diff options
| -rw-r--r-- | src/ChangeLog | 13 | ||||
| -rw-r--r-- | src/algebra/laurent.spad.pamphlet | 10 | ||||
| -rw-r--r-- | src/algebra/mts.spad.pamphlet | 10 | ||||
| -rw-r--r-- | src/algebra/padic.spad.pamphlet | 12 | ||||
| -rw-r--r-- | src/algebra/pscat.spad.pamphlet | 10 | ||||
| -rw-r--r-- | src/algebra/puiseux.spad.pamphlet | 10 | ||||
| -rw-r--r-- | src/algebra/strap/GCDDOM-.lsp | 86 | ||||
| -rw-r--r-- | src/algebra/strap/INT.lsp | 21 | ||||
| -rw-r--r-- | src/algebra/strap/ISTRING.lsp | 388 | ||||
| -rw-r--r-- | src/algebra/strap/LSAGG-.lsp | 131 | ||||
| -rw-r--r-- | src/algebra/strap/POLYCAT-.lsp | 86 | ||||
| -rw-r--r-- | src/algebra/strap/URAGG-.lsp | 216 | ||||
| -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 | 1329 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8662 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25976 |
17 files changed, 19517 insertions, 19477 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 52918b3c..a4a22fad 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,18 @@ 2010-06-13 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/laurent.spad.pamphlet + (UnivariateLaurentSeriesConstructor) [termsToOutputForm]: Tidy. + * algebra/mts.spad.pamphlet (SparseMultivariateTaylorSeries) + [coerce]: Likewise. + * algebra/padic.spad.pamphlet (PAdicIntegerCategory) [coerce]: + Likewise. + * algebra/pscat.spad.pamphlet + (UnivariateTaylorSeriesCategory)[coerce]: Likewise. + * algebra/puiseux.spad.pamphlet (UnivariatePuiseuxSeries) + [termsToOutputForm]: Likewise. + +2010-06-13 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/generic.spad.pamphlet (GenericNonAssociativeAlgebra)[generic]: Fix thinko. diff --git a/src/algebra/laurent.spad.pamphlet b/src/algebra/laurent.spad.pamphlet index a8f9337b..0a22f478 100644 --- a/src/algebra/laurent.spad.pamphlet +++ b/src/algebra/laurent.spad.pamphlet @@ -501,17 +501,21 @@ UnivariateLaurentSeriesConstructor(Coef,UTS):_ termsToOutputForm(m,uu,xxx) == l : L OUT := empty() empty? uu => (0$Coef) :: OUT - n : NNI ; count : NNI := _$streamCount$Lisp - for n in 0..count while not empty? uu repeat + count : NNI := _$streamCount$Lisp + n : NNI := 0 + while n <= count and not empty? uu repeat if frst(uu) ~= 0 then l := concat(termOutput((n :: I) + m,frst(uu),xxx),l) uu := rst uu + n := n + 1 if showAll?() then - for n in (count + 1).. while explicitEntries? uu and _ + n := count + 1 + while explicitEntries? uu and _ not eq?(uu,rst uu) repeat if frst(uu) ~= 0 then l := concat(termOutput((n::I) + m,frst(uu),xxx),l) uu := rst uu + n := n + 1 l := explicitlyEmpty? uu => l eq?(uu,rst uu) and frst uu = 0 => l diff --git a/src/algebra/mts.spad.pamphlet b/src/algebra/mts.spad.pamphlet index 00b1b68b..1f232c31 100644 --- a/src/algebra/mts.spad.pamphlet +++ b/src/algebra/mts.spad.pamphlet @@ -253,16 +253,18 @@ SparseMultivariateTaylorSeries(Coef,Var,SMP):_ coerce(s:%):OUT == uu := s pretend Stream(SMP) empty? uu => (0$SMP) :: OUT - n : NNI; count : NNI := _$streamCount$Lisp + count : NNI := _$streamCount$Lisp l : List OUT := empty() - for n in 0..count while not empty? uu repeat + n : NNI := 0 + while n <= count and not empty? uu repeat if frst(uu) ~= 0 then l := concat(tout frst uu,l) uu := rst uu + n := n + 1 if showAll?