T) ((-1306 . -102) T) ((-1013 . -891) 180580) ((-1013 . -893) 180562) ((-1221 . -723) 180459) ((-629 . -233) 180443) ((-627 . -21) T) ((-293 . -562) T) ((-627 . -25) T) ((-1207 . -1109) T) ((-717 . -723) 180408) ((-242 . -382) 180377) ((-1013 . -1047) 180337) ((-384 . -1058) T) ((-225 . -1067) T) ((-118 . -233) 180314) ((-59 . -290) 180266) ((-153 . -23) T) ((-522 . -290) 180218) ((-331 . -520) 180151) ((-502 . -290) 180103) ((-384 . -245) T) ((-384 . -235) T) ((-842 . -1058) T) ((-833 . -1058) T) ((-718 . -956) 180072) ((-707 . -856) T) ((-480 . -619) 180054) ((-1263 . -1060) 179959) ((-586 . -652) 179931) ((-570 . -652) 179903) ((-501 . -652) 179853) ((-833 . -235) 179832) ((-135 . -856) T) ((-1263 . -646) 179724) ((-664 . -1109) T) ((-1199 . -610) 179703) ((-556 . -1203) 179682) ((-341 . -1109) T) ((-323 . -368) 179661) ((-413 . -148) 179640) ((-413 . -146) 179619) ((-971 . -1121) 179518) ((-242 . -907) 179450) ((-821 . -1121) 179360) ((-660 . -858) 179344) ((-485 . -610) 179323) ((-556 . -107) 179273) ((-1013 . -382) 179255) ((-1013 . -343) 179237) ((-97 . -1109) T) ((-971 . -23) 179048) ((-483 . -21) T) ((-483 . -25) T) ((-821 . -23) 178918) ((-1186 . -619) 178900) ((-59 . -19) 178884) ((-1186 . -620) 178806) ((-1182 . -732) T) ((-1134 . -732) T) ((-522 . -19) 178790) ((-502 . -19) 178774) ((-59 . -610) 178751) ((-1096 . -1109) T) ((-908 . -102) 178729) ((-860 . -732) T) ((-788 . -1109) T) ((-522 . -610) 178706) ((-502 . -610) 178683) ((-786 . -1109) T) ((-786 . -1074) 178650) ((-467 . -1109) T) ((-460 . -1109) T) ((-592 . -723) 178625) ((-655 . -1109) T) ((-1269 . -47) 178602) ((-1263 . -102) T) ((-1262 . -47) 178572) ((-1241 . -47) 178549) ((-1221 . -174) 178500) ((-1183 . -311) 178479) ((-1177 . -311) 178458) ((-1105 . -622) 178439) ((-1099 . -622) 178420) ((-1089 . -562) 178371) ((-1013 . -907) NIL) ((-1089 . -1231) 178322) ((-676 . -132) T) ((-633 . -1121) T) ((-1082 . -622) 178303) ((-1075 . -622) 178284) ((-1045 . -622) 178265) ((-1028 . -622) 178246) ((-705 . -652) 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174850) ((-227 . -732) T) ((-522 . -620) 174811) ((-522 . -619) 174723) ((-503 . -619) 174655) ((-502 . -620) 174616) ((-502 . -619) 174528) ((-1089 . -368) 174479) ((-40 . -417) 174456) ((-77 . -1227) T) ((-877 . -916) NIL) ((-364 . -333) 174440) ((-364 . -368) T) ((-358 . -333) 174424) ((-358 . -368) T) ((-350 . -333) 174408) ((-350 . -368) T) ((-320 . -288) 174387) ((-108 . -368) T) ((-70 . -1227) T) ((-1241 . -343) 174339) ((-877 . -654) 174284) ((-1241 . -382) 174236) ((-971 . -132) 174091) ((-821 . -132) 173961) ((-965 . -657) 173945) ((-1096 . -174) 173856) ((-965 . -378) 173840) ((-1071 . -800) T) ((-1071 . -797) T) ((-878 . -622) 173738) ((-788 . -174) 173629) ((-786 . -174) 173540) ((-822 . -47) 173502) ((-1071 . -732) T) ((-331 . -495) 173486) ((-959 . -732) T) ((-1290 . -313) 173424) ((-460 . -174) 173335) ((-247 . -290) 173287) ((-1269 . -907) 173200) ((-1262 . -907) 173106) ((-1261 . -1065) 172941) ((-487 . -732) T) ((-1241 . -907) 172774) ((-1240 . -1065) 172582) ((-1221 . -294) 172561) ((-1196 . -1227) T) ((-1193 . -373) T) ((-1192 . -373) T) ((-1155 . -152) 172545) ((-1129 . -102) T) ((-1127 . -1109) T) ((-1089 . -23) T) ((-1089 . -1121) T) ((-1084 . -102) T) ((-1066 . -619) 172512) ((-934 . -962) T) ((-743 . -313) 172450) ((-75 . -1227) T) ((-670 . -387) 172422) ((-171 . -916) 172375) ((-30 . -962) T) ((-112 . -850) T) ((-1 . -619) 172357) ((-1012 . -415) 172329) ((-129 . -657) 172311) ((-50 . -626) 172295) ((-700 . -652) 172230) ((-601 . -907) 172143) ((-444 . -102) T) ((-129 . -378) 172125) ((-142 . -313) NIL) ((-878 . -1058) T) ((-839 . -856) 172104) ((-81 . -1227) T) ((-717 . -294) T) ((-40 . -1067) T) ((-587 . -174) T) ((-524 . -174) T) ((-517 . -619) 172086) ((-171 . -654) 171996) ((-513 . -619) 171978) ((-356 . -148) 171960) ((-356 . -146) T) ((-364 . -1121) T) ((-358 . -1121) T) ((-350 . -1121) T) ((-1013 . -311) T) ((-921 . -311) T) ((-878 . -245) T) ((-108 . -1121) T) ((-878 . -235) 171939) ((-1261 . -111) 171760) ((-1240 . -111) 171549) 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. -562) 165479) ((-254 . -1047) 165306) ((-253 . -1047) 165133) ((-127 . -120) 165117) ((-917 . -1065) 165082) ((-718 . -102) T) ((-705 . -1067) T) ((-603 . -622) 165063) ((-591 . -622) 165044) ((-542 . -624) 164947) ((-348 . -174) T) ((-88 . -619) 164929) ((-153 . -21) T) ((-153 . -25) T) ((-917 . -111) 164885) ((-40 . -723) 164830) ((-876 . -1109) T) ((-670 . -622) 164807) ((-651 . -622) 164788) ((-360 . -622) 164725) ((-357 . -622) 164662) ((-553 . -1109) T) ((-349 . -622) 164599) ((-331 . -620) 164560) ((-331 . -619) 164472) ((-267 . -622) 164225) ((-249 . -622) 164010) ((-1240 . -798) 163963) ((-1240 . -801) 163916) ((-254 . -382) 163885) ((-253 . -382) 163854) ((-660 . -38) 163824) ((-614 . -34) T) ((-488 . -1121) 163734) ((-481 . -34) T) ((-1122 . -132) 163604) ((-971 . -25) 163415) ((-917 . -622) 163365) ((-880 . -619) 163347) ((-971 . -21) 163302) ((-821 . -21) 163212) ((-821 . -25) 163063) ((-1233 . -373) T) ((-629 . -1067) T) ((-1188 . -562) 163042) ((-1182 . -47) 163019) 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. -25) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1036 . -152) 130825) ((-878 . -826) 130804) ((-878 . -927) T) ((-718 . -290) 130731) ((-602 . -21) T) ((-344 . -652) 130690) ((-602 . -25) T) ((-601 . -21) T) ((-176 . -652) 130607) ((-40 . -732) T) ((-224 . -520) 130540) ((-601 . -25) T) ((-482 . -152) 130524) ((-469 . -152) 130508) ((-928 . -800) T) ((-928 . -732) T) ((-777 . -799) T) ((-777 . -800) T) ((-512 . -1109) T) ((-508 . -1109) T) ((-777 . -732) T) ((-227 . -368) T) ((-1299 . -1060) 130492) ((-1297 . -1060) 130476) ((-1299 . -646) 130446) ((-1166 . -1109) 130424) ((-877 . -1231) T) ((-1297 . -646) 130394) ((-660 . -619) 130376) ((-877 . -562) T) ((-700 . -373) NIL) ((-44 . -1060) 130360) ((-1306 . -622) 130342) ((-1300 . -1109) T) ((-676 . -102) T) ((-364 . -1284) 130326) ((-358 . -1284) 130310) ((-44 . -646) 130294) ((-350 . -1284) 130278) ((-554 . -102) T) ((-526 . -856) 130257) ((-1055 . -1109) T) ((-823 . -458) 130236) ((-153 . -1060) 130220) ((-1055 . -1080) 130149) 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119999) ((-839 . -417) 119983) ((-1129 . -801) T) ((-1129 . -798) T) ((-707 . -1109) T) ((-584 . -619) 119965) ((-384 . -368) T) ((-171 . -499) 119943) ((-224 . -619) 119875) ((-135 . -1109) T) ((-117 . -1109) T) ((-973 . -1227) T) ((-48 . -732) T) ((-1055 . -495) 119840) ((-142 . -431) 119822) ((-142 . -373) T) ((-1036 . -102) T) ((-518 . -515) 119801) ((-718 . -622) 119557) ((-482 . -102) T) ((-469 . -102) T) ((-1043 . -1121) T) ((-1234 . -619) 119539) ((-1191 . -1047) 119475) ((-1184 . -35) 119441) ((-1184 . -95) 119407) ((-1184 . -1215) 119373) ((-1184 . -1212) 119339) ((-1183 . -1212) 119305) ((-1168 . -313) NIL) ((-89 . -402) T) ((-89 . -401) T) ((-1089 . -1161) 119284) ((-1183 . -1215) 119250) ((-1183 . -95) 119216) ((-1043 . -23) T) ((-1183 . -35) 119182) ((-577 . -499) T) ((-1177 . -1212) 119148) ((-1177 . -1215) 119114) ((-1177 . -95) 119080) ((-1177 . -35) 119046) ((-366 . -1121) T) ((-364 . -1161) 119025) ((-358 . -1161) 119004) ((-350 . -1161) 118983) ((-1113 . -290) 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. -1060) 114008) ((-45 . -102) T) ((-823 . -102) T) ((-1188 . -646) 113905) ((-1250 . -25) T) ((-1250 . -21) T) ((-861 . -25) T) ((-44 . -372) 113889) ((-861 . -21) T) ((-737 . -458) 113840) ((-1300 . -619) 113822) ((-1289 . -1060) 113792) ((-1063 . -313) 113730) ((-677 . -1092) T) ((-612 . -1092) T) ((-396 . -1109) T) ((-577 . -25) T) ((-577 . -21) T) ((-182 . -1092) T) ((-162 . -1092) T) ((-157 . -1092) T) ((-155 . -1092) T) ((-1289 . -646) 113700) ((-627 . -1109) T) ((-705 . -893) 113682) ((-1277 . -1227) T) ((-229 . -313) 113620) ((-145 . -373) T) ((-1055 . -620) 113562) ((-1055 . -619) 113505) ((-317 . -916) NIL) ((-1235 . -850) T) ((-705 . -1047) 113450) ((-717 . -927) T) ((-480 . -1231) 113429) ((-1183 . -458) 113408) ((-1177 . -458) 113387) ((-334 . -102) T) ((-878 . -1121) T) ((-323 . -652) 113269) ((-320 . -654) 113090) ((-317 . -654) 113019) ((-480 . -562) 112970) ((-344 . -520) 112936) ((-556 . -152) 112886) ((-40 . -311) T) ((-849 . -619) 112868) ((-707 . -294) T) ((-878 . 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. -1237) 105497) ((-521 . -25) T) ((-501 . -306) T) ((-517 . -23) T) ((-516 . -25) T) ((-514 . -25) T) ((-513 . -23) T) ((-424 . -1060) 105471) ((-413 . -1058) T) ((-323 . -1067) T) ((-700 . -311) T) ((-424 . -646) 105445) ((-108 . -854) T) ((-718 . -732) T) ((-413 . -245) T) ((-413 . -235) 105424) ((-493 . -38) 105374) ((-219 . -38) 105324) ((-480 . -499) 105290) ((-1234 . -373) T) ((-1168 . -1153) T) ((-1110 . -102) T) ((-707 . -619) 105272) ((-707 . -620) 105187) ((-720 . -21) T) ((-720 . -25) T) ((-1144 . -102) T) ((-488 . -652) 104937) ((-135 . -619) 104919) ((-117 . -619) 104901) ((-158 . -25) T) ((-1299 . -1109) T) ((-878 . -645) 104849) ((-1297 . -1109) T) ((-970 . -102) T) ((-741 . -102) T) ((-721 . -102) T) ((-459 . -102) T) ((-822 . -458) 104800) ((-44 . -1109) T) ((-1097 . -856) T) ((-1072 . -313) 104651) ((-670 . -132) T) ((-1063 . -652) 104620) ((-676 . -723) 104604) ((-293 . -1067) T) ((-360 . -132) T) ((-357 . -132) T) ((-349 . -132) T) ((-267 . -132) T) ((-249 . -132) 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-657) 100403) ((-1135 . -646) 100300) ((-1221 . -562) 100279) ((-825 . -391) 100263) ((-717 . -562) T) ((-320 . -891) 100247) ((-320 . -893) 100172) ((-137 . -1227) T) ((-317 . -891) 100133) ((-317 . -893) NIL) ((-805 . -313) 100098) ((-323 . -723) 99939) ((-392 . -391) 99923) ((-328 . -327) 99900) ((-491 . -102) T) ((-480 . -25) T) ((-480 . -21) T) ((-424 . -38) 99874) ((-320 . -1047) 99537) ((-227 . -1212) T) ((-227 . -1215) T) ((-3 . -619) 99519) ((-317 . -1047) 99449) ((-2 . -1109) T) ((-2 . |RecordCategory|) T) ((-839 . -619) 99431) ((-1122 . -1067) 99361) ((-586 . -927) T) ((-570 . -826) T) ((-570 . -927) T) ((-501 . -927) T) ((-137 . -1047) 99345) ((-227 . -95) T) ((-171 . -148) 99324) ((-75 . -447) T) ((0 . -619) 99306) ((-75 . -401) T) ((-171 . -146) 99257) ((-227 . -35) T) ((-49 . -619) 99239) ((-483 . -1067) T) ((-493 . -233) 99221) ((-490 . -977) 99205) ((-488 . -854) 99184) ((-219 . -233) 99166) ((-81 . -447) T) ((-81 . -401) T) ((-1155 . -34) T) ((-821 . -174) 99145) 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-38) 98261) ((-267 . -645) 98209) ((-249 . -645) 98157) ((-707 . -1065) 98144) ((-601 . -1255) 98121) ((-1135 . -288) 98087) ((-323 . -174) 98018) ((-364 . -1109) T) ((-358 . -1109) T) ((-350 . -1109) T) ((-506 . -19) 98000) ((-1129 . -1047) 97982) ((-1111 . -152) 97966) ((-108 . -1109) T) ((-117 . -1065) 97953) ((-717 . -368) T) ((-506 . -610) 97928) ((-707 . -111) 97913) ((-442 . -102) T) ((-882 . -1272) T) ((-252 . -102) T) ((-45 . -1158) 97863) ((-117 . -111) 97848) ((-1302 . -619) 97815) ((-641 . -726) T) ((-613 . -726) T) ((-1302 . -496) 97797) ((-1279 . -619) 97779) ((-1235 . -619) 97761) ((-1233 . -856) T) ((-1221 . -1121) T) ((-821 . -520) 97694) ((-1044 . -1227) T) ((-242 . -1060) 97591) ((-1221 . -23) T) ((-1182 . -458) 97522) ((-950 . -152) 97506) ((-1177 . -313) 97391) ((-1176 . -1109) T) ((-242 . -646) 97333) ((-1168 . -1109) T) ((-1151 . -654) 97307) ((-1135 . -313) 97294) ((-531 . -102) T) ((-526 . -102) 97244) ((-1134 . -458) 97195) ((-1096 . -562) 97126) ((-1096 . -1231) 97105) ((-788 . -1231) 97084) ((-786 . -1231) 97063) ((-62 . -1227) T) ((-483 . -619) 97015) ((-483 . -620) 96937) ((-1089 . -723) 96805) ((-1003 . -1109) T) ((-788 . -562) 96716) ((-786 . -562) 96647) ((-488 . -417) 96616) ((-629 . -927) 96595) ((-460 . -1231) 96574) ((-737 . -313) 96561) ((-707 . -622) 96533) ((-404 . -619) 96515) ((-681 . -520) 96448) ((-670 . -25) T) ((-670 . -21) T) ((-460 . -562) 96379) ((-360 . -25) T) ((-360 . -21) T) ((-118 . -927) T) ((-118 . -826) NIL) ((-357 . -25) T) ((-357 . -21) T) ((-349 . -25) T) ((-349 . -21) T) ((-267 . -25) T) ((-267 . -21) T) ((-249 . -25) T) ((-249 . -21) T) ((-83 . -389) T) ((-83 . -401) T) ((-135 . -622) 96361) ((-117 . -622) 96333) ((-1013 . -1060) 96283) ((-1013 . -646) 96233) ((-950 . -989) 96217) ((-921 . -646) 96169) ((-921 . -1060) 96121) ((-917 . -21) T) ((-917 . -25) T) ((-878 . -856) 96072) ((-872 . -654) 96032) ((-717 . -1121) T) ((-717 . -23) T) ((-707 . -1058) T) ((-293 . -174) T) ((-707 . -235) T) ((-315 . 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88680) ((-483 . -1065) 88645) ((-664 . -132) T) ((-627 . -622) 88614) ((-1122 . -520) 88547) ((-341 . -132) T) ((-171 . -408) 88526) ((-488 . -723) 88468) ((-821 . -290) 88445) ((-483 . -111) 88401) ((-659 . -1067) T) ((-822 . -1060) 88244) ((-1288 . -1092) T) ((-1250 . -458) 88175) ((-822 . -646) 88024) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87966) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87899) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-1008 . -1227) 87868) ((-45 . -1109) T) ((-390 . -723) 87838) ((-823 . -1109) T) ((-482 . -520) 87771) ((-469 . -520) 87704) ((-1302 . -622) 87686) ((-459 . -372) 87656) ((-45 . -616) 87635) ((-320 . -306) T) ((-483 . -622) 87585) ((-1241 . -313) 87470) ((-676 . -619) 87432) ((-59 . -856) 87411) ((-1013 . -406) 87393) ((-554 . -619) 87375) ((-805 . -652) 87334) ((-821 . -610) 87311) ((-522 . -856) 87290) ((-502 . -856) 87269) ((-40 . -1231) T) ((-1008 . 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-313) 81728) ((-970 . -417) 81712) ((-705 . -1231) T) ((-638 . -290) 81665) ((-1096 . -645) 81613) ((-788 . -645) 81561) ((-786 . -645) 81509) ((-348 . -132) T) ((-293 . -619) 81491) ((-912 . -1109) T) ((-705 . -562) T) ((-130 . -622) 81473) ((-876 . -1121) T) ((-460 . -645) 81421) ((-912 . -910) 81405) ((-384 . -458) T) ((-493 . -1109) T) ((-950 . -313) 81343) ((-707 . -654) 81330) ((-555 . -850) T) ((-219 . -1109) T) ((-320 . -927) 81309) ((-317 . -927) T) ((-317 . -826) NIL) ((-396 . -726) T) ((-876 . -23) T) ((-117 . -654) 81296) ((-480 . -146) 81275) ((-424 . -417) 81259) ((-480 . -148) 81238) ((-110 . -495) 81220) ((-315 . -622) 81201) ((-2 . -619) 81183) ((-188 . -102) T) ((-1168 . -19) 81165) ((-1168 . -610) 81140) ((-664 . -21) T) ((-664 . -25) T) ((-599 . -1153) T) ((-1122 . -290) 81117) ((-341 . -25) T) ((-341 . -21) T) ((-242 . -652) 80867) ((-501 . -368) T) ((-1292 . -38) 80837) ((-1182 . -1060) 80660) ((-1151 . -1227) T) ((-1134 . -1060) 80503) ((-860 . -1060) 80487) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 1a1ae0b1..e6ac108b 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3481665218) +(30 . 3485084667) (4455 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -484,665 +484,665 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |raisePolynomial| |rationalPoints| |reduction| - |whileLoop| |imagj| |leftFactor| |denom| |irreducibleFactor| - |doubleResultant| |digamma| |leftTrace| |minGbasis| |normalForm| - |plot| |tanintegrate| |possiblyNewVariety?| |makeCos| |generate| - |rightTraceMatrix| |numericalIntegration| |ffactor| |f07aef| - |iterationVar| |cond| |HenselLift| |perfectNthRoot| |d01asf| |pi| - |polynomialZeros| |nthRootIfCan| |graphStates| |lookupFunction| - |solveInField| |sqfree| |totalDifferential| |log10| |shape| |infinity| - |viewDefaults| |Is| |incrementBy| |nor| |e01sef| |cCsch| - |removeSinhSq| |antisymmetricTensors| |uncouplingMatrices| |bitand| - |replaceKthElement| |closed?| |iiasec| |expand| |sparsityIF| - |OMreadStr| |unvectorise| |adjoint| |messagePrint| |eulerPhi| - |flatten| |maxPoints| |bitior| |setButtonValue| |approximants| - |OMcloseConn| |filterWhile| |map| |isobaric?| |OMgetAtp| |poisson| - |internalSubQuasiComponent?| |transcendenceDegree| |OMputString| - |checkForZero| |linearAssociatedLog| |putProperty| |kernel| - |outputBinaryFile| |filterUntil| |connectTo| |isQuotient| - |reduceByQuasiMonic| |sech2cosh| |squareFreePart| - |removeRedundantFactors| |draw| |comment| |tan2cot| |number?| |updatD| - |processTemplate| |select| |even?| |stoseInvertible?reg| |block| - |hostPlatform| |permutationGroup| |symbol| |basisOfMiddleNucleus| - |zeroDimPrime?| |outputList| |radicalEigenvector| - |commutativeEquality| |currentEnv| |difference| |e01daf| |llprop| - |f01qdf| |romberg| |setMinPoints| |expression| |airyAi| |leadingIdeal| - |d01apf| |setrest!| |decompose| |mainKernel| |OMwrite| |dmpToHdmp| - |transcendentalDecompose| |radicalSimplify| |integer| |fTable| - |extractBottom!| |roughBase?| |eisensteinIrreducible?| |convert| - |d01akf| |quoted?| |numberOfChildren| |divisor| |bivariate?| - |changeWeightLevel| |setClipValue| |check| |makeObject| |implies| - |vedf2vef| |makeSketch| |cosIfCan| |height| |closedCurve?| |rotatez| - |minColIndex| |wordInGenerators| |meshPar2Var| |setCondition!| - |changeMeasure| |coef| |harmonic| ** |scaleRoots| |setEmpty!| - |expintfldpoly| |upperCase| |parents| |leaf?| |mkIntegral| - |intcompBasis| |frobenius| |iFTable| |makeRecord| |kroneckerDelta| - |preprocess| |skewSFunction| |rewriteIdealWithRemainder| - |primitivePart| |outerProduct| |getProperties| |sturmSequence| - |removeRedundantFactorsInPols| |fprindINFO| |leftLcm| |vspace| - |acothIfCan| |argumentList!| |e02gaf| |rightGcd| |numberOfOperations| - |csc2sin| |viewPosDefault| |reciprocalPolynomial| |subresultantVector| - |const| |bracket| |low| |bat| |validExponential| |hue| |OMgetBind| - |label| |palgint| |selectIntegrationRoutines| |f2df| |torsion?| - |axesColorDefault| |lo| |writeLine!| |cAcsch| |wronskianMatrix| - |toseLastSubResultant| |sumOfSquares| |primeFrobenius| |compdegd| - |dmpToP| |useSingleFactorBound?| |incr| |polarCoordinates| - |semiIndiceSubResultantEuclidean| |product| |mapSolve| |initial| - |someBasis| |solve1| |c05adf| |acsch| |concat!| |makeSeries| - |fortranComplex| |bombieriNorm| |insertionSort!| |approxSqrt| Y - |degreePartition| |signatureAst| |trigs2explogs| - |countRealRootsMultiple| |presuper| |getProperty| |cSin| |d02raf| - |fortranReal| |OMsupportsCD?| |headRemainder| |sizeMultiplication| - |e02ddf| |cross| |removeSinSq| |dictionary| |makeYoungTableau| - |tanh2trigh| |doubleRank| |endSubProgram| |nextPrimitiveNormalPoly| - |copyInto!| |lowerCase?| |LyndonBasis| |edf2efi| |subResultantGcd| - |postfix| |countable?| |LazardQuotient2| |viewSizeDefault| - |RemainderList| |constructor| |safeCeiling| |sh| |setprevious!| - |f01qef| |ocf2ocdf| |linearAssociatedExp| |antiCommutative?| |mesh| - |hostByteOrder| |nothing| |s17dhf| |irreducible?| |gbasis| |makeTerm| - |tail| |option| |dual| |arrayStack| |showSummary| - |genericRightTraceForm| |medialSet| |supersub| |rules| |cAcos| - |redPol| |curryRight| |laurentIfCan| - |unprotectedRemoveRedundantFactors| |bandedJacobian| |e02aef| - |remainder| |radicalRoots| |tableau| |complexForm| |multiset| |f02bbf| - |listYoungTableaus| |distance| |hexDigit?| |s13aaf| - |selectODEIVPRoutines| |aCubic| |showAttributes| |setPrologue!| - |powers| |macroExpand| |hermiteH| |knownInfBasis| |f02adf| - |inverseIntegralMatrix| |changeNameToObjf| |se2rfi| |groebgen| |rk4qc| - |create3Space| |rightTrim| |iiasech| |head| - |stoseIntegralLastSubResultant| |isOpen?| |qinterval| - |generateIrredPoly| |toseInvertibleSet| |assign| |rank| |drawStyle| - |leftTrim| |yCoordinates| |unknown| |stFunc1| |prod| |pascalTriangle| - |OMclose| |listConjugateBases| |isAbsolutelyIrreducible?| - |tryFunctionalDecomposition?| |asin| |direction| |plotPolar| - |createRandomElement| |sec2cos| |atom?| |lift| |lfintegrate| |c02agf| - |pToDmp| |fmecg| |mix| F |nextPrimitivePoly| |acos| |setRealSteps| - |createPrimitiveNormalPoly| |f01bsf| |minPoints3D| |sort| |reduce| - |complementaryBasis| |cAcosh| |transcendent?| |entries| |f04jgf| |ord| - |linearDependence| |atan| |OMgetInteger| |topPredicate| - |setMinPoints3D| |say| |randomLC| |f04axf| |coefficients| |quickSort| - |acot| |rootPower| |elliptic| |linear| |numberOfVariables| - |horizConcat| |remove| |function| |removeRedundantFactorsInContents| - |alternating| |writable?| |movedPoints| |relationsIdeal| |double?| - |asec| |complexIntegrate| |resultantReduit| |decreasePrecision| - |generalizedInverse| |OMgetApp| |monomial| |operators| |explimitedint| - |setAdaptive3D| |open| |factorSFBRlcUnit| |computeBasis| |acsc| - |outputSpacing| |leftPower| |f04mcf| |polynomial| |e02ajf| |random| - |multivariate| |last| |subCase?| |eval| |heap| |reducedSystem| |lists| - |insert!| |generalInfiniteProduct| |stopTableGcd!| |sinh| |assoc| - |null| |mathieu24| |semiDiscriminantEuclidean| |variables| - |getPickedPoints| |result| |rightLcm| |hspace| |refine| |unitVector| - |regime| |cosh| |dihedralGroup| |froot| |intensity| |rename!| - |pattern| |not| |alphanumeric?| |typeLists| |returns| |reset| - |character?| |probablyZeroDim?| |scale| |subset?| |tanh| |rischDE| - |simplify| |increment| |and| |nthExpon| |gcdPolynomial| |solid| - |divisorCascade| |float?| |fortranCharacter| |exprToGenUPS| |coth| - |s14aaf| |fixedPointExquo| |parseString| |operations| |or| |orbits| - |definingEquations| |write| |innerEigenvectors| |groebner?| - |clearTheFTable| |sech| |depth| |makeCrit| |imagE| |monomRDEsys| - |rotatey| |xor| |removeSquaresIfCan| |inverseColeman| |save| |d01amf| - |roughEqualIdeals?| |lagrange| |balancedBinaryTree| |csch| - |monomialIntegrate| |c06ecf| |inverseLaplace| |message| |df2mf| |case| - |pdct| |taylor| |leadingCoefficientRicDE| |positive?| |lintgcd| - |computePowers| |asinh| |factorPolynomial| |collect| |byte| - |numFunEvals3D| |quotient| |Zero| |bitCoef| |laurent| |rename| UP2UTS - |subQuasiComponent?| |leftRegularRepresentation| |acosh| - |integralLastSubResultant| |rationalPower| |stop| |irCtor| |One| - |mainDefiningPolynomial| |puiseux| |colorFunction| |generic| - |mapExponents| |iomode| |atanh| |psolve| |deref| |leftZero| - |compBound| |c05pbf| |OMParseError?| |curve?| |getSyntaxFormsFromFile| - |formula| |belong?| |acoth| |hi| |outlineRender| |squareFree| - |unitsColorDefault| |dioSolve| |lcm| |normalizedDivide| |inv| - |cot2trig| |makeViewport3D| |lexico| |asech| |symFunc| - |drawComplexVectorField| |OMgetError| |sortConstraints| |ground?| - |sumSquares| |semiResultantEuclideannaif| |curveColorPalette| - |curryLeft| |universe| |pleskenSplit| |range| |tubePlot| - |characteristicSet| |constant| |ground| |append| - |semiDegreeSubResultantEuclidean| |contractSolve| |biRank| |scopes| - |sumOfKthPowerDivisors| |univariateSolve| |multiple| |diagonal?| - |intChoose| |noKaratsuba| |c06fuf| |zeroOf| |powerSum| |elt| - |leadingMonomial| |gcd| |removeConstantTerm| |OMgetVariable| |f04arf| - |s17adf| |applyQuote| |leadingIndex| |associator| |nrows| |ode1| - |firstDenom| |int| |conjunction| |false| |leadingCoefficient| |mindeg| - |littleEndian| |cotIfCan| |putGraph| |patternVariable| - |createMultiplicationTable| |innerSolve| |back| |ncols| |ran| - |bezoutResultant| |primitiveMonomials| |zCoord| |output| - |primPartElseUnitCanonical| |monicModulo| |basisOfRightAnnihilator| - |green| |separate| |predicates| |binomial| |meatAxe| |reducedQPowers| - |eulerE| |reductum| |constantOperator| |swapRows!| |primaryDecomp| - |cscIfCan| |intPatternMatch| |ruleset| |shallowExpand| |quotientByP| - |equiv| |numberOfHues| |showArrayValues| |hclf| |exQuo| |content| - |modulus| |numberOfIrreduciblePoly| |nextNormalPoly| |qualifier| - |fortranLogical| |hcrf| |subSet| |cAtan| |square?| - |functionIsOscillatory| |idealiserMatrix| |leftRecip| - |increasePrecision| |bitLength| |splitDenominator| - |integralBasisAtInfinity| |coth2tanh| |quote| |high| |mkcomm| |real?| - |numericIfCan| |suchThat| |kmax| |laplacian| |every?| |lfextendedint| - |transform| |sdf2lst| |leadingSupport| |nextSubsetGray| - |quasiRegular?| |overset?| |d02ejf| |setScreenResolution3D| - |internalIntegrate| |bfEntry| |singRicDE| |regularRepresentation| - |genericRightDiscriminant| |OMputObject| |linearPolynomials| - |cyclotomicDecomposition| |halfExtendedSubResultantGcd2| |invmod| - |showTheRoutinesTable| |infix| |genericPosition| |asimpson| - |normDeriv2| |ode2| |iiatanh| |OMread| |partialNumerators| - |LagrangeInterpolation| |fi2df| |getMultiplicationTable| - |rightExactQuotient| |rightFactorCandidate| |setVariableOrder| - |insertRoot!| |c06eaf| |mvar| |startTableGcd!| |printInfo!| - |functorData| |f01qcf| |diagonalMatrix| |entry?| |supDimElseRittWu?| - |acosIfCan| |getVariableOrder| |logpart| |monomRDE| |figureUnits| - |plusInfinity| |OMencodingBinary| |rotate!| |clearDenominator| - |shiftRoots| |d01gbf| |bivariatePolynomials| |exactQuotient| |lex| - |pseudoRemainder| |backOldPos| |minusInfinity| |coshIfCan| |tab1| - |semiLastSubResultantEuclidean| |updatF| |power!| |tablePow| - |wordInStrongGenerators| |mapdiv| |part?| |argument| |basisOfCentroid| - |stoseInvertibleSet| |BasicMethod| |integer?| |superscript| - |computeCycleLength| |rightCharacteristicPolynomial| |goodnessOfFit| - |integralBasis| |quartic| |rowEch| |wholeRagits| |insertMatch| |key| - |ptFunc| |algebraicSort| |irreducibleRepresentation| |stFunc2| - |genericLeftMinimalPolynomial| |OMputEndObject| |expressIdealMember| - |solve| |cartesian| |associatedSystem| |hconcat| |maximumExponent| - |ParCondList| |f04mbf| |unmakeSUP| |laguerre| - |selectOptimizationRoutines| |mainExpression| |filename| |denominator| - |quatern| |binaryTournament| |lazyPremWithDefault| |triangSolve| - |type| |univariate?| |tanQ| |hdmpToDmp| |nand| |inHallBasis?| - |OMputFloat| |iilog| |prinpolINFO| |decrease| |sort!| |f07fdf| - |setMaxPoints| |weakBiRank| |parse| |maxrank| |quasiAlgebraicSet| - |size?| |elseBranch| |linearDependenceOverZ| |limitedint| |forLoop| - |coleman| |jacobi| |next| |minimalPolynomial| |rationalFunction| - |stopTable!| |outputAsScript| |expenseOfEvaluation| |leftNorm| - |c06gqf| |variationOfParameters| |airyBi| |iflist2Result| - |pseudoDivide| |rationalApproximation| |more?| |position!| |component| - |getRef| |f01maf| |ideal| |separant| |iiacsch| |quadraticNorm| - |reseed| |cap| |putColorInfo| |tableForDiscreteLogarithm| |evaluate| - |sequences| |ramified?| |palgRDE| |startTable!| |arbitrary| |identity| - |trailingCoefficient| EQ |OMputAtp| |ScanArabic| |particularSolution| - |ramifiedAtInfinity?| |setright!| |numberOfComponents| |overbar| - |semiResultantEuclidean2| |cycleEntry| |zerosOf| - |leftMinimalPolynomial| |deleteRoutine!| |bringDown| |lhs| - |palginfieldint| FG2F |quotedOperators| |smith| |bernoulliB| |credPol| - |mainForm| |evenInfiniteProduct| |prem| |rhs| |gcdPrimitive| - |rewriteIdealWithHeadRemainder| |Aleph| |setFieldInfo| |mathieu22| - |symmetricSquare| |goto| |OMgetEndBind| |reduced?| - |basisOfRightNucleus| |pdf2ef| |splitLinear| |bumptab1| |shiftRight| - |reduceLODE| |numberOfFactors| |fixedPoints| |antisymmetric?| - |createLowComplexityNormalBasis| |isPlus| |binding| |iisin| |janko2| - |localIntegralBasis| |splitSquarefree| |currentScope| |setleft!| - |generalizedContinuumHypothesisAssumed?| |children| |omError| - |quoByVar| |sinh2csch| |constantOpIfCan| |rootSimp| |iprint| - |lowerCase| |index| |s21bbf| |cycleSplit!| |semiResultantEuclidean1| - |fractionPart| |basicSet| |maxint| |rule| |distFact| |leftRemainder| - |invertIfCan| |alphabetic?| |univcase| |modularGcdPrimitive| - |totalLex| |anticoord| |closeComponent| |pointColor| |modifyPoint| - |showFortranOutputStack| |f02abf| |isNot| |unitCanonical| - |sumOfDivisors| |symmetric?| |extendIfCan| |accuracyIF| |fibonacci| - |readUInt32!| |pair| |monomialIntPoly| |taylorQuoByVar| |csubst| - |graphCurves| |evenlambert| |value| |nullity| |expintegrate| - |branchIfCan| |numberOfMonomials| |categoryMode| |split!| |cAsinh| - |characteristicSerie| |mappingAst| |realSolve| |subMatrix| |rotate| - |imagi| |iiacosh| |seriesSolve| |generalizedEigenvector| - |normalElement| |elaborate| |datalist| |e02zaf| |compactFraction| - |mainMonomial| |cAcsc| |nonLinearPart| |lowerBound| |showTheIFTable| - |constant?| |recolor| |entry| |tube| |subResultantGcdEuclidean| - |getGraph| |select!| |rischDEsys| |loopPoints| |leftOne| |complement| - |mathieu11| |radicalSolve| |Frobenius| |atanIfCan| |doubleDisc| - |cycleLength| |setLabelValue| |pseudoQuotient| |outputMeasure| - |primextendedint| |c06gcf| |halfExtendedResultant2| |largest| - |idealSimplify| |numberOfComposites| |d02bhf| |f07fef| |sn| |makeop| - |ricDsolve| |exponential1| |repeating?| |digits| |setProperties| - |reducedDiscriminant| |dn| |rarrow| |weight| |vark| |reverse| - |coordinate| |birth| |numerators| |e02adf| |inverse| |option?| |rquo| - |pointPlot| |makingStats?| |lexGroebner| |call| |f04qaf| - |viewPhiDefault| |rootNormalize| |univariatePolynomial| |makeEq| - |extract!| |graeffe| |createZechTable| |bindings| |screenResolution3D| - |mainPrimitivePart| |c06ebf| |divide| |sup| |edf2ef| - |exprHasLogarithmicWeights| |e01bgf| |s17ajf| |setsubMatrix!| |iroot| - |useEisensteinCriterion| |tubePoints| |discriminant| |f02bjf| |iisech| - |index?| |iisqrt2| |tree| |e02ahf| |besselY| |interactiveEnv| - |mapUnivariate| |highCommonTerms| |nextPrime| |fortranInteger| - |isEquiv| |shrinkable| |sncndn| |rightUnit| |meshPar1Var| |leftGcd| - |extendedSubResultantGcd| |sinhIfCan| |sPol| |integerIfCan| - |extendedIntegrate| |binarySearchTree| |extractPoint| |matrixConcat3D| - |slash| |sizeLess?| |algebraicCoefficients?| |noLinearFactor?| - |mpsode| |rootPoly| |groebSolve| |nextItem| |typeForm| |rspace| - |OMputApp| |rischNormalize| |f01rdf| |dequeue!| |flexibleArray| - |errorKind| |readUInt16!| |traverse| |OMbindTCP| |internal?| - |quasiMonic?| |extractSplittingLeaf| |completeHermite| |subtractIfCan| - |OMputEndBind| |positiveRemainder| |defineProperty| |coerceP| - |useEisensteinCriterion?| |minPoly| |unitNormalize| |generator| - |charthRoot| |fullDisplay| |changeVar| |patternMatchTimes| - |countRealRoots| |representationType| |degreeSubResultant| |search| - |d01anf| |f02awf| |keys| |singular?| |repSq| |nary?| |factorsOfDegree| - |column| |functionIsFracPolynomial?| |rem| - |semiSubResultantGcdEuclidean1| |findBinding| |lieAdmissible?| - |sinIfCan| |region| |rdregime| |algebraic?| |exponents| |s17ahf| - |split| |quo| |maxColIndex| |fractionFreeGauss!| |d01bbf| - |symmetricRemainder| |simplifyExp| |dihedral| |inputBinaryFile| - |HermiteIntegrate| |solveRetract| |mesh?| |stack| |s17aef| - |normalDeriv| |e04gcf| |bat1| |exprHasAlgebraicWeight| |plus!| - |setTex!| |internalLastSubResultant| |internalInfRittWu?| - |exprHasWeightCosWXorSinWX| |push!| |div| |henselFact| - |basisOfLeftAnnihilator| |s18acf| |jacobiIdentity?| |addBadValue| - |virtualDegree| |viewWriteDefault| |negative?| |pointColorDefault| - |acoshIfCan| |condition| |fortranCompilerName| |powerAssociative?| - |exquo| |computeCycleEntry| |divideIfCan!| |palglimint0| |badValues| - |member?| |returnTypeOf| |open?| |setEpilogue!| |infRittWu?| - |toseInvertible?| |normInvertible?| ~= - |solveLinearPolynomialEquationByFractions| |s01eaf| |d02gaf| - |denomLODE| |Beta| |style| |OMencodingSGML| |OMsend| |bivariateSLPEBR| - |mainValue| |#| |dim| |lambert| |deepestTail| |coth2trigh| - |dualSignature| |divideExponents| |droot| |makeFloatFunction| - |uniform01| |invertible?| |nlde| |euclideanGroebner| ~ |viewport3D| - |rroot| |composites| |idealiser| |acscIfCan| |concat| - |factorsOfCyclicGroupSize| |exp1| |setOfMinN| |normalized?| |inR?| - |diagonals| |totolex| |newReduc| |s18def| |move| |matrix| |algint| - |magnitude| |lSpaceBasis| |rightDivide| |nextNormalPrimitivePoly| - |bandedHessian| |d01ajf| |cubic| |rightMult| |readLine!| |reflect| - |f02aaf| |getExplanations| |viewDeltaYDefault| |contains?| |shiftLeft| - |clearCache| |explicitlyFinite?| |dequeue| |surface| |e04dgf| - |cyclotomicFactorization| |symbolTable| |presub| |child?| |Gamma| - |generalSqFr| |jokerMode| |laplace| |OMreadFile| |innerSolve1| - |UpTriBddDenomInv| |partialQuotients| |youngGroup| - |selectNonFiniteRoutines| |augment| |thenBranch| |perfectSquare?| - |lifting| |pile| |lastSubResultantEuclidean| |padicFraction| - |subResultantChain| |standardBasisOfCyclicSubmodule| |att2Result| - |complexElementary| |symmetricProduct| |upDateBranches| - |pushFortranOutputStack| |solveLinearPolynomialEquationByRecursion| - |char| |OMgetFloat| |cRationalPower| |divergence| |toScale| |setlast!| - |fortranDouble| |failed| |level| |popFortranOutputStack| |acotIfCan| - |d02bbf| |restorePrecision| |factorSquareFreePolynomial| - |roughUnitIdeal?| |e02dff| |paren| |relativeApprox| |unravel| - |bubbleSort!| |setTopPredicate| |basisOfNucleus| |LazardQuotient| - |central?| |readable?| |distribute| |outputAsFortran| |s17agf| - |cyclicSubmodule| |subspace| |parabolicCylindrical| |linkToFortran| - |rootsOf| |e02daf| |s19abf| |pole?| |elaborateFile| |limitedIntegrate| - |controlPanel| |summation| |eigenvectors| |isMult| |nil?| - |getBadValues| |tanhIfCan| |s17dcf| |taylorIfCan| |expint| - |removeCosSq| |leadingBasisTerm| |createNormalPrimitivePoly| |f04faf| - |leftDivide| |rightFactorIfCan| |diagonalProduct| |imaginary| - |wordsForStrongGenerators| |supRittWu?| |prinb| |An| - |basisOfLeftNucloid| |maxRowIndex| |elColumn2!| - |semiSubResultantGcdEuclidean2| |changeName| |compile| - |nextIrreduciblePoly| |absolutelyIrreducible?| |B1solve| |expandPower| - |contract| |expandLog| |stopMusserTrials| |chineseRemainder| - |lazyPrem| |isExpt| |selectMultiDimensionalRoutines| |float| |polyRDE| - |nextColeman| |noValueMode| |unparse| |zero?| |deepCopy| |elem?| - |pair?| |clipBoolean| |antiAssociative?| |moebius| - |resultantEuclideannaif| |normal01| |tan2trig| - |removeSuperfluousQuasiComponents| |simplifyPower| |BumInSepFFE| - |primextintfrac| |second| |exprToXXP| |partialFraction| - |getIdentifier| |d01aqf| |mainVariable?| |derivative| - |leftRankPolynomial| |powmod| |nthCoef| |FormatArabic| - |removeSuperfluousCases| |third| |getDatabase| |minPoints| - |alphanumeric| |solid?| |categories| |enqueue!| |testDim| |varselect| - |binaryFunction| |degree| |constantRight| |imagI| |normalise| - |enterPointData| |setRow!| |mathieu23| |blue| |outputAsTex| |cAsech| - |void| |exactQuotient!| |primintegrate| |e01bhf| |generalLambert| - |gramschmidt| |row| |redPo| |string?| |stosePrepareSubResAlgo| - |genericRightMinimalPolynomial| |f01ref| |conjugate| |dimensionsOf| - |rowEchelonLocal| |node?| |setAttributeButtonStep| |measure| |expr| - |meshFun2Var| |alternatingGroup| |printTypes| |getButtonValue| - |OMconnectTCP| |consnewpol| |identification| |mapDown!| |cycle| - |recoverAfterFail| |coefficient| |encodingDirectory| |substring?| - |changeBase| |positiveSolve| |lyndon?| |removeCoshSq| |isConnected?| - |complexEigenvectors| |leviCivitaSymbol| |s21bcf| |frst| |rootOf| - |integralAtInfinity?| |randomR| |mapmult| GE |cup| |zag| |readUInt8!| - |sorted?| |currentSubProgram| |monicDivide| |OMgetSymbol| |hdmpToP| - |chvar| |showTheFTable| |suffix?| |log| |stopTableInvSet!| GT - |setFormula!| |readIfCan!| |externalList| |hasoln| |rightZero| - |Hausdorff| |internalSubPolSet?| |nonQsign| |variable| |setProperty| - |indicialEquationAtInfinity| |goodPoint| LE |relerror| |quadraticForm| - |deleteProperty!| |setImagSteps| |identitySquareMatrix| - |leastAffineMultiple| |discreteLog| |OMsupportsSymbol?| - |squareFreeFactors| |iterators| BY |minset| |prefix?| |coefChoose| LT - |removeDuplicates!| |scan| |quasiMonicPolynomials| |writeInt8!| - |exponential| |graphState| |quadratic?| |extend| |iiasinh| |argscript| - |fracPart| |cCot| |weighted| |delta| |coerceImages| |d02kef| - |multinomial| |notelem| |eof?| |clearTheSymbolTable| |polyRicDE| - |OMputError| |mirror| |chiSquare| |multiplyCoefficients| |acschIfCan| - |s18dcf| |complexNormalize| |oddlambert| |abelianGroup| |closedCurve| - |wreath| |iiatan| |possiblyInfinite?| |modTree| |d01alf| |aQuadratic| - |critM| |insertBottom!| |reverse!| |iiacoth| |pToHdmp| |tanSum| - |printStatement| |listOfMonoms| |exprToUPS| |e02bcf| |inRadical?| - |evaluateInverse| |mkPrim| |pushdown| |ScanFloatIgnoreSpacesIfCan| - |rur| |lexTriangular| |realEigenvectors| |subResultantsChain| - |exponentialOrder| |axes| |lazy?| - |rewriteIdealWithQuasiMonicGenerators| |unknownEndian| |solveid| - |binomThmExpt| |OMmakeConn| |myDegree| |infix?| |in?| |resultant| - |indices| |prepareDecompose| |tensorProduct| NOT |less?| |iipow| - |light| |createIrreduciblePoly| |UnVectorise| |mask| |normalDenom| - |primlimintfrac| |atanhIfCan| |hMonic| |c06fpf| |trueEqual| OR - |patternMatch| |basis| |asecIfCan| |cSech| |replace| |pdf2df| |d02gbf| - |sqfrFactor| |lambda| |primlimitedint| |OMputEndBVar| |bit?| AND - |nodeOf?| |drawToScale| |OMgetEndApp| |rightUnits| |infinite?| - |stoseInvertibleSetreg| |quasiComponent| |partialDenominators| - |s20adf| |rombergo| |mapUnivariateIfCan| |commutator| |OMgetEndAttr| - |queue| |quadratic| |iifact| |e02bef| |indicialEquations| |terms| - |toroidal| |dmp2rfi| |setnext!| |binary| |orthonormalBasis| - |LiePolyIfCan| |checkPrecision| |outputGeneral| - |stoseLastSubResultant| |bigEndian| |s15aef| |fill!| |debug| - |setLegalFortranSourceExtensions| |whitePoint| |subscript| |rootSplit| - |cyclePartition| |s20acf| |quasiRegular| |legendreP| |qqq| - |simplifyLog| D |safeFloor| |copy!| |musserTrials| |repeating| - |readInt8!| |latex| |directSum| |youngDiagram| |isAtom| - |nextPartition| |discriminantEuclidean| |collectUpper| |c06gbf| - |Lazard2| |useNagFunctions| |po| |e02akf| |cosSinInfo| |listexp| - |listOfLists| |topFortranOutputStack| |OMputSymbol| - |coerceListOfPairs| |tanNa| |combineFeatureCompatibility| |firstNumer| - |degreeSubResultantEuclidean| |components| |octon| |principal?| - |sizePascalTriangle| |minimumDegree| |OMgetObject| |headReduce| - |primitiveElement| |merge| |factorList| |dAndcExp| |escape| - |generalPosition| |bipolarCylindrical| |totalfract| |elementary| - |insertTop!| |socf2socdf| |polygamma| |s14baf| |lfinfieldint| * - |readInt32!| GF2FG |leadingExponent| |hasPredicate?| |complexLimit| - |rightPower| |delete!| |showRegion| |trunc| |tanh2coth| |minus!| - |doubleFloatFormat| |safetyMargin| |sign| |f02ajf| |getOperator| - |genericLeftDiscriminant| |nsqfree| |c06ekf| |optimize| |symbolIfCan| - |f04atf| |mainContent| |f04asf| |sample| |pack!| |wrregime| |center| - |invmultisect| |anfactor| |e01bef| |e04ucf| = |branchPoint?| - |triangularSystems| |copies| |squareFreePolynomial| |properties| - |firstSubsetGray| |f01mcf| |makeSUP| |print| |stripCommentsAndBlanks| - |rk4| |subNodeOf?| |element?| |completeSmith| |LyndonCoordinates| - |nodes| |translate| |explicitlyEmpty?| |complete| |gensym| |resolve| - |ratPoly| |extractTop!| < |isList| |inrootof| |cExp| |heapSort| - |pr2dmp| |prefixRagits| |localAbs| |selectfirst| > |fixPredicate| - |physicalLength| |purelyAlgebraic?| |mergeFactors| |OMputInteger| - |cSec| |prime| |internalDecompose| |OMreceive| <= |radicalEigenvalues| - |primitivePart!| |s14abf| |symbolTableOf| |nextsousResultant2| |tanAn| - |rightNorm| |typeList| |printInfo| |gderiv| |addPointLast| - |separateDegrees| |s15adf| >= |returnType!| |e01saf| |laurentRep| - |iiacot| |OMputEndError| |f02aef| |ParCond| |increase| |pomopo!| - |lllp| |leftMult| |qroot| |close!| |e04jaf| |gcdcofactprim| - |viewport2D| |getMeasure| |upperCase!| - |removeRoughlyRedundantFactorsInPol| |aQuartic| |ldf2lst| |cCos| - |diag| |OMgetEndError| |palglimint| |approxNthRoot| |ratDenom| |has?| - |cPower| |mapMatrixIfCan| + |mappingMode| |partition| |irForm| - |normal?| |true| |univariatePolynomialsGcds| |useSingleFactorBound| - |e01sbf| |capacity| - |upperBound| |numberOfFractionalTerms| - |fractRagits| |order| |extensionDegree| |sylvesterMatrix| |f02wef| - |graphs| |usingTable?| |solveLinearlyOverQ| |interpret| - |brillhartTrials| |mantissa| |writeBytes!| / |ListOfTerms| |compose| - |inGroundField?| |rightRemainder| |overlabel| |jordanAlgebra?| - |karatsubaOnce| |read!| |selectAndPolynomials| |brillhartIrreducible?| - |extendedint| |twist| |viewpoint| |rightRankPolynomial| |OMputAttr| - |ScanRoman| |OMlistCDs| |category| |algintegrate| |nil| |parametersOf| - |coord| |OMconnOutDevice| |ipow| |createPrimitivePoly| |dark| - |remove!| |localUnquote| |listRepresentation| |domain| |odd?| - |algebraicVariables| |s19aaf| |generic?| |singularAtInfinity?| - |leftFactorIfCan| |OMsetEncoding| |internalAugment| |legendre| - |disjunction| |package| |shade| |init| |viewZoomDefault| - |halfExtendedSubResultantGcd1| |multiplyExponents| |closed| - |torsionIfCan| |shift| |zeroDim?| |exprex| |numberOfCycles| - |selectsecond| |var2StepsDefault| |beauzamyBound| |approximate| - |LyndonWordsList1| |trim| |curveColor| |lyndon| |ddFact| - |chainSubResultants| |outputForm| |unexpand| |makeFR| |complex| - |e04mbf| |explogs2trigs| |viewWriteAvailable| |rowEchLocal| - |mainMonomials| |inspect| |OMUnknownSymbol?| |pureLex| |allRootsOf| - |showAll?| |inf| |reify| |solveLinearPolynomialEquation| |list?| - |cycleTail| |show| |OMgetBVar| |purelyAlgebraicLeadingMonomial?| - |showIntensityFunctions| |zeroSetSplit| |coordinates| |property| - |upperCase?| |e01sff| |environment| |varList| |logical?| - |stoseInvertible?| |denominators| |firstUncouplingMatrix| |recur| - |ratDsolve| |polygon?| |zeroDimPrimary?| |newLine| - |permutationRepresentation| |algDsolve| |resize| |trace| |geometric| - |printStats!| |printingInfo?| |initials| |nthRoot| |qPot| |empty| - |removeZeroes| |rightMinimalPolynomial| |realEigenvalues| |ignore?| - |top!| |OMgetAttr| |nullary| |parts| |bothWays| |units| |ldf2vmf| - |exponent| |pushNewContour| |localReal?| |rootBound| |minrank| - |interReduce| |drawComplex| |expextendedint| |resultantnaif| - |duplicates| |bfKeys| |df2ef| |imports| |zeroMatrix| |retract| |exp| - |branchPointAtInfinity?| |power| |finiteBound| |stoseSquareFreePart| - |commonDenominator| |numericalOptimization| |rootRadius| |factorset| - |makeMulti| |factorSquareFree| |GospersMethod| |listLoops| |any?| - |truncate| |linearlyDependentOverZ?| |seed| |createNormalElement| - |clipPointsDefault| |iiGamma| |seriesToOutputForm| |complexZeros| - |plenaryPower| |swap| |leftQuotient| |host| |module| |flagFactor| - |indiceSubResultantEuclidean| |setMaxPoints3D| |setOrder| - |intermediateResultsIF| |bumprow| |lazyEvaluate| |characteristic| - |LyndonWordsList| |code| |modifyPointData| |rightScalarTimes!| - |c05nbf| |iCompose| |initiallyReduced?| |PDESolve| |bernoulli| - |unary?| |semicolonSeparate| |prindINFO| |qelt| |rationalPoint?| - |strongGenerators| |primPartElseUnitCanonical!| |one?| |totalDegree| - |aLinear| |coHeight| |linearlyDependent?| |ScanFloatIgnoreSpaces| - |qsetelt| |setStatus!| |df2fi| |integralDerivationMatrix| - |createPrimitiveElement| |isOp| |bumptab| |freeOf?| |ceiling| - |groebnerIdeal| |cos2sec| |clearTable!| |xRange| |traceMatrix| - |modularGcd| |sechIfCan| |cycleElt| |hitherPlane| |specialTrigs| - |setref| |oblateSpheroidal| |e04naf| |multiEuclideanTree| |yRange| - |iiasin| |getStream| |atrapezoidal| |eigenvector| |front| - |OMUnknownCD?| |subPolSet?| |genericLeftTraceForm| |twoFactor| - |prevPrime| |zRange| |dom| |createNormalPoly| |Ei| |plus| - |componentUpperBound| |corrPoly| |mdeg| |minimize| |addiag| |find| - |writeUInt8!| |map!| |coerceS| |charClass| |genericLeftNorm| - |simpsono| |getMultiplicationMatrix| |inputOutputBinaryFile| |rst| - |delay| |f02agf| |f04adf| |qsetelt!| |e02bdf| |push| |iicoth| |s17akf| - |associatedEquations| |lyndonIfCan| |linearMatrix| |getCode| - |screenResolution| |stronglyReduce| |sin?| |doubleComplex?| - |OMputVariable| |isAnd| |leftScalarTimes!| |padicallyExpand| - |stirling1| |gethi| LODO2FUN |top| |hasHi| |finiteBasis| - |constantToUnaryFunction| |jacobian| |times| |definingPolynomial| - |d01fcf| |OMserve| |dflist| |ref| |iicsc| |roman| |perfectSqrt| - |title| |comp| |finite?| |subscriptedVariables| |lazyPquo| |s17dgf| - |permanent| |generalizedEigenvectors| |status| |cyclicCopy| |fortran| - |eq?| |polar| |constantLeft| |fglmIfCan| |systemCommand| |s21bdf| - |complexEigenvalues| |lastSubResultant| - |removeIrreducibleRedundantFactors| |cosh2sech| |options| |continue| - |noncommutativeJordanAlgebra?| |complexRoots| |expIfCan| |child| - |categoryFrame| |rightRank| |cCsc| |getGoodPrime| |wholeRadix| - |basisOfLeftNucleus| |cLog| |realElementary| |leftExactQuotient| - |rightRegularRepresentation| |adaptive| |euclideanNormalForm| |e| - |ranges| |erf| |e02agf| |RittWuCompare| |monom| |lowerPolynomial| - |splitNodeOf!| |node| |mapCoef| |hessian| |stoseInvertible?sqfreg| - |s21baf| |list| |f04maf| |completeEval| |lazyPseudoRemainder| - |OMunhandledSymbol| |normal| |adaptive3D?| |empty?| |string| - |rootKerSimp| |expPot| |karatsubaDivide| |complexNumericIfCan| |car| - |dot| |symbol?| |var2Steps| |f01rcf| |leastPower| - |monicRightFactorIfCan| |conical| |iicot| |certainlySubVariety?| - |bsolve| |cdr| |mat| |tubeRadius| |dilog| |rational| |common| |imagk| - |packageCall| |s13acf| |attributeData| |createMultiplicationMatrix| - |besselJ| |setDifference| |shallowCopy| |df2st| - |conditionsForIdempotents| |sin| |invertibleSet| |determinant| - |oddInfiniteProduct| |lighting| |setIntersection| |lifting1| - |resetNew| |numFunEvals| |mainCharacterization| |iExquo| |cos| - |getOrder| |functionIsContinuousAtEndPoints| |pointLists| - |basisOfCenter| |xCoord| |paraboloidal| |matrixGcd| |parametric?| - |makeSin| |setUnion| |linears| |genericRightNorm| |tan| |lfextlimint| - |dimensionOfIrreducibleRepresentation| |principalAncestors| - |enumerate| |lflimitedint| |rightRecip| - |removeRoughlyRedundantFactorsInPols| |e01baf| |apply| |pushuconst| - |isImplies| |cot| |singularitiesOf| |zeroDimensional?| - |OMencodingUnknown| |removeRoughlyRedundantFactorsInContents| |genus| - |unaryFunction| |spherical| |perspective| |moebiusMu| |cycleRagits| - |routines| |sec| |lazyIntegrate| |zero| |multiEuclidean| - |listBranches| |genericRightTrace| |double| |failed?| - |radicalEigenvectors| |solveLinear| |size| |expenseOfEvaluationIF| - |extendedResultant| |csc| |e04ycf| |mindegTerm| |commutative?| |cAcot| - |createLowComplexityTable| |width| |irVar| |script| |chebyshevT| - |rdHack1| |trapezoidalo| |extension| |subHeight| |And| |innerint| - |makeprod| |completeHensel| |coercePreimagesImages| |pquo| - |removeZero| |constDsolve| |setScreenResolution| |readBytes!| - |scanOneDimSubspaces| |Or| |pmComplexintegrate| |internalZeroSetSplit| - |algSplitSimple| |fillPascalTriangle| |pol| |s18adf| |SturmHabicht| - |first| |e02dcf| |commaSeparate| |charpol| |nextLatticePermutation| - |Not| |outputFixed| |s17def| |setPoly| |tex| |prime?| |equation| - |stFuncN| |nativeModuleExtension| |composite| |rest| |nullary?| - |pastel| |palgextint0| |clearTheIFTable| |c02aff| |round| |complex?| - |super| |headAst| |substitute| |log2| |changeThreshhold| |convergents| - |scripted?| |polyred| |resetVariableOrder| |secIfCan| |hash| - |removeDuplicates| |signAround| |f02xef| |comparison| |appendPoint| - |triangulate| |purelyTranscendental?| |outputFloating| |fixedDivisor| - |shellSort| |count| |declare!| |morphism| |nthFractionalTerm| - |rubiksGroup| |associative?| |mr| |setErrorBound| |newSubProgram| - |SturmHabichtSequence| |getCurve| |digit?| |modularFactor| |name| - |optional| |constantCoefficientRicDE| |blankSeparate| |unit?| |just| - |multiple?| |showAllElements| |UP2ifCan| |body| |cardinality| - |crushedSet| |polyPart| |maxdeg| |integerBound| |infLex?| |prinshINFO| - |infiniteProduct| |OMopenFile| |iidsum| |parent| |lazyVariations| - |viewThetaDefault| |cylindrical| |readLineIfCan!| |rk4a| |clipSurface| - |splitConstant| |elaboration| |ODESolve| |wholePart| |retractable?| - |bits| |key?| |makeResult| |debug3D| |setStatus| |null?| |lowerCase!| - |over| |autoReduced?| |printCode| |numberOfPrimitivePoly| - |initiallyReduce| |fortranLiteral| |sub| - |stoseInternalLastSubResultant| |max| |cyclic| |selectOrPolynomials| - |tryFunctionalDecomposition| |extractIfCan| |box| |startStats!| - |segment| |cTanh| |writeByte!| |error| |initTable!| |drawCurves| - SEGMENT |gradient| |cot2tan| |critB| |symmetricTensors| |port| - |generalTwoFactor| |numberOfNormalPoly| |incrementKthElement| |dec| - |xn| |balancedFactorisation| |boundOfCauchy| |assert| - |tubeRadiusDefault| |redmat| |bezoutMatrix| |s18aff| |extractProperty| - |expt| |basisOfCommutingElements| |ReduceOrder| |perfectNthPower?| - |indicialEquation| |createGenericMatrix| |collectQuasiMonic| - |lieAlgebra?| |t| |submod| |karatsuba| |maxPoints3D| |applyRules| - |linSolve| |yellow| |rightTrace| |tower| |monomials| |e02def| - |triangular?| |asechIfCan| |palgintegrate| |loadNativeModule| |f2st| - |makeVariable| |selectPolynomials| |rotatex| |measure2Result| |subst| - |s18aef| |totalGroebner| |predicate| |buildSyntax| |extendedEuclidean| - |d03edf| |monicLeftDivide| |critMTonD1| |aspFilename| |factorFraction| - |cAcoth| |var1StepsDefault| |errorInfo| |integralMatrixAtInfinity| - |OMputEndAtp| |recip| |rightOne| |limitPlus| |cyclotomic| - |mainSquareFreePart| |root?| |leastMonomial| |decomposeFunc| - |palgint0| |viewDeltaXDefault| |prolateSpheroidal| |findConstructor| - |weierstrass| |voidMode| |constantKernel| |decimal| - |generalizedContinuumHypothesisAssumed| |roughBasicSet| - |squareFreeLexTriangular| |addMatch| |complexNumeric| |transpose| - |lookup| |conjugates| |startTableInvSet!| |elliptic?| |epilogue| - |iicosh| |sylvesterSequence| |iteratedInitials| |compound?| |cons| - |stoseInvertibleSetsqfreg| |limit| |mapGen| |asinhIfCan| |permutation| - |getConstant| |reopen!| |integers| |kernels| |asinIfCan| |step| - |satisfy?| |objects| |d02cjf| |antiCommutator| |associates?| - |operator| |OMlistSymbols| |indiceSubResultant| |companionBlocks| - |nullSpace| |points| |base| |expandTrigProducts| |uniform| - |interpretString| |diophantineSystem| |rootProduct| |tracePowMod| - |makeViewport2D| |mkAnswer| |laguerreL| |bezoutDiscriminant| |factor1| - |inconsistent?| |optpair| |clipParametric| |iibinom| |integral?| - |roughSubIdeal?| |univariate| |selectSumOfSquaresRoutines| - |reducedContinuedFraction| |iiacos| |zeroSquareMatrix| |parameters| - |numeric| |setClosed| |coerce| |trace2PowMod| |setleaves!| - |rewriteSetByReducingWithParticularGenerators| |OMconnInDevice| - |deepestInitial| |repeatUntilLoop| |saturate| |radical| |merge!| - |rangePascalTriangle| |construct| |subTriSet?| |factorGroebnerBasis| - |gcdprim| |byteBuffer| |tRange| |source| |explicitEntries?| - |stiffnessAndStabilityFactor| |leftUnits| - |factorSquareFreeByRecursion| |alternative?| |pointData| - |mapBivariate| |exptMod| |factor| |mainVariable| |extractClosed| - |irDef| |setvalue!| |SturmHabichtCoefficients| |space| |sts2stst| |Ci| - |sincos| |sqrt| |thetaCoord| |iisqrt3| |schwerpunkt| - |nextsubResultant2| |digit| |cn| |critMonD1| |pushdterm| |linGenPos| - |besselI| |real| |OMputEndApp| |directory| |reverseLex| - |lazyResidueClass| |monic?| |iitanh| |precision| |d03eef| |integrate| - |imag| |cyclicParents| |eigenMatrix| |polygon| |fortranDoubleComplex| - |OMencodingXML| |OMReadError?| |yCoord| |setLength!| |systemSizeIF| - |directProduct| |diff| |getZechTable| |readInt16!| |target| |bitTruth| - |updateStatus!| |connect| |simpleBounds?| |monomial?| |external?| - |minimumExponent| |complexExpand| |vertConcat| |outputArgs| - |shanksDiscLogAlgorithm| |scalarMatrix| |rootOfIrreduciblePoly| - |groebnerFactorize| |resultantReduitEuclidean| |moreAlgebraic?| - |csch2sinh| |brace| |setPredicates| |ptree| |kind| |previous| |red| - |inverseIntegralMatrixAtInfinity| |integral| |lquo| - |differentialVariables| |lineColorDefault| |nonSingularModel| - |normFactors| |destruct| |vconcat| |swapColumns!| |op| |e02baf| - |cyclicEntries| |singleFactorBound| |makeGraphImage| |interval| - |ip4Address| |basisOfRightNucloid| |pmintegrate| |iicsch| - |OMgetString| |opeval| |minIndex| |unitNormal| |d03faf| - |symmetricGroup| |besselK| |createThreeSpace| |ravel| |leadingTerm| - |euclideanSize| |leftTraceMatrix| |cyclicGroup| |trivialIdeal?| - |reindex| |rowEchelon| |oneDimensionalArray| |radix| |reshape| - |numberOfComputedEntries| |infinityNorm| |factorByRecursion| |edf2fi| - |setelt| |bipolar| |OMgetEndAtp| |operation| |integralCoordinates| - |problemPoints| |euler| |minRowIndex| |linearAssociatedOrder| - |members| |btwFact| |diagonal| |cAtanh| |rewriteSetWithReduction| - |separateFactors| |tanIfCan| |simpson| |isTimes| |areEquivalent?| - |minordet| |randnum| |copy| |exportedOperators| |showTheSymbolTable| - |leader| |palgLODE0| |fixedPoint| UTS2UP |union| |pop!| - |hyperelliptic| |ratpart| |cothIfCan| |pushup| |Si| |isOr| - |integralRepresents| |redpps| |linearPart| |startPolynomial| - |getMatch| |lfunc| |fortranTypeOf| |invertibleElseSplit?| |prologue| - |reduceBasisAtInfinity| |kovacic| |update| |PollardSmallFactor| - |exteriorDifferential| |root| |rootDirectory| |any| |autoCoerce| - |factorOfDegree| |selectFiniteRoutines| |lastSubResultantElseSplit| - |internalIntegrate0| |rCoord| |computeInt| |factorAndSplit| - |cyclicEqual?| |vector| |identityMatrix| |norm| |lazyPseudoDivide| - |sin2csc| |normalizedAssociate| |deriv| |primitive?| |userOrdered?| - |rectangularMatrix| |differentiate| |hasTopPredicate?| |imagJ| - |midpoint| |tab| |permutations| |point?| |f01brf| |variable?| |c06fqf| - |binaryTree| |interpolate| |cCoth| |s17aff| |fullPartialFraction| - |lazyGintegrate| |dimension| |sequence| |setAdaptive| |addPoint2| - |padecf| |moduloP| |mainVariables| |edf2df| |KrullNumber| |position| - |scalarTypeOf| |irreducibleFactors| |prepareSubResAlgo| - |rightExtendedGcd| |powern| |dfRange| |npcoef| |rightQuotient| - |partitions| |match?| |normalize| |critBonD| |maxrow| |pade| - |continuedFraction| |factorials| |crest| |var1Steps| |testModulus| - |optional?| |denomRicDE| |showClipRegion| |before?| |vectorise| - |ef2edf| |OMputEndAttr| |infieldIntegrate| |cCosh| |mathieu12| - |associatorDependence| |principalIdeal| |callForm?| |divisors| |sum| - |ellipticCylindrical| |e01bff| |moduleSum| |realZeros| - |sturmVariationsOf| |f02fjf| |create| |imagK| |cyclic?| |sayLength| - |Lazard| |derivationCoordinates| |s19adf| |fortranCarriageReturn| - |logGamma| |monicRightDivide| |subresultantSequence| |symmetricPower| - |pushucoef| |completeEchelonBasis| |generators| |divideIfCan| |leaves| - |declare| |dimensions| |rightDiscriminant| |lllip| |setchildren!| - |abs| |infieldint| |withPredicates| |reducedForm| |phiCoord| |radPoly| - |lp| |hex| |choosemon| |setPosition| |whatInfinity| |trigs| |is?| - |LowTriBddDenomInv| |cycles| |complexSolve| - |numberOfImproperPartitions| |physicalLength!| |doublyTransitive?| - |cAsin| |printHeader| |colorDef| |setColumn!| |clip| |graphImage| - |arg1| |endOfFile?| |characteristicPolynomial| |conditionP| |aromberg| - |zeroSetSplitIntoTriangularSystems| |close| |hermite| |primeFactor| - |calcRanges| |arg2| |enterInCache| |write!| |orbit| |iisinh| - |squareMatrix| |tValues| |lazyIrreducibleFactors| |nthr| |chiSquare1| - |tubePointsDefault| |radicalOfLeftTraceForm| |untab| |display| F2FG - |bright| |baseRDE| |clikeUniv| |stirling2| |conditions| |length| - |eigenvalues| |initializeGroupForWordProblem| |cTan| |d01gaf| - |superHeight| |genericLeftTrace| |matrixDimensions| |groebner| |match| - |scripts| |weights| |symmetricDifference| |critpOrder| - |pointSizeDefault| |taylorRep| |neglist| |adaptive?| |factorial| - |schema| |contours| |duplicates?| |exists?| |li| |zoom| |e02bbf| - |nthFlag| |cfirst| |selectPDERoutines| |bounds| |pow| |constantIfCan| - |oddintegers| |color| |nthFactor| |numerator| |jordanAdmissible?| - |critT| |input| |swap!| |leftCharacteristicPolynomial| |represents| - |leftDiscriminant| |extractIndex| |htrigs| |domainTemplate| - |currentCategoryFrame| |library| |mainCoefficients| |leftExtendedGcd| - |integralMatrix| |newTypeLists| |clipWithRanges| |ksec| |mapExpon| - |bottom!| |curry| |polCase| |iiexp| |shuffle| |factors| |linear?| - |OMgetType| |getlo| |lprop| RF2UTS |LiePoly| |stronglyReduced?| - |logIfCan| |revert| |maxIndex| |unit| |dominantTerm| - |fortranLinkerArgs| |Nul| |f02aff| |set| |addMatchRestricted| |mulmod| - |ridHack1| |resultantEuclidean| |iisec| |inc| |monicCompleteDecompose| - |optAttributes| |algebraicDecompose| |id| |iidprod| - |semiResultantReduitEuclidean| |eyeDistance| |primes| |build| - |reorder| |addmod| |s17acf| |monicDecomposeIfCan| |SFunction| |ode| - |algebraicOf| |test| |isPower| |setValue!| |cAsec| |OMopenString| - |table| |floor| |homogeneous?| |Vectorise| |rightAlternative?| - |squareFreePrim| |leftAlternative?| |makeUnit| |insert| |new| - |equality| |iitan| |s19acf| |definingInequation| |obj| - |normalizeIfCan| |mightHaveRoots| |iiabs| |rk4f| |gcdcofact| |elRow1!| - |c06frf| |deepExpand| |cache| |s13adf| |unrankImproperPartitions1| - |f07adf| |trapezoidal| |iicos| |curve| |addPoint| |arity| - |clearFortranOutputStack| |OMputBind| |realRoots| |conjug| |lepol| - |delete| |coerceL| |eq| |signature| |structuralConstants| |point| - |normalizeAtInfinity| |prefix| |palgRDE0| |baseRDEsys| - |fortranLiteralLine| |palgLODE| |resetBadValues| |iter| |chebyshevU| - |mapUp!| |leftUnit| |middle| |putProperties| |cschIfCan| |palgextint| - |headReduced?| |hasSolution?| |setfirst!| |f02axf| - |unrankImproperPartitions0| |iiperm| |s17dlf| |showScalarValues| - |leftRank| |lazyPseudoQuotient| |mergeDifference| |alphabetic| - |hexDigit| |minPol| |series| |nextSublist| |primintfldpoly| - |univariatePolynomials| |zeroVector| |toseSquareFreePart| |OMputBVar| - |intersect| |cSinh| |argumentListOf| |fractRadix| |compiledFunction| - |SturmHabichtMultiple| |elRow2!| |badNum| |collectUnder| - |stiffnessAndStabilityOfODEIF| |resetAttributeButtons| |e04fdf| - |nthExponent| |readByte!| |subNode?| |nilFactor| |findCycle| - |getOperands| |flexible?| |qfactor| |OMgetEndBVar| |parabolic| - |setelt!| |multisect| |hypergeometric0F1| |multMonom| |arguments| - |rangeIsFinite| |left| |distdfact| |rationalIfCan| |min| |rational?| - |sinhcosh| |retractIfCan| |squareTop| |fintegrate| |overlap| - |midpoints| |c06gsf| |/\\| |right| |f02akf| |bytes| |slex| - |numberOfDivisors| |halfExtendedResultant1| |shufflein| |iiacsc| - |elements| |bag| |\\/| |checkRur| |atoms| |OMgetEndObject| |numer| - |times!| |pointColorPalette| |FormatRoman| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |primeFrobenius| |fixedPoints| |printingInfo?| + |rangePascalTriangle| |exponential| |biRank| |unaryFunction| |Beta| + |graphImage| |compdegd| |antisymmetric?| |initials| |subTriSet?| + |graphState| |spherical| |scopes| |match?| |style| |rule| |endOfFile?| + |createLowComplexityNormalBasis| |dmpToP| |autoCoerce| |nthRoot| + |quadratic?| |factorGroebnerBasis| |sumOfKthPowerDivisors| + |OMencodingSGML| |perspective| |characteristicPolynomial| + |macroExpand| |useSingleFactorBound?| |qPot| |isPlus| |gcdprim| + |extend| |initial| |univariateSolve| |moebiusMu| |OMsend| |conditionP| + |polarCoordinates| |binding| |empty| |byteBuffer| |iiasinh| + |diagonal?| |bivariateSLPEBR| |cycleRagits| |aromberg| |numeric| + |semiIndiceSubResultantEuclidean| |iisin| |removeZeroes| |tRange| + |argscript| |ravel| |intChoose| |mainValue| |routines| + |zeroSetSplitIntoTriangularSystems| |radical| |product| + |rightMinimalPolynomial| |janko2| |fracPart| |explicitEntries?| + |reshape| |close| |noKaratsuba| |lazyIntegrate| |lambert| |hermite| + |mapSolve| F |realEigenvalues| |localIntegralBasis| + |stiffnessAndStabilityFactor| |cCot| |c06fuf| |multiEuclidean| + |deepestTail| |primeFactor| |someBasis| |depth| |ignore?| + |splitSquarefree| |leftUnits| |weighted| |reverse| |box| |zeroOf| + |display| |listBranches| |coth2trigh| |calcRanges| |top!| |solve1| + |entry| |void| |currentScope| |coerceImages| + |factorSquareFreeByRecursion| |powerSum| |dualSignature| + |genericRightTrace| |enterInCache| |c05adf| |setleft!| |OMgetAttr| + |alternative?| |d02kef| |removeConstantTerm| |failed?| + |divideExponents| |write!| |concat!| + |generalizedContinuumHypothesisAssumed?| |nullary| |multinomial| + |pointData| |OMgetVariable| |update| |droot| |radicalEigenvectors| + |orbit| |makeSeries| |bothWays| |children| |mapBivariate| |notelem| + |f04arf| ** |solveLinear| |makeFloatFunction| |iisinh| |tree| + |fortranComplex| |ldf2vmf| |omError| |eof?| |exptMod| |input| |s17adf| + |expenseOfEvaluationIF| |uniform01| |squareMatrix| |bombieriNorm| + |exponent| |quoByVar| |mainVariable| |clearTheSymbolTable| + |leadingIndex| |library| |extendedResultant| |invertible?| |tValues| + |pushNewContour| |sinh2csch| |polyRicDE| |extractClosed| |associator| + |e04ycf| |nlde| |lazyIrreducibleFactors| |constantOpIfCan| + |localReal?| |irDef| |OMputError| |iiasec| |position| |ode1| + |euclideanGroebner| |mindegTerm| |nthr| |rootSimp| |rootBound| + |setvalue!| |mirror| |sparsityIF| |firstDenom| |commutative?| + |viewport3D| |chiSquare1| |even?| |iprint| |minrank| |chiSquare| + |SturmHabichtCoefficients| |set| |cAcot| |rroot| |tubePointsDefault| + |stoseInvertible?reg| |interReduce| |lowerCase| |space| + |multiplyCoefficients| |rename!| |createLowComplexityTable| + |composites| |radicalOfLeftTraceForm| |block| |drawComplex| |s21bbf| + |acschIfCan| |sts2stst| |alphanumeric?| |idealiser| |irVar| |untab| + |hostPlatform| |properties| |expextendedint| |cycleSplit!| |Ci| + |s18dcf| |typeLists| |chebyshevT| |acscIfCan| F2FG |expr| + |permutationGroup| |sincos| |complexNormalize| |translate| |returns| + |factorsOfCyclicGroupSize| |rdHack1| |baseRDE| |basisOfMiddleNucleus| + |nand| |karatsubaOnce| |thetaCoord| |oddlambert| |character?| |exp1| + |trapezoidalo| |true| |clikeUniv| |raisePolynomial| |zeroDimPrime?| + |read!| |inHallBasis?| |iisqrt3| |abelianGroup| |probablyZeroDim?| + |stirling2| |extension| |setOfMinN| |category| |size| |rationalPoints| + |radicalEigenvector| |OMputFloat| |selectAndPolynomials| |schwerpunkt| + |closedCurve| |scale| |brillhartIrreducible?| |eigenvalues| |variable| + |domain| |commutativeEquality| |iilog| |reduction| |wreath| + |nextsubResultant2| |cLog| |subset?| |insert| |traverse| |package| + |whileLoop| |initializeGroupForWordProblem| |iterators| |precision| + |difference| |prinpolINFO| |extendedint| |digit| |iiatan| |rischDE| + |realElementary| |OMbindTCP| |cTan| |decrease| |e01daf| |twist| + |imagj| |critMonD1| |possiblyInfinite?| |leftExactQuotient| |simplify| + |internal?| |show| |d01gaf| |sort!| |llprop| |leftFactor| |viewpoint| + |rightRegularRepresentation| |increment| |quasiMonic?| |varList| + |irreducibleFactor| |superHeight| |rightRankPolynomial| |f01qdf| + |f07fdf| |lp| |cAcoth| |mathieu23| |adaptive| |nthExpon| + |extractSplittingLeaf| |trace| |genericLeftTrace| |doubleResultant| + |romberg| |OMputAttr| |setMaxPoints| |blue| |var1StepsDefault| + |gcdPolynomial| |euclideanNormalForm| |completeHermite| |matrix| + |matrixDimensions| |weakBiRank| |setMinPoints| |ScanRoman| |digamma| + |errorInfo| |outputAsTex| |solid| |subtractIfCan| |ranges| |leftTrace| + |airyAi| |OMlistCDs| |maxrank| |integralMatrixAtInfinity| |cAsech| + |divisorCascade| |e02agf| |OMputEndBind| |irreducibleFactors| + |minGbasis| |leadingIdeal| |algintegrate| |quasiAlgebraicSet| + |OMputEndAtp| |exactQuotient!| |float?| |positiveRemainder| + |RittWuCompare| |prepareSubResAlgo| |size?| |d01apf| |normalForm| + |parametersOf| |primintegrate| |recip| |fortranCharacter| + |lowerPolynomial| |defineProperty| |rightExtendedGcd| |elseBranch| + |setrest!| |coord| |plot| |rightOne| |e01bhf| |exprToGenUPS| |coerceP| + |splitNodeOf!| |powern| |tanintegrate| |decompose| |OMconnOutDevice| + |linearDependenceOverZ| |limitPlus| |generalLambert| |subNode?| + |s14aaf| |mapCoef| |useEisensteinCriterion?| |dfRange| |ipow| + |mainKernel| |limitedint| |possiblyNewVariety?| |cyclotomic| + |gramschmidt| |nilFactor| |fixedPointExquo| |minPoly| |hessian| + |npcoef| |forLoop| |OMwrite| |createPrimitivePoly| |makeCos| |row| + |mainSquareFreePart| |findCycle| |parseString| |unitNormalize| + |stoseInvertible?sqfreg| |rightQuotient| |rightTraceMatrix| + |dmpToHdmp| |dark| |coleman| |redPo| |root?| |getOperands| |orbits| + |s21baf| |charthRoot| |log10| |partitions| |jacobi| + |transcendentalDecompose| |numericalIntegration| |remove!| + |leastMonomial| |string?| |flexible?| |definingEquations| + |fullDisplay| |f04maf| |normalize| |bitand| |localUnquote| + |radicalSimplify| |ffactor| |minimalPolynomial| + |stosePrepareSubResAlgo| |decomposeFunc| |qfactor| |completeEval| + |innerEigenvectors| |plus| |changeVar| |critBonD| |bitior| |fTable| + |f07aef| |listRepresentation| |rationalFunction| + |genericRightMinimalPolynomial| |palgint0| |OMgetEndBVar| |groebner?| + |lazyPseudoRemainder| |patternMatchTimes| |maxrow| |obj| + |extractBottom!| |odd?| |stopTable!| |iterationVar| |f01ref| + |viewDeltaXDefault| |parabolic| |clearTheFTable| |OMunhandledSymbol| + |countRealRoots| |pade| |HenselLift| |cache| |roughBase?| + |outputAsScript| |algebraicVariables| |prolateSpheroidal| |conjugate| + |setelt!| |makeCrit| |representationType| |adaptive3D?| + |continuedFraction| |expenseOfEvaluation| |eisensteinIrreducible?| + |perfectNthRoot| |s19aaf| |findConstructor| |dimensionsOf| |multisect| + |imagE| |times| |degreeSubResultant| |empty?| |factorials| |leftNorm| + |d01akf| |d01asf| |generic?| |rowEchelonLocal| |weierstrass| + |hypergeometric0F1| |monomRDEsys| |rootKerSimp| |d01anf| |crest| + |polynomialZeros| |quoted?| |singularAtInfinity?| |c06gqf| |voidMode| + |node?| |multMonom| |rotatey| |expPot| |f02awf| |var1Steps| + |numberOfChildren| |variationOfParameters| |nthRootIfCan| + |leftFactorIfCan| |setAttributeButtonStep| |constantKernel| + |rangeIsFinite| |declare!| |removeSquaresIfCan| |singular?| + |karatsubaDivide| |testModulus| |divisor| |OMsetEncoding| |airyBi| + |graphStates| |decimal| |measure| |distdfact| |repSq| |inverseColeman| + |complexNumericIfCan| |monom| |optional?| |iflist2Result| |bivariate?| + |lookupFunction| |internalAugment| + |generalizedContinuumHypothesisAssumed| |meshFun2Var| |rationalIfCan| + |d01amf| |nary?| |car| |denomRicDE| |shift| |changeWeightLevel| + |solveInField| |legendre| |pseudoDivide| |alternatingGroup| + |roughBasicSet| |rational?| |print| |roughEqualIdeals?| + |factorsOfDegree| |dot| |showClipRegion| |dom| |setClipValue| + |rationalApproximation| |sqfree| |disjunction| + |squareFreeLexTriangular| |printTypes| |sinhcosh| |resolve| |common| + |lagrange| |column| |symbol?| |before?| |getButtonValue| |check| + |shade| |more?| |addMatch| Y |squareTop| |balancedBinaryTree| + |var2Steps| |functionIsFracPolynomial?| |vectorise| |implies| + |position!| |viewZoomDefault| |OMconnectTCP| |transpose| |fintegrate| + |monomialIntegrate| |f01rcf| |semiSubResultantGcdEuclidean1| |ef2edf| + |vedf2vef| |label| |component| |halfExtendedSubResultantGcd1| |lookup| + |consnewpol| |overlap| |segment| |c06ecf| |leastPower| |findBinding| + |OMputEndAttr| |makeSketch| |getRef| |multiplyExponents| + |identification| |conjugates| |midpoints| |inverseLaplace| |mantissa| + |lieAdmissible?| |monicRightFactorIfCan| |infieldIntegrate| |cosIfCan| + |closed| |f01maf| |mapDown!| |startTableInvSet!| |c06gsf| |df2mf| + |conical| |sinIfCan| |cCosh| |closedCurve?| |ideal| |torsionIfCan| + |elliptic?| |cycle| |f02akf| |pdct| |iicot| |region| |mathieu12| + |rotatez| |eulerPhi| |separant| |zeroDim?| |recoverAfterFail| + |epilogue| |bytes| |leadingCoefficientRicDE| |rdregime| + |certainlySubVariety?| |associatorDependence| |totalDifferential| + |maxPoints| |minColIndex| |iiacsch| |exprex| |iicosh| |coefficient| + |slex| |positive?| |bsolve| |algebraic?| |principalIdeal| + |quadraticNorm| |wordInGenerators| |numberOfCycles| |shape| + |encodingDirectory| |sylvesterSequence| |numberOfDivisors| + |constructor| |lintgcd| |exponents| |cdr| |callForm?| |dec| + |meshPar2Var| |selectsecond| |reseed| |changeBase| |iteratedInitials| + |halfExtendedResultant1| |computePowers| |mat| |s17ahf| |divisors| + |option| |setCondition!| |cap| |var2StepsDefault| |compound?| + |positiveSolve| |shufflein| |showSummary| |keys| |factorPolynomial| + |tubeRadius| |split| |ellipticCylindrical| |changeMeasure| + |beauzamyBound| |putColorInfo| |lyndon?| |stoseInvertibleSetsqfreg| + |iiacsc| |collect| |rational| |maxColIndex| |e01bff| + |tableForDiscreteLogarithm| |harmonic| |LyndonWordsList1| |center| + |limit| |removeCoshSq| |elements| |showAttributes| |numFunEvals3D| + |fractionFreeGauss!| |imagk| |moduleSum| |scaleRoots| |evaluate| + |trim| |mapGen| |isConnected?| |bag| |quotient| |packageCall| |d01bbf| + |linearAssociatedLog| |realZeros| |setEmpty!| |curveColor| |sequences| + |complexEigenvectors| |asinhIfCan| |checkRur| |previous| |putProperty| + |bitCoef| |symmetricRemainder| |s13acf| |sturmVariationsOf| |name| + |expintfldpoly| |ramified?| |lyndon| |leviCivitaSymbol| |permutation| + |atoms| |rename| |attributeData| |simplifyExp| |f02fjf| |body| + |upperCase| |palgRDE| |ddFact| |getConstant| |s21bcf| |OMgetEndObject| + UP2UTS |dihedral| |createMultiplicationMatrix| |create| |leaf?| + |chainSubResultants| |startTable!| |reopen!| |frst| |times!| |units| + |subQuasiComponent?| |inputBinaryFile| |besselJ| |imagK| |arbitrary| + |null| |outputForm| EQ |rootOf| |integers| |pointColorPalette| + |leftRegularRepresentation| |HermiteIntegrate| |setDifference| + |cyclic?| |identity| |unexpand| |not| |integralAtInfinity?| + |asinIfCan| |FormatRoman| |OMgetAtp| |integralLastSubResultant| + |solveRetract| |shallowCopy| |sayLength| |makeFR| + |trailingCoefficient| |and| |satisfy?| |randomR| |poisson| |df2st| + |rationalPower| |squareFreePart| |mesh?| |Lazard| |e04mbf| |OMputAtp| + |or| |d02cjf| |mapmult| |conditionsForIdempotents| |s17aef| + |derivationCoordinates| |explogs2trigs| |ScanArabic| |xor| |cup| + |antiCommutator| |assert| |code| |minPoints3D| |tower| |normalDeriv| + |invertibleSet| |s19adf| |port| |particularSolution| |pattern| + |viewWriteAvailable| |case| |associates?| |zag| |complementaryBasis| + |e04gcf| |determinant| |fortranCarriageReturn| |ramifiedAtInfinity?| + |rowEchLocal| |Zero| |readUInt8!| |OMlistSymbols| |cAcosh| + |oddInfiniteProduct| |bat1| |logGamma| |t| |One| |sorted?| + |indiceSubResultant| |search| |transcendent?| |exprHasAlgebraicWeight| + |eq| |lighting| |monicRightDivide| |shiftRoots| |returnType!| + |companionBlocks| |currentSubProgram| |predicate| |entries| + |setIntersection| |iter| |plus!| |dim| |subresultantSequence| |d01gbf| + |e01saf| |message| |nullSpace| |monicDivide| |f04jgf| |lifting1| + |complexNumeric| |setTex!| |symmetricPower| |bivariatePolynomials| + |laurentRep| |OMgetSymbol| |points| |ord| |OMreadStr| |pushucoef| + |iiacot| |exactQuotient| |hdmpToP| |expandTrigProducts| + |linearDependence| |unvectorise| |bindings| |iicoth| |kernels| + |completeEchelonBasis| |OMputEndError| |lex| |elt| |chvar| |uniform| + |OMgetInteger| |sum| |s17akf| |screenResolution3D| |operator| + |generators| |f02aef| |pseudoRemainder| |showTheFTable| + |interpretString| |delta| |topPredicate| |associatedEquations| + |mainPrimitivePart| |divideIfCan| |typeForm| |backOldPos| |ParCond| + |lyndonIfCan| |setMinPoints3D| |c06ebf| |cons| |univariate| + |dimensions| |increase| |coshIfCan| |tryFunctionalDecomposition| + |semiSubResultantGcdEuclidean2| |randomLC| |linearMatrix| |divide| + |rightDiscriminant| |pomopo!| |tab1| |changeName| |extractIfCan| + |f04axf| |getCode| |sup| |lllip| |cn| |semiLastSubResultantEuclidean| + |lllp| |nextIrreduciblePoly| |startStats!| |parameters| |coefficients| + |edf2ef| |screenResolution| |factor| |updatF| |leftMult| + |absolutelyIrreducible?| |cTanh| |exprHasLogarithmicWeights| + |quickSort| |useNagFunctions| |stronglyReduce| |redpps| |sqrt| + |power!| |qroot| |writeByte!| |B1solve| |rootPower| |linearPart| + |sin?| |e01bgf| |po| |real| |close!| |tablePow| |initTable!| + |expandPower| |startPolynomial| |lambda| |elliptic| |doubleComplex?| + |s17ajf| |source| |e02akf| |imag| |retract| |e04jaf| + |wordInStrongGenerators| |contract| |drawCurves| |directProduct| + |nothing| |numberOfVariables| |setsubMatrix!| |OMputVariable| + |getMatch| |cosSinInfo| |gcdcofactprim| |mapdiv| |gradient| + |expandLog| |addPoint| |iroot| |lfunc| |horizConcat| |zero| |isAnd| + |listexp| |plusInfinity| |part?| |viewport2D| |stopMusserTrials| + |cot2tan| |arity| |useEisensteinCriterion| |leftScalarTimes!| + |removeRedundantFactorsInContents| |minusInfinity| |fortranTypeOf| + |listOfLists| |brace| |argument| |getMeasure| |critB| + |chineseRemainder| |char| |clearFortranOutputStack| |alternating| + |tubePoints| |topFortranOutputStack| |padicallyExpand| |And| + |invertibleElseSplit?| |destruct| |basisOfCentroid| |upperCase!| + |symmetricTensors| |lazyPrem| |OMputBind| |stirling1| |writable?| + |discriminant| |target| |Or| |OMputSymbol| |prologue| + |removeRoughlyRedundantFactorsInPol| |stoseInvertibleSet| |isExpt| + |generalTwoFactor| |realRoots| |gethi| |reduceBasisAtInfinity| + |checkPrecision| |movedPoints| |f02bjf| |Not| |coerceListOfPairs| + |substring?| |setButtonValue| |BasicMethod| |aQuartic| + |numberOfNormalPoly| |selectMultiDimensionalRoutines| |conjug| + |relationsIdeal| |iisech| LODO2FUN |kovacic| |tanNa| |approximants| + |ldf2lst| |integer?| |polyRDE| |incrementKthElement| |lepol| + |combineFeatureCompatibility| |type| |double?| |PollardSmallFactor| + |index?| |hasHi| |monomial| |suffix?| |xn| |cCos| |superscript| + |stack| |nextColeman| |coerceL| |exteriorDifferential| + |complexIntegrate| |iisqrt2| |finiteBasis| |firstNumer| |multivariate| + |computeCycleLength| |diag| |balancedFactorisation| |noValueMode| + |structuralConstants| |float| |constantToUnaryFunction| |e02ahf| + |resultantReduit| |root| |degreeSubResultantEuclidean| |variables| + |prefix?| |rightCharacteristicPolynomial| |OMgetEndError| |unparse| + |boundOfCauchy| |normalizeAtInfinity| |decreasePrecision| |jacobian| + |besselY| |components| |rootDirectory| |palglimint| |goodnessOfFit| + |zero?| |tubeRadiusDefault| |palgRDE0| |generalizedInverse| + |interactiveEnv| |definingPolynomial| |factorOfDegree| |octon| + |approxNthRoot| |integralBasis| |redmat| |deepCopy| |baseRDEsys| + |OMgetApp| |mapUnivariate| |d01fcf| |principal?| + |selectFiniteRoutines| |ratDenom| |quartic| |bezoutMatrix| |elem?| + |fortranLiteralLine| |operators| |highCommonTerms| |OMserve| + |sizePascalTriangle| |lastSubResultantElseSplit| |has?| |rowEch| + |s18aff| |pair?| |palgLODE| |dflist| |explimitedint| + |internalIntegrate0| |nextPrime| |minimumDegree| |taylor| |cPower| + |wholeRagits| |clipBoolean| |extractProperty| |resetBadValues| + |fortranInteger| |ref| |setAdaptive3D| |OMgetObject| |rCoord| |infix?| + |laurent| |mapMatrixIfCan| |insertMatch| |antiAssociative?| |expt| + |computeInt| |chebyshevU| |iicsc| |lift| |factorSFBRlcUnit| |init| + |mask| |isEquiv| |headReduce| |puiseux| |ptree| |mappingMode| |ptFunc| + |basisOfCommutingElements| |moebius| |mapUp!| GE |reduce| |flatten| + |computeBasis| |shrinkable| |roman| |factorAndSplit| + |primitiveElement| |partition| |algebraicSort| + |resultantEuclideannaif| |ReduceOrder| |leftUnit| GT |sncndn| + |outputSpacing| |perfectSqrt| |merge| |cyclicEqual?| |inv| |operation| + |irForm| |irreducibleRepresentation| |perfectNthPower?| |normal01| + |middle| LE |rightUnit| |leftPower| |ground?| |finite?| |factorList| + |identityMatrix| |normal?| |stFunc2| |indicialEquation| |tan2trig| + |putProperties| LT |subscriptedVariables| |f04mcf| |ground| + |meshPar1Var| |dAndcExp| |norm| |point| |genericLeftMinimalPolynomial| + |univariatePolynomialsGcds| |createGenericMatrix| + |removeSuperfluousQuasiComponents| |cschIfCan| |e02ajf| |leftGcd| + |lazyPquo| |escape| |lazyPseudoDivide| |useSingleFactorBound| + |OMputEndObject| |simplifyPower| |collectQuasiMonic| |palgextint| + |subCase?| |s17dgf| |extendedSubResultantGcd| |generalPosition| + |sin2csc| |e01sbf| |expressIdealMember| |lieAlgebra?| |BumInSepFFE| + |headReduced?| |heap| |permanent| |sinhIfCan| |bipolarCylindrical| + |normalizedAssociate| |series| |capacity| |solve| |submod| + |primextintfrac| |hasSolution?| |reducedSystem| + |generalizedEigenvectors| |sPol| |totalfract| |deriv| |cartesian| + |index| |upperBound| |exprToXXP| |karatsuba| |setfirst!| |insert!| + |integerIfCan| |status| |elementary| |primitive?| |associatedSystem| + |numberOfFractionalTerms| |partialFraction| |maxPoints3D| |f02axf| + |generalInfiniteProduct| |outerProduct| |extendedIntegrate| + |cyclicCopy| |insertTop!| |userOrdered?| |hconcat| |fractRagits| + |applyRules| |getIdentifier| |unrankImproperPartitions0| + |stopTableGcd!| |rightTrim| |eq?| |binarySearchTree| |socf2socdf| + |rectangularMatrix| |min| |maximumExponent| |pair| |order| |linSolve| + |d01aqf| |iiperm| |byte| |polar| |mathieu24| |leftTrim| |extractPoint| + |bright| |hasTopPredicate?| |polygamma| |ParCondList| + |extensionDegree| |yellow| |mainVariable?| |s17dlf| + |semiDiscriminantEuclidean| |matrixConcat3D| |constantLeft| |s14baf| + |imagJ| |sylvesterMatrix| |f04mbf| |derivative| |rightTrace| + |showScalarValues| |lfinfieldint| |getPickedPoints| |fglmIfCan| + |slash| |midpoint| |eval| |f02wef| |unmakeSUP| |leftRankPolynomial| + |monomials| |leftRank| |rightLcm| |sizeLess?| |s21bdf| |readInt32!| + |tab| |laguerre| |graphs| |powmod| |e02def| |lazyPseudoQuotient| + |hspace| |complexEigenvalues| |algebraicCoefficients?| GF2FG + |permutations| |selectOptimizationRoutines| |usingTable?| |nthCoef| + |triangular?| |mergeDifference| |noLinearFactor?| |refine| |error| + |lastSubResultant| |leadingExponent| |point?| |mainExpression| + |solveLinearlyOverQ| |FormatArabic| |asechIfCan| |alphabetic| + |unitVector| |removeIrreducibleRedundantFactors| |mpsode| |f01brf| + |hasPredicate?| |brillhartTrials| |denominator| |palgintegrate| + |removeSuperfluousCases| |hexDigit| |regime| |rootPoly| |cosh2sech| + |variable?| |complexLimit| |writeBytes!| |quatern| |f2st| + |getDatabase| |minPol| |function| |optimize| |dihedralGroup| + |noncommutativeJordanAlgebra?| |groebSolve| |rightPower| |c06fqf| + |binaryTournament| |makeVariable| |ListOfTerms| |sn| |minPoints| + |nextSublist| |froot| BY |complexRoots| |nextItem| |binaryTree| + |delete!| |lazyPremWithDefault| |compose| |alphanumeric| + |selectPolynomials| |primintfldpoly| |intensity| |rspace| |expIfCan| + |interpolate| |showRegion| |inGroundField?| |triangSolve| |solid?| + |rotatex| |univariatePolynomials| |OMputApp| |child| |cCoth| |trunc| + |rightRemainder| |univariate?| |measure2Result| |enqueue!| + |zeroVector| |bandedJacobian| |rischNormalize| |categoryFrame| + |s17aff| |tanh2coth| |tanQ| |overlabel| |testDim| |s18aef| + |toseSquareFreePart| |e02aef| |rightRank| |f01rdf| + |fullPartialFraction| |minus!| |jordanAlgebra?| |hdmpToDmp| + |varselect| |totalGroebner| |OMputBVar| |remainder| |cCsc| |dequeue!| + |doubleFloatFormat| |lazyGintegrate| |binaryFunction| |buildSyntax| + |intersect| |radicalRoots| |flexibleArray| |rem| |result| + |getGoodPrime| |safetyMargin| |dimension| |f04asf| |numericIfCan| NOT + |extendedEuclidean| |degree| |cSinh| |li| |tableau| |quo| |errorKind| + |wholeRadix| |sequence| |sign| |kmax| |sample| OR |constantRight| + |d03edf| |argumentListOf| |complexForm| |basisOfLeftNucleus| + |readUInt16!| |f02ajf| |setAdaptive| |pack!| |laplacian| AND + |monicLeftDivide| |imagI| |fractRadix| |multiset| |div| |addPoint2| + |getOperator| |every?| |wrregime| |critMTonD1| |normalise| |lcm| + |compiledFunction| |f02bbf| |recolor| |aLinear| + |genericLeftDiscriminant| |exquo| |delete| |padecf| |lfextendedint| + |id| |invmultisect| |aspFilename| |enterPointData| + |SturmHabichtMultiple| |listYoungTableaus| |coHeight| |tube| ~= + |nsqfree| |moduloP| |anfactor| |transform| |lo| |setRow!| + |factorFraction| |append| |elRow2!| |distance| |linearlyDependent?| + |subResultantGcdEuclidean| |#| |c06ekf| |mainVariables| |sdf2lst| + |e01bef| |badNum| |gcd| |hexDigit?| |ScanFloatIgnoreSpaces| |getGraph| + ~ |edf2df| |symbolIfCan| |leadingSupport| |e04ucf| |divergence| + |nthFractionalTerm| |false| |collectUnder| |s13aaf| |select!| + |setStatus!| |f04atf| |KrullNumber| |branchPoint?| |nextSubsetGray| + |toScale| |rubiksGroup| |stiffnessAndStabilityOfODEIF| + |selectODEIVPRoutines| |df2fi| |rischDEsys| |test| |scalarTypeOf| + |mainContent| |triangularSystems| |viewDefaults| |quasiRegular?| + |associative?| |setlast!| |resetAttributeButtons| |aCubic| + |integralDerivationMatrix| |loopPoints| |/\\| |copies| |Is| |overset?| + |setErrorBound| |fortranDouble| |e04fdf| |basisOfRightNucloid| + |setPrologue!| |leftOne| |createPrimitiveElement| |\\/| |OMputEndBVar| + |d02ejf| |acotIfCan| |numer| |squareFreePolynomial| |newSubProgram| * + |nthExponent| |retractIfCan| |powers| |complement| |isOp| |bit?| + |pmintegrate| |firstSubsetGray| |d02bbf| |denom| + |setScreenResolution3D| |SturmHabichtSequence| |coerce| |readByte!| + |hermiteH| |mathieu11| |bumptab| |iicsch| |nodeOf?| + |internalIntegrate| |f01mcf| |restorePrecision| |getCurve| |construct| + |knownInfBasis| |freeOf?| |radicalSolve| |drawToScale| |OMgetString| + |bfEntry| |digit?| |makeSUP| |factorSquareFreePolynomial| |pi| = + |revert| |prefix| |f02adf| |ceiling| |Frobenius| |OMgetEndApp| + |opeval| |modularFactor| |singRicDE| |stripCommentsAndBlanks| + |infinity| |roughUnitIdeal?| |maxIndex| |inverseIntegralMatrix| + |groebnerIdeal| |atanIfCan| |rightUnits| |minIndex| + |regularRepresentation| |rk4| |e02dff| |constantCoefficientRicDE| + |unit| < |changeNameToObjf| |doubleDisc| |cos2sec| |unitNormal| + |infinite?| |genericRightDiscriminant| |subNodeOf?| |blankSeparate| + |paren| > |dominantTerm| |se2rfi| |clearTable!| |cycleLength| |d03faf| + |stoseInvertibleSetreg| |element?| |outputList| |unit?| |OMputObject| + |kernel| |relativeApprox| |fortranLinkerArgs| <= |groebgen| + |setLabelValue| |traceMatrix| |symmetricGroup| |quasiComponent| + |unravel| |declare| |sort| |linearPolynomials| |completeSmith| |just| + |list| |Nul| >= |map| |rk4qc| |modularGcd| |pseudoQuotient| + |partialDenominators| |besselK| |cyclotomicDecomposition| |draw| + |LyndonCoordinates| |multiple?| |bubbleSort!| |f02aff| |tan2cot| + |leader| |create3Space| |outputMeasure| |sechIfCan| |s20adf| + |createThreeSpace| |nodes| |halfExtendedSubResultantGcd2| + |setTopPredicate| |showAllElements| |number?| |addMatchRestricted| + |cycleElt| |iiasech| |leadingTerm| |primextendedint| |categories| + |rombergo| |basisOfNucleus| |invmod| |explicitlyEmpty?| |UP2ifCan| + |updatD| |mulmod| + |head| |value| |c06gcf| |hitherPlane| + |euclideanSize| |mapUnivariateIfCan| |subst| |cardinality| |width| + |complete| |random| |showTheRoutinesTable| |processTemplate| + |LazardQuotient| - |ridHack1| |stoseIntegralLastSubResultant| + |specialTrigs| |halfExtendedResultant2| |leftTraceMatrix| |commutator| + |central?| |gensym| |infix| |makeObject| |crushedSet| / + |resultantEuclidean| |convert| |isOpen?| |level| |setref| |largest| + |OMgetEndAttr| |cyclicGroup| |ratPoly| |readable?| |genericPosition| + |polyPart| |coef| |iisec| |qinterval| |oblateSpheroidal| + |idealSimplify| |trivialIdeal?| |queue| |extractTop!