() then - for n in n.. while explicitEntries? uu and _ - not eq?(uu,rst uu) repeat + while explicitEntries? uu and not eq?(uu,rst uu) repeat if frst(uu) ~= 0 then l := concat(tout frst uu,l) uu := rst uu + n := n + 1 l := explicitlyEmpty? uu => l eq?(uu,rst uu) and frst uu = 0 => l diff --git a/src/algebra/padic.spad.pamphlet b/src/algebra/padic.spad.pamphlet index 6b3481d1..47c53e8a 100644 --- a/src/algebra/padic.spad.pamphlet +++ b/src/algebra/padic.spad.pamphlet @@ -293,7 +293,7 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where count : NNI := _$streamCount$Lisp l : L OUT := empty() n : NNI := 0 - while n <= count while not empty? st repeat + while n <= count and not empty? st repeat if frst(st) ~= 0 then l := concat(termOutput(n :: I,frst st),l) st := rst st @@ -516,17 +516,21 @@ PAdicRationalConstructor(p,PADIC): Exports == Implementation where uu := digits zp l : L OUT := empty() empty? uu => 0 :: OUT - n : NNI ; count : NNI := _$streamCount$Lisp - for n in 0..count while not empty? uu repeat + count : NNI := _$streamCount$Lisp + n : NNI := 0 + while n <= count and not empty? uu repeat if frst(uu) ~= 0 then l := concat(termOutput((n :: I) + m,frst(uu)),l) uu := rst uu + n := n + 1 if showAll?() then - for n in (count + 1).. while explicitEntries? uu and _ + n := count + 1 + while explicitEntries? uu and _ not eq?(uu,rst uu) repeat if frst(uu) ~= 0 then l := concat(termOutput((n::I) + m,frst(uu)),l) uu := rst uu + n := n + 1 l := explicitlyEmpty? uu => l eq?(uu,rst uu) and frst uu = 0 => l diff --git a/src/algebra/pscat.spad.pamphlet b/src/algebra/pscat.spad.pamphlet index 37f63dd1..c27f6e61 100644 --- a/src/algebra/pscat.spad.pamphlet +++ b/src/algebra/pscat.spad.pamphlet @@ -294,18 +294,22 @@ UnivariateTaylorSeriesCategory(Coef): Category == Definition where vv := zero? cen => var :: OUT paren(var :: OUT - cen :: OUT) - n : NNI ; count : NNI := _$streamCount$Lisp + count : NNI := _$streamCount$Lisp l : L OUT := empty() - for n in 0..count while not empty? uu repeat + n : NNI := 0 + while n <= count and not empty? uu repeat if frst(uu) ~= 0 then l := concat(termOutput(n :: I,frst uu,vv),l) uu := rst uu + n := n + 1 if showAll?() then - for n in (count + 1).. while explicitEntries? uu and _ + n := count + 1 + while explicitEntries? uu and _ not eq?(uu,rst uu) repeat if frst(uu) ~= 0 then l := concat(termOutput(n :: I,frst uu,vv),l) uu := rst uu + n := n + 1 l := explicitlyEmpty? uu => l eq?(uu,rst uu) and frst uu = 0 => l diff --git a/src/algebra/puiseux.spad.pamphlet b/src/algebra/puiseux.spad.pamphlet index a38a3301..fc5321ec 100644 --- a/src/algebra/puiseux.spad.pamphlet +++ b/src/algebra/puiseux.spad.pamphlet @@ -535,17 +535,21 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where termsToOutputForm(m,rat,uu,xxx) == l : L OUT := empty() empty? uu => 0 :: OUT - n : NNI; count : NNI := _$streamCount$Lisp - for n in 0..count while not empty? uu repeat + count : NNI := _$streamCount$Lisp + n : NNI := 0 + while n <= count and not empty? uu repeat if frst(uu) ~= 0 then l := concat(termOutput((n :: I) * rat + m,frst uu,xxx),l) uu := rst uu + n := n + 1 if showAll?() then - for n in (count + 1).. while explicitEntries? uu and _ + n := count + 1 + while explicitEntries? uu and _ not eq?