| |distribute| + |asimpson| |log| |maxdeg| |monicCompleteDecompose| |generateIrredPoly| + |e04naf| |numberOfComposites| |reindex| |quadratic| |normDeriv2| + |isList| |integerBound| |s17agf| |optAttributes| |toseInvertibleSet| + |multiEuclideanTree| |d02bhf| |iifact| |rowEchelon| |inrootof| + |cyclicSubmodule| |ode2| |infLex?| |setelt| |algebraicDecompose| + |assign| |iiasin| |f07fef| |oneDimensionalArray| |e02bef| |iiatanh| + |prinshINFO| |cExp| |subspace| |objects| |iidprod| |drawStyle| |mr| + |getStream| |makeop| |indicialEquations| |radix| + |parabolicCylindrical| |heapSort| |infiniteProduct| |OMread| + |optional| |base| |copy| |semiResultantReduitEuclidean| |yCoordinates| + |atrapezoidal| |ricDsolve| |numberOfComputedEntries| |terms| + |partialNumerators| |pr2dmp| |qelt| |linkToFortran| |OMopenFile| + |eyeDistance| |stFunc1| |eigenvector| |exponential1| |toroidal| + |infinityNorm| |qsetelt| |LagrangeInterpolation| |prefixRagits| + |rootsOf| |iidsum| |primes| |prod| |front| |repeating?| + |factorByRecursion| |dmp2rfi| |fi2df| |localAbs| |xRange| |e02daf| + |parent| |build| |pascalTriangle| |OMUnknownCD?| |digits| |setnext!| + |edf2fi| |getMultiplicationTable| |selectfirst| |yRange| |s19abf| + |lazyVariations| |reorder| |OMclose| |setProperties| |subPolSet?| + |bipolar| |binary| |rightExactQuotient| |fixPredicate| |zRange| + |pole?| |viewThetaDefault| |addmod| |listConjugateBases| + |genericLeftTraceForm| |reducedDiscriminant| |OMgetEndAtp| + |orthonormalBasis| |map!| |physicalLength| |rightFactorCandidate| + |elaborateFile| |cylindrical| |s17acf| |isAbsolutelyIrreducible?| |dn| + |twoFactor| |integralCoordinates| |LiePolyIfCan| |systemCommand| + |qsetelt!| |signature| |purelyAlgebraic?| |setVariableOrder| + |limitedIntegrate| |readLineIfCan!| |monicDecomposeIfCan| + |tryFunctionalDecomposition?| |rarrow| |prevPrime| |problemPoints| + |outputGeneral| |insertRoot!| |mergeFactors| |rk4a| |controlPanel| + |SFunction| |direction| |weight| |createNormalPoly| |euler| + |stoseLastSubResultant| |c06eaf| |OMputInteger| |summation| + |clipSurface| |ode| |plotPolar| |vark| |Ei| |bigEndian| |minRowIndex| + |normal| |cSec| |mvar| |eigenvectors| |splitConstant| |algebraicOf| + |createRandomElement| |coordinate| |componentUpperBound| + |linearAssociatedOrder| |s15aef| |prime| |startTableGcd!| + |elaboration| |isMult| |isPower| |sec2cos| |corrPoly| |birth| |fill!| + |members| |unknown| |internalDecompose| |acsch| |printInfo!| + |ODESolve| |nil?| |setValue!| |super| |atom?| |numerators| |mdeg| + |setLegalFortranSourceExtensions| |btwFact| |functorData| |OMreceive| + |getBadValues| |wholePart| |cAsec| |lfintegrate| |minimize| |e02adf| + |whitePoint| |diagonal| |f01qcf| |retractable?| |radicalEigenvalues| + |tanhIfCan| |remove| |OMopenString| |c02agf| |lhs| |addiag| |inverse| + |cAtanh| |subscript| |removeRedundantFactors| |primitivePart!| + |diagonalMatrix| |bits| |s17dcf| |floor| |find| |pToDmp| |option?| + |rhs| |rootSplit| |rewriteSetWithReduction| |entry?| |key?| |s14abf| + |taylorIfCan| |last| |homogeneous?| |fmecg| |writeUInt8!| |rquo| + |separateFactors| |cyclePartition| |assoc| |supDimElseRittWu?| + |symbolTableOf| |expint| |makeResult| |Vectorise| |currentEnv| |mix| + |coerceS| |pointPlot| |s20acf| |tanIfCan| |nor| |nextsousResultant2| + |acosIfCan| |debug3D| |removeCosSq| |rightAlternative?| + |nextPrimitivePoly| |charClass| |makingStats?| |simpson| + |quasiRegular| |cond| |e01sef| |tanAn| |getVariableOrder| + |leadingBasisTerm| |setStatus| |squareFreePrim| |setRealSteps| + |genericLeftNorm| |lexGroebner| |legendreP| |isTimes| |rightNorm| + |logpart| |cCsch| |createNormalPrimitivePoly| |null?| + |leftAlternative?| |datalist| |createPrimitiveNormalPoly| |call| + |simpsono| |areEquivalent?| |qqq| |monomRDE| |typeList| |removeSinhSq| + |f04faf| |lowerCase!| |makeUnit| |f01bsf| |getMultiplicationMatrix| + |f04qaf| |minordet| |simplifyLog| |figureUnits| |antisymmetricTensors| + |gderiv| |leftDivide| |over| |equality| |inputOutputBinaryFile| + |viewPhiDefault| |safeFloor| |randnum| |uncouplingMatrices| + |OMencodingBinary| |addPointLast| |autoReduced?| |rightFactorIfCan| + |iitan| |insertionSort!| |rootNormalize| |rst| |exportedOperators| + |copy!| |separateDegrees| |rotate!| |replaceKthElement| |printCode| + |diagonalProduct| |s19acf| |approxSqrt| |delay| |univariatePolynomial| + |musserTrials| |showTheSymbolTable| |imaginary| |s15adf| |closed?| + |clearDenominator| |numberOfPrimitivePoly| |symbolTable| + |definingInequation| |degreePartition| |makeEq| |f02agf| |palgLODE0| + |repeating| |wordsForStrongGenerators| |initiallyReduce| + |normalizeIfCan| |signatureAst| |extract!| |f04adf| |readInt8!| + |fixedPoint| |conjunction| |pushFortranOutputStack| |fortranLiteral| + |supRittWu?| |mightHaveRoots| |trigs2explogs| |graeffe| |e02bdf| + |latex| UTS2UP |mindeg| |popFortranOutputStack| |prinb| |sub| |iiabs| + |countRealRootsMultiple| |push| |createZechTable| |directSum| |pop!| + |say| |littleEndian| |An| |outputAsFortran| + |stoseInternalLastSubResultant| |rk4f| |presuper| |hyperelliptic| + |youngDiagram| |cotIfCan| |basisOfLeftNucloid| |max| |gcdcofact| + |getProperty| |semiResultantEuclidean1| |resultantnaif| + |leadingMonomial| |ratpart| |reset| |isAtom| |putGraph| |cyclic| + |maxRowIndex| |elRow1!| |cSin| |duplicates| |fractionPart| + |leadingCoefficient| |nil| |cothIfCan| |nextPartition| |inc| + |patternVariable| |elColumn2!| |selectOrPolynomials| |c06frf| |bfKeys| + |d02raf| |primitiveMonomials| |basicSet| |write| |rules| + |discriminantEuclidean| |pushup| |createMultiplicationTable| + |deepExpand| |df2ef| |fortranReal| |maxint| |reductum| |save| |Si| + |collectUpper| |innerSolve| |subHeight| |normalized?| |stop| |s13adf| + |OMsupportsCD?| |imports| |distFact| |approximate| |c06gbf| |isOr| + |back| |innerint| |inR?| |unrankImproperPartitions1| |headRemainder| + |zeroMatrix| |leftRemainder| |complex| |integralRepresents| |Lazard2| + |ran| |makeprod| |diagonals| |f07adf| |sizeMultiplication| + |branchPointAtInfinity?| |invertIfCan| |bezoutResultant| + |completeHensel| |totolex| |trapezoidal| |e02ddf| |adjoint| + |alphabetic?| |power| |modTree| |pushdterm| |zCoord| |newReduc| + |coercePreimagesImages| |iicos| |messagePrint| |cross| |finiteBound| + |univcase| |linGenPos| |d01alf| |primPartElseUnitCanonical| |s18def| + |pquo| |curve| |modularGcdPrimitive| |removeSinSq| |failed| + |stoseSquareFreePart| |aQuadratic| |besselI| |monicModulo| + |removeZero| |move| |dictionary| |totalLex| |commonDenominator| + |critM| |OMputEndApp| |basisOfRightAnnihilator| |algint| |constDsolve| + |groebner| |vector| |makeYoungTableau| |anticoord| + |numericalOptimization| |insertBottom!| |reverseLex| |double| |node| + |green| |setScreenResolution| |magnitude| |weights| |differentiate| + |tanh2trigh| |rootRadius| |closeComponent| |reverse!| + |lazyResidueClass| |separate| |lSpaceBasis| |readBytes!| + |symmetricDifference| |doubleRank| |constant| |pointColor| |factorset| + |iiacoth| |monic?| |predicates| |rightDivide| |scanOneDimSubspaces| + |critpOrder| |exp| |endSubProgram| |makeMulti| |modifyPoint| |iitanh| + |pToHdmp| |binomial| |nextNormalPrimitivePoly| |pmComplexintegrate| + |pointSizeDefault| |nextPrimitiveNormalPoly| |debug| + |showFortranOutputStack| |factorSquareFree| |d03eef| |tanSum| + |bandedHessian| |meatAxe| |internalZeroSetSplit| |second| |taylorRep| + |copyInto!| D |GospersMethod| |f02abf| |printStatement| |integrate| + |algSplitSimple| |reducedQPowers| |d01ajf| |third| |neglist| + |lowerCase?| |isNot| |listLoops| |listOfMonoms| |cyclicParents| + |eulerE| |fillPascalTriangle| |cubic| |adaptive?| |any| |LyndonBasis| + |any?| |unitCanonical| |exprToUPS| |eigenMatrix| |constantOperator| + |pol| |rightMult| |key| |factorial| |edf2efi| |sumOfDivisors| + |truncate| |e02bcf| |polygon| |parents| |leaves| |swapRows!| |s18adf| + |readLine!| |schema| |subResultantGcd| |symmetric?| + |linearlyDependentOverZ?| |fortranDoubleComplex| |inRadical?| + |reflect| |primaryDecomp| |filename| |SturmHabicht| |contours| + |OMencodingXML| |postfix| |seed| |extendIfCan| |evaluateInverse| + |isQuotient| |cscIfCan| |loadNativeModule| |e02dcf| |f02aaf| + |duplicates?| |open| |countable?| |accuracyIF| |createNormalElement| + |mkPrim| |OMReadError?| |intPatternMatch| |commaSeparate| + |getExplanations| |parse| |exists?| |LazardQuotient2| + |clipPointsDefault| |fibonacci| |yCoord| |pushdown| |shallowExpand| + |charpol| |viewDeltaYDefault| |equation| |zoom| |viewSizeDefault| + |iiGamma| |readUInt32!| |setLength!| |ScanFloatIgnoreSpacesIfCan| + |quotientByP| |contains?| |nextLatticePermutation| |e02bbf| + |RemainderList| |monomialIntPoly| |seriesToOutputForm| |systemSizeIF| + |rur| |equiv| |outputFixed| |shiftLeft| |nthFlag| |operations| + |complexZeros| |safeCeiling| |taylorQuoByVar| |lexTriangular| |diff| + |height| |numberOfHues| |s17def| |explicitlyFinite?| |cfirst| |sh| + |plenaryPower| |csubst| |getZechTable| |realEigenvectors| + |showArrayValues| |dequeue| |setPoly| |selectPDERoutines| + |setprevious!| |swap| |graphCurves| |readInt16!| |subResultantsChain| + |hclf| |generator| |surface| |prime?| |bounds| + |internalSubQuasiComponent?| |f01qef| |leftQuotient| |evenlambert| + |exponentialOrder| |bitTruth| |exQuo| |e04dgf| |stFuncN| |pow| + |transcendenceDegree| |ocf2ocdf| |host| |nullity| |updateStatus!| + |axes| |options| |content| |cyclotomicFactorization| + |nativeModuleExtension| |constantIfCan| |linearAssociatedExp| |module| + |expintegrate| |lazy?| |connect| |modulus| |presub| |composite| + |oddintegers| |antiCommutative?| |flagFactor| |branchIfCan| + |simpleBounds?| |rewriteIdealWithQuasiMonicGenerators| |table| + |numberOfIrreduciblePoly| |nullary?| |child?| |color| |mesh| + |numberOfMonomials| |indiceSubResultantEuclidean| |unknownEndian| + |monomial?| |string| |new| |nextNormalPoly| |pastel| |Gamma| + |nthFactor| |hostByteOrder| |categoryMode| |setMaxPoints3D| + |external?| |solveid| |qualifier| |palgextint0| |generalSqFr| + |numerator| |length| |s17dhf| |setOrder| |split!| |binomThmExpt| + |minimumExponent| |fortranLogical| |jokerMode| |clearTheIFTable| + |jordanAdmissible?| |scripts| |intermediateResultsIF| |irreducible?| + |cAsinh| |title| |complexExpand| |OMmakeConn| |hcrf| |laplace| + |c02aff| |critT| |arg1| |gbasis| |bumprow| |characteristicSerie| + |vertConcat| |myDegree| |incr| |subSet| |OMreadFile| |round| |swap!| + |arg2| |makeTerm| |lazyEvaluate| |mappingAst| |in?| |outputArgs| + |cAtan| |hi| |complex?| |innerSolve1| |leftCharacteristicPolynomial| + |tail| |e| |shanksDiscLogAlgorithm| |dual| |characteristic| + |realSolve| |printInfo| |resultant| |square?| |headAst| + |UpTriBddDenomInv| |represents| |conditions| |arrayStack| + |LyndonWordsList| |subMatrix| |indices| |scalarMatrix| + |functionIsOscillatory| |partialQuotients| |substitute| + |leftDiscriminant| |parts| |match| |genericRightTraceForm| |rotate| + |modifyPointData| |rootOfIrreduciblePoly| |prepareDecompose| + |idealiserMatrix| |log2| |youngGroup| |apply| |extractIndex| + |medialSet| |rightScalarTimes!| |imagi| |groebnerFactorize| + |tensorProduct| |comment| |leftRecip| |changeThreshhold| + |selectNonFiniteRoutines| |htrigs| |first| |supersub| |iiacosh| + |c05nbf| |resultantReduitEuclidean| |less?| |left| |convergents| + |increasePrecision| |domainTemplate| |augment| |fortran| |rest| + |cAcos| |seriesSolve| |iCompose| |iipow| |moreAlgebraic?| |right| + |thenBranch| |bitLength| |scripted?| |hash| |currentCategoryFrame| + |generalizedEigenvector| |redPol| |comp| |initiallyReduced?| |light| + |csch2sinh| |count| |splitDenominator| |perfectSquare?| |polyred| + |mainCoefficients| |curryRight| |normalElement| |PDESolve| + |createIrreduciblePoly| |setPredicates| |integralBasisAtInfinity| + |lifting| |resetVariableOrder| |leftExtendedGcd| |laurentIfCan| + |elaborate| |bernoulli| |UnVectorise| |red| |coth2tanh| |pile| + |secIfCan| |integralMatrix| |unprotectedRemoveRedundantFactors| + |unary?| |e02zaf| |inverseIntegralMatrixAtInfinity| |normalDenom| + |quote| |removeDuplicates| |lastSubResultantEuclidean| |newTypeLists| + |semicolonSeparate| |compactFraction| |primlimintfrac| |integral| + |OMcloseConn| |high| |signAround| |padicFraction| |clipWithRanges| + |mkIntegral| |prindINFO| |mainMonomial| |atanhIfCan| |lquo| + |isobaric?| |mkcomm| |generate| |f02xef| |subResultantChain| |ksec| + |intcompBasis| |rationalPoint?| |cAcsc| |differentialVariables| + |hMonic| |real?| |comparison| |standardBasisOfCyclicSubmodule| + |mapExpon| |frobenius| |nonLinearPart| |strongGenerators| |c06fpf| + |lineColorDefault| |incrementBy| |att2Result| |appendPoint| |bottom!| + |iFTable| |primPartElseUnitCanonical!| |lowerBound| |nonSingularModel| + |trueEqual| |irCtor| |expand| |triangulate| |complexElementary| + |arguments| |curry| |kroneckerDelta| |one?| |showTheIFTable| + |normFactors| |patternMatch| |mainDefiningPolynomial| |symbol| + |filterWhile| |symmetricProduct| |purelyTranscendental?| |polCase| + |next| |preprocess| |totalDegree| |constant?| |basis| |vconcat| + |colorFunction| |erf| |expression| |filterUntil| |outputFloating| + |upDateBranches| |iiexp| |script| |skewSFunction| |swapColumns!| + |asecIfCan| |generic| |integer| |select| + |solveLinearPolynomialEquationByRecursion| |fixedDivisor| |shuffle| + |rewriteIdealWithRemainder| |setright!| |mainMonomials| |cSech| + |e02baf| |mapExponents| |shellSort| |OMgetFloat| |factors| + |primitivePart| |inspect| |numberOfComponents| |replace| + |cyclicEntries| |iomode| |dilog| |morphism| |cRationalPower| |linear?| + |tex| |getProperties| |OMUnknownSymbol?| |overbar| |pdf2df| + |singleFactorBound| |psolve| |sin| |OMgetType| |pureLex| + |sturmSequence| |semiResultantEuclidean2| |top| |makeGraphImage| + |d02gbf| |deref| |cos| |internalLastSubResultant| |resetNew| |getlo| + |continue| |removeRedundantFactorsInPols| |allRootsOf| |cycleEntry| + |sqfrFactor| |interval| |leftZero| |tan| |numFunEvals| + |internalInfRittWu?| |lprop| |fprindINFO| |zerosOf| |showAll?| + |primlimitedint| |ip4Address| |exprHasWeightCosWXorSinWX| |compBound| + |cot| |makeRecord| |mainCharacterization| |step| RF2UTS |leftLcm| + |leftMinimalPolynomial| |inf| |iExquo| |c05pbf| |push!| |sec| |int| + |concat| |LiePoly| |vspace| |reify| |deleteRoutine!| + |stopTableInvSet!| |diophantineSystem| |OMParseError?| |csc| + |getOrder| |henselFact| |stronglyReduced?| |rootProduct| |acothIfCan| + |bringDown| |solveLinearPolynomialEquation| |setFormula!| |output| + |condition| |curve?| |asin| |basisOfLeftAnnihilator| + |functionIsContinuousAtEndPoints| |logIfCan| |argumentList!| + |palginfieldint| |list?| |tracePowMod| |readIfCan!| + |getSyntaxFormsFromFile| |acos| |pointLists| |s18acf| |e02gaf| FG2F + |cycleTail| |externalList| |makeViewport2D| |interpret| |belong?| + |atan| |basisOfCenter| |jacobiIdentity?| |setchildren!| |rightGcd| + |OMgetBVar| |quotedOperators| |mkAnswer| |hasoln| |acot| + |outlineRender| |addBadValue| |xCoord| |abs| |numberOfOperations| + |purelyAlgebraicLeadingMonomial?| |smith| |rightZero| |laguerreL| + |asec| |squareFree| |paraboloidal| |virtualDegree| |infieldint| + |csc2sin| |bernoulliB| |showIntensityFunctions| |bezoutDiscriminant| + |Hausdorff| |outputBinaryFile| |acsc| |unitsColorDefault| |matrixGcd| + |viewWriteDefault| |withPredicates| |viewPosDefault| |credPol| + |zeroSetSplit| |factor1| |internalSubPolSet?| |connectTo| |dioSolve| + |sinh| |parametric?| |negative?| |reducedForm| |reciprocalPolynomial| + |mainForm| |coordinates| |inconsistent?| |nonQsign| |normalizedDivide| + |cosh| |makeSin| |pointColorDefault| |phiCoord| |subresultantVector| + |property| |evenInfiniteProduct| |setProperty| |optpair| |rank| |tanh| + |cot2trig| |setUnion| |acoshIfCan| |radPoly| |const| |upperCase?| + |prem| |clipParametric| |indicialEquationAtInfinity| |coth| + |makeViewport3D| |linears| |fortranCompilerName| |hex| |OMputString| + |bracket| |e01sff| |gcdPrimitive| |goodPoint| |iibinom| |lexico| + |sech| |powerAssociative?| |genericRightNorm| |choosemon| + |checkForZero| |environment| |low| |integral?| + |rewriteIdealWithHeadRemainder| |relerror| SEGMENT + |reduceByQuasiMonic| |csch| |symFunc| |computeCycleEntry| + |lfextlimint| |setPosition| |kind| |bat| |Aleph| |logical?| + |roughSubIdeal?| |quadraticForm| |sech2cosh| |drawComplexVectorField| + |asinh| |divideIfCan!| |dimensionOfIrreducibleRepresentation| |op| + |whatInfinity| |linear| |validExponential| |setFieldInfo| + |stoseInvertible?| |deleteProperty!| |selectSumOfSquaresRoutines| + |OMgetError| |acosh| |principalAncestors| |palglimint0| |trigs| |hue| + |denominators| |mathieu22| |reducedContinuedFraction| |setImagSteps| + |sortConstraints| |atanh| |badValues| |enumerate| |is?| |polynomial| + |OMgetBind| |symmetricSquare| |firstUncouplingMatrix| |iiacos| + |identitySquareMatrix| |compile| |lists| |sumSquares| |acoth| + |lflimitedint| |member?| |LowTriBddDenomInv| |palgint| |goto| |recur| + |zeroSquareMatrix| |leastAffineMultiple| |semiResultantEuclideannaif| + |asech| |rightRecip| |returnTypeOf| |cycles| + |selectIntegrationRoutines| |ratDsolve| |OMgetEndBind| |discreteLog| + |setClosed| |curveColorPalette| |removeRoughlyRedundantFactorsInPols| + |open?| |complexSolve| |f2df| |polygon?| |reduced?| |trace2PowMod| + |OMsupportsSymbol?| |curryLeft| |multiple| |e01baf| |setEpilogue!| + |union| |numberOfImproperPartitions| |torsion?| |basisOfRightNucleus| + |zeroDimPrimary?| |setleaves!| |squareFreeFactors| |universe| + |applyQuote| |pushuconst| |infRittWu?| |physicalLength!| + |axesColorDefault| |newLine| |pdf2ef| |minset| + |rewriteSetByReducingWithParticularGenerators| |formula| + |pleskenSplit| |isImplies| |toseInvertible?| |doublyTransitive?| + |splitLinear| |writeLine!| |permutationRepresentation| |clearCache| + |coefChoose| |OMconnInDevice| |range| |singularitiesOf| + |normInvertible?| |cAsin| |cAcsch| |algDsolve| |bumptab1| + |removeDuplicates!| |deepestInitial| |tubePlot| |ruleset| + |zeroDimensional?| |solveLinearPolynomialEquationByFractions| + |printHeader| |wronskianMatrix| |shiftRight| |resize| + |repeatUntilLoop| |scan| |characteristicSet| |s01eaf| + |OMencodingUnknown| |colorDef| |toseLastSubResultant| |reduceLODE| + |geometric| |saturate| |quasiMonicPolynomials| |nrows| + |semiDegreeSubResultantEuclidean| |d02gaf| + |removeRoughlyRedundantFactorsInContents| |setColumn!| |sumOfSquares| + |numberOfFactors| |printStats!| |writeInt8!| |merge!| |directory| + |ncols| |suchThat| |contractSolve| |genus| |denomLODE| |clip| |nil| + |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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(|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2854 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -2854 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2854 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2854 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1277 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2854 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2854 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2854 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2854 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2854 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2854 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2854 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2854 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2854 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) -((-2771 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-1661 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-1376 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) -(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -2771 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1661 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1376 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) -((-1376 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-1661 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-2771 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) -(-10 -7 (-15 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|%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-732)) (PROGN (-6 (-732)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-373)) (-6 (-373)) |%noBranch|) (IF (|has| |t#2| (-174)) (PROGN (-6 (-38 |t#2|)) (-6 (-174))) |%noBranch|) (IF (|has| |t#2| (-6 -4449)) (-6 -4449) |%noBranch|) (IF (|has| |t#2| (-854)) (-6 (-854)) |%noBranch|) (IF (|has| |t#2| (-799)) (-6 (-799)) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-1284 |t#2|)) |%noBranch|))) +(((-21) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-23) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-25) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2811 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -2811 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2811 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2811 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1277 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2811 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2811 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2811 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2811 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2811 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2811 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2811 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2811 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2811 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) +((-4406 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-2507 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-3025 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) +(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -4406 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -2507 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -3025 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) +((-3025 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-2507 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-4406 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-174) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#3| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#3| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#3| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) |has| |#1| (-235)) ((-294) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -2854 (|has| |#1| (-916)) (|has| |#1| (-458))) ((-520 |#2| |#1|) |has| |#1| (-235)) ((-520 |#2| $) |has| |#1| (-235)) ((-520 |#3| |#1|) . T) ((-520 |#3| $) . T) ((-520 $ $) . T) ((-562) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-652 #0#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #0#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-732) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-907 |#3|) . T) ((-893 (-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#3| (-893 (-384)))) ((-893 (-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#3| (-893 (-570)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1047 |#2|) . T) ((-1047 |#3|) . T) ((-1060 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2854 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1231) |has| |#1| (-916))) -((-2462 (((-112) $ $) 19 (|has| |#1| (-1109)))) (-3222 ((|#1| $) 55)) (-3378 ((|#1| $) 45)) (-2088 (((-112) $ (-777)) 8)) (-2984 (($) 7 T CONST)) (-2013 (($ $) 61)) (-2809 (($ $) 49)) (-2435 ((|#1| |#1| $) 47)) (-4005 ((|#1| $) 46)) (-3225 (((-650 |#1|) $) 31 (|has| $ (-6 -4452)))) (-2108 (((-112) $ (-777)) 9)) (-3985 (((-650 |#1|) $) 30 (|has| $ (-6 -4452)))) (-2455 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3347 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4453)))) (-1376 (($ (-1 |#1| |#1|) $) 36)) (-2842 (((-112) $ (-777)) 10)) (-4191 (((-777) $) 62)) (-2916 (((-1168) $) 22 (|has| |#1| (-1109)))) (-3177 ((|#1| $) 40)) (-2954 ((|#1| |#1| $) 53)) (-2808 ((|#1| |#1| $) 52)) (-1719 (($ |#1| $) 41)) (-1450 (((-777) $) 56)) (-3611 (((-1129) $) 21 (|has| |#1| (-1109)))) (-3329 ((|#1| $) 63)) (-3015 ((|#1| $) 51)) (-1433 ((|#1| $) 50)) (-2309 ((|#1| $) 42)) (-1961 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4452)))) (-1715 (($ $ (-650 (-298 |#1|))) 27 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-298 |#1|)) 26 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-650 |#1|) (-650 |#1|)) 24 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))))) (-3403 (((-112) $ $) 14)) (-2668 ((|#1| |#1| $) 59)) (-3451 (((-112) $) 11)) (-3217 (($) 12)) (-2366 ((|#1| $) 60)) (-2522 (($) 58) (($ (-650 |#1|)) 57)) (-1775 (((-777) $) 44)) (-3622 (((-777) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4452))) (((-777) |#1| $) 29 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3997 (($ $) 13)) (-3838 (((-868) $) 18 (|has| |#1| (-619 (-868))))) (-4246 ((|#1| $) 54)) (-4096 (((-112) $ $) 23 (|has| |#1| (-1109)))) (-4424 (($ (-650 |#1|)) 43)) (-1904 ((|#1| $) 64)) (-3257 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4452)))) (-2992 (((-112) $ $) 20 (|has| |#1| (-1109)))) (-2473 (((-777) $) 6 (|has| $ (-6 -4452))))) +((-2726 (*1 *2 *3) (-12 (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-1 *1 (-777))) (-4 *1 (-256 *4 *3 *5 *6)))) (-4014 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-650 *4)))) (-2629 (*1 *2 *1 *3) (-12 (-4 *1 (-256 *4 *3 *5 *6)) (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-777)))) (-2629 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-777)))) (-2800 (*1 *2 *1 *3) (-12 (-4 *1 (-256 *4 *3 *5 *6)) (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-777)))) (-3608 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-650 (-777))))) (-3251 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-777)))) (-3608 (*1 *2 *1 *3) (-12 (-4 *1 (-256 *4 *3 *5 *6)) (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-650 (-777))))) (-3251 (*1 *2 *1 *3) (-12 (-4 *1 (-256 *4 *3 *5 *6)) (-4 *4 (-1058)) (-4 *3 (-856)) (-4 *5 (-269 *3)) (-4 *6 (-799)) (-5 *2 (-777)))) (-4005 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-112)))) (-3038 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *2 *5)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-799)) (-4 *2 (-269 *4)))) (-1347 (*1 *1 *1) (-12 (-4 *1 (-256 *2 *3 *4 *5)) (-4 *2 (-1058)) (-4 *3 (-856)) (-4 *4 (-269 *3)) (-4 *5 (-799)))) (-1956 (*1 *1 *1) (-12 (-4 *1 (-256 *2 *3 *4 *5)) (-4 *2 (-1058)) (-4 *3 (-856)) (-4 *4 (-269 *3)) (-4 *5 (-799)))) (-2726 (*1 *2 *1) (-12 (-4 *3 (-235)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-269 *4)) (-4 *6 (-799)) (-5 *2 (-1 *1 (-777))) (-4 *1 (-256 *3 *4 *5 *6))))) +(-13 (-956 |t#1| |t#4| |t#3|) (-233 |t#1|) (-1047 |t#2|) (-10 -8 (-15 -2726 ((-1 $ (-777)) |t#2|)) (-15 -4014 ((-650 |t#2|) $)) (-15 -2629 ((-777) $ |t#2|)) (-15 -2629 ((-777) $)) (-15 -2800 ((-777) $ |t#2|)) (-15 -3608 ((-650 (-777)) $)) (-15 -3251 ((-777) $)) (-15 -3608 ((-650 (-777)) $ |t#2|)) (-15 -3251 ((-777) $ |t#2|)) (-15 -4005 ((-112) $)) (-15 -3038 (|t#3| $)) (-15 -1347 ($ $)) (-15 -1956 ($ $)) (IF (|has| |t#1| (-235)) (PROGN (-6 (-520 |t#2| |t#1|)) (-6 (-520 |t#2| $)) (-6 (-313 $)) (-15 -2726 ((-1 $ (-777)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-413 (-570)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #0#) -2811 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 |#1|) . T) ((-622 |#2|) . T) ((-622 |#3|) . T) ((-622 $) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-619 (-868)) . T) ((-174) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#3| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#3| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#3| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) |has| |#1| (-235)) ((-294) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -2811 (|has| |#1| (-916)) (|has| |#1| (-458))) ((-520 |#2| |#1|) |has| |#1| (-235)) ((-520 |#2| $) |has| |#1| (-235)) ((-520 |#3| |#1|) . T) ((-520 |#3| $) . T) ((-520 $ $) . T) ((-562) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-652 #0#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #0#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-732) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-907 |#3|) . T) ((-893 (-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#3| (-893 (-384)))) ((-893 (-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#3| (-893 (-570)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1047 |#2|) . T) ((-1047 |#3|) . T) ((-1060 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2811 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1231) |has| |#1| (-916))) +((-2852 (((-112) $ $) 19 (|has| |#1| (-1109)))) (-1407 ((|#1| $) 55)) (-4105 ((|#1| $) 45)) (-1669 (((-112) $ (-777)) 8)) (-2810 (($) 7 T CONST)) (-3424 (($ $) 61)) (-3613 (($ $) 49)) (-4141 ((|#1| |#1| $) 47)) (-3473 ((|#1| $) 46)) (-3907 (((-650 |#1|) $) 31 (|has| $ (-6 -4452)))) (-1893 (((-112) $ (-777)) 9)) (-3285 (((-650 |#1|) $) 30 (|has| $ (-6 -4452)))) (-4330 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3221 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4453)))) (-3025 (($ (-1 |#1| |#1|) $) 36)) (-3934 (((-112) $ (-777)) 10)) (-3842 (((-777) $) 62)) (-3462 (((-1168) $) 22 (|has| |#1| (-1109)))) (-4084 ((|#1| $) 40)) (-2613 ((|#1| |#1| $) 53)) (-3601 ((|#1| |#1| $) 52)) (-2599 (($ |#1| $) 41)) (-3758 (((-777) $) 56)) (-3951 (((-1129) $) 21 (|has| |#1| (-1109)))) (-3184 ((|#1| $) 63)) (-3109 ((|#1| $) 51)) (-1771 ((|#1| $) 50)) (-3450 ((|#1| $) 42)) (-2830 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4452)))) (-2661 (($ $ (-650 (-298 |#1|))) 27 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-298 |#1|)) 26 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (($ $ (-650 |#1|) (-650 |#1|)) 24 (-12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))))) (-2622 (((-112) $ $) 14)) (-2759 ((|#1| |#1| $) 59)) (-1804 (((-112) $) 11)) (-1354 (($) 12)) (-2783 ((|#1| $) 60)) (-3769 (($) 58) (($ (-650 |#1|)) 57)) (-1395 (((-777) $) 44)) (-3959 (((-777) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4452))) (((-777) |#1| $) 29 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3159 (($ $) 13)) (-2940 (((-868) $) 18 (|has| |#1| (-619 (-868))))) (-4028 ((|#1| $) 54)) (-1889 (((-112) $ $) 23 (|has| |#1| (-1109)))) (-2040 (($ (-650 |#1|)) 43)) (-3538 ((|#1| $) 64)) (-3672 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4452)))) (-2962 (((-112) $ $) 20 (|has| |#1| (-1109)))) (-2865 (((-777) $) 6 (|has| $ (-6 -4452))))) (((-257 |#1|) (-141) (-1227)) (T -257)) -((-2522 (*1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2522 (*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-257 *3)))) (-1450 (*1 *2 *1) (-12 (-4 *1 (-257 *3)) (-4 *3 (-1227)) (-5 *2 (-777)))) (-3222 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-4246 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2954 (*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2808 (*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-3015 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-1433 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2809 (*1 *1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227))))) -(-13 (-1130 |t#1|) (-1004 |t#1|) (-10 -8 (-15 -2522 ($)) (-15 -2522 ($ (-650 |t#1|))) (-15 -1450 ((-777) $)) (-15 -3222 (|t#1| $)) (-15 -4246 (|t#1| $)) (-15 -2954 (|t#1| |t#1| $)) (-15 -2808 (|t#1| |t#1| $)) (-15 -3015 (|t#1| $)) (-15 -1433 (|t#1| $)) (-15 -2809 ($ $)))) -(((-34) . 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"Range not yet evaluated")))))))) 26)) (-1409 (((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -4388 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) (|:| -4388 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 38)) (-2179 (((-650 (-2 (|:| -3679 (-2 (|:| |var| (-1186)) (|:| |fn| 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T) ((-646 #1#) -2811 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-646 |#1|) |has| |#1| (-174)) ((-646 |#2|) |has| |#1| (-368)) ((-646 $) -2811 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-645 (-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((-645 |#2|) |has| |#1| (-368)) ((-723 #1#) -2811 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-723 |#1|) |has| |#1| (-174)) ((-723 |#2|) |has| |#1| (-368)) ((-723 $) -2811 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-732) . 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T) ((-23) . T) ((-47 |#1| #0=(-413 (-570))) . T) ((-25) . T) ((-38 #1=(-413 (-570))) -2854 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2854 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-35) |has| |#1| (-38 (-413 (-570)))) ((-95) |has| |#1| (-38 (-413 (-570)))) ((-102) . T) ((-111 #1# #1#) -2854 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2854 (|has| |#1| (-562)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #1#) -2854 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 |#1|) |has| |#1| (-174)) ((-622 $) -2854 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-619 (-868)) . T) ((-174) -2854 (|has| |#1| (-562)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-235) |has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) ((-245) |has| |#1| (-368)) ((-288) |has| |#1| (-38 (-413 (-570)))) ((-290 #0# |#1|) . 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"TS" 2941657 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2925274 2929393 2929490 "TSETCAT" 2934759 NIL TSETCAT (NIL T T T T) -9 NIL 2936290 NIL) (-1219 2920006 2921606 2923497 "TSETCAT-" 2923502 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2914645 2915492 2916421 "TRMANIP" 2919142 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914086 2914149 2914312 "TRIMAT" 2914577 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2911952 2912189 2912546 "TRIGMNIP" 2913835 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2911472 2911585 2911615 "TRIGCAT" 2911828 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911141 2911220 2911361 "TRIGCAT-" 2911366 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2907986 2909999 2910280 "TREE" 2910895 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2907260 2907788 2907818 "TRANFUN" 2907853 T TRANFUN (NIL) -9 NIL 2907919 NIL) (-1211 2906539 2906730 2907010 "TRANFUN-" 2907015 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2906343 2906375 2906436 "TOPSP" 2906500 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2905691 2905806 2905960 "TOOLSIGN" 2906224 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2904325 2904868 2905107 "TEXTFILE" 2905474 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2902237 2902778 2903207 "TEX" 2903918 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902018 2902049 2902121 "TEX1" 2902200 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2901666 2901729 2901819 "TEMUTL" 2901950 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2899820 2900100 2900425 "TBCMPPK" 2901389 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2891597 2897980 2898036 "TBAGG" 2898436 NIL TBAGG (NIL T T) -9 NIL 2898647 NIL) (-1202 2886667 2888155 2889909 "TBAGG-" 2889914 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886051 2886158 2886303 "TANEXP" 2886556 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2885562 2885826 2885916 "TALGOP" 2885996 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2878952 2885419 2885512 "TABLE" 2885517 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2878364 2878463 2878601 "TABLEAU" 2878849 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2872972 2874192 2875440 "TABLBUMP" 2877150 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872194 2872341 2872522 "SYSTEM" 2872813 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2868653 2869352 2870135 "SYSSOLP" 2871445 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2868451 2868608 2868639 "SYSPTR" 2868644 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2867495 2868000 2868119 "SYSNNI" 2868305 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868390) (-1192 2866802 2867261 2867340 "SYSINT" 2867400 NIL SYSINT (NIL NIL) -8 NIL NIL 2867445) (-1191 2863134 2864080 2864790 "SYNTAX" 2866114 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2860292 2860894 2861526 "SYMTAB" 2862524 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2855541 2856443 2857426 "SYMS" 2859331 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2852776 2854999 2855229 "SYMPOLY" 2855346 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2852293 2852368 2852491 "SYMFUNC" 2852688 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2848313 2849605 2850418 "SYMBOL" 2851502 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2841852 2843541 2845261 "SWITCH" 2846615 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835086 2840673 2840976 "SUTS" 2841607 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827152 2834333 2834606 "SUPXS" 2834871 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2818911 2826770 2826896 "SUP" 2827061 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818070 2818197 2818414 "SUPFRACF" 2818779 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2817691 2817750 2817863 "SUP2" 2818005 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816139 2816413 2816769 "SUMRF" 2817390 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2815474 2815540 2815732 "SUMFS" 2816060 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2799441 2814651 2814902 "SULS" 2815281 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799043 2799263 2799333 "SUCHTAST" 2799393 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2798338 2798568 2798708 "SUCH" 2798951 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792205 2793244 2794203 "SUBSPACE" 2797426 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2791635 2791725 2791889 "SUBRESP" 2792093 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785003 2786300 2787611 "STTF" 2790371 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779176 2780296 2781443 "STTFNC" 2783903 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2770489 2772358 2774152 "STTAYLOR" 2777417 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2763619 2770353 2770436 "STRTBL" 2770441 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2758983 2763574 2763605 "STRING" 2763610 T STRING (NIL) -8 NIL NIL NIL) (-1167 2753812 2758326 2758356 "STRICAT" 2758415 T STRICAT (NIL) -9 NIL 2758477 NIL) (-1166 2746565 2751431 2752042 "STREAM" 2753236 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746075 2746152 2746296 "STREAM3" 2746482 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745057 2745240 2745475 "STREAM2" 2745888 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2744745 2744797 2744890 "STREAM1" 2744999 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2743761 2743942 2744173 "STINPROD" 2744561 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2743313 2743523 2743553 "STEP" 2743633 T STEP (NIL) -9 NIL 2743711 NIL) (-1160 2742500 2742802 2742950 "STEPAST" 2743187 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2735932 2742399 2742476 "STBL" 2742481 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731027 2735123 2735166 "STAGG" 2735319 NIL STAGG (NIL T) -9 NIL 2735408 NIL) (-1157 2728729 2729331 2730203 "STAGG-" 2730208 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2726876 2728499 2728591 "STACK" 2728672 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2719571 2725017 2725473 "SREGSET" 2726506 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2711996 2713365 2714878 "SRDCMPK" 2718177 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2704881 2709406 2709436 "SRAGG" 2710739 T SRAGG (NIL) -9 NIL 2711347 NIL) (-1152 2703898 2704153 2704532 "SRAGG-" 2704537 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2698358 2702845 2703266 "SQMATRIX" 2703524 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692043 2695076 2695803 "SPLTREE" 2697703 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688006 2688699 2689345 "SPLNODE" 2691469 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687053 2687286 2687316 "SPFCAT" 2687760 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2685790 2686000 2686264 "SPECOUT" 2686811 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2676900 2678772 2678802 "SPADXPT" 2683478 T SPADXPT (NIL) -9 NIL 2685642 NIL) (-1145 2676661 2676701 2676770 "SPADPRSR" 2676853 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2674710 2676616 2676647 "SPADAST" 2676652 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2666655 2668428 2668471 "SPACEC" 2672844 NIL SPACEC (NIL T) -9 NIL 2674660 NIL) (-1142 2664785 2666587 2666636 "SPACE3" 2666641 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2663537 2663708 2663999 "SORTPAK" 2664590 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2661629 2661932 2662344 "SOLVETRA" 2663201 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2660679 2660901 2661162 "SOLVESER" 2661402 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2655983 2656871 2657866 "SOLVERAD" 2659731 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2651798 2652407 2653136 "SOLVEFOR" 2655350 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646068 2651147 2651244 "SNTSCAT" 2651249 NIL SNTSCAT (NIL T T T T) -9 NIL 2651319 NIL) (-1135 2640174 2644391 2644782 "SMTS" 2645758 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2634859 2640062 2640139 "SMP" 2640144 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633018 2633319 2633717 "SMITH" 2634556 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2625731 2629927 2630030 "SMATCAT" 2631381 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631931 NIL) (-1131 2622671 2623494 2624672 "SMATCAT-" 2624677 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2620337 2621907 2621950 "SKAGG" 2622211 NIL SKAGG (NIL T) -9 NIL 2622346 NIL) (-1129 2616663 2619810 2619994 "SINT" 2620146 T SINT (NIL) -8 NIL NIL 2620308) (-1128 2616435 2616473 2616539 "SIMPAN" 2616619 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2615714 2615970 2616110 "SIG" 2616317 T SIG (NIL) -8 NIL NIL NIL) (-1126 2614552 2614773 2615048 "SIGNRF" 2615473 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2613385 2613536 2613820 "SIGNEF" 2614381 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2612691 2612968 2613092 "SIGAST" 2613283 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2610381 2610835 2611341 "SHP" 2612232 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2604233 2610282 2610358 "SHDP" 2610363 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2603806 2603998 2604028 "SGROUP" 2604121 T SGROUP (NIL) -9 NIL 2604183 NIL) (-1120 2603664 2603690 2603763 "SGROUP-" 2603768 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2600455 2601153 2601876 "SGCF" 2602963 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2594823 2599902 2599999 "SFRTCAT" 2600004 NIL SFRTCAT (NIL T T T T) -9 NIL 2600043 NIL) (-1117 2588244 2589262 2590398 "SFRGCD" 2593806 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2581370 2582443 2583629 "SFQCMPK" 2587177 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2580990 2581079 2581190 "SFORT" 2581311 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2580108 2580830 2580951 "SEXOF" 2580956 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2579215 2579989 2580057 "SEX" 2580062 T SEX (NIL) -8 NIL NIL NIL) (-1112 2574996 2575711 2575806 "SEXCAT" 2578428 NIL SEXCAT (NIL T T T T T) -9 NIL 2578988 NIL) (-1111 2572149 2574930 2574978 "SET" 2574983 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570373 2570862 2571167 "SETMN" 2571890 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2569869 2570021 2570051 "SETCAT" 2570227 T SETCAT (NIL) -9 NIL 2570337 NIL) (-1108 2569561 2569639 2569769 "SETCAT-" 2569774 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2565922 2568022 2568065 "SETAGG" 2568935 NIL SETAGG (NIL T) -9 NIL 2569275 NIL) (-1106 2565380 2565496 2565733 "SETAGG-" 2565738 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2564823 2565076 2565177 "SEQAST" 2565301 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564022 2564316 2564377 "SEGXCAT" 2564663 NIL SEGXCAT (NIL T T) -9 NIL 2564783 NIL) (-1103 2563028 2563688 2563870 "SEG" 2563875 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562007 2562221 2562264 "SEGCAT" 2562786 NIL SEGCAT (NIL T) -9 NIL 2563007 NIL) (-1101 2560939 2561370 2561578 "SEGBIND" 2561834 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2560560 2560619 2560732 "SEGBIND2" 2560874 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560133 2560361 2560438 "SEGAST" 2560505 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559352 2559478 2559682 "SEG2" 2559977 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2558762 2559287 2559334 "SDVAR" 2559339 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551289 2558532 2558662 "SDPOL" 2558667 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2549882 2550148 2550467 "SCPKG" 2551004 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549046 2549218 2549410 "SCOPE" 2549712 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548266 2548400 2548579 "SCACHE" 2548901 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2547912 2548098 2548128 "SASTCAT" 2548133 T SASTCAT (NIL) -9 NIL 2548146 NIL) (-1091 2547399 2547747 2547823 "SAOS" 2547858 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2546964 2546999 2547172 "SAERFFC" 2547358 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2540903 2546861 2546941 "SAE" 2546946 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2540496 2540531 2540690 "SAEFACT" 2540862 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2538817 2539131 2539532 "RURPK" 2540162 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2537454 2537760 2538065 "RULESET" 2538651 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2534677 2535207 2535665 "RULE" 2537135 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534289 2534471 2534554 "RULECOLD" 2534629 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534079 2534107 2534178 "RTVALUE" 2534240 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2533550 2533796 2533890 "RSTRCAST" 2534007 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528398 2529193 2530113 "RSETGCD" 2532749 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2517628 2522707 2522804 "RSETCAT" 2526923 NIL RSETCAT (NIL T T T T) -9 NIL 2528020 NIL) (-1079 2515555 2516094 2516918 "RSETCAT-" 2516923 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2507941 2509317 2510837 "RSDCMPK" 2514154 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505920 2506387 2506461 "RRCC" 2507547 NIL RRCC (NIL T T) -9 NIL 2507891 NIL) (-1076 2505271 2505445 2505724 "RRCC-" 2505729 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2504714 2504967 2505068 "RPTAST" 2505192 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2478560 2487919 2487986 "RPOLCAT" 2498652 NIL RPOLCAT (NIL T T T) -9 NIL 2501812 NIL) (-1073 2470058 2472398 2475520 "RPOLCAT-" 2475525 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2460989 2468269 2468751 "ROUTINE" 2469598 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2457787 2460615 2460755 "ROMAN" 2460871 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456031 2456647 2456907 "ROIRC" 2457592 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452263 2454547 2454577 "RNS" 2454881 T RNS (NIL) -9 NIL 2455155 NIL) (-1068 2450772 2451155 2451689 "RNS-" 2451764 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450175 2450583 2450613 "RNG" 2450618 T RNG (NIL) -9 NIL 2450639 NIL) (-1066 2449178 2449540 2449742 "RNGBIND" 2450026 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2448577 2448965 2449008 "RMODULE" 2449013 NIL RMODULE (NIL T) -9 NIL 2449040 NIL) (-1064 2447413 2447507 2447843 "RMCAT2" 2448478 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444263 2446759 2447056 "RMATRIX" 2447175 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437090 2439350 2439465 "RMATCAT" 2442824 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443806 NIL) (-1061 2436465 2436612 2436919 "RMATCAT-" 2436924 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2435866 2436087 2436130 "RLINSET" 2436324 NIL RLINSET (NIL T) -9 NIL 2436415 NIL) (-1059 2435433 2435508 2435636 "RINTERP" 2435785 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2434491 2435045 2435075 "RING" 2435131 T RING (NIL) -9 NIL 2435223 NIL) (-1057 2434283 2434327 2434424 "RING-" 2434429 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433124 2433361 2433619 "RIDIST" 2434047 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2424413 2432592 2432798 "RGCHAIN" 2432972 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2423763 2424169 2424210 "RGBCSPC" 2424268 NIL RGBCSPC (NIL T) -9 NIL 2424320 NIL) (-1053 2422921 2423302 2423343 "RGBCMDL" 2423575 NIL RGBCMDL (NIL T) -9 NIL 2423689 NIL) (-1052 2419915 2420529 2421199 "RF" 2422285 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2419561 2419624 2419727 "RFFACTOR" 2419846 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419286 2419321 2419418 "RFFACT" 2419520 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2417403 2417767 2418149 "RFDIST" 2418926 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2416856 2416948 2417111 "RETSOL" 2417305 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2416492 2416572 2416615 "RETRACT" 2416748 NIL RETRACT (NIL T) -9 NIL 2416835 NIL) (-1046 2416341 2416366 2416453 "RETRACT-" 2416458 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2415943 2416163 2416233 "RETAST" 2416293 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2408681 2415596 2415723 "RESULT" 2415838 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407272 2407950 2408149 "RESRING" 2408584 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2406908 2406957 2407055 "RESLATC" 2407209 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2406613 2406648 2406755 "REPSQ" 2406867 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404035 2404615 2405217 "REP" 2406033 T REP (NIL) -7 NIL NIL NIL) (-1039 2403732 2403767 2403878 "REPDB" 2403994 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2397632 2399021 2400244 "REP2" 2402544 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394009 2394690 2395498 "REP1" 2396859 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2386705 2392150 2392606 "REGSET" 2393639 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2385470 2385853 2386103 "REF" 2386490 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2384847 2384950 2385117 "REDORDER" 2385354 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2380815 2384060 2384287 "RECLOS" 2384675 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2379867 2380048 2380263 "REALSOLV" 2380622 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2379713 2379754 2379784 "REAL" 2379789 T REAL (NIL) -9 NIL 2379824 NIL) (-1030 2376196 2376998 2377882 "REAL0Q" 2378878 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2371797 2372785 2373846 "REAL0" 2375177 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371268 2371514 2371608 "RDUCEAST" 2371725 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2370673 2370745 2370952 "RDIV" 2371190 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2369741 2369915 2370128 "RDIST" 2370495 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368338 2368625 2368997 "RDETRS" 2369449 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366150 2366604 2367142 "RDETR" 2367880 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2364775 2365053 2365450 "RDEEFS" 2365866 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363284 2363590 2364015 "RDEEF" 2364463 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357345 2360265 2360295 "RCFIELD" 2361590 T RCFIELD (NIL) -9 NIL 2362321 NIL) (-1020 2355409 2355913 2356609 "RCFIELD-" 2356684 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2351678 2353510 2353553 "RCAGG" 2354637 NIL RCAGG (NIL T) -9 NIL 2355102 NIL) (-1018 2351306 2351400 2351563 "RCAGG-" 2351568 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2350641 2350753 2350918 "RATRET" 2351190 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350194 2350261 2350382 "RATFACT" 2350569 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2349502 2349622 2349774 "RANDSRC" 2350064 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349236 2349280 2349353 "RADUTIL" 2349451 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2342350 2348067 2348378 "RADIX" 2348959 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2333969 2342192 2342322 "RADFF" 2342327 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2333616 2333691 2333721 "RADCAT" 2333881 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2333398 2333446 2333546 "RADCAT-" 2333551 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2331496 2333168 2333260 "QUEUE" 2333341 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328033 2331429 2331477 "QUAT" 2331482 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2327664 2327707 2327838 "QUATCT2" 2327984 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321075 2324420 2324462 "QUATCAT" 2325253 NIL QUATCAT (NIL T) -9 NIL 2326019 NIL) (-1005 2317214 2318251 2319641 "QUATCAT-" 2319737 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2314679 2316290 2316333 "QUAGG" 2316714 NIL QUAGG (NIL T) -9 NIL 2316889 NIL) (-1003 2314281 2314501 2314571 "QQUTAST" 2314631 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313294 2313794 2313959 "QFORM" 2314162 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304287 2309526 2309568 "QFCAT" 2310236 NIL QFCAT (NIL T) -9 NIL 2311237 NIL) (-1000 2299854 2301055 2302649 "QFCAT-" 2302745 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2299488 2299531 2299660 "QFCAT2" 2299805 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2298948 2299058 2299188 "QEQUAT" 2299378 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2292094 2293167 2294351 "QCMPACK" 2297881 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2289643 2290091 2290519 "QALGSET" 2291749 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2288888 2289062 2289294 "QALGSET2" 2289463 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2287578 2287802 2288119 "PWFFINTB" 2288661 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2285760 2285928 2286282 "PUSHVAR" 2287392 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2281678 2282732 2282773 "PTRANFN" 2284657 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280080 2280371 2280693 "PTPACK" 2281389 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2279712 2279769 2279878 "PTFUNC2" 2280017 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274157 2278554 2278595 "PTCAT" 2278891 NIL PTCAT (NIL T) -9 NIL 2279044 NIL) (-988 2273815 2273850 2273974 "PSQFR" 2274116 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272410 2272708 2273042 "PSEUDLIN" 2273513 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259173 2261544 2263868 "PSETPK" 2270170 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252191 2254931 2255027 "PSETCAT" 2258048 NIL PSETCAT (NIL T T T T) -9 NIL 2258862 NIL) (-984 2250027 2250661 2251482 "PSETCAT-" 2251487 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2249376 2249541 2249569 "PSCURVE" 2249837 T PSCURVE (NIL) -9 NIL 2250004 NIL) (-982 2245374 2246890 2246955 "PSCAT" 2247799 NIL PSCAT (NIL T T T) -9 NIL 2248039 NIL) (-981 2244437 2244653 2245053 "PSCAT-" 2245058 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2242796 2243506 2243769 "PRTITION" 2244194 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2242271 2242517 2242609 "PRTDAST" 2242724 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2231361 2233575 2235763 "PRS" 2240133 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2229172 2230711 2230751 "PRQAGG" 2230934 NIL PRQAGG (NIL T) -9 NIL 2231036 NIL) (-976 2228508 2228813 2228841 "PROPLOG" 2228980 T PROPLOG (NIL) -9 NIL 2229095 NIL) (-975 2228112 2228169 2228292 "PROPFUN2" 2228431 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2227427 2227548 2227720 "PROPFUN1" 2227973 NIL 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2064774 2065617 2065645 "PDECAT" 2066432 T PDECAT (NIL) -9 NIL 2067145 NIL) (-901 2064525 2064558 2064648 "PCOMP" 2064735 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-900 2062703 2063326 2063623 "PBWLB" 2064254 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-899 2055176 2056776 2058114 "PATTERN" 2061386 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-898 2054808 2054865 2054974 "PATTERN2" 2055113 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2052565 2052953 2053410 "PATTERN1" 2054397 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2049933 2050514 2050995 "PATRES" 2052130 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-895 2049497 2049564 2049696 "PATRES2" 2049860 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2047380 2047785 2048192 "PATMATCH" 2049164 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-893 2046890 2047099 2047140 "PATMAB" 2047247 NIL PATMAB (NIL T) -9 NIL 2047330 NIL) (-892 2045408 2045744 2046002 "PATLRES" 2046695 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-891 2044954 2045077 2045118 "PATAB" 2045123 NIL PATAB (NIL T) -9 NIL 2045295 NIL) (-890 2043136 2043531 2043954 "PARTPERM" 2044551 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2042757 2042820 2042922 "PARSURF" 2043067 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042389 2042446 2042555 "PARSU2" 2042694 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042153 2042193 2042260 "PARSER" 2042342 T PARSER (NIL) -7 NIL NIL NIL) (-886 2041774 2041837 2041939 "PARSCURV" 2042084 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041406 2041463 2041572 "PARSC2" 2041711 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041045 2041103 2041200 "PARPCURV" 2041342 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2040677 2040734 2040843 "PARPC2" 2040982 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2039738 2040050 2040232 "PARAMAST" 2040515 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039258 2039344 2039463 "PAN2EXPR" 2039639 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038035 2038379 2038607 "PALETTE" 2039050 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036428 2037040 2037400 "PAIR" 2037721 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030296 2035685 2035880 "PADICRC" 2036282 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023523 2029640 2029825 "PADICRAT" 2030143 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2021838 2023460 2023505 "PADIC" 2023510 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2018948 2020512 2020552 "PADICCT" 2021133 NIL PADICCT (NIL NIL) -9 NIL 2021415 NIL) (-874 2017905 2018105 2018373 "PADEPAC" 2018735 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017117 2017250 2017456 "PADE" 2017767 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015504 2016325 2016605 "OWP" 2016921 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2014997 2015210 2015307 "OVERSET" 2015427 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014043 2014602 2014774 "OVAR" 2014865 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013307 2013428 2013589 "OUT" 2013902 T OUT (NIL) -7 NIL NIL NIL) (-868 2002179 2004416 2006616 "OUTFORM" 2011127 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001515 2001776 2001903 "OUTBFILE" 2002072 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2000822 2000987 2001015 "OUTBCON" 2001333 T OUTBCON (NIL) -9 NIL 2001499 NIL) (-865 2000423 2000535 2000692 "OUTBCON-" 2000697 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1999803 2000152 2000241 "OSI" 2000354 T OSI (NIL) -8 NIL NIL NIL) (-863 1999333 1999671 1999699 "OSGROUP" 1999704 T OSGROUP (NIL) -9 NIL 1999726 NIL) (-862 1998078 1998305 1998590 "ORTHPOL" 1999080 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995629 1997913 1998034 "OREUP" 1998039 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993032 1995320 1995447 "ORESUP" 1995571 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990560 1991060 1991621 "OREPCTO" 1992521 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984246 1986447 1986488 "OREPCAT" 1988836 NIL OREPCAT (NIL T) -9 NIL 1989940 NIL) (-857 1981393 1982175 1983233 "OREPCAT-" 1983238 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980544 1980842 1980870 "ORDSET" 1981179 T ORDSET (NIL) -9 NIL 1981343 NIL) (-855 1979975 1980123 1980347 "ORDSET-" 1980352 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978540 1979331 1979359 "ORDRING" 1979561 T ORDRING (NIL) -9 NIL 1979686 NIL) (-853 1978185 1978279 1978423 "ORDRING-" 1978428 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977565 1978028 1978056 "ORDMON" 1978061 T ORDMON (NIL) -9 NIL 1978082 NIL) (-851 1976727 1976874 1977069 "ORDFUNS" 1977414 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976065 1976484 1976512 "ORDFIN" 1976577 T ORDFIN (NIL) -9 NIL 1976651 NIL) (-849 1972624 1974651 1975060 "ORDCOMP" 1975689 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1971890 1972017 1972203 "ORDCOMP2" 1972484 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968471 1969381 1970195 "OPTPROB" 1971096 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965273 1965912 1966616 "OPTPACK" 1967787 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1962960 1963726 1963754 "OPTCAT" 1964573 T OPTCAT (NIL) -9 NIL 1965223 NIL) (-844 1962344 1962637 1962742 "OPSIG" 1962875 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962112 1962151 1962217 "OPQUERY" 1962298 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959243 1960423 1960927 "OP" 1961641 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958617 1958843 1958884 "OPERCAT" 1959096 NIL OPERCAT (NIL T) -9 NIL 1959193 NIL) (-840 1958372 1958428 1958545 "OPERCAT-" 1958550 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955185 1957169 1957538 "ONECOMP" 1958036 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954490 1954605 1954779 "ONECOMP2" 1955057 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953909 1954015 1954145 "OMSERVER" 1954380 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1950771 1953349 1953389 "OMSAGG" 1953450 NIL OMSAGG (NIL T) -9 NIL 1953514 NIL) (-835 1949394 1949657 1949939 "OMPKG" 1950509 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1948824 1948927 1948955 "OM" 1949254 T OM (NIL) -9 NIL NIL NIL) (-833 1947371 1948373 1948542 "OMLO" 1948705 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946331 1946478 1946698 "OMEXPR" 1947197 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945622 1945877 1946013 "OMERR" 1946215 T OMERR (NIL) -8 NIL NIL NIL) (-830 1944773 1945043 1945203 "OMERRK" 1945482 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944224 1944450 1944558 "OMENC" 1944685 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938119 1939304 1940475 "OMDEV" 1943073 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937188 1937359 1937553 "OMCONN" 1937945 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1935709 1936685 1936713 "OINTDOM" 1936718 T OINTDOM (NIL) -9 NIL 1936739 NIL) (-825 1933047 1934397 1934734 "OFMONOID" 1935404 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932458 1932984 1933029 "ODVAR" 1933034 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1929881 1932203 1932358 "ODR" 1932363 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922462 1929657 1929783 "ODPOL" 1929788 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916284 1922334 1922439 "ODP" 1922444 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915050 1915265 1915540 "ODETOOLS" 1916058 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912017 1912675 1913391 "ODESYS" 1914383 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1906899 1907807 1908832 "ODERTRIC" 1911092 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906325 1906407 1906601 "ODERED" 1906811 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903213 1903761 1904438 "ODERAT" 1905748 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900172 1900637 1901234 "ODEPRRIC" 1902742 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898115 1898711 1899197 "ODEPROB" 1899706 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894635 1895120 1895767 "ODEPRIM" 1897594 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1893884 1893986 1894246 "ODEPAL" 1894527 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890046 1890837 1891701 "ODEPACK" 1893040 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889107 1889214 1889436 "ODEINT" 1889935 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883208 1884633 1886080 "ODEIFTBL" 1887680 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878606 1879392 1880344 "ODEEF" 1882367 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1877955 1878044 1878267 "ODECONST" 1878511 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876080 1876741 1876769 "ODECAT" 1877374 T ODECAT (NIL) -9 NIL 1877905 NIL) (-805 1872935 1875785 1875907 "OCT" 1875990 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872573 1872616 1872743 "OCTCT2" 1872886 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867184 1869619 1869659 "OC" 1870756 NIL OC (NIL T) -9 NIL 1871614 NIL) (-802 1864411 1865159 1866149 "OC-" 1866243 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1863763 1864231 1864259 "OCAMON" 1864264 T OCAMON (NIL) -9 NIL 1864285 NIL) (-800 1863294 1863635 1863663 "OASGP" 1863668 T OASGP (NIL) -9 NIL 1863688 NIL) (-799 1862555 1863044 1863072 "OAMONS" 1863112 T OAMONS (NIL) -9 NIL 1863155 NIL) (-798 1861969 1862402 1862430 "OAMON" 1862435 T OAMON (NIL) -9 NIL 1862455 NIL) (-797 1861227 1861745 1861773 "OAGROUP" 1861778 T OAGROUP (NIL) -9 NIL 1861798 NIL) (-796 1860917 1860967 1861055 "NUMTUBE" 1861171 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854490 1856008 1857544 "NUMQUAD" 1859401 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850246 1851234 1852259 "NUMODE" 1853485 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847601 1848481 1848509 "NUMINT" 1849432 T NUMINT (NIL) -9 NIL 1850196 NIL) (-792 1846549 1846746 1846964 "NUMFMT" 1847403 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1832908 1835853 1838385 "NUMERIC" 1844056 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827278 1832357 1832452 "NTSCAT" 1832457 NIL NTSCAT (NIL T T T T) -9 NIL 1832496 NIL) (-789 1826472 1826637 1826830 "NTPOLFN" 1827117 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814549 1823297 1824109 "NSUP" 1825693 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814181 1814238 1814347 "NSUP2" 1814486 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804407 1813955 1814088 "NSMP" 1814093 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1802839 1803140 1803497 "NREP" 1804095 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801430 1801682 1802040 "NPCOEF" 1802582 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800496 1800611 1800827 "NORMRETR" 1801311 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798537 1798827 1799236 "NORMPK" 1800204 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798222 1798250 1798374 "NORMMA" 1798503 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798022 1798179 1798208 "NONE" 1798213 T NONE (NIL) -8 NIL NIL NIL) (-779 1797811 1797840 1797909 "NONE1" 1797986 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797308 1797370 1797549 "NODE1" 1797743 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795593 1796444 1796699 "NNI" 1797046 T NNI (NIL) -8 NIL NIL 1797281) (-776 1794013 1794326 1794690 "NLINSOL" 1795261 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790254 1791249 1792148 "NIPROB" 1793134 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789011 1789245 1789547 "NFINTBAS" 1790016 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788185 1788661 1788702 "NETCLT" 1788874 NIL NETCLT (NIL T) -9 NIL 1788956 NIL) (-772 1786893 1787124 1787405 "NCODIV" 1787953 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786655 1786692 1786767 "NCNTFRAC" 1786850 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1784835 1785199 1785619 "NCEP" 1786280 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1783686 1784459 1784487 "NASRING" 1784597 T NASRING (NIL) -9 NIL 1784677 NIL) (-768 1783481 1783525 1783619 "NASRING-" 1783624 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782588 1783113 1783141 "NARNG" 1783258 T NARNG (NIL) -9 NIL 1783349 NIL) (-766 1782280 1782347 1782481 "NARNG-" 1782486 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781159 1781366 1781601 "NAGSP" 1782065 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772431 1774115 1775788 "NAGS" 1779506 T NAGS (NIL) -7 NIL NIL NIL) (-763 1770979 1771287 1771618 "NAGF07" 1772120 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765517 1766808 1768115 "NAGF04" 1769692 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758485 1760099 1761732 "NAGF02" 1763904 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1753709 1754809 1755926 "NAGF01" 1757388 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747337 1748903 1750488 "NAGE04" 1752144 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738506 1740627 1742757 "NAGE02" 1745227 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734459 1735406 1736370 "NAGE01" 1737562 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732254 1732788 1733346 "NAGD03" 1733921 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724004 1725932 1727886 "NAGD02" 1730320 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1717815 1719240 1720680 "NAGD01" 1722584 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714024 1714846 1715683 "NAGC06" 1716998 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712489 1712821 1713177 "NAGC05" 1713688 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1711865 1711984 1712128 "NAGC02" 1712365 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1710824 1711407 1711447 "NAALG" 1711526 NIL NAALG (NIL T) -9 NIL 1711587 NIL) (-749 1710659 1710688 1710778 "NAALG-" 1710783 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704609 1705717 1706904 "MULTSQFR" 1709555 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1703928 1704003 1704187 "MULTFACT" 1704521 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696652 1700565 1700618 "MTSCAT" 1701688 NIL MTSCAT (NIL T T) -9 NIL 1702203 NIL) (-745 1696364 1696418 1696510 "MTHING" 1696592 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696156 1696189 1696249 "MSYSCMD" 1696324 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692238 1694911 1695231 "MSET" 1695869 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689307 1691799 1691840 "MSETAGG" 1691845 NIL MSETAGG (NIL T) -9 NIL 1691879 NIL) (-741 1685149 1686686 1687431 "MRING" 1688607 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1684715 1684782 1684913 "MRF2" 1685076 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684333 1684368 1684512 "MRATFAC" 1684674 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1681945 1682240 1682671 "MPRFF" 1684038 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676242 1681799 1681896 "MPOLY" 1681901 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1675732 1675767 1675975 "MPCPF" 1676201 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675246 1675289 1675473 "MPC3" 1675683 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674441 1674522 1674743 "MPC2" 1675161 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1672742 1673079 1673469 "MONOTOOL" 1674101 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1671967 1672284 1672312 "MONOID" 1672531 T MONOID (NIL) -9 NIL 1672678 NIL) (-731 1671513 1671632 1671813 "MONOID-" 1671818 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1661988 1667939 1667998 "MONOGEN" 1668672 NIL MONOGEN (NIL T T) -9 NIL 1669128 NIL) (-729 1659206 1659941 1660941 "MONOGEN-" 1661060 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658039 1658485 1658513 "MONADWU" 1658905 T MONADWU (NIL) -9 NIL 1659143 NIL) (-727 1657411 1657570 1657818 "MONADWU-" 1657823 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1656770 1657014 1657042 "MONAD" 1657249 T MONAD (NIL) -9 NIL 1657361 NIL) (-725 1656455 1656533 1656665 "MONAD-" 1656670 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1654744 1655368 1655647 "MOEBIUS" 1656208 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654022 1654426 1654466 "MODULE" 1654471 NIL MODULE (NIL T) -9 NIL 1654510 NIL) (-722 1653590 1653686 1653876 "MODULE-" 1653881 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651270 1651954 1652281 "MODRING" 1653414 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648214 1649375 1649896 "MODOP" 1650799 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1646802 1647281 1647558 "MODMONOM" 1648077 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1636846 1645093 1645507 "MODMON" 1646439 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634002 1635690 1635966 "MODFIELD" 1636721 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1632979 1633283 1633473 "MMLFORM" 1633832 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632505 1632548 1632727 "MMAP" 1632930 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630584 1631351 1631392 "MLO" 1631815 NIL MLO (NIL T) -9 NIL 1632057 NIL) (-713 1627950 1628466 1629068 "MLIFT" 1630065 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627341 1627425 1627579 "MKUCFUNC" 1627861 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1626940 1627010 1627133 "MKRECORD" 1627264 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1625987 1626149 1626377 "MKFUNC" 1626751 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625375 1625479 1625635 "MKFLCFN" 1625870 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624652 1624754 1624939 "MKBCFUNC" 1625268 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621359 1624206 1624342 "MINT" 1624536 T MINT (NIL) -8 NIL NIL NIL) (-706 1620171 1620414 1620691 "MHROWRED" 1621114 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615551 1618706 1619111 "MFLOAT" 1619786 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1614908 1614984 1615155 "MFINFACT" 1615463 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611223 1612071 1612955 "MESH" 1614044 T MESH (NIL) -7 NIL NIL NIL) (-702 1609613 1609925 1610278 "MDDFACT" 1610910 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606408 1608772 1608813 "MDAGG" 1609068 NIL MDAGG (NIL T) -9 NIL 1609211 NIL) (-700 1596148 1605701 1605908 "MCMPLX" 1606221 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595285 1595431 1595632 "MCDEN" 1595997 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593175 1593445 1593825 "MCALCFN" 1595015 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592100 1592340 1592573 "MAYBE" 1592981 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1589712 1590235 1590797 "MATSTOR" 1591571 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1585669 1589084 1589332 "MATRIX" 1589497 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581435 1582142 1582878 "MATLIN" 1585026 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571541 1574727 1574804 "MATCAT" 1579684 NIL MATCAT (NIL T T T) -9 NIL 1581101 NIL) (-692 1567897 1568918 1570274 "MATCAT-" 1570279 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566491 1566644 1566977 "MATCAT2" 1567732 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564603 1564927 1565311 "MAPPKG3" 1566166 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563584 1563757 1563979 "MAPPKG2" 1564427 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562083 1562367 1562694 "MAPPKG1" 1563290 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561162 1561489 1561666 "MAPPAST" 1561926 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1560773 1560831 1560954 "MAPHACK3" 1561098 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560365 1560426 1560540 "MAPHACK2" 1560705 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1559803 1559906 1560048 "MAPHACK1" 1560256 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1557882 1558503 1558807 "MAGMA" 1559531 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557361 1557606 1557697 "MACROAST" 1557811 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1553779 1555600 1556061 "M3D" 1556933 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1547854 1552118 1552159 "LZSTAGG" 1552941 NIL LZSTAGG (NIL T) -9 NIL 1553236 NIL) (-679 1543812 1544985 1546442 "LZSTAGG-" 1546447 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1540899 1541703 1542190 "LWORD" 1543357 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540475 1540703 1540778 "LSTAST" 1540844 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1533641 1540246 1540380 "LSQM" 1540385 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1532865 1533004 1533232 "LSPP" 1533496 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1530677 1530978 1531434 "LSMP" 1532554 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527456 1528130 1528860 "LSMP1" 1529979 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521302 1526593 1526634 "LSAGG" 1526696 NIL LSAGG (NIL T) -9 NIL 1526774 NIL) (-671 1517997 1518921 1520134 "LSAGG-" 1520139 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515596 1517141 1517390 "LPOLY" 1517792 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515178 1515263 1515386 "LPEFRAC" 1515505 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513499 1514272 1514525 "LO" 1515010 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513151 1513263 1513291 "LOGIC" 1513402 T LOGIC (NIL) -9 NIL 1513483 NIL) (-666 1513013 1513036 1513107 "LOGIC-" 1513112 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512206 1512346 1512539 "LODOOPS" 1512869 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1509629 1512122 1512188 "LODO" 1512193 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508167 1508402 1508755 "LODOF" 1509376 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504371 1506802 1506843 "LODOCAT" 1507281 NIL LODOCAT (NIL T) -9 NIL 1507492 NIL) (-661 1504104 1504162 1504289 "LODOCAT-" 1504294 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501424 1503945 1504063 "LODO2" 1504068 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1498859 1501361 1501406 "LODO1" 1501411 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1497740 1497905 1498210 "LODEEF" 1498682 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493043 1495934 1495975 "LNAGG" 1496837 NIL LNAGG (NIL T) -9 NIL 1497272 NIL) (-656 1492190 1492404 1492746 "LNAGG-" 1492751 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488326 1489115 1489754 "LMOPS" 1491605 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1487729 1488117 1488158 "LMODULE" 1488163 NIL LMODULE (NIL T) -9 NIL 1488189 NIL) (-653 1484927 1487374 1487497 "LMDICT" 1487639 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484333 1484554 1484595 "LLINSET" 1484786 NIL LLINSET (NIL T) -9 NIL 1484877 NIL) (-651 1484032 1484241 1484301 "LITERAL" 1484306 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477195 1482966 1483270 "LIST" 1483761 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1476720 1476794 1476933 "LIST3" 1477115 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1475727 1475905 1476133 "LIST2" 1476538 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1473861 1474173 1474572 "LIST2MAP" 1475374 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473457 1473694 1473735 "LINSET" 1473740 NIL LINSET (NIL T) -9 NIL 1473774 NIL) (-645 1472118 1472788 1472829 "LINEXP" 1473084 NIL LINEXP (NIL T) -9 NIL 1473233 NIL) (-644 1470765 1471025 1471322 "LINDEP" 1471870 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467532 1468251 1469028 "LIMITRF" 1470020 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1465835 1466131 1466540 "LIMITPS" 1467227 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460263 1465346 1465574 "LIE" 1465656 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459211 1459680 1459720 "LIECAT" 1459860 NIL LIECAT (NIL T) -9 NIL 1460011 NIL) (-639 1459052 1459079 1459167 "LIECAT-" 1459172 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451639 1458592 1458748 "LIB" 1458916 T LIB (NIL) -8 NIL NIL NIL) (-637 1447274 1448157 1449092 "LGROBP" 1450756 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445272 1445546 1445896 "LF" 1446995 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444112 1444804 1444832 "LFCAT" 1445039 T LFCAT (NIL) -9 NIL 1445178 NIL) (-634 1441014 1441644 1442332 "LEXTRIPK" 1443476 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1437758 1438584 1439087 "LEXP" 1440594 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437234 1437479 1437571 "LETAST" 1437686 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435632 1435945 1436346 "LEADCDET" 1436916 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1434822 1434896 1435125 "LAZM3PK" 1435553 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429739 1432899 1433437 "LAUPOL" 1434334 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429318 1429362 1429523 "LAPLACE" 1429689 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427257 1428419 1428670 "LA" 1429151 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426251 1426835 1426876 "LALG" 1426938 NIL LALG (NIL T) -9 NIL 1426997 NIL) (-625 1425965 1426024 1426160 "LALG-" 1426165 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1425800 1425824 1425865 "KVTFROM" 1425927 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424723 1425167 1425352 "KTVLOGIC" 1425635 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424558 1424582 1424623 "KRCFROM" 1424685 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423462 1423649 1423948 "KOVACIC" 1424358 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423297 1423321 1423362 "KONVERT" 1423424 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423132 1423156 1423197 "KOERCE" 1423259 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1420962 1421725 1422102 "KERNEL" 1422788 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420458 1420539 1420671 "KERNEL2" 1420876 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414228 1418997 1419051 "KDAGG" 1419428 NIL KDAGG (NIL T T) -9 NIL 1419634 NIL) (-615 1413757 1413881 1414086 "KDAGG-" 1414091 