(uu,rst uu) repeat if frst(uu) ~= 0 then l := concat(termOutput((n :: I) * rat + m,frst uu,xxx),l) uu := rst uu + n := n + 1 l := explicitlyEmpty? uu => l eq?(uu,rst uu) and frst uu = 0 => l diff --git a/src/algebra/strap/GCDDOM-.lsp b/src/algebra/strap/GCDDOM-.lsp index f1d298cf..1248c146 100644 --- a/src/algebra/strap/GCDDOM-.lsp +++ b/src/algebra/strap/GCDDOM-.lsp @@ -43,7 +43,7 @@ (|getShellEntry| $ 19))) (DEFUN |GCDDOM-;gcdPolynomial;3Sup;4| (|p1| |p2| $) - (PROG (|e2| |e1| |c1| |p| |c2| #0=#:G1418) + (PROG (|e2| |e1| |c1| |p| |c2|) (RETURN (SEQ (COND ((SPADCALL |p1| (|getShellEntry| $ 24)) @@ -56,26 +56,23 @@ (LETT |c2| (SPADCALL |p2| (|getShellEntry| $ 26)) |GCDDOM-;gcdPolynomial;3Sup;4|) (LETT |p1| - (PROG2 (LETT #0# - (SPADCALL |p1| |c1| - (|getShellEntry| $ 27)) - |GCDDOM-;gcdPolynomial;3Sup;4|) - (CDR #0#) + (LET ((#0=#:G1418 + (SPADCALL |p1| |c1| + (|getShellEntry| $ 27)))) (|check-union| (EQL (CAR #0#) 0) (|SparseUnivariatePolynomial| (|getShellEntry| $ 6)) - #0#)) + #0#) + (CDR #0#)) |GCDDOM-;gcdPolynomial;3Sup;4|) (LETT |p2| - (PROG2 (LETT #0# - (SPADCALL |p2| |c2| - (|getShellEntry| $ 27)) - |GCDDOM-;gcdPolynomial;3Sup;4|) - (CDR #0#) + (LET ((#0# (SPADCALL |p2| |c2| + (|getShellEntry| $ 27)))) (|check-union| (EQL (CAR #0#) 0) (|SparseUnivariatePolynomial| (|getShellEntry| $ 6)) - #0#)) + #0#) + (CDR #0#)) |GCDDOM-;gcdPolynomial;3Sup;4|) (SEQ (LETT |e1| (SPADCALL |p1| (|getShellEntry| $ 29)) @@ -83,20 +80,19 @@ (EXIT (COND ((> |e1| 0) (LETT |p1| - (PROG2 - (LETT #0# - (SPADCALL |p1| - (SPADCALL - (|spadConstant| $ 16) |e1| - (|getShellEntry| $ 34)) - (|getShellEntry| $ 35)) - |GCDDOM-;gcdPolynomial;3Sup;4|) - (CDR #0#) + (LET + ((#0# + (SPADCALL |p1| + (SPADCALL + (|spadConstant| $ 16) |e1| + (|getShellEntry| $ 34)) + (|getShellEntry| $ 35)))) (|check-union| (EQL (CAR #0#) 0) (|SparseUnivariatePolynomial| (|getShellEntry| $ 6)) - #0#)) + #0#) + (CDR #0#)) |GCDDOM-;gcdPolynomial;3Sup;4|))))) (SEQ (LETT |e2| (SPADCALL |p2| (|getShellEntry| $ 29)) @@ -104,20 +100,19 @@ (EXIT (COND ((> |e2| 0) (LETT |p2| - (PROG2 - (LETT #0# - (SPADCALL |p2| - (SPADCALL - (|spadConstant| $ 16) |e2| - (|getShellEntry| $ 34)) - (|getShellEntry| $ 35)) - |GCDDOM-;gcdPolynomial;3Sup;4|) - (CDR #0#) + (LET + ((#0# + (SPADCALL |p2| + (SPADCALL + (|spadConstant| $ 16) |e2| + (|getShellEntry| $ 34)) + (|getShellEntry| $ 35)))) (|check-union| (EQL (CAR #0#) 0) (|SparseUnivariatePolynomial| (|getShellEntry| $ 6)) - #0#)) + #0#) + (CDR #0#)) |GCDDOM-;gcdPolynomial;3Sup;4|))))) (LETT |e1| (MIN |e1| |e2|) |GCDDOM-;gcdPolynomial;3Sup;4|) @@ -159,25 +154,24 @@ (SPADCALL (SPADCALL |c1| (SPADCALL - (PROG2 - (LETT #0# - (SPADCALL - (SPADCALL |c2| |p| + (LET + ((#0# + (SPADCALL + (SPADCALL |c2| |p| + (|getShellEntry| $ + 41)) + (SPADCALL |p| + (|getShellEntry| $ + 40)) (|getShellEntry| $ - 41)) - (SPADCALL |p| - (|getShellEntry| $ - 40)) - (|getShellEntry| $ - 27)) - |GCDDOM-;gcdPolynomial;3Sup;4|) - (CDR #0#) + 27)))) (|check-union| (EQL (CAR #0#) 0) (|SparseUnivariatePolynomial| (|getShellEntry| $ 6)) - #0#)) + #0#) + (CDR #0#)) (|getShellEntry| $ 42)) (|getShellEntry| $ 41)) (|getShellEntry| $ 25)))))))))) diff --git a/src/algebra/strap/INT.lsp b/src/algebra/strap/INT.lsp index 38e24e3d..80d2f9e7 100644 --- a/src/algebra/strap/INT.lsp +++ b/src/algebra/strap/INT.lsp @@ -474,7 +474,7 @@ (SPADCALL |p| (|getShellEntry| $ 106))) (DEFUN |INT;factorPolynomial| (|p| $) - (PROG (|pp| #0=#:G1499) + (PROG (|pp|) (RETURN (SEQ (LETT |pp| (SPADCALL |p| (|getShellEntry| $ 107)) |INT;factorPolynomial|) @@ -486,17 +486,16 @@ (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 110)) (SPADCALL (CONS #'|INT;factorPolynomial!0| $) (SPADCALL - (PROG2 (LETT #0# - (SPADCALL - (SPADCALL |p| - (|getShellEntry| $ 108)) - (SPADCALL |pp| - (|getShellEntry| $ 108)) - (|getShellEntry| $ 112)) - |INT;factorPolynomial|) - (CDR #0#) + (LET ((#0=#:G1499 + (SPADCALL + (SPADCALL |p| + (|getShellEntry| $ 108)) + (SPADCALL |pp| + (|getShellEntry| $ 108)) + (|getShellEntry| $ 112)))) (|check-union| (EQL (CAR #0#) 0) $ - #0#)) + #0#) + (CDR #0#)) (|getShellEntry| $ 114)) (|getShellEntry| $ 118)) (|getShellEntry| $ 120))))))))) diff --git a/src/algebra/strap/ISTRING.lsp b/src/algebra/strap/ISTRING.lsp index 23b54d95..a5dce2d9 100644 --- a/src/algebra/strap/ISTRING.lsp +++ b/src/algebra/strap/ISTRING.lsp @@ -178,7 +178,7 @@ (STRCONC "\\mbox{``" (STRCONC |s| "''}"))) (DEFUN |ISTRING;replace;$Us2$;15| (|s| |sg| |t| $) - (PROG (|l| |m| |n| |h| |r| #0=#:G1532 #1=#:G1533 |i| #2=#:G1534 |k|) + (PROG (|l| |m| |n| |h| |r| #0=#:G1535 #1=#:G1536 |i| #2=#:G1537 |k|) (RETURN (SEQ (LETT |l| (- (SPADCALL |sg| (|getShellEntry| $ 44)) @@ -200,33 +200,34 @@ (EXIT (|error| "index out of range")))) (LETT |r| (MAKE-FULL-CVEC - (LET ((#3=#:G1441 + (LET ((#3=#:G1444 (+ (- |m| (+ (- |h| |l|) 1)) |n|))) (|check-subtype| (>= #3# 0) '(|NonNegativeInteger|) #3#)) (|spadConstant| $ 53)) |ISTRING;replace;$Us2$;15|) + (LETT |k| 0 |ISTRING;replace;$Us2$;15|) (SEQ (LETT |i| 0 |ISTRING;replace;$Us2$;15|) - (LETT #0# (- |l| 1) |ISTRING;replace;$Us2$;15|) - (LETT |k| 0 |ISTRING;replace;$Us2$;15|) G190 + (LETT #0# (- |l| 1) |ISTRING;replace;$Us2$;15|) G190 (COND ((QSGREATERP |i| #0#) (GO G191))) - (SEQ (EXIT (QESET |r| |k| (CHAR |s| |i|)))) - (SETQ |k| (PROG1 (QSADD1 |k|) (SETQ |i| (QSADD1 |i|)))) - (GO G190) G191 (EXIT NIL)) + (SEQ (QESET |r| |k| (CHAR |s| |i|)) + (EXIT (LETT |k| (+ |k| 1) + |ISTRING;replace;$Us2$;15|))) + (SETQ |i| (QSADD1 |i|)) (GO G190) G191 (EXIT NIL)) (SEQ (LETT |i| 0 |ISTRING;replace;$Us2$;15|) - (LETT #1# (- |n| 1) |ISTRING;replace;$Us2$;15|) - (LETT |k| |k| |ISTRING;replace;$Us2$;15|) G190 + (LETT #1# (- |n| 1) |ISTRING;replace;$Us2$;15|) G190 (COND ((QSGREATERP |i| #1#) (GO G191))) - (SEQ (EXIT (QESET |r| |k| (CHAR |t| |i|)))) - (SETQ |k| (PROG1 (+ |k| 1) (SETQ |i| (QSADD1 |i|)))) - (GO G190) G191 (EXIT NIL)) + (SEQ (QESET |r| |k| (CHAR |t| |i|)) + (EXIT (LETT |k| (+ |k| 1) + |ISTRING;replace;$Us2$;15|))) + (SETQ |i| (QSADD1 |i|)) (GO G190) G191 (EXIT NIL)) (SEQ (LETT |i| (+ |h| 1) |ISTRING;replace;$Us2$;15|) - (LETT #2# (- |m| 1) |ISTRING;replace;$Us2$;15|) - (LETT |k| |k| |ISTRING;replace;$Us2$;15|) G190 + (LETT #2# (- |m| 1) |ISTRING;replace;$Us2$;15|) G190 (COND ((> |i| #2#) (GO G191))) - (SEQ (EXIT (QESET |r| |k| (CHAR |s| |i|)))) - (SETQ |k| (PROG1 (+ |k| 1) (SETQ |i| (+ |i| 1)))) - (GO G190) G191 (EXIT NIL)) + (SEQ (QESET |r| |k| (CHAR |s| |i|)) + (EXIT (LETT |k| (+ |k| 1) + |ISTRING;replace;$Us2$;15|))) + (SETQ |i| (+ |i| 1)) (GO G190) G191 (EXIT NIL)) (EXIT |r|))))) (DEFUN |ISTRING;setelt;$I2C;16| (|s| |i| |c| $) @@ -239,7 +240,7 @@ (EXIT |c|)))))) (DEFUN |ISTRING;substring?;2$IB;17| (|part| |whole| |startpos| $) - (PROG (|np| |nw| |iw| |ip| #0=#:G1535) + (PROG (|np| |nw| |iw| |ip| #0=#:G1538) (RETURN (SEQ (LETT |np| (QCSIZE |part|) |ISTRING;substring?;2$IB;17|) (LETT |nw| (QCSIZE |whole|) |ISTRING;substring?;2$IB;17|) @@ -289,7 +290,7 @@ ('T (+ |r| (|getShellEntry| $ 6))))))))))))) (DEFUN |ISTRING;position;C$2I;19| (|c| |t| |startpos| $) - (PROG (|r| #0=#:G1536) + (PROG (|r| #0=#:G1539) (RETURN (SEQ (LETT |startpos| (- |startpos| (|getShellEntry| $ 6)) |ISTRING;position;C$2I;19|) @@ -314,7 +315,7 @@ (EXIT (- (|getShellEntry| $ 6) 1)))))))))) (DEFUN |ISTRING;position;Cc$2I;20| (|cc| |t| |startpos| $) - (PROG (|r| #0=#:G1537) + (PROG (|r| #0=#:G1540) (RETURN (SEQ (LETT |startpos| (- |startpos| (|getShellEntry| $ 6)) |ISTRING;position;Cc$2I;20|) @@ -331,7 +332,7 @@ (SEQ (EXIT (COND ((SPADCALL (CHAR |t| |r|) |cc| - (|getShellEntry| $ 64)) + (|getShellEntry| $ 65)) (RETURN-FROM |ISTRING;position;Cc$2I;20| (+ |r| (|getShellEntry| $ 6))))))) @@ -357,15 +358,17 @@ (RETURN (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;split;$CL;22|) - (SEQ (LETT |i| (|getShellEntry| $ 6) |ISTRING;split;$CL;22|) - G190 + (LETT |i| (|getShellEntry| $ 6) |ISTRING;split;$CL;22|) + (SEQ G190 (COND - ((OR (> |i| |n|) - (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |c| (|getShellEntry| $ 68)))) + ((NULL (COND + ((> |i| |n|) NIL) + ('T + (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) + |c| (|getShellEntry| $ 69))))) (GO G191))) - (SEQ (EXIT 0)) (SETQ |i| (+ |i| 1)) (GO G190) G191 - (EXIT NIL)) + (SEQ (EXIT (LETT |i| (+ |i| 1) |ISTRING;split;$CL;22|))) + NIL (GO G190) G191 (EXIT NIL)) (LETT |l| NIL |ISTRING;split;$CL;22|) (SEQ G190 (COND @@ -384,19 +387,24 @@ (SPADCALL |i| (- |j| 1) (|getShellEntry| $ 24)) $) - |l| (|getShellEntry| $ 71)) + |l| (|getShellEntry| $ 72)) |ISTRING;split;$CL;22|) - (EXIT (SEQ (LETT |i| |j| |ISTRING;split;$CL;22|) - G190 + (LETT |i| |j| |ISTRING;split;$CL;22|) + (EXIT (SEQ G190 (COND - ((OR (> |i| |n|) - (NULL - (SPADCALL - (|ISTRING;elt;$IC;30| |s| |i| $) - |c| (|getShellEntry| $ 68)))) + ((NULL + (COND + ((> |i| |n|) NIL) + ('T + (SPADCALL + (|ISTRING;elt;$IC;30| |s| |i| + $) + |c| (|getShellEntry| $ 69))))) (GO G191))) - (SEQ (EXIT 0)) (SETQ |i| (+ |i| 1)) - (GO G190) G191 (EXIT NIL)))) + (SEQ (EXIT + (LETT |i| (+ |i| 1) + |ISTRING;split;$CL;22|))) + NIL (GO G190) G191 (EXIT NIL)))) NIL (GO G190) G191 (EXIT NIL)) (COND ((NOT (> |i| |n|)) @@ -405,7 +413,7 @@ (|ISTRING;elt;$Us$;31| |s| (SPADCALL |i| |n| (|getShellEntry| $ 24)) $) - |l| (|getShellEntry| $ 71)) + |l| (|getShellEntry| $ 72)) |ISTRING;split;$CL;22|))) (EXIT (NREVERSE |l|)))))) @@ -414,16 +422,17 @@ (RETURN (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;split;$CcL;23|) - (SEQ (LETT |i| (|getShellEntry| $ 6) - |ISTRING;split;$CcL;23|) - G190 + (LETT |i| (|getShellEntry| $ 6) |ISTRING;split;$CcL;23|) + (SEQ G190 (COND - ((OR (> |i| |n|) - (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |cc| (|getShellEntry| $ 64)))) + ((NULL (COND + ((> |i| |n|) NIL) + ('T + (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) + |cc| (|getShellEntry| $ 65))))) (GO G191))) - (SEQ (EXIT 0)) (SETQ |i| (+ |i| 1)) (GO G190) G191 - (EXIT