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1406905 1413418 1413573 "KAFILE" 1413635 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401333 1406416 1406644 "JORDAN" 1406726 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400712 1400982 1401103 "JOINAST" 1401232 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400558 1400617 1400672 "JAVACODE" 1400677 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1396810 1398763 1398817 "IXAGG" 1399746 NIL IXAGG (NIL T T) -9 NIL 1400205 NIL) (-609 1395729 1396035 1396454 "IXAGG-" 1396459 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391259 1395651 1395710 "IVECTOR" 1395715 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390025 1390262 1390528 "ITUPLE" 1391026 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388527 1388704 1388999 "ITRIGMNP" 1389847 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387272 1387476 1387759 "ITFUN3" 1388303 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1386904 1386961 1387070 "ITFUN2" 1387209 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386063 1386384 1386558 "ITFORM" 1386750 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384024 1385083 1385361 "ITAYLOR" 1385818 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1372969 1378161 1379324 "ISUPS" 1382894 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372073 1372213 1372449 "ISUMP" 1372816 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367448 1372018 1372059 "ISTRING" 1372064 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1366924 1367169 1367261 "ISAST" 1367376 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366133 1366215 1366431 "IRURPK" 1366838 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365069 1365270 1365510 "IRSN" 1365913 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363140 1363495 1363924 "IRRF2F" 1364707 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1362887 1362925 1363001 "IRREDFFX" 1363096 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361502 1361761 1362060 "IROOT" 1362620 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358106 1359186 1359878 "IR" 1360842 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357311 1357599 1357750 "IRFORM" 1357975 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1354924 1355419 1355985 "IR2" 1356789 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354024 1354137 1354351 "IR2F" 1354807 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1353815 1353849 1353909 "IPRNTPK" 1353984 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350396 1353704 1353773 "IPF" 1353778 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348723 1350321 1350378 "IPADIC" 1350383 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348035 1348283 1348413 "IP4ADDR" 1348613 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347409 1347664 1347796 "IOMODE" 1347923 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346482 1347006 1347133 "IOBFILE" 1347302 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1345970 1346386 1346414 "IOBCON" 1346419 T IOBCON (NIL) -9 NIL 1346440 NIL) (-581 1345481 1345539 1345722 "INVLAPLA" 1345906 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335129 1337483 1339869 "INTTR" 1343145 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331464 1332206 1333071 "INTTOOLS" 1334314 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331050 1331141 1331258 "INTSLPE" 1331367 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329003 1330973 1331032 "INTRVL" 1331037 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326605 1327117 1327692 "INTRF" 1328488 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326016 1326113 1326255 "INTRET" 1326503 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324013 1324402 1324872 "INTRAT" 1325624 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321276 1321859 1322478 "INTPM" 1323498 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318021 1318620 1319358 "INTPAF" 1320662 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313200 1314162 1315213 "INTPACK" 1316990 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310148 1312997 1313106 "INT" 1313111 T INT (NIL) -8 NIL NIL NIL) (-569 1309400 1309552 1309760 "INTHERTR" 1309990 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1308839 1308919 1309107 "INTHERAL" 1309314 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306685 1307128 1307585 "INTHEORY" 1308402 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298091 1299712 1301484 "INTG0" 1305037 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278664 1283454 1288264 "INTFTBL" 1293301 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1277913 1278051 1278224 "INTFACT" 1278523 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275340 1275786 1276343 "INTEF" 1277467 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273707 1274446 1274474 "INTDOM" 1274775 T INTDOM (NIL) -9 NIL 1274982 NIL) (-561 1273076 1273250 1273492 "INTDOM-" 1273497 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269464 1271392 1271446 "INTCAT" 1272245 NIL INTCAT (NIL T) -9 NIL 1272566 NIL) (-559 1268936 1269039 1269167 "INTBIT" 1269356 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267635 1267789 1268096 "INTALG" 1268781 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267118 1267208 1267365 "INTAF" 1267539 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260461 1266928 1267068 "INTABL" 1267073 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1259802 1260268 1260333 "INT8" 1260367 T INT8 (NIL) -8 NIL NIL 1260412) (-554 1259142 1259608 1259673 "INT64" 1259707 T INT64 (NIL) -8 NIL NIL 1259752) (-553 1258482 1258948 1259013 "INT32" 1259047 T INT32 (NIL) -8 NIL NIL 1259092) (-552 1257822 1258288 1258353 "INT16" 1258387 T INT16 (NIL) -8 NIL NIL 1258432) (-551 1252732 1255445 1255473 "INS" 1256407 T INS (NIL) -9 NIL 1257072 NIL) (-550 1249972 1250743 1251717 "INS-" 1251790 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1248747 1248974 1249272 "INPSIGN" 1249725 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1247865 1247982 1248179 "INPRODPF" 1248627 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1246759 1246876 1247113 "INPRODFF" 1247745 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1245759 1245911 1246171 "INNMFACT" 1246595 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1244956 1245053 1245241 "INMODGCD" 1245658 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243464 1243709 1244033 "INFSP" 1244701 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242648 1242765 1242948 "INFPROD0" 1243344 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239503 1240713 1241228 "INFORM" 1242141 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239113 1239173 1239271 "INFORM1" 1239438 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238636 1238725 1238839 "INFINITY" 1239019 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1237812 1238356 1238457 "INETCLTS" 1238555 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236428 1236678 1236999 "INEP" 1237560 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235677 1236325 1236390 "INDE" 1236395 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235241 1235309 1235426 "INCRMAPS" 1235604 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234059 1234510 1234716 "INBFILE" 1235055 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229358 1230295 1231239 "INBFF" 1233147 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228266 1228535 1228563 "INBCON" 1229076 T INBCON (NIL) -9 NIL 1229342 NIL) (-532 1227518 1227741 1228017 "INBCON-" 1228022 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1226997 1227242 1227333 "INAST" 1227447 T INAST (NIL) -8 NIL NIL NIL) (-530 1226424 1226676 1226782 "IMPTAST" 1226911 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1222870 1226268 1226372 "IMATRIX" 1226377 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221578 1221701 1222017 "IMATQF" 1222726 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1219798 1220025 1220362 "IMATLIN" 1221334 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214376 1219722 1219780 "ILIST" 1219785 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212281 1214236 1214349 "IIARRAY2" 1214354 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207679 1212192 1212256 "IFF" 1212261 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207026 1207296 1207412 "IFAST" 1207583 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202021 1206318 1206506 "IFARRAY" 1206883 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201201 1201925 1201998 "IFAMON" 1202003 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1200785 1200850 1200904 "IEVALAB" 1201111 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200460 1200528 1200688 "IEVALAB-" 1200693 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200091 1200374 1200437 "IDPO" 1200442 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199341 1199980 1200055 "IDPOAMS" 1200060 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198648 1199230 1199305 "IDPOAM" 1199310 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197707 1197983 1198036 "IDPC" 1198449 NIL IDPC (NIL T T) -9 NIL 1198598 NIL) (-514 1197176 1197599 1197672 "IDPAM" 1197677 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196552 1197068 1197141 "IDPAG" 1197146 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196197 1196388 1196463 "IDENT" 1196497 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192452 1193300 1194195 "IDECOMP" 1195354 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185290 1186375 1187422 "IDEAL" 1191488 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184450 1184562 1184762 "ICDEN" 1185174 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183521 1183930 1184077 "ICARD" 1184323 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181581 1181894 1182299 "IBPTOOLS" 1183198 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177188 1181201 1181314 "IBITS" 1181500 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1173911 1174487 1175182 "IBATOOL" 1176605 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171690 1172152 1172685 "IBACHIN" 1173446 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169519 1171536 1171639 "IARRAY2" 1171644 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165625 1169445 1169502 "IARRAY1" 1169507 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159734 1164037 1164518 "IAN" 1165164 T IAN (NIL) -8 NIL NIL NIL) (-500 1159245 1159302 1159475 "IALGFACT" 1159671 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1158773 1158886 1158914 "HYPCAT" 1159121 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158311 1158428 1158614 "HYPCAT-" 1158619 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1157906 1158106 1158189 "HOSTNAME" 1158248 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1157751 1157788 1157829 "HOMOTOP" 1157834 NIL HOMOTOP (NIL T) -9 NIL 1157867 NIL) (-495 1154383 1155761 1155802 "HOAGG" 1156783 NIL HOAGG (NIL T) -9 NIL 1157462 NIL) (-494 1152977 1153376 1153902 "HOAGG-" 1153907 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1146979 1152570 1152720 "HEXADEC" 1152847 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145727 1145949 1146212 "HEUGCD" 1146756 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1144803 1145564 1145694 "HELLFDIV" 1145699 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1142982 1144580 1144668 "HEAP" 1144747 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142245 1142534 1142668 "HEADAST" 1142868 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136111 1142160 1142222 "HDP" 1142227 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130099 1135746 1135898 "HDMP" 1136012 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129423 1129563 1129727 "HB" 1129955 T HB (NIL) -7 NIL NIL NIL) (-485 1122809 1129269 1129373 "HASHTBL" 1129378 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122285 1122530 1122622 "HASAST" 1122737 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120063 1121907 1122089 "HACKPI" 1122123 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115731 1119916 1120029 "GTSET" 1120034 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109146 1115609 1115707 "GSTBL" 1115712 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101424 1108177 1108442 "GSERIES" 1108937 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100565 1100982 1101010 "GROUP" 1101213 T GROUP (NIL) -9 NIL 1101347 NIL) (-478 1099931 1100090 1100341 "GROUP-" 1100346 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098298 1098619 1099006 "GROEBSOL" 1099608 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097212 1097500 1097551 "GRMOD" 1098080 NIL GRMOD (NIL T T) -9 NIL 1098248 NIL) (-475 1096980 1097016 1097144 "GRMOD-" 1097149 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092270 1093334 1094334 "GRIMAGE" 1096000 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090736 1090997 1091321 "GRDEF" 1091966 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090180 1090296 1090437 "GRAY" 1090615 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089367 1089773 1089824 "GRALG" 1089977 NIL GRALG (NIL T T) -9 NIL 1090070 NIL) (-470 1089028 1089101 1089264 "GRALG-" 1089269 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1085805 1088613 1088791 "GPOLSET" 1088935 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085159 1085216 1085474 "GOSPER" 1085742 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1080891 1081597 1082123 "GMODPOL" 1084858 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1079896 1080080 1080318 "GHENSEL" 1080703 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074052 1074895 1075915 "GENUPS" 1078980 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1073749 1073800 1073889 "GENUFACT" 1073995 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073161 1073238 1073403 "GENPGCD" 1073667 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072635 1072670 1072883 "GENMFACT" 1073120 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071201 1071458 1071765 "GENEEZ" 1072378 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065349 1070812 1070974 "GDMP" 1071124 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054692 1059120 1060226 "GCNAALG" 1064332 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053019 1053881 1053909 "GCDDOM" 1054164 T GCDDOM (NIL) -9 NIL 1054321 NIL) (-457 1052489 1052616 1052831 "GCDDOM-" 1052836 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051161 1051346 1051650 "GB" 1052268 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1039777 1042107 1044499 "GBINTERN" 1048852 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037614 1037906 1038327 "GBF" 1039452 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036395 1036560 1036827 "GBEUCLID" 1037430 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1035744 1035869 1036018 "GAUSSFAC" 1036266 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034111 1034413 1034727 "GALUTIL" 1035463 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032419 1032693 1033017 "GALPOLYU" 1033838 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1029784 1030074 1030481 "GALFACTU" 1032116 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021590 1023089 1024697 "GALFACT" 1028216 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1018978 1019636 1019664 "FVFUN" 1020820 T FVFUN (NIL) -9 NIL 1021540 NIL) (-446 1018244 1018426 1018454 "FVC" 1018745 T FVC (NIL) -9 NIL 1018928 NIL) (-445 1017887 1018069 1018137 "FUNDESC" 1018196 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017502 1017684 1017765 "FUNCTION" 1017839 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015246 1015824 1016290 "FT" 1017056 T FT (NIL) -8 NIL NIL NIL) (-442 1014037 1014547 1014750 "FTEM" 1015063 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012328 1012617 1013014 "FSUPFACT" 1013728 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010725 1011014 1011346 "FST" 1012016 T FST (NIL) -8 NIL NIL NIL) (-439 1009924 1010030 1010218 "FSRED" 1010607 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008623 1008879 1009226 "FSPRMELT" 1009639 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1005929 1006367 1006853 "FSPECF" 1008186 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987567 995898 995939 "FS" 999823 NIL FS (NIL T) -9 NIL 1002112 NIL) (-435 976210 979203 983260 "FS-" 983560 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975738 975792 975962 "FSINT" 976151 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974030 974731 975034 "FSERIES" 975517 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973072 973188 973412 "FSCINT" 973910 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969280 972016 972057 "FSAGG" 972427 NIL FSAGG (NIL T) -9 NIL 972686 NIL) (-430 967042 967643 968439 "FSAGG-" 968534 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966084 966227 966454 "FSAGG2" 966895 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 963766 964046 964593 "FS2UPS" 965802 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963400 963443 963572 "FS2" 963717 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962278 962449 962751 "FS2EXPXP" 963225 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961704 961819 961971 "FRUTIL" 962158 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953117 957199 958557 "FR" 960378 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948131 950806 950846 "FRNAALG" 952166 NIL FRNAALG (NIL T) -9 NIL 952764 NIL) (-422 943804 944880 946155 "FRNAALG-" 946905 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943442 943485 943612 "FRNAAF2" 943755 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 941817 942291 942587 "FRMOD" 943254 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939560 940192 940510 "FRIDEAL" 941608 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938751 938838 939129 "FRIDEAL2" 939467 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 937884 938298 938339 "FRETRCT" 938344 NIL FRETRCT (NIL T) -9 NIL 938520 NIL) (-416 936996 937227 937578 "FRETRCT-" 937583 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934084 935294 935353 "FRAMALG" 936235 NIL FRAMALG (NIL T T) -9 NIL 936527 NIL) (-414 932218 932673 933303 "FRAMALG-" 933526 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926137 931691 931968 "FRAC" 931973 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925773 925830 925937 "FRAC2" 926074 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925409 925466 925573 "FR2" 925710 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 919922 922815 922843 "FPS" 923962 T FPS (NIL) -9 NIL 924519 NIL) (-409 919371 919480 919644 "FPS-" 919790 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916673 918342 918370 "FPC" 918595 T FPC (NIL) -9 NIL 918737 NIL) (-407 916466 916506 916603 "FPC-" 916608 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915256 915954 915995 "FPATMAB" 916000 NIL FPATMAB (NIL T) -9 NIL 916152 NIL) (-405 912929 913432 913858 "FPARFRAC" 914893 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908323 908821 909503 "FORTRAN" 912361 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906039 906539 907078 "FORT" 907804 T FORT (NIL) -7 NIL NIL NIL) (-402 903715 904277 904305 "FORTFN" 905365 T FORTFN (NIL) -9 NIL 905989 NIL) (-401 903479 903529 903557 "FORTCAT" 903616 T FORTCAT (NIL) -9 NIL 903678 NIL) (-400 901585 902095 902485 "FORMULA" 903109 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901373 901403 901472 "FORMULA1" 901549 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 900896 900948 901121 "FORDER" 901315 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 899992 900156 900349 "FOP" 900723 T FOP (NIL) -7 NIL NIL NIL) (-396 898573 899272 899446 "FNLA" 899874 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897302 897717 897745 "FNCAT" 898205 T FNCAT (NIL) -9 NIL 898465 NIL) (-394 896841 897261 897289 "FNAME" 897294 T FNAME (NIL) -8 NIL NIL NIL) (-393 895404 896367 896395 "FMTC" 896400 T FMTC (NIL) -9 NIL 896436 NIL) (-392 894150 895340 895386 "FMONOID" 895391 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 890978 892146 892187 "FMONCAT" 893404 NIL FMONCAT (NIL T) -9 NIL 894009 NIL) (-390 890170 890720 890869 "FM" 890874 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887594 888240 888268 "FMFUN" 889412 T FMFUN (NIL) -9 NIL 890120 NIL) (-388 886863 887044 887072 "FMC" 887362 T FMC (NIL) -9 NIL 887544 NIL) (-387 883942 884802 884856 "FMCAT" 886051 NIL FMCAT (NIL T T) -9 NIL 886546 NIL) (-386 882808 883708 883808 "FM1" 883887 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880582 880998 881492 "FLOATRP" 882359 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874160 878311 878932 "FLOAT" 879981 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871598 872098 872676 "FLOATCP" 873627 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870338 871176 871217 "FLINEXP" 871222 NIL FLINEXP (NIL T) -9 NIL 871315 NIL) (-381 869492 869727 870055 "FLINEXP-" 870060 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868568 868712 868936 "FLASORT" 869344 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865684 866552 866604 "FLALG" 867831 NIL FLALG (NIL T T) -9 NIL 868298 NIL) (-378 859388 863140 863181 "FLAGG" 864443 NIL FLAGG (NIL T) -9 NIL 865095 NIL) (-377 858114 858453 858943 "FLAGG-" 858948 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857156 857299 857526 "FLAGG2" 857967 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854007 855015 855074 "FINRALG" 856202 NIL FINRALG (NIL T T) -9 NIL 856710 NIL) (-374 853167 853396 853735 "FINRALG-" 853740 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852547 852786 852814 "FINITE" 853010 T FINITE (NIL) -9 NIL 853117 NIL) (-372 844904 847091 847131 "FINAALG" 850798 NIL FINAALG (NIL T) -9 NIL 852251 NIL) (-371 840236 841286 842430 "FINAALG-" 843809 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839604 839991 840094 "FILE" 840166 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838262 838600 838654 "FILECAT" 839338 NIL FILECAT (NIL T T) -9 NIL 839554 NIL) (-368 835978 837506 837534 "FIELD" 837574 T FIELD (NIL) -9 NIL 837654 NIL) (-367 834598 834983 835494 "FIELD-" 835499 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832448 833233 833580 "FGROUP" 834284 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831538 831702 831922 "FGLMICPK" 832280 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827370 831463 831520 "FFX" 831525 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 826971 827032 827167 "FFSLPE" 827303 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 822961 823743 824539 "FFPOLY" 826207 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822465 822501 822710 "FFPOLY2" 822919 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818311 822384 822447 "FFP" 822452 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813709 818222 818286 "FF" 818291 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 808835 813052 813242 "FFNBX" 813563 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 803763 807970 808228 "FFNBP" 808689 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798396 803047 803258 "FFNB" 803596 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797228 797426 797741 "FFINTBAS" 798193 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793297 795517 795545 "FFIELDC" 796165 T FFIELDC (NIL) -9 NIL 796541 NIL) (-353 791959 792330 792827 "FFIELDC-" 792832 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791528 791574 791698 "FFHOM" 791901 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789223 789710 790227 "FFF" 791043 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 784841 788965 789066 "FFCGX" 789166 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780463 784573 784680 "FFCGP" 784784 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775646 780190 780298 "FFCG" 780399 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757042 766123 766209 "FFCAT" 771374 NIL FFCAT (NIL T T T) -9 NIL 772825 NIL) (-346 752239 753287 754601 "FFCAT-" 755831 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751650 751693 751928 "FFCAT2" 752190 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 740973 744622 745842 "FEXPR" 750502 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 739935 740370 740411 "FEVALAB" 740495 NIL FEVALAB (NIL T) -9 NIL 740756 NIL) (-342 739094 739304 739642 "FEVALAB-" 739647 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737660 738477 738680 "FDIV" 738993 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734680 735421 735536 "FDIVCAT" 737104 NIL FDIVCAT (NIL T T T T) -9 NIL 737541 NIL) (-339 734442 734469 734639 "FDIVCAT-" 734644 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733662 733749 734026 "FDIV2" 734349 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732636 732957 733159 "FCTRDATA" 733480 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731322 731581 731870 "FCPAK1" 732367 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730421 730822 730963 "FCOMP" 731213 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714126 717571 721109 "FC" 726903 T FC (NIL) -8 NIL NIL NIL) (-333 706489 710517 710557 "FAXF" 712359 NIL FAXF (NIL T) -9 NIL 713051 NIL) (-332 703766 704423 705248 "FAXF-" 705713 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 698818 703142 703318 "FARRAY" 703623 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693712 695779 695832 "FAMR" 696855 NIL FAMR (NIL T T) -9 NIL 697315 NIL) (-329 692602 692904 693339 "FAMR-" 693344 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 691771 692524 692577 "FAMONOID" 692582 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689557 690267 690320 "FAMONC" 691261 NIL FAMONC (NIL T T) -9 NIL 691647 NIL) (-326 688221 689311 689448 "FAGROUP" 689453 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686016 686335 686738 "FACUTIL" 687902 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685115 685300 685522 "FACTFUNC" 685826 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677537 684418 684617 "EXPUPXS" 684971 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675020 675560 676146 "EXPRTUBE" 676971 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671291 671883 672613 "EXPRODE" 674359 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 656776 669940 670369 "EXPR" 670895 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651330 651917 652723 "EXPR2UPS" 656074 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 650962 651019 651128 "EXPR2" 651267 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642350 650113 650404 "EXPEXPAN" 650798 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642150 642307 642336 "EXIT" 642341 T EXIT (NIL) -8 NIL NIL NIL) (-315 641630 641874 641965 "EXITAST" 642079 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641257 641319 641432 "EVALCYC" 641562 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 640798 640916 640957 "EVALAB" 641127 NIL EVALAB (NIL T) -9 NIL 641231 NIL) (-312 640279 640401 640622 "EVALAB-" 640627 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637647 638949 638977 "EUCDOM" 639532 T EUCDOM (NIL) -9 NIL 639882 NIL) (-310 636052 636494 637084 "EUCDOM-" 637089 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623591 626350 629100 "ESTOOLS" 633322 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623223 623280 623389 "ESTOOLS2" 623528 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 622974 623016 623096 "ESTOOLS1" 623175 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617011 618619 618647 "ES" 621415 T ES (NIL) -9 NIL 622825 NIL) (-305 611958 613245 615062 "ES-" 615226 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608332 609093 609873 "ESCONT" 611198 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608077 608109 608191 "ESCONT1" 608294 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 607752 607802 607902 "ES2" 608021 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607382 607440 607549 "ES1" 607688 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606598 606727 606903 "ERROR" 607226 T ERROR (NIL) -7 NIL NIL NIL) (-299 599990 606457 606548 "EQTBL" 606553 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592493 595304 596753 "EQ" 598574 NIL -2129 (NIL T) -8 NIL NIL NIL) (-297 592125 592182 592291 "EQ2" 592430 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587416 588463 589556 "EP" 591064 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586016 586307 586613 "ENV" 587130 T ENV (NIL) -8 NIL NIL NIL) (-294 585110 585664 585692 "ENTIRER" 585697 T ENTIRER (NIL) -9 NIL 585743 NIL) (-293 581804 583292 583653 "EMR" 584918 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 580934 581119 581173 "ELTAGG" 581553 NIL ELTAGG (NIL T T) -9 NIL 581764 NIL) (-291 580653 580715 580856 "ELTAGG-" 580861 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580417 580446 580500 "ELTAB" 580584 NIL ELTAB (NIL T T) -9 NIL 580636 NIL) (-289 579543 579689 579888 "ELFUTS" 580268 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579285 579341 579369 "ELEMFUN" 579474 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579155 579176 579244 "ELEMFUN-" 579249 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 573969 577225 577266 "ELAGG" 578206 NIL ELAGG (NIL T) -9 NIL 578669 NIL) (-285 572254 572688 573351 "ELAGG-" 573356 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571566 571703 571859 "ELABOR" 572118 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570227 570506 570800 "ELABEXPR" 571292 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563091 564894 565721 "EFUPXS" 569503 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556541 558342 559152 "EFULS" 562367 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554026 554384 554856 "EFSTRUC" 556173 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543817 545383 546931 "EF" 552541 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 542891 543302 543451 "EAB" 543688 T EAB (NIL) -8 NIL NIL NIL) (-277 542073 542850 542878 "E04UCFA" 542883 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541255 542032 542060 "E04NAFA" 542065 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540437 541214 541242 "E04MBFA" 541247 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539619 540396 540424 "E04JAFA" 540429 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538803 539578 539606 "E04GCFA" 539611 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 537987 538762 538790 "E04FDFA" 538795 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537169 537946 537974 "E04DGFA" 537979 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531342 532694 534058 "E04AGNT" 535825 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530022 530528 530568 "DVARCAT" 531043 NIL DVARCAT (NIL T) -9 NIL 531242 NIL) (-268 529226 529438 529752 "DVARCAT-" 529757 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522363 529025 529154 "DSMP" 529159 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517144 518308 519376 "DROPT" 521315 T DROPT (NIL) -8 NIL NIL NIL) (-265 516809 516868 516966 "DROPT1" 517079 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 511924 513050 514187 "DROPT0" 515692 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510269 510594 510980 "DRAWPT" 511558 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504856 505779 506858 "DRAW" 509243 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504489 504542 504660 "DRAWHACK" 504797 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503220 503489 503780 "DRAWCX" 504218 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502735 502804 502955 "DRAWCURV" 503146 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493203 495165 497280 "DRAWCFUN" 500640 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 489967 491896 491937 "DQAGG" 492566 NIL DQAGG (NIL T) -9 NIL 492840 NIL) (-256 478091 484560 484643 "DPOLCAT" 486495 NIL DPOLCAT (NIL T T T T) -9 NIL 487040 NIL) (-255 472928 474276 476234 "DPOLCAT-" 476239 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466050 472789 472887 "DPMO" 472892 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459075 465830 465997 "DPMM" 466002 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458645 458859 458948 "DOMTMPLT" 459006 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458078 458447 458527 "DOMCTOR" 458585 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457290 457558 457709 "DOMAIN" 457947 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451278 456925 457077 "DMP" 457191 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450878 450934 451078 "DLP" 451216 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444700 450205 450395 "DLIST" 450720 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441497 443553 443594 "DLAGG" 444144 NIL DLAGG (NIL T) -9 NIL 444374 NIL) (-245 440173 440837 440865 "DIVRING" 440957 T DIVRING (NIL) -9 NIL 441040 NIL) (-244 439410 439600 439900 "DIVRING-" 439905 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437512 437869 438275 "DISPLAY" 439024 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431400 437426 437489 "DIRPROD" 437494 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430248 430451 430716 "DIRPROD2" 431193 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419023 425029 425082 "DIRPCAT" 425492 NIL DIRPCAT (NIL NIL T) -9 NIL 426332 NIL) (-239 416349 416991 417872 "DIRPCAT-" 418209 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415636 415796 415982 "DIOSP" 416183 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412291 414548 414589 "DIOPS" 415023 NIL DIOPS (NIL T) -9 NIL 415252 NIL) (-236 411840 411954 412145 "DIOPS-" 412150 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410663 411291 411319 "DIFRING" 411506 T DIFRING (NIL) -9 NIL 411616 NIL) (-234 410309 410386 410538 "DIFRING-" 410543 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408045 409317 409358 "DIFEXT" 409721 NIL DIFEXT (NIL T) -9 NIL 410015 NIL) (-232 406330 406758 407424 "DIFEXT-" 407429 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403605 405862 405903 "DIAGG" 405908 NIL DIAGG (NIL T) -9 NIL 405928 NIL) (-230 402989 403146 403398 "DIAGG-" 403403 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398406 401948 402225 "DHMATRIX" 402758 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394018 394927 395937 "DFSFUN" 397416 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389097 392949 393261 "DFLOAT" 393726 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387360 387641 388030 "DFINTTLS" 388805 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384389 385381 385781 "DERHAM" 387026 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382190 384164 384253 "DEQUEUE" 384333 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381444 381577 381760 "DEGRED" 382052 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377874 378619 379465 "DEFINTRF" 380672 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375429 375898 376490 "DEFINTEF" 377393 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374779 375049 375164 "DEFAST" 375334 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368781 374372 374522 "DECIMAL" 374649 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366293 366751 367257 "DDFACT" 368325 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365889 365932 366083 "DBLRESP" 366244 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363761 364122 364482 "DBASE" 365656 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363003 363241 363387 "DATAARY" 363660 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362109 362962 362990 "D03FAFA" 362995 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361216 362068 362096 "D03EEFA" 362101 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359166 359632 360121 "D03AGNT" 360747 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358455 359125 359153 "D02EJFA" 359158 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357744 358414 358442 "D02CJFA" 358447 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357033 357703 357731 "D02BHFA" 357736 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356322 356992 357020 "D02BBFA" 357025 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349519 351108 352714 "D02AGNT" 354736 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347287 347810 348356 "D01WGTS" 348993 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346354 347246 347274 "D01TRNS" 347279 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345422 346313 346341 "D01GBFA" 346346 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344490 345381 345409 "D01FCFA" 345414 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343558 344449 344477 "D01ASFA" 344482 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342626 343517 343545 "D01AQFA" 343550 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341694 342585 342613 "D01APFA" 342618 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340762 341653 341681 "D01ANFA" 341686 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339830 340721 340749 "D01AMFA" 340754 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338898 339789 339817 "D01ALFA" 339822 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 337966 338857 338885 "D01AKFA" 338890 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337034 337925 337953 "D01AJFA" 337958 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330329 331882 333443 "D01AGNT" 335493 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329666 329794 329946 "CYCLOTOM" 330197 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326399 327114 327841 "CYCLES" 328959 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325711 325845 326016 "CVMP" 326260 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323552 323810 324179 "CTRIGMNP" 325439 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 322988 323346 323419 "CTOR" 323499 T CTOR (NIL) -8 NIL NIL NIL) (-188 322497 322719 322820 "CTORKIND" 322907 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321788 322104 322132 "CTORCAT" 322314 T CTORCAT (NIL) -9 NIL 322427 NIL) (-186 321386 321497 321656 "CTORCAT-" 321661 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320848 321060 321168 "CTORCALL" 321310 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320222 320321 320474 "CSTTOOLS" 320745 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316021 316678 317436 "CRFP" 319534 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315496 315742 315834 "CRCEAST" 315949 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314543 314728 314956 "CRAPACK" 315300 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313927 314028 314232 "CPMATCH" 314419 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313652 313680 313786 "CPIMA" 313893 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310000 310672 311391 "COORDSYS" 312987 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309412 309533 309675 "CONTOUR" 309878 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305303 307415 307907 "CONTFRAC" 308952 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305183 305204 305232 "CONDUIT" 305269 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304271 304825 304853 "COMRING" 304858 T COMRING (NIL) -9 NIL 304910 NIL) (-173 303325 303629 303813 "COMPPROP" 304107 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 302986 303021 303149 "COMPLPAT" 303284 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293277 302795 302904 "COMPLEX" 302909 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292913 292970 293077 "COMPLEX2" 293214 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292252 292373 292533 "COMPILER" 292773 T COMPILER (NIL) -8 NIL NIL NIL) (-168 291970 292005 292103 "COMPFACT" 292211 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276050 286044 286084 "COMPCAT" 287088 NIL COMPCAT (NIL T) -9 NIL 288436 NIL) (-166 265562 268489 272116 "COMPCAT-" 272472 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265291 265319 265422 "COMMUPC" 265528 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265085 265119 265178 "COMMONOP" 265252 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264641 264836 264923 "COMM" 265018 T COMM (NIL) -8 NIL NIL NIL) (-162 264217 264445 264520 "COMMAAST" 264586 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263466 263660 263688 "COMBOPC" 264026 T COMBOPC (NIL) -9 NIL 264201 NIL) (-160 262362 262572 262814 "COMBINAT" 263256 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258819 259393 260020 "COMBF" 261784 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257577 257935 258170 "COLOR" 258604 T COLOR (NIL) -8 NIL NIL NIL) (-157 257053 257298 257390 "COLONAST" 257505 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256693 256740 256865 "CMPLXRT" 257000 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256141 256393 256492 "CLLCTAST" 256614 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251643 252671 253751 "CLIP" 255081 T CLIP (NIL) -7 NIL NIL NIL) (-153 249984 250744 250984 "CLIF" 251470 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246159 248130 248171 "CLAGG" 249100 NIL CLAGG (NIL T) -9 NIL 249636 NIL) (-151 244581 245038 245621 "CLAGG-" 245626 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244125 244210 244350 "CINTSLPE" 244490 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241626 242097 242645 "CHVAR" 243653 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240800 241354 241382 "CHARZ" 241387 T CHARZ (NIL) -9 NIL 241402 NIL) (-147 240554 240594 240672 "CHARPOL" 240754 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239612 240199 240227 "CHARNZ" 240274 T CHARNZ (NIL) -9 NIL 240330 NIL) (-145 237518 238266 238619 "CHAR" 239279 T CHAR (NIL) -8 NIL NIL NIL) (-144 237244 237305 237333 "CFCAT" 237444 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236485 236596 236779 "CDEN" 237128 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232450 235638 235918 "CCLASS" 236225 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231701 231858 232035 "CATEGORY" 232293 T -10 (NIL) -8 NIL NIL NIL) (-140 231274 231620 231668 "CATCTOR" 231673 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230725 230977 231075 "CATAST" 231196 T CATAST (NIL) -8 NIL NIL NIL) (-138 230201 230446 230538 "CASEAST" 230653 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225339 226358 227102 "CARTEN" 229513 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224447 224595 224816 "CARTEN2" 225186 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222763 223597 223854 "CARD" 224210 T CARD (NIL) -8 NIL NIL NIL) (-134 222339 222567 222642 "CAPSLAST" 222708 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221843 222051 222079 "CACHSET" 222211 T CACHSET (NIL) -9 NIL 222289 NIL) (-132 221313 221635 221663 "CABMON" 221713 T CABMON (NIL) -9 NIL 221769 NIL) (-131 220786 221017 221127 "BYTEORD" 221223 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219768 220320 220462 "BYTE" 220625 T BYTE (NIL) -8 NIL NIL 220747) (-129 215118 219273 219445 "BYTEBUF" 219616 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212627 214810 214917 "BTREE" 215044 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 210076 212275 212397 "BTOURN" 212537 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207446 209546 209587 "BTCAT" 209655 NIL BTCAT (NIL T) -9 NIL 209732 NIL) (-125 207113 207193 207342 "BTCAT-" 207347 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202492 206372 206400 "BTAGG" 206514 T BTAGG (NIL) -9 NIL 206624 NIL) (-123 201982 202107 202313 "BTAGG-" 202318 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198977 201260 201475 "BSTREE" 201799 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198115 198241 198425 "BRILL" 198833 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194767 196841 196882 "BRAGG" 197531 NIL BRAGG (NIL T) -9 NIL 197789 NIL) (-119 193296 193702 194257 "BRAGG-" 194262 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186523 192640 192825 "BPADICRT" 193143 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184838 186460 186505 "BPADIC" 186510 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184536 184566 184680 "BOUNDZRO" 184802 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179764 180962 181874 "BOP" 183644 T BOP (NIL) -8 NIL NIL NIL) (-114 177545 177949 178424 "BOP1" 179322 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177246 177307 177335 "BOOLE" 177446 T BOOLE (NIL) -9 NIL 177528 NIL) (-112 176071 176820 176969 "BOOLEAN" 177117 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175350 175754 175808 "BMODULE" 175813 NIL BMODULE (NIL T T) -9 NIL 175878 NIL) (-110 171151 175148 175221 "BITS" 175297 T BITS (NIL) -8 NIL NIL NIL) (-109 170572 170691 170831 "BINDING" 171031 T BINDING (NIL) -8 NIL NIL NIL) (-108 164577 170167 170316 "BINARY" 170443 T BINARY (NIL) -8 NIL NIL NIL) (-107 162357 163832 163873 "BGAGG" 164133 NIL BGAGG (NIL T) -9 NIL 164270 NIL) (-106 162188 162220 162311 "BGAGG-" 162316 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161259 161572 161777 "BFUNCT" 162003 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159949 160127 160415 "BEZOUT" 161083 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156418 158801 159131 "BBTREE" 159652 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156152 156205 156233 "BASTYPE" 156352 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156004 156033 156106 "BASTYPE-" 156111 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155438 155514 155666 "BALFACT" 155915 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154294 154853 155039 "AUTOMOR" 155283 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154020 154025 154051 "ATTREG" 154056 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152272 152717 153069 "ATTRBUT" 153686 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151880 152100 152166 "ATTRAST" 152224 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151416 151529 151555 "ATRIG" 151756 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151225 151266 151353 "ATRIG-" 151358 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150870 151056 151082 "ASTCAT" 151087 T ASTCAT (NIL) -9 NIL 151117 NIL) (-92 150597 150656 150775 "ASTCAT-" 150780 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148746 150373 150461 "ASTACK" 150540 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147251 147548 147913 "ASSOCEQ" 148428 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146283 146910 147034 "ASP9" 147158 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146046 146231 146270 "ASP8" 146275 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144914 145651 145793 "ASP80" 145935 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143812 144549 144681 "ASP7" 144813 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142766 143489 143607 "ASP78" 143725 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141735 142446 142563 "ASP77" 142680 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140647 141373 141504 "ASP74" 141635 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139547 140282 140414 "ASP73" 140546 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138651 139373 139473 "ASP6" 139478 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137598 138328 138446 "ASP55" 138564 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136547 137272 137391 "ASP50" 137510 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135635 136248 136358 "ASP4" 136468 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134723 135336 135446 "ASP49" 135556 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133507 134262 134430 "ASP42" 134612 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132284 133040 133210 "ASP41" 133394 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131234 131961 132079 "ASP35" 132197 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130999 131182 131221 "ASP34" 131226 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130736 130803 130879 "ASP33" 130954 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129630 130371 130503 "ASP31" 130635 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129395 129578 129617 "ASP30" 129622 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129130 129199 129275 "ASP29" 129350 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128895 129078 129117 "ASP28" 129122 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128660 128843 128882 "ASP27" 128887 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127744 128358 128469 "ASP24" 128580 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126821 127546 127658 "ASP20" 127663 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125909 126522 126632 "ASP1" 126742 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124852 125583 125702 "ASP19" 125821 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124589 124656 124732 "ASP12" 124807 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123441 124188 124332 "ASP10" 124476 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121292 123285 123376 "ARRAY2" 123381 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117057 120940 121054 "ARRAY1" 121209 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116089 116262 116483 "ARRAY12" 116880 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110401 112319 112394 "ARR2CAT" 115024 NIL ARR2CAT (NIL T T T) -9 NIL 115782 NIL) (-56 107835 108579 109533 "ARR2CAT-" 109538 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107152 107462 107587 "ARITY" 107728 T ARITY (NIL) -8 NIL NIL NIL) (-54 105928 106080 106379 "APPRULE" 106988 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105579 105627 105746 "APPLYORE" 105874 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104933 105172 105292 "ANY" 105477 T ANY (NIL) -8 NIL NIL NIL) (-51 104211 104334 104491 "ANY1" 104807 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101741 102648 102975 "ANTISYM" 103935 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101233 101448 101544 "ANON" 101663 T ANON (NIL) -8 NIL NIL NIL) (-48 95482 99772 100226 "AN" 100797 T AN (NIL) -8 NIL NIL NIL) (-47 91380 92768 92819 "AMR" 93567 NIL AMR (NIL T T) -9 NIL 94167 NIL) (-46 90492 90713 91076 "AMR-" 91081 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74931 90409 90470 "ALIST" 90475 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71736 74525 74694 "ALGSC" 74849 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68292 68846 69453 "ALGPKG" 71176 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67569 67670 67854 "ALGMFACT" 68178 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63604 64183 64777 "ALGMANIP" 67153 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54974 63230 63380 "ALGFF" 63537 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54170 54301 54480 "ALGFACT" 54832 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53111 53711 53749 "ALGEBRA" 53754 NIL ALGEBRA (NIL T) -9 NIL 53795 NIL) (-37 52829 52888 53020 "ALGEBRA-" 53025 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34892 50801 50853 "ALAGG" 50989 NIL ALAGG (NIL T T) -9 NIL 51150 NIL) (-35 34428 34541 34567 "AHYP" 34768 T AHYP (NIL) -9 NIL NIL NIL) (-34 33359 33607 33633 "AGG" 34132 T AGG (NIL) -9 NIL 34411 NIL) (-33 32793 32955 33169 "AGG-" 33174 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30599 31022 31427 "AF" 32435 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30079 30324 30414 "ADDAST" 30527 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29347 29606 29762 "ACPLOT" 29941 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26474 26512 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3228527 3228532 3228537 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3228512 3228517 3228522 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3228497 3228502 3228507 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3228482 3228487 3228492 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1306 3227625 3228357 3228434 "ZMOD" 3228439 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1305 3226735 3226899 3227108 "ZLINDEP" 3227457 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1304 3216035 3217803 3219775 "ZDSOLVE" 3224865 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1303 3215281 3215422 3215611 "YSTREAM" 3215881 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1302 3214709 3214955 3215068 "YDIAGRAM" 3215190 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1301 3212483 3214010 3214214 "XRPOLY" 3214552 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3209036 3210354 3210929 "XPR" 3211955 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3206757 3208367 3208571 "XPOLY" 3208867 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3204410 3205778 3205833 "XPOLYC" 3206121 NIL XPOLYC (NIL T T) -9 NIL 3206234 NIL) (-1297 3200786 3202927 3203315 "XPBWPOLY" 3204068 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3196481 3198776 3198818 "XF" 3199439 NIL XF (NIL T) -9 NIL 3199839 NIL) (-1295 3196102 3196190 3196359 "XF-" 3196364 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191298 3192587 3192642 "XFALG" 3194814 NIL XFALG (NIL T T) -9 NIL 3195603 NIL) (-1293 3190431 3190535 3190740 "XEXPPKG" 3191190 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3188540 3190281 3190377 "XDPOLY" 3190382 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3187347 3187947 3187990 "XALG" 3187995 NIL XALG (NIL T) -9 NIL 3188106 NIL) (-1290 3180789 3185324 3185818 "WUTSET" 3186939 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3179045 3179841 3180164 "WP" 3180600 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3178647 3178867 3178937 "WHILEAST" 3178997 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178119 3178364 3178458 "WHEREAST" 3178575 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3177005 3177203 3177498 "WFFINTBS" 3177916 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3174909 3175336 3175798 "WEIER" 3176577 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3173955 3174405 3174447 "VSPACE" 3174583 NIL VSPACE (NIL T) -9 NIL 3174657 NIL) (-1283 3173793 3173820 3173911 "VSPACE-" 3173916 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3173602 3173644 3173712 "VOID" 3173747 T VOID (NIL) -8 NIL NIL NIL) (-1281 3171738 3172097 3172503 "VIEW" 3173218 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168162 3168801 3169538 "VIEWDEF" 3171023 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3157466 3159710 3161883 "VIEW3D" 3166011 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3149717 3151377 3152956 "VIEW2D" 3155909 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3145070 3149487 3149579 "VECTOR" 3149660 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3143647 3143906 3144224 "VECTOR2" 3144800 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3137089 3141398 3141441 "VECTCAT" 3142436 NIL VECTCAT (NIL T) -9 NIL 3143023 NIL) (-1274 3136103 3136357 3136747 "VECTCAT-" 3136752 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3135557 3135754 3135874 "VARIABLE" 3136018 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3135490 3135495 3135525 "UTYPE" 3135530 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3134320 3134474 3134736 "UTSODETL" 3135316 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3131760 3132220 3132744 "UTSODE" 3133861 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3123598 3129386 3129875 "UTS" 3131329 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3114435 3119803 3119846 "UTSCAT" 3120958 NIL UTSCAT (NIL T) -9 NIL 3121716 NIL) (-1267 3111783 3112505 3113494 "UTSCAT-" 3113499 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3111410 3111453 3111586 "UTS2" 3111734 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3105636 3108248 3108291 "URAGG" 3110361 NIL URAGG (NIL T) -9 NIL 3111084 NIL) (-1264 3102575 3103438 3104561 "URAGG-" 3104566 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3098284 3101210 3101675 "UPXSSING" 3102239 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3090350 3097531 3097804 "UPXS" 3098069 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3083423 3090254 3090326 "UPXSCONS" 3090331 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073131 3079925 3079987 "UPXSCCA" 3080561 NIL UPXSCCA (NIL T T) -9 NIL 3080794 NIL) (-1259 3072769 3072854 3073028 "UPXSCCA-" 3073033 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3062329 3068896 3068939 "UPXSCAT" 3069587 NIL UPXSCAT (NIL T) -9 NIL 3070196 NIL) (-1257 3061759 3061838 3062017 "UPXS2" 3062244 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3060413 3060666 3061017 "UPSQFREE" 3061502 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3053886 3056944 3056999 "UPSCAT" 3058079 NIL UPSCAT (NIL T T) -9 NIL 3058844 NIL) (-1254 3053090 3053297 3053624 "UPSCAT-" 3053629 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3038731 3046499 3046542 "UPOLYC" 3048643 NIL UPOLYC (NIL T) -9 NIL 3049864 NIL) (-1252 3030059 3032485 3035632 "UPOLYC-" 3035637 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3029686 3029729 3029862 "UPOLYC2" 3030010 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3021497 3029369 3029498 "UP" 3029605 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3020836 3020943 3021107 "UPMP" 3021386 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3020389 3020470 3020609 "UPDIVP" 3020749 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3018957 3019206 3019522 "UPDECOMP" 3020138 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018188 3018300 3018486 "UPCDEN" 3018841 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3017707 3017776 3017925 "UP2" 3018113 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016174 3016911 3017188 "UNISEG" 3017465 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3015389 3015516 3015721 "UNISEG2" 3016017 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3014449 3014629 3014855 "UNIFACT" 3015205 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2998381 3013626 3013877 "ULS" 3014256 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2986379 2998285 2998357 "ULSCONS" 2998362 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2968387 2980373 2980435 "ULSCCAT" 2981073 NIL ULSCCAT (NIL T T) -9 NIL 2981362 NIL) (-1238 2967437 2967682 2968070 "ULSCCAT-" 2968075 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2956774 2963255 2963298 "ULSCAT" 2964161 NIL ULSCAT (NIL T) -9 NIL 2964892 NIL) (-1236 2956204 2956283 2956462 "ULS2" 2956689 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2955331 2955841 2955948 "UINT8" 2956059 T UINT8 (NIL) -8 NIL NIL 2956144) (-1234 2954457 2954967 2955074 "UINT64" 2955185 T UINT64 (NIL) -8 NIL NIL 2955270) (-1233 2953583 2954093 2954200 "UINT32" 2954311 T UINT32 (NIL) -8 NIL NIL 2954396) (-1232 2952709 2953219 2953326 "UINT16" 2953437 T UINT16 (NIL) -8 NIL NIL 2953522) (-1231 2951012 2951969 2951999 "UFD" 2952211 T UFD (NIL) -9 NIL 2952325 NIL) (-1230 2950806 2950852 2950947 "UFD-" 2950952 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2949888 2950071 2950287 "UDVO" 2950612 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2947704 2948113 2948584 "UDPO" 2949452 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2947637 2947642 2947672 "TYPE" 2947677 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2947397 2947592 2947623 "TYPEAST" 2947628 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2946368 2946570 2946810 "TWOFACT" 2947191 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2945391 2945777 2946012 "TUPLE" 2946168 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2943082 2943601 2944140 "TUBETOOL" 2944874 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2941931 2942136 2942377 "TUBE" 2942875 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2936660 2940903 2941186 "TS" 2941683 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2925300 2929419 2929516 "TSETCAT" 2934785 NIL TSETCAT (NIL T T T T) -9 NIL 2936316 NIL) (-1219 2920032 2921632 2923523 "TSETCAT-" 2923528 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2914671 2915518 2916447 "TRMANIP" 2919168 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914112 2914175 2914338 "TRIMAT" 2914603 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2911978 2912215 2912572 "TRIGMNIP" 2913861 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2911498 2911611 2911641 "TRIGCAT" 2911854 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911167 2911246 2911387 "TRIGCAT-" 2911392 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2908012 2910025 2910306 "TREE" 2910921 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2907286 2907814 2907844 "TRANFUN" 2907879 T TRANFUN (NIL) -9 NIL 2907945 NIL) (-1211 2906565 2906756 2907036 "TRANFUN-" 2907041 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2906369 2906401 2906462 "TOPSP" 2906526 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2905717 2905832 2905986 "TOOLSIGN" 2906250 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2904351 2904894 2905133 "TEXTFILE" 2905500 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2902263 2902804 2903233 "TEX" 2903944 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902044 2902075 2902147 "TEX1" 2902226 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2901692 2901755 2901845 "TEMUTL" 2901976 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2899846 2900126 2900451 "TBCMPPK" 2901415 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2891623 2898006 2898062 "TBAGG" 2898462 NIL TBAGG (NIL T T) -9 NIL 2898673 NIL) (-1202 2886693 2888181 2889935 "TBAGG-" 2889940 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886077 2886184 2886329 "TANEXP" 2886582 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2885588 2885852 2885942 "TALGOP" 2886022 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2878978 2885445 2885538 "TABLE" 2885543 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2878390 2878489 2878627 "TABLEAU" 2878875 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2872998 2874218 2875466 "TABLBUMP" 2877176 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872220 2872367 2872548 "SYSTEM" 2872839 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2868679 2869378 2870161 "SYSSOLP" 2871471 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2868477 2868634 2868665 "SYSPTR" 2868670 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2867516 2868021 2868140 "SYSNNI" 2868326 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868411) (-1192 2866818 2867277 2867356 "SYSINT" 2867416 NIL SYSINT (NIL NIL) -8 NIL NIL 2867461) (-1191 2863150 2864096 2864806 "SYNTAX" 2866130 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2860308 2860910 2861542 "SYMTAB" 2862540 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2855557 2856459 2857442 "SYMS" 2859347 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2852792 2855015 2855245 "SYMPOLY" 2855362 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2852309 2852384 2852507 "SYMFUNC" 2852704 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2848329 2849621 2850434 "SYMBOL" 2851518 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2841868 2843557 2845277 "SWITCH" 2846631 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835102 2840689 2840992 "SUTS" 2841623 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827168 2834349 2834622 "SUPXS" 2834887 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2818927 2826786 2826912 "SUP" 2827077 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818086 2818213 2818430 "SUPFRACF" 2818795 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2817707 2817766 2817879 "SUP2" 2818021 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816155 2816429 2816785 "SUMRF" 2817406 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2815490 2815556 2815748 "SUMFS" 2816076 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2799457 2814667 2814918 "SULS" 2815297 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799059 2799279 2799349 "SUCHTAST" 2799409 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2798354 2798584 2798724 "SUCH" 2798967 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792221 2793260 2794219 "SUBSPACE" 2797442 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2791651 2791741 2791905 "SUBRESP" 2792109 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785019 2786316 2787627 "STTF" 2790387 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779192 2780312 2781459 "STTFNC" 2783919 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2770505 2772374 2774168 "STTAYLOR" 2777433 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2763635 2770369 2770452 "STRTBL" 2770457 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2758999 2763590 2763621 "STRING" 2763626 T STRING (NIL) -8 NIL NIL NIL) (-1167 2753828 2758342 2758372 "STRICAT" 2758431 T STRICAT (NIL) -9 NIL 2758493 NIL) (-1166 2746581 2751447 2752058 "STREAM" 2753252 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746091 2746168 2746312 "STREAM3" 2746498 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745073 2745256 2745491 "STREAM2" 2745904 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2744761 2744813 2744906 "STREAM1" 2745015 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2743777 2743958 2744189 "STINPROD" 2744577 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2743329 2743539 2743569 "STEP" 2743649 T STEP (NIL) -9 NIL 2743727 NIL) (-1160 2742516 2742818 2742966 "STEPAST" 2743203 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2735948 2742415 2742492 "STBL" 2742497 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731043 2735139 2735182 "STAGG" 2735335 NIL STAGG (NIL T) -9 NIL 2735424 NIL) (-1157 2728745 2729347 2730219 "STAGG-" 2730224 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2726892 2728515 2728607 "STACK" 2728688 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2719587 2725033 2725489 "SREGSET" 2726522 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712012 2713381 2714894 "SRDCMPK" 2718193 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2704897 2709422 2709452 "SRAGG" 2710755 T SRAGG (NIL) -9 NIL 2711363 NIL) (-1152 2703914 2704169 2704548 "SRAGG-" 2704553 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2698374 2702861 2703282 "SQMATRIX" 2703540 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692059 2695092 2695819 "SPLTREE" 2697719 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688022 2688715 2689361 "SPLNODE" 2691485 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687069 2687302 2687332 "SPFCAT" 2687776 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2685806 2686016 2686280 "SPECOUT" 2686827 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2676916 2678788 2678818 "SPADXPT" 2683494 T SPADXPT (NIL) -9 NIL 2685658 NIL) (-1145 2676677 2676717 2676786 "SPADPRSR" 2676869 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2674726 2676632 2676663 "SPADAST" 2676668 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2666671 2668444 2668487 "SPACEC" 2672860 NIL SPACEC (NIL T) -9 NIL 2674676 NIL) (-1142 2664801 2666603 2666652 "SPACE3" 2666657 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2663553 2663724 2664015 "SORTPAK" 2664606 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2661645 2661948 2662360 "SOLVETRA" 2663217 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2660695 2660917 2661178 "SOLVESER" 2661418 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2655999 2656887 2657882 "SOLVERAD" 2659747 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2651814 2652423 2653152 "SOLVEFOR" 2655366 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646084 2651163 2651260 "SNTSCAT" 2651265 NIL SNTSCAT (NIL T T T T) -9 NIL 2651335 NIL) (-1135 2640190 2644407 2644798 "SMTS" 2645774 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2634875 2640078 2640155 "SMP" 2640160 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633034 2633335 2633733 "SMITH" 2634572 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2625747 2629943 2630046 "SMATCAT" 2631397 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631947 NIL) (-1131 2622687 2623510 2624688 "SMATCAT-" 2624693 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2620353 2621923 2621966 "SKAGG" 2622227 NIL SKAGG (NIL T) -9 NIL 2622362 NIL) (-1129 2616679 2619826 2620010 "SINT" 2620162 T SINT (NIL) -8 NIL NIL 2620324) (-1128 2616451 2616489 2616555 "SIMPAN" 2616635 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2615730 2615986 2616126 "SIG" 2616333 T SIG (NIL) -8 NIL NIL NIL) (-1126 2614568 2614789 2615064 "SIGNRF" 2615489 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2613401 2613552 2613836 "SIGNEF" 2614397 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2612707 2612984 2613108 "SIGAST" 2613299 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2610397 2610851 2611357 "SHP" 2612248 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2604249 2610298 2610374 "SHDP" 2610379 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2603822 2604014 2604044 "SGROUP" 2604137 T SGROUP (NIL) -9 NIL 2604199 NIL) (-1120 2603680 2603706 2603779 "SGROUP-" 2603784 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2600471 2601169 2601892 "SGCF" 2602979 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2594839 2599918 2600015 "SFRTCAT" 2600020 NIL SFRTCAT (NIL T T T T) -9 NIL 2600059 NIL) (-1117 2588260 2589278 2590414 "SFRGCD" 2593822 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2581386 2582459 2583645 "SFQCMPK" 2587193 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581006 2581095 2581206 "SFORT" 2581327 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2580124 2580846 2580967 "SEXOF" 2580972 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2579231 2580005 2580073 "SEX" 2580078 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575012 2575727 2575822 "SEXCAT" 2578444 NIL SEXCAT (NIL T T T T T) -9 NIL 2579004 NIL) (-1111 2572165 2574946 2574994 "SET" 2574999 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570389 2570878 2571183 "SETMN" 2571906 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2569885 2570037 2570067 "SETCAT" 2570243 T SETCAT (NIL) -9 NIL 2570353 NIL) (-1108 2569577 2569655 2569785 "SETCAT-" 2569790 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2565938 2568038 2568081 "SETAGG" 2568951 NIL SETAGG (NIL T) -9 NIL 2569291 NIL) (-1106 2565396 2565512 2565749 "SETAGG-" 2565754 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2564839 2565092 2565193 "SEQAST" 2565317 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564038 2564332 2564393 "SEGXCAT" 2564679 NIL SEGXCAT (NIL T T) -9 NIL 2564799 NIL) (-1103 2563044 2563704 2563886 "SEG" 2563891 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562023 2562237 2562280 "SEGCAT" 2562802 NIL SEGCAT (NIL T) -9 NIL 2563023 NIL) (-1101 2560955 2561386 2561594 "SEGBIND" 2561850 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2560576 2560635 2560748 "SEGBIND2" 2560890 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560149 2560377 2560454 "SEGAST" 2560521 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559368 2559494 2559698 "SEG2" 2559993 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2558778 2559303 2559350 "SDVAR" 2559355 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551305 2558548 2558678 "SDPOL" 2558683 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2549898 2550164 2550483 "SCPKG" 2551020 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549062 2549234 2549426 "SCOPE" 2549728 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548282 2548416 2548595 "SCACHE" 2548917 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2547928 2548114 2548144 "SASTCAT" 2548149 T SASTCAT (NIL) -9 NIL 2548162 NIL) (-1091 2547415 2547763 2547839 "SAOS" 2547874 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2546980 2547015 2547188 "SAERFFC" 2547374 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2540919 2546877 2546957 "SAE" 2546962 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2540512 2540547 2540706 "SAEFACT" 2540878 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2538833 2539147 2539548 "RURPK" 2540178 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2537470 2537776 2538081 "RULESET" 2538667 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2534693 2535223 2535681 "RULE" 2537151 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534305 2534487 2534570 "RULECOLD" 2534645 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534095 2534123 2534194 "RTVALUE" 2534256 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2533566 2533812 2533906 "RSTRCAST" 2534023 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528414 2529209 2530129 "RSETGCD" 2532765 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2517644 2522723 2522820 "RSETCAT" 2526939 NIL RSETCAT (NIL T T T T) -9 NIL 2528036 NIL) (-1079 2515571 2516110 2516934 "RSETCAT-" 2516939 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2507957 2509333 2510853 "RSDCMPK" 2514170 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505936 2506403 2506477 "RRCC" 2507563 NIL RRCC (NIL T T) -9 NIL 2507907 NIL) (-1076 2505287 2505461 2505740 "RRCC-" 2505745 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2504730 2504983 2505084 "RPTAST" 2505208 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2478576 2487935 2488002 "RPOLCAT" 2498668 NIL RPOLCAT (NIL T T T) -9 NIL 2501828 NIL) (-1073 2470074 2472414 2475536 "RPOLCAT-" 2475541 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461005 2468285 2468767 "ROUTINE" 2469614 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2457803 2460631 2460771 "ROMAN" 2460887 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456047 2456663 2456923 "ROIRC" 2457608 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452279 2454563 2454593 "RNS" 2454897 T RNS (NIL) -9 NIL 2455171 NIL) (-1068 2450788 2451171 2451705 "RNS-" 2451780 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450191 2450599 2450629 "RNG" 2450634 T RNG (NIL) -9 NIL 2450655 NIL) (-1066 2449194 2449556 2449758 "RNGBIND" 2450042 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2448593 2448981 2449024 "RMODULE" 2449029 NIL RMODULE (NIL T) -9 NIL 2449056 NIL) (-1064 2447429 2447523 2447859 "RMCAT2" 2448494 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444279 2446775 2447072 "RMATRIX" 2447191 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437106 2439366 2439481 "RMATCAT" 2442840 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443822 NIL) (-1061 2436481 2436628 2436935 "RMATCAT-" 2436940 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2435882 2436103 2436146 "RLINSET" 2436340 NIL RLINSET (NIL T) -9 NIL 2436431 NIL) (-1059 2435449 2435524 2435652 "RINTERP" 2435801 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2434507 2435061 2435091 "RING" 2435147 T RING (NIL) -9 NIL 2435239 NIL) (-1057 2434299 2434343 2434440 "RING-" 2434445 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433140 2433377 2433635 "RIDIST" 2434063 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2424429 2432608 2432814 "RGCHAIN" 2432988 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2423779 2424185 2424226 "RGBCSPC" 2424284 NIL RGBCSPC (NIL T) -9 NIL 2424336 NIL) (-1053 2422937 2423318 2423359 "RGBCMDL" 2423591 NIL RGBCMDL (NIL T) -9 NIL 2423705 NIL) (-1052 2419931 2420545 2421215 "RF" 2422301 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2419577 2419640 2419743 "RFFACTOR" 2419862 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419302 2419337 2419434 "RFFACT" 2419536 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2417419 2417783 2418165 "RFDIST" 2418942 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2416872 2416964 2417127 "RETSOL" 2417321 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2416508 2416588 2416631 "RETRACT" 2416764 NIL RETRACT (NIL T) -9 NIL 2416851 NIL) (-1046 2416357 2416382 2416469 "RETRACT-" 2416474 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2415959 2416179 2416249 "RETAST" 2416309 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2408697 2415612 2415739 "RESULT" 2415854 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407288 2407966 2408165 "RESRING" 2408600 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2406924 2406973 2407071 "RESLATC" 2407225 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2406629 2406664 2406771 "REPSQ" 2406883 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404051 2404631 2405233 "REP" 2406049 T REP (NIL) -7 NIL NIL NIL) (-1039 2403748 2403783 2403894 "REPDB" 2404010 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2397648 2399037 2400260 "REP2" 2402560 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394025 2394706 2395514 "REP1" 2396875 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2386721 2392166 2392622 "REGSET" 2393655 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2385486 2385869 2386119 "REF" 2386506 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2384863 2384966 2385133 "REDORDER" 2385370 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2380831 2384076 2384303 "RECLOS" 2384691 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2379883 2380064 2380279 "REALSOLV" 2380638 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2379729 2379770 2379800 "REAL" 2379805 T REAL (NIL) -9 NIL 2379840 NIL) (-1030 2376212 2377014 2377898 "REAL0Q" 2378894 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2371813 2372801 2373862 "REAL0" 2375193 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371284 2371530 2371624 "RDUCEAST" 2371741 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2370689 2370761 2370968 "RDIV" 2371206 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2369757 2369931 2370144 "RDIST" 2370511 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368354 2368641 2369013 "RDETRS" 2369465 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366166 2366620 2367158 "RDETR" 2367896 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2364791 2365069 2365466 "RDEEFS" 2365882 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363300 2363606 2364031 "RDEEF" 2364479 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357361 2360281 2360311 "RCFIELD" 2361606 T RCFIELD (NIL) -9 NIL 2362337 NIL) (-1020 2355425 2355929 2356625 "RCFIELD-" 2356700 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2351694 2353526 2353569 "RCAGG" 2354653 NIL RCAGG (NIL T) -9 NIL 2355118 NIL) (-1018 2351322 2351416 2351579 "RCAGG-" 2351584 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2350657 2350769 2350934 "RATRET" 2351206 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350210 2350277 2350398 "RATFACT" 2350585 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2349518 2349638 2349790 "RANDSRC" 2350080 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349252 2349296 2349369 "RADUTIL" 2349467 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2342366 2348083 2348394 "RADIX" 2348975 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2333985 2342208 2342338 "RADFF" 2342343 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2333632 2333707 2333737 "RADCAT" 2333897 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2333414 2333462 2333562 "RADCAT-" 2333567 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2331512 2333184 2333276 "QUEUE" 2333357 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328049 2331445 2331493 "QUAT" 2331498 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2327680 2327723 2327854 "QUATCT2" 2328000 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321091 2324436 2324478 "QUATCAT" 2325269 NIL QUATCAT (NIL T) -9 NIL 2326035 NIL) (-1005 2317230 2318267 2319657 "QUATCAT-" 2319753 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2314695 2316306 2316349 "QUAGG" 2316730 NIL QUAGG (NIL T) -9 NIL 2316905 NIL) (-1003 2314297 2314517 2314587 "QQUTAST" 2314647 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313310 2313810 2313975 "QFORM" 2314178 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304303 2309542 2309584 "QFCAT" 2310252 NIL QFCAT (NIL T) -9 NIL 2311253 NIL) (-1000 2299870 2301071 2302665 "QFCAT-" 2302761 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2299504 2299547 2299676 "QFCAT2" 2299821 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2298964 2299074 2299204 "QEQUAT" 2299394 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2292110 2293183 2294367 "QCMPACK" 2297897 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2289659 2290107 2290535 "QALGSET" 2291765 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2288904 2289078 2289310 "QALGSET2" 2289479 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2287594 2287818 2288135 "PWFFINTB" 2288677 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2285776 2285944 2286298 "PUSHVAR" 2287408 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2281694 2282748 2282789 "PTRANFN" 2284673 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2280096 2280387 2280709 "PTPACK" 2281405 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2279728 2279785 2279894 "PTFUNC2" 2280033 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274173 2278570 2278611 "PTCAT" 2278907 NIL PTCAT (NIL T) -9 NIL 2279060 NIL) (-988 2273831 2273866 2273990 "PSQFR" 2274132 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272426 2272724 2273058 "PSEUDLIN" 2273529 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259189 2261560 2263884 "PSETPK" 2270186 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252207 2254947 2255043 "PSETCAT" 2258064 NIL PSETCAT (NIL T T T T) -9 NIL 2258878 NIL) (-984 2250043 2250677 2251498 "PSETCAT-" 2251503 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2249392 2249557 2249585 "PSCURVE" 2249853 T PSCURVE (NIL) -9 NIL 2250020 NIL) (-982 2245390 2246906 2246971 "PSCAT" 2247815 NIL PSCAT (NIL T T T) -9 NIL 2248055 NIL) (-981 2244453 2244669 2245069 "PSCAT-" 2245074 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2242812 2243522 2243785 "PRTITION" 2244210 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2242287 2242533 2242625 "PRTDAST" 2242740 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2231377 2233591 2235779 "PRS" 2240149 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2229188 2230727 2230767 "PRQAGG" 2230950 NIL PRQAGG (NIL T) -9 NIL 2231052 NIL) (-976 2228524 2228829 2228857 "PROPLOG" 2228996 T PROPLOG (NIL) -9 NIL 2229111 NIL) (-975 2228128 2228185 2228308 "PROPFUN2" 2228447 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2227443 2227564 2227736 "PROPFUN1" 2227989 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-973 2225624 2226190 2226487 "PROPFRML" 2227179 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-972 2225093 2225200 2225328 "PROPERTY" 2225516 T PROPERTY (NIL) -8 NIL NIL NIL) (-971 2219151 2223259 2224079 "PRODUCT" 2224319 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-970 2216429 2218609 2218843 "PR" 2218962 NIL PR (NIL T T) -8 NIL NIL NIL) (-969 2216225 2216257 2216316 "PRINT" 2216390 T PRINT (NIL) -7 NIL NIL NIL) (-968 2215565 2215682 2215834 "PRIMES" 2216105 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2213630 2214031 2214497 "PRIMELT" 2215144 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2213359 2213408 2213436 "PRIMCAT" 2213560 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2209474 2213297 2213342 "PRIMARR" 2213347 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-964 2208481 2208659 2208887 "PRIMARR2" 2209292 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-963 2208124 2208180 2208291 "PREASSOC" 2208419 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2207599 2207732 2207760 "PPCURVE" 2207965 T PPCURVE (NIL) -9 NIL 2208101 NIL) (-961 2207194 2207394 2207477 "PORTNUM" 2207536 T PORTNUM (NIL) -8 NIL NIL NIL) (-960 2204553 2204952 2205544 "POLYROOT" 2206775 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-959 2198735 2204157 2204317 "POLY" 2204426 NIL POLY (NIL T) -8 NIL NIL NIL) (-958 2198118 2198176 2198410 "POLYLIFT" 2198671 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2194393 2194842 2195471 "POLYCATQ" 2197663 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2181105 2186233 2186298 "POLYCAT" 2189812 NIL POLYCAT (NIL T T T) -9 NIL 2191690 NIL) (-955 2174554 2176416 2178800 "POLYCAT-" 2178805 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2174141 2174209 2174329 "POLY2UP" 2174480 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2173773 2173830 2173939 "POLY2" 2174078 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2172458 2172697 2172973 "POLUTIL" 2173547 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-951 2170813 2171090 2171421 "POLTOPOL" 2172180 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-950 2166278 2170749 2170795 "POINT" 2170800 NIL POINT (NIL T) -8 NIL NIL NIL) (-949 2164465 2164822 2165197 "PNTHEORY" 2165923 T PNTHEORY (NIL) -7 NIL NIL NIL) (-948 2162923 2163220 2163619 "PMTOOLS" 2164163 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-947 2162516 2162594 2162711 "PMSYM" 2162839 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-946 2162024 2162093 2162268 "PMQFCAT" 2162441 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-945 2161379 2161489 2161645 "PMPRED" 2161901 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-944 2160772 2160858 2161020 "PMPREDFS" 2161280 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2159436 2159644 2160022 "PMPLCAT" 2160534 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-942 2158968 2159047 2159199 "PMLSAGG" 2159351 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-941 2158441 2158517 2158699 "PMKERNEL" 2158886 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-940 2158058 2158133 2158246 "PMINS" 2158360 NIL PMINS (NIL T) -7 NIL NIL NIL) (-939 2157500 2157569 2157778 "PMFS" 2157983 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-938 2156728 2156846 2157051 "PMDOWN" 2157377 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-937 2155895 2156053 2156234 "PMASS" 2156567 T PMASS (NIL) -7 NIL NIL NIL) (-936 2155168 2155278 2155441 "PMASSFS" 2155782 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2154823 2154891 2154985 "PLOTTOOL" 2155094 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-934 2149430 2150634 2151782 "PLOT" 2153695 T PLOT (NIL) -8 NIL NIL NIL) (-933 2145234 2146278 2147199 "PLOT3D" 2148529 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2144146 2144323 2144558 "PLOT1" 2145038 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2119537 2124212 2129063 "PLEQN" 2139412 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-930 2118855 2118977 2119157 "PINTERP" 2119402 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-929 2118548 2118595 2118698 "PINTERPA" 2118802 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2117764 2118312 2118399 "PI" 2118439 T PI (NIL) -8 NIL NIL 2118506) (-927 2116061 2117036 2117064 "PID" 2117246 T PID (NIL) -9 NIL 2117380 NIL) (-926 2115812 2115849 2115924 "PICOERCE" 2116018 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2115132 2115271 2115447 "PGROEB" 2115668 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-924 2110719 2111533 2112438 "PGE" 2114247 T PGE (NIL) -7 NIL NIL NIL) (-923 2108842 2109089 2109455 "PGCD" 2110436 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-922 2108180 2108283 2108444 "PFRPAC" 2108726 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-921 2104820 2106728 2107081 "PFR" 2107859 NIL PFR (NIL T) -8 NIL NIL NIL) (-920 2103209 2103453 2103778 "PFOTOOLS" 2104567 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-919 2101742 2101981 2102332 "PFOQ" 2102966 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-918 2100243 2100455 2100811 "PFO" 2101526 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-917 2096796 2100132 2100201 "PF" 2100206 NIL PF (NIL NIL) -8 NIL NIL NIL) (-916 2094130 2095401 2095429 "PFECAT" 2096014 T PFECAT (NIL) -9 NIL 2096398 NIL) (-915 2093575 2093729 2093943 "PFECAT-" 2093948 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2092178 2092430 2092731 "PFBRU" 2093324 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2090044 2090396 2090828 "PFBR" 2091829 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2085926 2087420 2088096 "PERM" 2089401 NIL PERM (NIL T) -8 NIL NIL NIL) (-911 2081160 2082133 2083003 "PERMGRP" 2085089 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2079266 2080223 2080264 "PERMCAT" 2080710 NIL PERMCAT (NIL T) -9 NIL 2081015 NIL) (-909 2078919 2078960 2079084 "PERMAN" 2079219 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2076407 2078584 2078706 "PENDTREE" 2078830 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-907 2074431 2075199 2075240 "PDRING" 2075897 NIL PDRING (NIL T) -9 NIL 2076183 NIL) (-906 2073534 2073752 2074114 "PDRING-" 2074119 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-905 2070749 2071527 2072195 "PDEPROB" 2072886 T PDEPROB (NIL) -8 NIL NIL NIL) (-904 2068294 2068798 2069353 "PDEPACK" 2070214 T PDEPACK (NIL) -7 NIL NIL NIL) (-903 2067206 2067396 2067647 "PDECOMP" 2068093 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-902 2064785 2065628 2065656 "PDECAT" 2066443 T PDECAT (NIL) -9 NIL 2067156 NIL) (-901 2064536 2064569 2064659 "PCOMP" 2064746 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-900 2062714 2063337 2063634 "PBWLB" 2064265 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-899 2055187 2056787 2058125 "PATTERN" 2061397 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-898 2054819 2054876 2054985 "PATTERN2" 2055124 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2052576 2052964 2053421 "PATTERN1" 2054408 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2049944 2050525 2051006 "PATRES" 2052141 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-895 2049508 2049575 2049707 "PATRES2" 2049871 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2047391 2047796 2048203 "PATMATCH" 2049175 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-893 2046901 2047110 2047151 "PATMAB" 2047258 NIL PATMAB (NIL T) -9 NIL 2047341 NIL) (-892 2045419 2045755 2046013 "PATLRES" 2046706 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-891 2044965 2045088 2045129 "PATAB" 2045134 NIL PATAB (NIL T) -9 NIL 2045306 NIL) (-890 2043147 2043542 2043965 "PARTPERM" 2044562 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2042768 2042831 2042933 "PARSURF" 2043078 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042400 2042457 2042566 "PARSU2" 2042705 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042164 2042204 2042271 "PARSER" 2042353 T PARSER (NIL) -7 NIL NIL NIL) (-886 2041785 2041848 2041950 "PARSCURV" 2042095 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041417 2041474 2041583 "PARSC2" 2041722 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041056 2041114 2041211 "PARPCURV" 2041353 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2040688 2040745 2040854 "PARPC2" 2040993 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2039749 2040061 2040243 "PARAMAST" 2040526 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039269 2039355 2039474 "PAN2EXPR" 2039650 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038046 2038390 2038618 "PALETTE" 2039061 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036439 2037051 2037411 "PAIR" 2037732 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030307 2035696 2035891 "PADICRC" 2036293 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023534 2029651 2029836 "PADICRAT" 2030154 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2021849 2023471 2023516 "PADIC" 2023521 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2018959 2020523 2020563 "PADICCT" 2021144 NIL PADICCT (NIL NIL) -9 NIL 2021426 NIL) (-874 2017916 2018116 2018384 "PADEPAC" 2018746 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017128 2017261 2017467 "PADE" 2017778 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015515 2016336 2016616 "OWP" 2016932 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2015008 2015221 2015318 "OVERSET" 2015438 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014054 2014613 2014785 "OVAR" 2014876 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013318 2013439 2013600 "OUT" 2013913 T OUT (NIL) -7 NIL NIL NIL) (-868 2002190 2004427 2006627 "OUTFORM" 2011138 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001526 2001787 2001914 "OUTBFILE" 2002083 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2000833 2000998 2001026 "OUTBCON" 2001344 T OUTBCON (NIL) -9 NIL 2001510 NIL) (-865 2000434 2000546 2000703 "OUTBCON-" 2000708 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1999814 2000163 2000252 "OSI" 2000365 T OSI (NIL) -8 NIL NIL NIL) (-863 1999344 1999682 1999710 "OSGROUP" 1999715 T OSGROUP (NIL) -9 NIL 1999737 NIL) (-862 1998089 1998316 1998601 "ORTHPOL" 1999091 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995640 1997924 1998045 "OREUP" 1998050 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993043 1995331 1995458 "ORESUP" 1995582 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990571 1991071 1991632 "OREPCTO" 1992532 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984257 1986458 1986499 "OREPCAT" 1988847 NIL OREPCAT (NIL T) -9 NIL 1989951 NIL) (-857 1981404 1982186 1983244 "OREPCAT-" 1983249 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980555 1980853 1980881 "ORDSET" 1981190 T ORDSET (NIL) -9 NIL 1981354 NIL) (-855 1979986 1980134 1980358 "ORDSET-" 1980363 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978551 1979342 1979370 "ORDRING" 1979572 T ORDRING (NIL) -9 NIL 1979697 NIL) (-853 1978196 1978290 1978434 "ORDRING-" 1978439 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977576 1978039 1978067 "ORDMON" 1978072 T ORDMON (NIL) -9 NIL 1978093 NIL) (-851 1976738 1976885 1977080 "ORDFUNS" 1977425 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976076 1976495 1976523 "ORDFIN" 1976588 T ORDFIN (NIL) -9 NIL 1976662 NIL) (-849 1972635 1974662 1975071 "ORDCOMP" 1975700 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1971901 1972028 1972214 "ORDCOMP2" 1972495 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968482 1969392 1970206 "OPTPROB" 1971107 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965284 1965923 1966627 "OPTPACK" 1967798 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1962971 1963737 1963765 "OPTCAT" 1964584 T OPTCAT (NIL) -9 NIL 1965234 NIL) (-844 1962355 1962648 1962753 "OPSIG" 1962886 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962123 1962162 1962228 "OPQUERY" 1962309 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959254 1960434 1960938 "OP" 1961652 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958628 1958854 1958895 "OPERCAT" 1959107 NIL OPERCAT (NIL T) -9 NIL 1959204 NIL) (-840 1958383 1958439 1958556 "OPERCAT-" 1958561 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955196 1957180 1957549 "ONECOMP" 1958047 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954501 1954616 1954790 "ONECOMP2" 1955068 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953920 1954026 1954156 "OMSERVER" 1954391 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1950782 1953360 1953400 "OMSAGG" 1953461 NIL OMSAGG (NIL T) -9 NIL 1953525 NIL) (-835 1949405 1949668 1949950 "OMPKG" 1950520 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1948835 1948938 1948966 "OM" 1949265 T OM (NIL) -9 NIL NIL NIL) (-833 1947382 1948384 1948553 "OMLO" 1948716 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946342 1946489 1946709 "OMEXPR" 1947208 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945633 1945888 1946024 "OMERR" 1946226 T OMERR (NIL) -8 NIL NIL NIL) (-830 1944784 1945054 1945214 "OMERRK" 1945493 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944235 1944461 1944569 "OMENC" 1944696 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938130 1939315 1940486 "OMDEV" 1943084 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937199 1937370 1937564 "OMCONN" 1937956 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1935720 1936696 1936724 "OINTDOM" 1936729 T OINTDOM (NIL) -9 NIL 1936750 NIL) (-825 1933058 1934408 1934745 "OFMONOID" 1935415 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932469 1932995 1933040 "ODVAR" 1933045 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1929892 1932214 1932369 "ODR" 1932374 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922473 1929668 1929794 "ODPOL" 1929799 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916295 1922345 1922450 "ODP" 1922455 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915061 1915276 1915551 "ODETOOLS" 1916069 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912028 1912686 1913402 "ODESYS" 1914394 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1906910 1907818 1908843 "ODERTRIC" 1911103 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906336 1906418 1906612 "ODERED" 1906822 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903224 1903772 1904449 "ODERAT" 1905759 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900183 1900648 1901245 "ODEPRRIC" 1902753 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898126 1898722 1899208 "ODEPROB" 1899717 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894646 1895131 1895778 "ODEPRIM" 1897605 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1893895 1893997 1894257 "ODEPAL" 1894538 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890057 1890848 1891712 "ODEPACK" 1893051 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889118 1889225 1889447 "ODEINT" 1889946 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883219 1884644 1886091 "ODEIFTBL" 1887691 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878617 1879403 1880355 "ODEEF" 1882378 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1877966 1878055 1878278 "ODECONST" 1878522 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876091 1876752 1876780 "ODECAT" 1877385 T ODECAT (NIL) -9 NIL 1877916 NIL) (-805 1872946 1875796 1875918 "OCT" 1876001 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872584 1872627 1872754 "OCTCT2" 1872897 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867195 1869630 1869670 "OC" 1870767 NIL OC (NIL T) -9 NIL 1871625 NIL) (-802 1864422 1865170 1866160 "OC-" 1866254 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1863774 1864242 1864270 "OCAMON" 1864275 T OCAMON (NIL) -9 NIL 1864296 NIL) (-800 1863305 1863646 1863674 "OASGP" 1863679 T OASGP (NIL) -9 NIL 1863699 NIL) (-799 1862566 1863055 1863083 "OAMONS" 1863123 T OAMONS (NIL) -9 NIL 1863166 NIL) (-798 1861980 1862413 1862441 "OAMON" 1862446 T OAMON (NIL) -9 NIL 1862466 NIL) (-797 1861238 1861756 1861784 "OAGROUP" 1861789 T OAGROUP (NIL) -9 NIL 1861809 NIL) (-796 1860928 1860978 1861066 "NUMTUBE" 1861182 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854501 1856019 1857555 "NUMQUAD" 1859412 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850257 1851245 1852270 "NUMODE" 1853496 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847612 1848492 1848520 "NUMINT" 1849443 T NUMINT (NIL) -9 NIL 1850207 NIL) (-792 1846560 1846757 1846975 "NUMFMT" 1847414 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1832919 1835864 1838396 "NUMERIC" 1844067 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827289 1832368 1832463 "NTSCAT" 1832468 NIL NTSCAT (NIL T T T T) -9 NIL 1832507 NIL) (-789 1826483 1826648 1826841 "NTPOLFN" 1827128 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814560 1823308 1824120 "NSUP" 1825704 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814192 1814249 1814358 "NSUP2" 1814497 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804418 1813966 1814099 "NSMP" 1814104 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1802850 1803151 1803508 "NREP" 1804106 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801441 1801693 1802051 "NPCOEF" 1802593 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800507 1800622 1800838 "NORMRETR" 1801322 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798548 1798838 1799247 "NORMPK" 1800215 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798233 1798261 1798385 "NORMMA" 1798514 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798033 1798190 1798219 "NONE" 1798224 T NONE (NIL) -8 NIL NIL NIL) (-779 1797822 1797851 1797920 "NONE1" 1797997 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797319 1797381 1797560 "NODE1" 1797754 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795600 1796451 1796706 "NNI" 1797053 T NNI (NIL) -8 NIL NIL 1797288) (-776 1794020 1794333 1794697 "NLINSOL" 1795268 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790261 1791256 1792155 "NIPROB" 1793141 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789018 1789252 1789554 "NFINTBAS" 1790023 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788192 1788668 1788709 "NETCLT" 1788881 NIL NETCLT (NIL T) -9 NIL 1788963 NIL) (-772 1786900 1787131 1787412 "NCODIV" 1787960 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786662 1786699 1786774 "NCNTFRAC" 1786857 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1784842 1785206 1785626 "NCEP" 1786287 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1783693 1784466 1784494 "NASRING" 1784604 T NASRING (NIL) -9 NIL 1784684 NIL) (-768 1783488 1783532 1783626 "NASRING-" 1783631 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782595 1783120 1783148 "NARNG" 1783265 T NARNG (NIL) -9 NIL 1783356 NIL) (-766 1782287 1782354 1782488 "NARNG-" 1782493 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781166 1781373 1781608 "NAGSP" 1782072 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772438 1774122 1775795 "NAGS" 1779513 T NAGS (NIL) -7 NIL NIL NIL) (-763 1770986 1771294 1771625 "NAGF07" 1772127 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765524 1766815 1768122 "NAGF04" 1769699 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758492 1760106 1761739 "NAGF02" 1763911 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1753716 1754816 1755933 "NAGF01" 1757395 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747344 1748910 1750495 "NAGE04" 1752151 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738513 1740634 1742764 "NAGE02" 1745234 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734466 1735413 1736377 "NAGE01" 1737569 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732261 1732795 1733353 "NAGD03" 1733928 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724011 1725939 1727893 "NAGD02" 1730327 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1717822 1719247 1720687 "NAGD01" 1722591 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714031 1714853 1715690 "NAGC06" 1717005 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712496 1712828 1713184 "NAGC05" 1713695 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1711872 1711991 1712135 "NAGC02" 1712372 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1710831 1711414 1711454 "NAALG" 1711533 NIL NAALG (NIL T) -9 NIL 1711594 NIL) (-749 1710666 1710695 1710785 "NAALG-" 1710790 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704616 1705724 1706911 "MULTSQFR" 1709562 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1703935 1704010 1704194 "MULTFACT" 1704528 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696659 1700572 1700625 "MTSCAT" 1701695 NIL MTSCAT (NIL T T) -9 NIL 1702210 NIL) (-745 1696371 1696425 1696517 "MTHING" 1696599 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696163 1696196 1696256 "MSYSCMD" 1696331 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692245 1694918 1695238 "MSET" 1695876 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689314 1691806 1691847 "MSETAGG" 1691852 NIL MSETAGG (NIL T) -9 NIL 1691886 NIL) (-741 1685156 1686693 1687438 "MRING" 1688614 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1684722 1684789 1684920 "MRF2" 1685083 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684340 1684375 1684519 "MRATFAC" 1684681 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1681952 1682247 1682678 "MPRFF" 1684045 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676249 1681806 1681903 "MPOLY" 1681908 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1675739 1675774 1675982 "MPCPF" 1676208 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675253 1675296 1675480 "MPC3" 1675690 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674448 1674529 1674750 "MPC2" 1675168 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1672749 1673086 1673476 "MONOTOOL" 1674108 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1671974 1672291 1672319 "MONOID" 1672538 T MONOID (NIL) -9 NIL 1672685 NIL) (-731 1671520 1671639 1671820 "MONOID-" 1671825 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1661995 1667946 1668005 "MONOGEN" 1668679 NIL MONOGEN (NIL T T) -9 NIL 1669135 NIL) (-729 1659213 1659948 1660948 "MONOGEN-" 1661067 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658046 1658492 1658520 "MONADWU" 1658912 T MONADWU (NIL) -9 NIL 1659150 NIL) (-727 1657418 1657577 1657825 "MONADWU-" 1657830 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1656777 1657021 1657049 "MONAD" 1657256 T MONAD (NIL) -9 NIL 1657368 NIL) (-725 1656462 1656540 1656672 "MONAD-" 1656677 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1654751 1655375 1655654 "MOEBIUS" 1656215 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654029 1654433 1654473 "MODULE" 1654478 NIL MODULE (NIL T) -9 NIL 1654517 NIL) (-722 1653597 1653693 1653883 "MODULE-" 1653888 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651277 1651961 1652288 "MODRING" 1653421 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648221 1649382 1649903 "MODOP" 1650806 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1646809 1647288 1647565 "MODMONOM" 1648084 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1636853 1645100 1645514 "MODMON" 1646446 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634009 1635697 1635973 "MODFIELD" 1636728 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1632986 1633290 1633480 "MMLFORM" 1633839 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632512 1632555 1632734 "MMAP" 1632937 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630591 1631358 1631399 "MLO" 1631822 NIL MLO (NIL T) -9 NIL 1632064 NIL) (-713 1627957 1628473 1629075 "MLIFT" 1630072 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627348 1627432 1627586 "MKUCFUNC" 1627868 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1626947 1627017 1627140 "MKRECORD" 1627271 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1625994 1626156 1626384 "MKFUNC" 1626758 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625382 1625486 1625642 "MKFLCFN" 1625877 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624659 1624761 1624946 "MKBCFUNC" 1625275 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621366 1624213 1624349 "MINT" 1624543 T MINT (NIL) -8 NIL NIL NIL) (-706 1620178 1620421 1620698 "MHROWRED" 1621121 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615558 1618713 1619118 "MFLOAT" 1619793 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1614915 1614991 1615162 "MFINFACT" 1615470 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611230 1612078 1612962 "MESH" 1614051 T MESH (NIL) -7 NIL NIL NIL) (-702 1609620 1609932 1610285 "MDDFACT" 1610917 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606415 1608779 1608820 "MDAGG" 1609075 NIL MDAGG (NIL T) -9 NIL 1609218 NIL) (-700 1596155 1605708 1605915 "MCMPLX" 1606228 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595292 1595438 1595639 "MCDEN" 1596004 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593182 1593452 1593832 "MCALCFN" 1595022 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592107 1592347 1592580 "MAYBE" 1592988 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1589719 1590242 1590804 "MATSTOR" 1591578 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1585676 1589091 1589339 "MATRIX" 1589504 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581442 1582149 1582885 "MATLIN" 1585033 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571548 1574734 1574811 "MATCAT" 1579691 NIL MATCAT (NIL T T T) -9 NIL 1581108 NIL) (-692 1567904 1568925 1570281 "MATCAT-" 1570286 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566498 1566651 1566984 "MATCAT2" 1567739 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564610 1564934 1565318 "MAPPKG3" 1566173 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563591 1563764 1563986 "MAPPKG2" 1564434 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562090 1562374 1562701 "MAPPKG1" 1563297 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561169 1561496 1561673 "MAPPAST" 1561933 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1560780 1560838 1560961 "MAPHACK3" 1561105 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560372 1560433 1560547 "MAPHACK2" 1560712 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1559810 1559913 1560055 "MAPHACK1" 1560263 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1557889 1558510 1558814 "MAGMA" 1559538 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557368 1557613 1557704 "MACROAST" 1557818 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1553786 1555607 1556068 "M3D" 1556940 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1547861 1552125 1552166 "LZSTAGG" 1552948 NIL LZSTAGG (NIL T) -9 NIL 1553243 NIL) (-679 1543819 1544992 1546449 "LZSTAGG-" 1546454 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1540906 1541710 1542197 "LWORD" 1543364 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540482 1540710 1540785 "LSTAST" 1540851 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1533648 1540253 1540387 "LSQM" 1540392 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1532872 1533011 1533239 "LSPP" 1533503 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1530684 1530985 1531441 "LSMP" 1532561 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527463 1528137 1528867 "LSMP1" 1529986 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521309 1526600 1526641 "LSAGG" 1526703 NIL LSAGG (NIL T) -9 NIL 1526781 NIL) (-671 1518004 1518928 1520141 "LSAGG-" 1520146 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515603 1517148 1517397 "LPOLY" 1517799 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515185 1515270 1515393 "LPEFRAC" 1515512 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513506 1514279 1514532 "LO" 1515017 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513158 1513270 1513298 "LOGIC" 1513409 T LOGIC (NIL) -9 NIL 1513490 NIL) (-666 1513020 1513043 1513114 "LOGIC-" 1513119 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512213 1512353 1512546 "LODOOPS" 1512876 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1509636 1512129 1512195 "LODO" 1512200 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508174 1508409 1508762 "LODOF" 1509383 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504378 1506809 1506850 "LODOCAT" 1507288 NIL LODOCAT (NIL T) -9 NIL 1507499 NIL) (-661 1504111 1504169 1504296 "LODOCAT-" 1504301 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501431 1503952 1504070 "LODO2" 1504075 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1498866 1501368 1501413 "LODO1" 1501418 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1497747 1497912 1498217 "LODEEF" 1498689 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493050 1495941 1495982 "LNAGG" 1496844 NIL LNAGG (NIL T) -9 NIL 1497279 NIL) (-656 1492197 1492411 1492753 "LNAGG-" 1492758 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488333 1489122 1489761 "LMOPS" 1491612 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1487736 1488124 1488165 "LMODULE" 1488170 NIL LMODULE (NIL T) -9 NIL 1488196 NIL) (-653 1484934 1487381 1487504 "LMDICT" 1487646 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484340 1484561 1484602 "LLINSET" 1484793 NIL LLINSET (NIL T) -9 NIL 1484884 NIL) (-651 1484039 1484248 1484308 "LITERAL" 1484313 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477202 1482973 1483277 "LIST" 1483768 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1476727 1476801 1476940 "LIST3" 1477122 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1475734 1475912 1476140 "LIST2" 1476545 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1473868 1474180 1474579 "LIST2MAP" 1475381 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473464 1473701 1473742 "LINSET" 1473747 NIL LINSET (NIL T) -9 NIL 1473781 NIL) (-645 1472125 1472795 1472836 "LINEXP" 1473091 NIL LINEXP (NIL T) -9 NIL 1473240 NIL) (-644 1470772 1471032 1471329 "LINDEP" 1471877 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467539 1468258 1469035 "LIMITRF" 1470027 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1465842 1466138 1466547 "LIMITPS" 1467234 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460270 1465353 1465581 "LIE" 1465663 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459218 1459687 1459727 "LIECAT" 1459867 NIL LIECAT (NIL T) -9 NIL 1460018 NIL) (-639 1459059 1459086 1459174 "LIECAT-" 1459179 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451646 1458599 1458755 "LIB" 1458923 T LIB (NIL) -8 NIL NIL NIL) (-637 1447281 1448164 1449099 "LGROBP" 1450763 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445279 1445553 1445903 "LF" 1447002 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444119 1444811 1444839 "LFCAT" 1445046 T LFCAT (NIL) -9 NIL 1445185 NIL) (-634 1441021 1441651 1442339 "LEXTRIPK" 1443483 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1437765 1438591 1439094 "LEXP" 1440601 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437241 1437486 1437578 "LETAST" 1437693 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435639 1435952 1436353 "LEADCDET" 1436923 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1434829 1434903 1435132 "LAZM3PK" 1435560 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429746 1432906 1433444 "LAUPOL" 1434341 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429325 1429369 1429530 "LAPLACE" 1429696 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427264 1428426 1428677 "LA" 1429158 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426258 1426842 1426883 "LALG" 1426945 NIL LALG (NIL T) -9 NIL 1427004 NIL) (-625 1425972 1426031 1426167 "LALG-" 1426172 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1425807 1425831 1425872 "KVTFROM" 1425934 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424730 1425174 1425359 "KTVLOGIC" 1425642 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424565 1424589 1424630 "KRCFROM" 1424692 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423469 1423656 1423955 "KOVACIC" 1424365 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423304 1423328 1423369 "KONVERT" 1423431 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423139 1423163 1423204 "KOERCE" 1423266 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1420969 1421732 1422109 "KERNEL" 1422795 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420465 1420546 1420678 "KERNEL2" 1420883 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414235 1419004 1419058 "KDAGG" 1419435 NIL KDAGG (NIL T T) -9 NIL 1419641 NIL) (-615 1413764 1413888 1414093 "KDAGG-" 1414098 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1406912 1413425 1413580 "KAFILE" 1413642 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401340 1406423 1406651 "JORDAN" 1406733 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400719 1400989 1401110 "JOINAST" 1401239 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400565 1400624 1400679 "JAVACODE" 1400684 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1396817 1398770 1398824 "IXAGG" 1399753 NIL IXAGG (NIL T T) -9 NIL 1400212 NIL) (-609 1395736 1396042 1396461 "IXAGG-" 1396466 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391266 1395658 1395717 "IVECTOR" 1395722 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390032 1390269 1390535 "ITUPLE" 1391033 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388534 1388711 1389006 "ITRIGMNP" 1389854 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387279 1387483 1387766 "ITFUN3" 1388310 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1386911 1386968 1387077 "ITFUN2" 1387216 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386070 1386391 1386565 "ITFORM" 1386757 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384031 1385090 1385368 "ITAYLOR" 1385825 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1372976 1378168 1379331 "ISUPS" 1382901 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372080 1372220 1372456 "ISUMP" 1372823 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367455 1372025 1372066 "ISTRING" 1372071 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1366931 1367176 1367268 "ISAST" 1367383 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366140 1366222 1366438 "IRURPK" 1366845 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365076 1365277 1365517 "IRSN" 1365920 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363147 1363502 1363931 "IRRF2F" 1364714 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1362894 1362932 1363008 "IRREDFFX" 1363103 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361509 1361768 1362067 "IROOT" 1362627 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358113 1359193 1359885 "IR" 1360849 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357318 1357606 1357757 "IRFORM" 1357982 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1354931 1355426 1355992 "IR2" 1356796 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354031 1354144 1354358 "IR2F" 1354814 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1353822 1353856 1353916 "IPRNTPK" 1353991 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350403 1353711 1353780 "IPF" 1353785 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348730 1350328 1350385 "IPADIC" 1350390 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348042 1348290 1348420 "IP4ADDR" 1348620 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347416 1347671 1347803 "IOMODE" 1347930 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346489 1347013 1347140 "IOBFILE" 1347309 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1345977 1346393 1346421 "IOBCON" 1346426 T IOBCON (NIL) -9 NIL 1346447 NIL) (-581 1345488 1345546 1345729 "INVLAPLA" 1345913 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335136 1337490 1339876 "INTTR" 1343152 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331471 1332213 1333078 "INTTOOLS" 1334321 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331057 1331148 1331265 "INTSLPE" 1331374 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329010 1330980 1331039 "INTRVL" 1331044 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326612 1327124 1327699 "INTRF" 1328495 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326023 1326120 1326262 "INTRET" 1326510 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324020 1324409 1324879 "INTRAT" 1325631 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321283 1321866 1322485 "INTPM" 1323505 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318028 1318627 1319365 "INTPAF" 1320669 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313207 1314169 1315220 "INTPACK" 1316997 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310155 1313004 1313113 "INT" 1313118 T INT (NIL) -8 NIL NIL NIL) (-569 1309407 1309559 1309767 "INTHERTR" 1309997 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1308846 1308926 1309114 "INTHERAL" 1309321 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306692 1307135 1307592 "INTHEORY" 1308409 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298098 1299719 1301491 "INTG0" 1305044 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278671 1283461 1288271 "INTFTBL" 1293308 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1277920 1278058 1278231 "INTFACT" 1278530 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275347 1275793 1276350 "INTEF" 1277474 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273714 1274453 1274481 "INTDOM" 1274782 T INTDOM (NIL) -9 NIL 1274989 NIL) (-561 1273083 1273257 1273499 "INTDOM-" 1273504 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269471 1271399 1271453 "INTCAT" 1272252 NIL INTCAT (NIL T) -9 NIL 1272573 NIL) (-559 1268943 1269046 1269174 "INTBIT" 1269363 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267642 1267796 1268103 "INTALG" 1268788 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267125 1267215 1267372 "INTAF" 1267546 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260468 1266935 1267075 "INTABL" 1267080 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1259809 1260275 1260340 "INT8" 1260374 T INT8 (NIL) -8 NIL NIL 1260419) (-554 1259149 1259615 1259680 "INT64" 1259714 T INT64 (NIL) -8 NIL NIL 1259759) (-553 1258489 1258955 1259020 "INT32" 1259054 T INT32 (NIL) -8 NIL NIL 1259099) (-552 1257829 1258295 1258360 "INT16" 1258394 T INT16 (NIL) -8 NIL NIL 1258439) (-551 1252739 1255452 1255480 "INS" 1256414 T INS (NIL) -9 NIL 1257079 NIL) (-550 1249979 1250750 1251724 "INS-" 1251797 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1248754 1248981 1249279 "INPSIGN" 1249732 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1247872 1247989 1248186 "INPRODPF" 1248634 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1246766 1246883 1247120 "INPRODFF" 1247752 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1245766 1245918 1246178 "INNMFACT" 1246602 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1244963 1245060 1245248 "INMODGCD" 1245665 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243471 1243716 1244040 "INFSP" 1244708 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242655 1242772 1242955 "INFPROD0" 1243351 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239510 1240720 1241235 "INFORM" 1242148 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239120 1239180 1239278 "INFORM1" 1239445 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238643 1238732 1238846 "INFINITY" 1239026 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1237819 1238363 1238464 "INETCLTS" 1238562 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236435 1236685 1237006 "INEP" 1237567 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235684 1236332 1236397 "INDE" 1236402 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235248 1235316 1235433 "INCRMAPS" 1235611 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234066 1234517 1234723 "INBFILE" 1235062 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229365 1230302 1231246 "INBFF" 1233154 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228273 1228542 1228570 "INBCON" 1229083 T INBCON (NIL) -9 NIL 1229349 NIL) (-532 1227525 1227748 1228024 "INBCON-" 1228029 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227004 1227249 1227340 "INAST" 1227454 T INAST (NIL) -8 NIL NIL NIL) (-530 1226431 1226683 1226789 "IMPTAST" 1226918 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1222877 1226275 1226379 "IMATRIX" 1226384 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221585 1221708 1222024 "IMATQF" 1222733 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1219805 1220032 1220369 "IMATLIN" 1221341 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214383 1219729 1219787 "ILIST" 1219792 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212288 1214243 1214356 "IIARRAY2" 1214361 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207686 1212199 1212263 "IFF" 1212268 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207033 1207303 1207419 "IFAST" 1207590 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202028 1206325 1206513 "IFARRAY" 1206890 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201208 1201932 1202005 "IFAMON" 1202010 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1200792 1200857 1200911 "IEVALAB" 1201118 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200467 1200535 1200695 "IEVALAB-" 1200700 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200098 1200381 1200444 "IDPO" 1200449 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199348 1199987 1200062 "IDPOAMS" 1200067 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198655 1199237 1199312 "IDPOAM" 1199317 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197714 1197990 1198043 "IDPC" 1198456 NIL IDPC (NIL T T) -9 NIL 1198605 NIL) (-514 1197183 1197606 1197679 "IDPAM" 1197684 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196559 1197075 1197148 "IDPAG" 1197153 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196204 1196395 1196470 "IDENT" 1196504 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192459 1193307 1194202 "IDECOMP" 1195361 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185296 1186382 1187429 "IDEAL" 1191495 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184456 1184568 1184768 "ICDEN" 1185180 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183527 1183936 1184083 "ICARD" 1184329 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181587 1181900 1182305 "IBPTOOLS" 1183204 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177194 1181207 1181320 "IBITS" 1181506 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1173917 1174493 1175188 "IBATOOL" 1176611 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171696 1172158 1172691 "IBACHIN" 1173452 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169525 1171542 1171645 "IARRAY2" 1171650 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165631 1169451 1169508 "IARRAY1" 1169513 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159740 1164043 1164524 "IAN" 1165170 T IAN (NIL) -8 NIL NIL NIL) (-500 1159251 1159308 1159481 "IALGFACT" 1159677 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1158779 1158892 1158920 "HYPCAT" 1159127 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158317 1158434 1158620 "HYPCAT-" 1158625 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1157912 1158112 1158195 "HOSTNAME" 1158254 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1157757 1157794 1157835 "HOMOTOP" 1157840 NIL HOMOTOP (NIL T) -9 NIL 1157873 NIL) (-495 1154389 1155767 1155808 "HOAGG" 1156789 NIL HOAGG (NIL T) -9 NIL 1157468 NIL) (-494 1152983 1153382 1153908 "HOAGG-" 1153913 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1146985 1152576 1152726 "HEXADEC" 1152853 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145733 1145955 1146218 "HEUGCD" 1146762 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1144809 1145570 1145700 "HELLFDIV" 1145705 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1142988 1144586 1144674 "HEAP" 1144753 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142251 1142540 1142674 "HEADAST" 1142874 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136117 1142166 1142228 "HDP" 1142233 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130105 1135752 1135904 "HDMP" 1136018 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129429 1129569 1129733 "HB" 1129961 T HB (NIL) -7 NIL NIL NIL) (-485 1122815 1129275 1129379 "HASHTBL" 1129384 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122291 1122536 1122628 "HASAST" 1122743 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120069 1121913 1122095 "HACKPI" 1122129 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115737 1119922 1120035 "GTSET" 1120040 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109152 1115615 1115713 "GSTBL" 1115718 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101430 1108183 1108448 "GSERIES" 1108943 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100571 1100988 1101016 "GROUP" 1101219 T GROUP (NIL) -9 NIL 1101353 NIL) (-478 1099937 1100096 1100347 "GROUP-" 1100352 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098304 1098625 1099012 "GROEBSOL" 1099614 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097218 1097506 1097557 "GRMOD" 1098086 NIL GRMOD (NIL T T) -9 NIL 1098254 NIL) (-475 1096986 1097022 1097150 "GRMOD-" 1097155 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092276 1093340 1094340 "GRIMAGE" 1096006 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090742 1091003 1091327 "GRDEF" 1091972 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090186 1090302 1090443 "GRAY" 1090621 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089373 1089779 1089830 "GRALG" 1089983 NIL GRALG (NIL T T) -9 NIL 1090076 NIL) (-470 1089034 1089107 1089270 "GRALG-" 1089275 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1085811 1088619 1088797 "GPOLSET" 1088941 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085165 1085222 1085480 "GOSPER" 1085748 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1080897 1081603 1082129 "GMODPOL" 1084864 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1079902 1080086 1080324 "GHENSEL" 1080709 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074058 1074901 1075921 "GENUPS" 1078986 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1073755 1073806 1073895 "GENUFACT" 1074001 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073167 1073244 1073409 "GENPGCD" 1073673 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072641 1072676 1072889 "GENMFACT" 1073126 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071207 1071464 1071771 "GENEEZ" 1072384 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065355 1070818 1070980 "GDMP" 1071130 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054698 1059126 1060232 "GCNAALG" 1064338 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053025 1053887 1053915 "GCDDOM" 1054170 T GCDDOM (NIL) -9 NIL 1054327 NIL) (-457 1052495 1052622 1052837 "GCDDOM-" 1052842 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051167 1051352 1051656 "GB" 1052274 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1039783 1042113 1044505 "GBINTERN" 1048858 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037620 1037912 1038333 "GBF" 1039458 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036401 1036566 1036833 "GBEUCLID" 1037436 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1035750 1035875 1036024 "GAUSSFAC" 1036272 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034117 1034419 1034733 "GALUTIL" 1035469 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032425 1032699 1033023 "GALPOLYU" 1033844 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1029790 1030080 1030487 "GALFACTU" 1032122 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021596 1023095 1024703 "GALFACT" 1028222 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1018984 1019642 1019670 "FVFUN" 1020826 T FVFUN (NIL) -9 NIL 1021546 NIL) (-446 1018250 1018432 1018460 "FVC" 1018751 T FVC (NIL) -9 NIL 1018934 NIL) (-445 1017893 1018075 1018143 "FUNDESC" 1018202 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017508 1017690 1017771 "FUNCTION" 1017845 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015252 1015830 1016296 "FT" 1017062 T FT (NIL) -8 NIL NIL NIL) (-442 1014043 1014553 1014756 "FTEM" 1015069 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012334 1012623 1013020 "FSUPFACT" 1013734 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010731 1011020 1011352 "FST" 1012022 T FST (NIL) -8 NIL NIL NIL) (-439 1009930 1010036 1010224 "FSRED" 1010613 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008629 1008885 1009232 "FSPRMELT" 1009645 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1005935 1006373 1006859 "FSPECF" 1008192 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987573 995904 995945 "FS" 999829 NIL FS (NIL T) -9 NIL 1002118 NIL) (-435 976216 979209 983266 "FS-" 983566 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975744 975798 975968 "FSINT" 976157 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974036 974737 975040 "FSERIES" 975523 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973078 973194 973418 "FSCINT" 973916 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969286 972022 972063 "FSAGG" 972433 NIL FSAGG (NIL T) -9 NIL 972692 NIL) (-430 967048 967649 968445 "FSAGG-" 968540 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966090 966233 966460 "FSAGG2" 966901 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 963772 964052 964599 "FS2UPS" 965808 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963406 963449 963578 "FS2" 963723 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962284 962455 962757 "FS2EXPXP" 963231 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961710 961825 961977 "FRUTIL" 962164 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953123 957205 958563 "FR" 960384 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948137 950812 950852 "FRNAALG" 952172 NIL FRNAALG (NIL T) -9 NIL 952770 NIL) (-422 943810 944886 946161 "FRNAALG-" 946911 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943448 943491 943618 "FRNAAF2" 943761 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 941823 942297 942593 "FRMOD" 943260 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939566 940198 940516 "FRIDEAL" 941614 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938757 938844 939135 "FRIDEAL2" 939473 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 937890 938304 938345 "FRETRCT" 938350 NIL FRETRCT (NIL T) -9 NIL 938526 NIL) (-416 937002 937233 937584 "FRETRCT-" 937589 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934090 935300 935359 "FRAMALG" 936241 NIL FRAMALG (NIL T T) -9 NIL 936533 NIL) (-414 932224 932679 933309 "FRAMALG-" 933532 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926143 931697 931974 "FRAC" 931979 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925779 925836 925943 "FRAC2" 926080 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925415 925472 925579 "FR2" 925716 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 919928 922821 922849 "FPS" 923968 T FPS (NIL) -9 NIL 924525 NIL) (-409 919377 919486 919650 "FPS-" 919796 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916679 918348 918376 "FPC" 918601 T FPC (NIL) -9 NIL 918743 NIL) (-407 916472 916512 916609 "FPC-" 916614 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915262 915960 916001 "FPATMAB" 916006 NIL FPATMAB (NIL T) -9 NIL 916158 NIL) (-405 912935 913438 913864 "FPARFRAC" 914899 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908329 908827 909509 "FORTRAN" 912367 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906045 906545 907084 "FORT" 907810 T FORT (NIL) -7 NIL NIL NIL) (-402 903721 904283 904311 "FORTFN" 905371 T FORTFN (NIL) -9 NIL 905995 NIL) (-401 903485 903535 903563 "FORTCAT" 903622 T FORTCAT (NIL) -9 NIL 903684 NIL) (-400 901591 902101 902491 "FORMULA" 903115 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901379 901409 901478 "FORMULA1" 901555 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 900902 900954 901127 "FORDER" 901321 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 899998 900162 900355 "FOP" 900729 T FOP (NIL) -7 NIL NIL NIL) (-396 898579 899278 899452 "FNLA" 899880 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897308 897723 897751 "FNCAT" 898211 T FNCAT (NIL) -9 NIL 898471 NIL) (-394 896847 897267 897295 "FNAME" 897300 T FNAME (NIL) -8 NIL NIL NIL) (-393 895410 896373 896401 "FMTC" 896406 T FMTC (NIL) -9 NIL 896442 NIL) (-392 894156 895346 895392 "FMONOID" 895397 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 890984 892152 892193 "FMONCAT" 893410 NIL FMONCAT (NIL T) -9 NIL 894015 NIL) (-390 890176 890726 890875 "FM" 890880 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887600 888246 888274 "FMFUN" 889418 T FMFUN (NIL) -9 NIL 890126 NIL) (-388 886869 887050 887078 "FMC" 887368 T FMC (NIL) -9 NIL 887550 NIL) (-387 883948 884808 884862 "FMCAT" 886057 NIL FMCAT (NIL T T) -9 NIL 886552 NIL) (-386 882814 883714 883814 "FM1" 883893 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880588 881004 881498 "FLOATRP" 882365 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874166 878317 878938 "FLOAT" 879987 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871604 872104 872682 "FLOATCP" 873633 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870344 871182 871223 "FLINEXP" 871228 NIL FLINEXP (NIL T) -9 NIL 871321 NIL) (-381 869498 869733 870061 "FLINEXP-" 870066 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868574 868718 868942 "FLASORT" 869350 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865690 866558 866610 "FLALG" 867837 NIL FLALG (NIL T T) -9 NIL 868304 NIL) (-378 859394 863146 863187 "FLAGG" 864449 NIL FLAGG (NIL T) -9 NIL 865101 NIL) (-377 858120 858459 858949 "FLAGG-" 858954 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857162 857305 857532 "FLAGG2" 857973 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854013 855021 855080 "FINRALG" 856208 NIL FINRALG (NIL T T) -9 NIL 856716 NIL) (-374 853173 853402 853741 "FINRALG-" 853746 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852553 852792 852820 "FINITE" 853016 T FINITE (NIL) -9 NIL 853123 NIL) (-372 844910 847097 847137 "FINAALG" 850804 NIL FINAALG (NIL T) -9 NIL 852257 NIL) (-371 840242 841292 842436 "FINAALG-" 843815 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839610 839997 840100 "FILE" 840172 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838268 838606 838660 "FILECAT" 839344 NIL FILECAT (NIL T T) -9 NIL 839560 NIL) (-368 835984 837512 837540 "FIELD" 837580 T FIELD (NIL) -9 NIL 837660 NIL) (-367 834604 834989 835500 "FIELD-" 835505 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832454 833239 833586 "FGROUP" 834290 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831544 831708 831928 "FGLMICPK" 832286 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827376 831469 831526 "FFX" 831531 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 826977 827038 827173 "FFSLPE" 827309 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 822967 823749 824545 "FFPOLY" 826213 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822471 822507 822716 "FFPOLY2" 822925 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818317 822390 822453 "FFP" 822458 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813715 818228 818292 "FF" 818297 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 808841 813058 813248 "FFNBX" 813569 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 803769 807976 808234 "FFNBP" 808695 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798402 803053 803264 "FFNB" 803602 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797234 797432 797747 "FFINTBAS" 798199 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793303 795523 795551 "FFIELDC" 796171 T FFIELDC (NIL) -9 NIL 796547 NIL) (-353 791965 792336 792833 "FFIELDC-" 792838 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791534 791580 791704 "FFHOM" 791907 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789229 789716 790233 "FFF" 791049 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 784847 788971 789072 "FFCGX" 789172 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780469 784579 784686 "FFCGP" 784790 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775652 780196 780304 "FFCG" 780405 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757048 766129 766215 "FFCAT" 771380 NIL FFCAT (NIL T T T) -9 NIL 772831 NIL) (-346 752245 753293 754607 "FFCAT-" 755837 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751656 751699 751934 "FFCAT2" 752196 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 740979 744628 745848 "FEXPR" 750508 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 739941 740376 740417 "FEVALAB" 740501 NIL FEVALAB (NIL T) -9 NIL 740762 NIL) (-342 739100 739310 739648 "FEVALAB-" 739653 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737666 738483 738686 "FDIV" 738999 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734686 735427 735542 "FDIVCAT" 737110 NIL FDIVCAT (NIL T T T T) -9 NIL 737547 NIL) (-339 734448 734475 734645 "FDIVCAT-" 734650 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733668 733755 734032 "FDIV2" 734355 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732642 732963 733165 "FCTRDATA" 733486 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731328 731587 731876 "FCPAK1" 732373 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730427 730828 730969 "FCOMP" 731219 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714132 717577 721115 "FC" 726909 T FC (NIL) -8 NIL NIL NIL) (-333 706495 710523 710563 "FAXF" 712365 NIL FAXF (NIL T) -9 NIL 713057 NIL) (-332 703772 704429 705254 "FAXF-" 705719 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 698824 703148 703324 "FARRAY" 703629 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693718 695785 695838 "FAMR" 696861 NIL FAMR (NIL T T) -9 NIL 697321 NIL) (-329 692608 692910 693345 "FAMR-" 693350 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 691777 692530 692583 "FAMONOID" 692588 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689563 690273 690326 "FAMONC" 691267 NIL FAMONC (NIL T T) -9 NIL 691653 NIL) (-326 688227 689317 689454 "FAGROUP" 689459 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686022 686341 686744 "FACUTIL" 687908 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685121 685306 685528 "FACTFUNC" 685832 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677543 684424 684623 "EXPUPXS" 684977 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675026 675566 676152 "EXPRTUBE" 676977 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671297 671889 672619 "EXPRODE" 674365 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 656782 669946 670375 "EXPR" 670901 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651336 651923 652729 "EXPR2UPS" 656080 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 650968 651025 651134 "EXPR2" 651273 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642356 650119 650410 "EXPEXPAN" 650804 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642156 642313 642342 "EXIT" 642347 T EXIT (NIL) -8 NIL NIL NIL) (-315 641636 641880 641971 "EXITAST" 642085 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641263 641325 641438 "EVALCYC" 641568 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 640804 640922 640963 "EVALAB" 641133 NIL EVALAB (NIL T) -9 NIL 641237 NIL) (-312 640285 640407 640628 "EVALAB-" 640633 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637653 638955 638983 "EUCDOM" 639538 T EUCDOM (NIL) -9 NIL 639888 NIL) (-310 636058 636500 637090 "EUCDOM-" 637095 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623597 626356 629106 "ESTOOLS" 633328 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623229 623286 623395 "ESTOOLS2" 623534 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 622980 623022 623102 "ESTOOLS1" 623181 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617017 618625 618653 "ES" 621421 T ES (NIL) -9 NIL 622831 NIL) (-305 611964 613251 615068 "ES-" 615232 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608338 609099 609879 "ESCONT" 611204 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608083 608115 608197 "ESCONT1" 608300 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 607758 607808 607908 "ES2" 608027 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607388 607446 607555 "ES1" 607694 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606604 606733 606909 "ERROR" 607232 T ERROR (NIL) -7 NIL NIL NIL) (-299 599996 606463 606554 "EQTBL" 606559 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592499 595310 596759 "EQ" 598580 NIL -2094 (NIL T) -8 NIL NIL NIL) (-297 592131 592188 592297 "EQ2" 592436 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587422 588469 589562 "EP" 591070 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586022 586313 586619 "ENV" 587136 T ENV (NIL) -8 NIL NIL NIL) (-294 585116 585670 585698 "ENTIRER" 585703 T ENTIRER (NIL) -9 NIL 585749 NIL) (-293 581810 583298 583659 "EMR" 584924 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 580940 581125 581179 "ELTAGG" 581559 NIL ELTAGG (NIL T T) -9 NIL 581770 NIL) (-291 580659 580721 580862 "ELTAGG-" 580867 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580423 580452 580506 "ELTAB" 580590 NIL ELTAB (NIL T T) -9 NIL 580642 NIL) (-289 579549 579695 579894 "ELFUTS" 580274 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579291 579347 579375 "ELEMFUN" 579480 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579161 579182 579250 "ELEMFUN-" 579255 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 573975 577231 577272 "ELAGG" 578212 NIL ELAGG (NIL T) -9 NIL 578675 NIL) (-285 572260 572694 573357 "ELAGG-" 573362 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571572 571709 571865 "ELABOR" 572124 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570233 570512 570806 "ELABEXPR" 571298 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563097 564900 565727 "EFUPXS" 569509 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556547 558348 559158 "EFULS" 562373 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554032 554390 554862 "EFSTRUC" 556179 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543823 545389 546937 "EF" 552547 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 542897 543308 543457 "EAB" 543694 T EAB (NIL) -8 NIL NIL NIL) (-277 542079 542856 542884 "E04UCFA" 542889 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541261 542038 542066 "E04NAFA" 542071 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540443 541220 541248 "E04MBFA" 541253 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539625 540402 540430 "E04JAFA" 540435 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538809 539584 539612 "E04GCFA" 539617 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 537993 538768 538796 "E04FDFA" 538801 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537175 537952 537980 "E04DGFA" 537985 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531348 532700 534064 "E04AGNT" 535831 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530028 530534 530574 "DVARCAT" 531049 NIL DVARCAT (NIL T) -9 NIL 531248 NIL) (-268 529232 529444 529758 "DVARCAT-" 529763 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522369 529031 529160 "DSMP" 529165 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517150 518314 519382 "DROPT" 521321 T DROPT (NIL) -8 NIL NIL NIL) (-265 516815 516874 516972 "DROPT1" 517085 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 511930 513056 514193 "DROPT0" 515698 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510275 510600 510986 "DRAWPT" 511564 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504862 505785 506864 "DRAW" 509249 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504495 504548 504666 "DRAWHACK" 504803 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503226 503495 503786 "DRAWCX" 504224 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502741 502810 502961 "DRAWCURV" 503152 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493209 495171 497286 "DRAWCFUN" 500646 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 489973 491902 491943 "DQAGG" 492572 NIL DQAGG (NIL T) -9 NIL 492846 NIL) (-256 478097 484566 484649 "DPOLCAT" 486501 NIL DPOLCAT (NIL T T T T) -9 NIL 487046 NIL) (-255 472934 474282 476240 "DPOLCAT-" 476245 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466056 472795 472893 "DPMO" 472898 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459081 465836 466003 "DPMM" 466008 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458651 458865 458954 "DOMTMPLT" 459012 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458084 458453 458533 "DOMCTOR" 458591 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457296 457564 457715 "DOMAIN" 457953 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451284 456931 457083 "DMP" 457197 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450884 450940 451084 "DLP" 451222 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444706 450211 450401 "DLIST" 450726 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441503 443559 443600 "DLAGG" 444150 NIL DLAGG (NIL T) -9 NIL 444380 NIL) (-245 440179 440843 440871 "DIVRING" 440963 T DIVRING (NIL) -9 NIL 441046 NIL) (-244 439416 439606 439906 "DIVRING-" 439911 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437518 437875 438281 "DISPLAY" 439030 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431404 437432 437495 "DIRPROD" 437500 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430252 430455 430720 "DIRPROD2" 431197 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419027 425033 425086 "DIRPCAT" 425496 NIL DIRPCAT (NIL NIL T) -9 NIL 426336 NIL) (-239 416353 416995 417876 "DIRPCAT-" 418213 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415640 415800 415986 "DIOSP" 416187 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412295 414552 414593 "DIOPS" 415027 NIL DIOPS (NIL T) -9 NIL 415256 NIL) (-236 411844 411958 412149 "DIOPS-" 412154 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410667 411295 411323 "DIFRING" 411510 T DIFRING (NIL) -9 NIL 411620 NIL) (-234 410313 410390 410542 "DIFRING-" 410547 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408049 409321 409362 "DIFEXT" 409725 NIL DIFEXT (NIL T) -9 NIL 410019 NIL) (-232 406334 406762 407428 "DIFEXT-" 407433 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403609 405866 405907 "DIAGG" 405912 NIL DIAGG (NIL T) -9 NIL 405932 NIL) (-230 402993 403150 403402 "DIAGG-" 403407 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398410 401952 402229 "DHMATRIX" 402762 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394022 394931 395941 "DFSFUN" 397420 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389102 392953 393265 "DFLOAT" 393730 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387365 387646 388035 "DFINTTLS" 388810 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384394 385386 385786 "DERHAM" 387031 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382195 384169 384258 "DEQUEUE" 384338 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381449 381582 381765 "DEGRED" 382057 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377879 378624 379470 "DEFINTRF" 380677 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375434 375903 376495 "DEFINTEF" 377398 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374784 375054 375169 "DEFAST" 375339 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368786 374377 374527 "DECIMAL" 374654 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366298 366756 367262 "DDFACT" 368330 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365894 365937 366088 "DBLRESP" 366249 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363766 364127 364487 "DBASE" 365661 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363008 363246 363392 "DATAARY" 363665 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362114 362967 362995 "D03FAFA" 363000 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361221 362073 362101 "D03EEFA" 362106 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359171 359637 360126 "D03AGNT" 360752 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358460 359130 359158 "D02EJFA" 359163 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357749 358419 358447 "D02CJFA" 358452 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357038 357708 357736 "D02BHFA" 357741 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356327 356997 357025 "D02BBFA" 357030 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349524 351113 352719 "D02AGNT" 354741 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347292 347815 348361 "D01WGTS" 348998 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346359 347251 347279 "D01TRNS" 347284 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345427 346318 346346 "D01GBFA" 346351 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344495 345386 345414 "D01FCFA" 345419 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343563 344454 344482 "D01ASFA" 344487 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342631 343522 343550 "D01AQFA" 343555 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341699 342590 342618 "D01APFA" 342623 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340767 341658 341686 "D01ANFA" 341691 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339835 340726 340754 "D01AMFA" 340759 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338903 339794 339822 "D01ALFA" 339827 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 337971 338862 338890 "D01AKFA" 338895 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337039 337930 337958 "D01AJFA" 337963 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330334 331887 333448 "D01AGNT" 335498 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329671 329799 329951 "CYCLOTOM" 330202 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326404 327119 327846 "CYCLES" 328964 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325716 325850 326021 "CVMP" 326265 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323557 323815 324184 "CTRIGMNP" 325444 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 322993 323351 323424 "CTOR" 323504 T CTOR (NIL) -8 NIL NIL NIL) (-188 322502 322724 322825 "CTORKIND" 322912 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321793 322109 322137 "CTORCAT" 322319 T CTORCAT (NIL) -9 NIL 322432 NIL) (-186 321391 321502 321661 "CTORCAT-" 321666 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320853 321065 321173 "CTORCALL" 321315 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320227 320326 320479 "CSTTOOLS" 320750 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316026 316683 317441 "CRFP" 319539 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315501 315747 315839 "CRCEAST" 315954 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314548 314733 314961 "CRAPACK" 315305 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313932 314033 314237 "CPMATCH" 314424 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313657 313685 313791 "CPIMA" 313898 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310005 310677 311396 "COORDSYS" 312992 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309417 309538 309680 "CONTOUR" 309883 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305308 307420 307912 "CONTFRAC" 308957 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305188 305209 305237 "CONDUIT" 305274 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304276 304830 304858 "COMRING" 304863 T COMRING (NIL) -9 NIL 304915 NIL) (-173 303330 303634 303818 "COMPPROP" 304112 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 302991 303026 303154 "COMPLPAT" 303289 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293282 302800 302909 "COMPLEX" 302914 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292918 292975 293082 "COMPLEX2" 293219 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292257 292378 292538 "COMPILER" 292778 T COMPILER (NIL) -8 NIL NIL NIL) (-168 291975 292010 292108 "COMPFACT" 292216 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276055 286049 286089 "COMPCAT" 287093 NIL COMPCAT (NIL T) -9 NIL 288441 NIL) (-166 265567 268494 272121 "COMPCAT-" 272477 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265296 265324 265427 "COMMUPC" 265533 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265090 265124 265183 "COMMONOP" 265257 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264646 264841 264928 "COMM" 265023 T COMM (NIL) -8 NIL NIL NIL) (-162 264222 264450 264525 "COMMAAST" 264591 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263471 263665 263693 "COMBOPC" 264031 T COMBOPC (NIL) -9 NIL 264206 NIL) (-160 262367 262577 262819 "COMBINAT" 263261 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258824 259398 260025 "COMBF" 261789 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257582 257940 258175 "COLOR" 258609 T COLOR (NIL) -8 NIL NIL NIL) (-157 257058 257303 257395 "COLONAST" 257510 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256698 256745 256870 "CMPLXRT" 257005 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256146 256398 256497 "CLLCTAST" 256619 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251648 252676 253756 "CLIP" 255086 T CLIP (NIL) -7 NIL NIL NIL) (-153 249989 250749 250989 "CLIF" 251475 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246164 248135 248176 "CLAGG" 249105 NIL CLAGG (NIL T) -9 NIL 249641 NIL) (-151 244586 245043 245626 "CLAGG-" 245631 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244130 244215 244355 "CINTSLPE" 244495 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241631 242102 242650 "CHVAR" 243658 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240805 241359 241387 "CHARZ" 241392 T CHARZ (NIL) -9 NIL 241407 NIL) (-147 240559 240599 240677 "CHARPOL" 240759 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239617 240204 240232 "CHARNZ" 240279 T CHARNZ (NIL) -9 NIL 240335 NIL) (-145 237523 238271 238624 "CHAR" 239284 T CHAR (NIL) -8 NIL NIL NIL) (-144 237249 237310 237338 "CFCAT" 237449 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236490 236601 236784 "CDEN" 237133 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232455 235643 235923 "CCLASS" 236230 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231706 231863 232040 "CATEGORY" 232298 T -10 (NIL) -8 NIL NIL NIL) (-140 231279 231625 231673 "CATCTOR" 231678 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230730 230982 231080 "CATAST" 231201 T CATAST (NIL) -8 NIL NIL NIL) (-138 230206 230451 230543 "CASEAST" 230658 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225344 226363 227107 "CARTEN" 229518 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224452 224600 224821 "CARTEN2" 225191 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222768 223602 223859 "CARD" 224215 T CARD (NIL) -8 NIL NIL NIL) (-134 222344 222572 222647 "CAPSLAST" 222713 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221848 222056 222084 "CACHSET" 222216 T CACHSET (NIL) -9 NIL 222294 NIL) (-132 221318 221640 221668 "CABMON" 221718 T CABMON (NIL) -9 NIL 221774 NIL) (-131 220791 221022 221132 "BYTEORD" 221228 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219768 220320 220462 "BYTE" 220625 T BYTE (NIL) -8 NIL NIL 220747) (-129 215118 219273 219445 "BYTEBUF" 219616 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212627 214810 214917 "BTREE" 215044 NIL BTREE 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(|:| -1410 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-335 *4)) (-4 *4 (-13 (-856) (-21))) @@ -3476,14 +8310,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-440)) (-5 *1 (-443)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3280 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -2138 (-650 (-334))))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-1277 (-705))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3280 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -2138 (-650 (-334))))) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-447)))) @@ -3552,7 +8386,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-650 (-2 (|:| -1458 *3) (|:| -3436 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*3 (-570)) (-4 *1 (-286 *2)) (-4 *2 (-1227)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -3679 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -4388 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -1409 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4388 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| 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+ (-5 *3 + (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-777)) (|:| |poli| *2) + (|:| |polj| *2))) + (-4 *5 (-799)) (-4 *2 (-956 *4 *5 *6)) (-5 *1 (-455 *4 *5 *6 *2)) + (-4 *4 (-458)) (-4 *6 (-856))))) +(((*1 *2 *3) + (-12 (-4 *4 (-458)) + (-5 *2 + (-650 + (-2 (|:| |eigval| (-3 (-413 (-959 *4)) (-1175 (-1186) (-959 *4)))) + (|:| |geneigvec| (-650 (-695 (-413 (-959 *4)))))))) + (-5 *1 (-296 *4)) (-5 *3 (-695 (-413 (-959 *4))))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-695 *1)) (-5 *4 (-1277 *1)) (-4 *1 (-645 *5)) + (-4 *5 (-1058)) + (-5 *2 (-2 (|:| -1997 (-695 *5)) (|:| |vec| (-1277 *5)))))) + ((*1 *2 *3) + (-12 (-5 *3 (-695 *1)) (-4 *1 (-645 *4)) (-4 *4 (-1058)) + (-5 *2 (-695 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-695 *5)) (-5 *4 (-1277 *5)) (-4 *5 (-368)) + (-5 *2 (-112)) (-5 *1 (-673 *5)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 -4453)))) + (-4 *4 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-5 *2 (-112)) + (-5 *1 (-674 *5 *6 *4 *3)) (-4 *3 (-693 *5 *6 *4))))) +(((*1 *2 *3 *4 *3) + (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1253 *5)) (-4 *5 (-368)) + (-5 *2 (-2 (|:| -3491 (-413 *6)) (|:| |coeff| (-413 *6)))) + (-5 *1 (-580 *5 *6)) (-5 *3 (-413 *6))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-551)))) (((*1 *2 *3 *4) (-12 (-5 *3 (-650 (-413 (-959 (-570))))) (-5 *2 (-650 (-650 (-298 (-959 *4))))) (-5 *1 (-385 *4)) @@ -12253,7 +10471,7 @@ (|partial| -12 (-5 *5 (-1186)) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-4 *4 (-13 (-29 *6) (-1212) (-966))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -2856 (-650 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -4055 (-650 *4)))) (-5 *1 (-658 *6 *4 *3)) (-4 *3 (-662 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-650 *2)) @@ -12264,40 +10482,40 @@ (-12 (-5 *3 (-695 *5)) (-4 *5 (-368)) (-5 *2 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -2856 (-650 (-1277 *5))))) + (|:| -4055 (-650 (-1277 *5))))) (-5 *1 (-673 *5)) (-5 *4 (-1277 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-650 (-650 *5))) (-4 *5 (-368)) (-5 *2 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -2856 (-650 (-1277 *5))))) + (|:| -4055 (-650 (-1277 *5))))) (-5 *1 (-673 *5)) (-5 *4 (-1277 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-695 *5)) (-4 *5 (-368)) (-5 *2 (-650 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -2856 (-650 (-1277 *5)))))) + (|:| -4055 (-650 (-1277 *5)))))) (-5 *1 (-673 *5)) (-5 *4 (-650 (-1277 *5))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-650 (-650 *5))) (-4 *5 (-368)) (-5 *2 (-650 (-2 (|:| |particular| (-3 (-1277 *5) "failed")) - (|:| -2856 (-650 (-1277 *5)))))) + (|:| -4055 (-650 (-1277 *5)))))) (-5 *1 (-673 *5)) (-5 *4 (-650 (-1277 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-4 *4 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2856 (-650 *4)))) + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -4055 (-650 *4)))) (-5 *1 (-674 *5 *6 *4 *3)) (-4 *3 (-693 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-368)) (-4 *6 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-4 *7 (-13 (-378 *5) (-10 -7 (-6 -4453)))) (-5 *2 (-650 - (-2 (|:| |particular| (-3 *7 "failed")) (|:| -2856 (-650 *7))))) + (-2 (|:| |particular| (-3 *7 "failed")) (|:| -4055 (-650 *7))))) (-5 *1 (-674 *5 *6 *7 *3)) (-5 *4 (-650 *7)) (-4 *3 (-693 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -12315,7 +10533,7 @@ (-4 *7 (-13 (-29 *6) (-1212) (-966))) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1277 *7)) (|:| -2856 (-650 (-1277 *7))))) + (-2 (|:| |particular| (-1277 *7)) (|:| -4055 (-650 (-1277 *7))))) (-5 *1 (-808 *6 *7)) (-5 *4 (-1277 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-695 *6)) (-5 *4 (-1186)) @@ -12327,27 +10545,27 @@ (-5 *5 (-1186)) (-4 *7 (-13 (-29 *6) (-1212) (-966))) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1277 *7)) (|:| -2856 (-650 (-1277 *7))))) + (-2 (|:| |particular| (-1277 *7)) (|:| -4055 (-650 (-1277 *7))))) (-5 *1 (-808 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-650 *7)) (-5 *4 (-650 (-115))) (-5 *5 (-1186)) (-4 *7 (-13 (-29 *6) (-1212) (-966))) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1277 *7)) (|:| -2856 (-650 (-1277 *7))))) + (-2 (|:| |particular| (-1277 *7)) (|:| -4055 (-650 (-1277 *7))))) (-5 *1 (-808 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-298 *7)) (-5 *4 (-115)) (-5 *5 (-1186)) (-4 *7 (-13 (-29 *6) (-1212) (-966))) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-3 (-2 (|:| |particular| *7) (|:| -2856 (-650 *7))) *7 "failed")) + (-3 (-2 (|:| |particular| *7) (|:| -4055 (-650 *7))) *7 "failed")) (-5 *1 (-808 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-115)) (-5 *5 (-1186)) (-4 *6 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) (-5 *2 - (-3 (-2 (|:| |particular| *3) (|:| -2856 (-650 *3))) *3 "failed")) + (-3 (-2 (|:| |particular| *3) (|:| -4055 (-650 *3))) *3 "failed")) (-5 *1 (-808 *6 *3)) (-4 *3 (-13 (-29 *6) (-1212) (-966))))) ((*1 *2 *3 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