NIL)) + (SEQ (EXIT (LETT |i| (+ |i| 1) |ISTRING;split;$CcL;23|))) + NIL (GO G190) G191 (EXIT NIL)) (LETT |l| NIL |ISTRING;split;$CcL;23|) (SEQ G190 (COND @@ -442,19 +451,24 @@ (SPADCALL |i| (- |j| 1) (|getShellEntry| $ 24)) $) - |l| (|getShellEntry| $ 71)) + |l| (|getShellEntry| $ 72)) |ISTRING;split;$CcL;23|) - (EXIT (SEQ (LETT |i| |j| |ISTRING;split;$CcL;23|) - G190 + (LETT |i| |j| |ISTRING;split;$CcL;23|) + (EXIT (SEQ G190 (COND - ((OR (> |i| |n|) - (NULL - (SPADCALL - (|ISTRING;elt;$IC;30| |s| |i| $) - |cc| (|getShellEntry| $ 64)))) + ((NULL + (COND + ((> |i| |n|) NIL) + ('T + (SPADCALL + (|ISTRING;elt;$IC;30| |s| |i| + $) + |cc| (|getShellEntry| $ 65))))) (GO G191))) - (SEQ (EXIT 0)) (SETQ |i| (+ |i| 1)) - (GO G190) G191 (EXIT NIL)))) + (SEQ (EXIT + (LETT |i| (+ |i| 1) + |ISTRING;split;$CcL;23|))) + NIL (GO G190) G191 (EXIT NIL)))) NIL (GO G190) G191 (EXIT NIL)) (COND ((NOT (> |i| |n|)) @@ -463,7 +477,7 @@ (|ISTRING;elt;$Us$;31| |s| (SPADCALL |i| |n| (|getShellEntry| $ 24)) $) - |l| (|getShellEntry| $ 71)) + |l| (|getShellEntry| $ 72)) |ISTRING;split;$CcL;23|))) (EXIT (NREVERSE |l|)))))) @@ -472,16 +486,18 @@ (RETURN (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;leftTrim;$C$;24|) - (SEQ (LETT |i| (|getShellEntry| $ 6) - |ISTRING;leftTrim;$C$;24|) - G190 + (LETT |i| (|getShellEntry| $ 6) |ISTRING;leftTrim;$C$;24|) + (SEQ G190 (COND - ((OR (> |i| |n|) - (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |c| (|getShellEntry| $ 68)))) + ((NULL (COND + ((> |i| |n|) NIL) + ('T + (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) + |c| (|getShellEntry| $ 69))))) (GO G191))) - (SEQ (EXIT 0)) (SETQ |i| (+ |i| 1)) (GO G190) G191 - (EXIT NIL)) + (SEQ (EXIT (LETT |i| (+ |i| 1) + |ISTRING;leftTrim;$C$;24|))) + NIL (GO G190) G191 (EXIT NIL)) (EXIT (|ISTRING;elt;$Us$;31| |s| (SPADCALL |i| |n| (|getShellEntry| $ 24)) $)))))) @@ -490,71 +506,75 @@ (RETURN (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;leftTrim;$Cc$;25|) - (SEQ (LETT |i| (|getShellEntry| $ 6) - |ISTRING;leftTrim;$Cc$;25|) - G190 + (LETT |i| (|getShellEntry| $ 6) |ISTRING;leftTrim;$Cc$;25|) + (SEQ G190 (COND - ((OR (> |i| |n|) - (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |cc| (|getShellEntry| $ 64)))) + ((NULL (COND + ((> |i| |n|) NIL) + ('T + (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) + |cc| (|getShellEntry| $ 65))))) (GO G191))) - (SEQ (EXIT 0)) (SETQ |i| (+ |i| 1)) (GO G190) G191 - (EXIT NIL)) + (SEQ (EXIT (LETT |i| (+ |i| 1) + |ISTRING;leftTrim;$Cc$;25|))) + NIL (GO G190) G191 (EXIT NIL)) (EXIT (|ISTRING;elt;$Us$;31| |s| (SPADCALL |i| |n| (|getShellEntry| $ 24)) $)))))) (DEFUN |ISTRING;rightTrim;$C$;26| (|s| |c| $) - (PROG (|j| #0=#:G1538) + (PROG (|j|) (RETURN - (SEQ (SEQ (LETT |j| (SPADCALL |s| (|getShellEntry| $ 47)) - |ISTRING;rightTrim;$C$;26|) - (LETT #0# (|getShellEntry| $ 6) - |ISTRING;rightTrim;$C$;26|) - G190 + (SEQ (LETT |j| (SPADCALL |s| (|getShellEntry| $ 47)) + |ISTRING;rightTrim;$C$;26|) + (SEQ G190 (COND - ((OR (< |j| #0#) - (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |j| $) - |c| (|getShellEntry| $ 68)))) + ((NULL (COND + ((>= |j| (|getShellEntry| $ 6)) + (SPADCALL (|ISTRING;elt;$IC;30| |s| |j| $) + |c| (|getShellEntry| $ 69))) + ('T NIL))) (GO G191))) - (SEQ (EXIT 0)) (SETQ |j| (+ |j| -1)) (GO G190) G191 - (EXIT NIL)) + (SEQ (EXIT (LETT |j| (- |j| 1) + |ISTRING;rightTrim;$C$;26|))) + NIL (GO G190) G191 (EXIT NIL)) (EXIT (|ISTRING;elt;$Us$;31| |s| (SPADCALL (|ISTRING;minIndex;$I;11| |s| $) |j| (|getShellEntry| $ 24)) $)))))) (DEFUN |ISTRING;rightTrim;$Cc$;27| (|s| |cc| $) - (PROG (|j| #0=#:G1539) + (PROG (|j|) (RETURN - (SEQ (SEQ (LETT |j| (SPADCALL |s| (|getShellEntry| $ 47)) - |ISTRING;rightTrim;$Cc$;27|) - (LETT #0# (|getShellEntry| $ 6) - |ISTRING;rightTrim;$Cc$;27|) - G190 + (SEQ (LETT |j| (SPADCALL |s| (|getShellEntry| $ 47)) + |ISTRING;rightTrim;$Cc$;27|) + (SEQ G190 (COND - ((OR (< |j| #0#) - (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |j| $) - |cc| (|getShellEntry| $ 64)))) + ((NULL (COND + ((>= |j| (|getShellEntry| $ 6)) + (SPADCALL (|ISTRING;elt;$IC;30| |s| |j| $) + |cc| (|getShellEntry| $ 65))) + ('T NIL))) (GO G191))) - (SEQ (EXIT 0)) (SETQ |j| (+ |j| -1)) (GO G190) G191 - (EXIT NIL)) + (SEQ (EXIT (LETT |j| (- |j| 1) + |ISTRING;rightTrim;$Cc$;27|))) + NIL (GO G190) G191 (EXIT NIL)) (EXIT (|ISTRING;elt;$Us$;31| |s| (SPADCALL (|ISTRING;minIndex;$I;11| |s| $) |j| (|getShellEntry| $ 24)) $)))))) (DEFUN |ISTRING;concat;L$;28| (|l| $) - (PROG (|t| |s| #0=#:G1541 |i|) + (PROG (|t| |s| #0=#:G1542 |i|) (RETURN (SEQ (LETT |t| (MAKE-FULL-CVEC - (LET ((#1=#:G1494 NIL) (#2=#:G1495 T) - (#3=#:G1540 |l|)) + (LET ((#1=#:G1497 NIL) (#2=#:G1498 T) + (#3=#:G1541 |l|)) (LOOP (COND ((ATOM #3#) (RETURN (COND (#2# 0) (T #1#)))) (T (LET ((|s| (CAR #3#))) - (LET ((#4=#:G1493 (QCSIZE |s|))) + (LET ((#4=#:G1496 (QCSIZE |s|))) (COND (#2# (SETQ #1# #4#)) (T (SETQ #1# (+ #1# #4#)))) @@ -627,7 +647,7 @@ (SEQ (LETT |n| (SPADCALL |pattern| (|getShellEntry| $ 47)) |ISTRING;match?;2$CB;34|) (LETT |p| - (LET ((#0=#:G1522 + (LET ((#0=#:G1525 (|ISTRING;position;C$2I;19| |dontcare| |pattern| (LETT |m| @@ -642,18 +662,18 @@ ((EQL |p| (- |m| 1)) (EQUAL |pattern| |target|)) ('T (SEQ (COND - ((SPADCALL |p| |m| (|getShellEntry| $ 88)) + ((SPADCALL |p| |m| (|getShellEntry| $ 87)) (COND ((NOT (SPADCALL (|ISTRING;elt;$Us$;31| |pattern| (SPADCALL |m| (- |p| 1) (|getShellEntry| $ 24)) $) - |target| (|getShellEntry| $ 89))) + |target| (|getShellEntry| $ 88))) (EXIT NIL))))) (LETT |i| |p| |ISTRING;match?;2$CB;34|) (LETT |q| - (LET ((#1=#:G1523 + (LET ((#1=#:G1526 (|ISTRING;position;C$2I;19| |dontcare| |pattern| (+ |p| 1) $))) @@ -663,7 +683,7 @@ (SEQ G190 (COND ((NULL (SPADCALL |q| (- |m| 1) - (|getShellEntry| $ 88))) + (|getShellEntry| $ 87))) (GO G191))) (SEQ (LETT |s| (|ISTRING;elt;$Us$;31| |pattern| @@ -673,7 +693,7 @@ |ISTRING;match?;2$CB;34|) (LETT |i| (LET - ((#2=#:G1524 + ((#2=#:G1527 (|ISTRING;position;2$2I;18| |s| |target| |i| $))) (|check-subtype| (>= #2# 0) @@ -694,7 +714,7 @@ (EXIT (LETT |q| (LET - ((#3=#:G1525 + ((#3=#:G1528 (|ISTRING;position;C$2I;19| |dontcare| |pattern| (+ |q| 1) $))) @@ -704,7 +724,7 @@ |ISTRING;match?;2$CB;34|))))))) NIL (GO G190) G191 (EXIT NIL)) (COND - ((SPADCALL |p| |n| (|getShellEntry| $ 88)) + ((SPADCALL |p| |n| (|getShellEntry| $ 87)) (COND ((NOT (|ISTRING;suffix?;2$B;21| (|ISTRING;elt;$Us$;31| |pattern| @@ -715,8 +735,8 @@ (EXIT NIL))))) (EXIT T))))))))) -(DEFUN |IndexedString| (#0=#:G1542) - (PROG (#1=#:G1543) +(DEFUN |IndexedString| (#0=#:G1543) + (PROG (#1=#:G1544) (RETURN (COND ((SETQ #1# @@ -732,7 +752,7 @@ (DEFUN |IndexedString;| (|#1|) (LET* ((|dv$1| (|devaluate| |#1|)) - (|dv$| (LIST '|IndexedString| |dv$1|)) ($ (|newShell| 101)) + (|dv$| (LIST '|IndexedString| |dv$1|)) ($ (|newShell| 100)) (|pv$| (|buildPredVector| 0 0 (LIST (OR (AND (|HasCategory| (|Character|) '(|OrderedSet|)) @@ -791,43 +811,42 @@ |ISTRING;latex;$S;14| (66 . |lo|) (71 . |hasHi|) (76 . |hi|) (81 . |maxIndex|) (86 . |Zero|) (90 . <) (96 . >=) (102 . |One|) (106 . +) (112 . |space|) - (|PositiveInteger|) (116 . |One|) - |ISTRING;replace;$Us2$;15| (120 . >) - |ISTRING;setelt;$I2C;16| (126 . |false|) (130 . |true|) + (|PositiveInteger|) (116 . |One|) (120 . +) + |ISTRING;replace;$Us2$;15| (126 . >) + |ISTRING;setelt;$I2C;16| (132 . |false|) (136 . |true|) |ISTRING;substring?;2$IB;17| |ISTRING;position;2$2I;18| - |ISTRING;position;C$2I;19| (134 . |member?|) + |ISTRING;position;C$2I;19| (140 . |member?|) |ISTRING;position;Cc$2I;20| |ISTRING;suffix?;2$B;21| - |ISTRING;elt;$IC;30| (140 . =) (|List| $$) (146 . |empty|) - (150 . |concat|) (156 . |reverse!|) (|List| $) + |ISTRING;elt;$IC;30| (146 . =) (|List| $$) (152 . |empty|) + (156 . |concat|) (162 . |reverse!|) (|List| $) |ISTRING;split;$CL;22| |ISTRING;split;$CcL;23| |ISTRING;leftTrim;$C$;24| |ISTRING;leftTrim;$Cc$;25| - (161 . -) |ISTRING;rightTrim;$C$;26| - |ISTRING;rightTrim;$Cc$;27| (166 . +) + |ISTRING;rightTrim;$C$;26| |ISTRING;rightTrim;$Cc$;27| |ISTRING;copyInto!;2$I$;29| |ISTRING;concat;L$;28| - (172 . |max|) (|SingleInteger|) |ISTRING;hash;$Si;32| - |ISTRING;match;2$CNni;33| (178 . ~=) (184 . |prefix?|) + (167 . |max|) (|SingleInteger|) |ISTRING;hash;$Si;32| + |ISTRING;match;2$CNni;33| (173 . ~=) (179 . |prefix?|) |ISTRING;match?;2$CB;34| (|List| 8) (|Equation| 8) - (|List| 92) (|Mapping| 8 8 8) (|InputForm|) + (|List| 91) (|Mapping| 8 8 8) (|InputForm|) (|Mapping| 13 8) (|Mapping| 13 8 8) (|Void|) (|Union| 8 '"failed") (|List| 11)) - '#(~= 190 |upperCase!| 196 |upperCase| 201 |trim| 206 |swap!| - 218 |suffix?| 225 |substring?| 231 |split| 238 |sorted?| - 250 |sort!| 261 |sort| 272 |size?| 283 |setelt| 289 - |select| 303 |sample| 309 |rightTrim| 313 |reverse!| 325 - |reverse| 330 |replace| 335 |removeDuplicates| 342 - |remove| 347 |reduce| 359 |qsetelt!| 380 |qelt| 387 - |prefix?| 393 |position| 399 |parts| 432 |new| 437 |more?| - 443 |minIndex| 449 |min| 454 |merge| 460 |members| 473 - |member?| 478 |maxIndex| 484 |max| 489 |match?| 495 - |match| 502 |map!| 509 |map| 515 |lowerCase!| 528 - |lowerCase| 533 |less?| 538 |leftTrim| 544 |latex| 556 - |insert| 561 |indices| 575 |index?| 580 |hash| 586 |first| - 591 |find| 596 |fill!| 602 |every?| 608 |eval| 614 |eq?| - 640 |entry?| 646 |entries| 652 |empty?| 657 |empty| 662 - |elt| 666 |delete| 691 |count| 703 |copyInto!| 715 |copy| - 722 |convert| 727 |construct| 732 |concat| 737 |coerce| - 760 |before?| 770 |any?| 776 >= 782 > 788 = 794 <= 800 < - 806 |#| 812) + '#(~= 185 |upperCase!| 191 |upperCase| 196 |trim| 201 |swap!| + 213 |suffix?| 220 |substring?| 226 |split| 233 |sorted?| + 245 |sort!| 256 |sort| 267 |size?| 278 |setelt| 284 + |select| 298 |sample| 304 |rightTrim| 308 |reverse!| 320 + |reverse| 325 |replace| 330 |removeDuplicates| 337 + |remove| 342 |reduce| 354 |qsetelt!| 375 |qelt| 382 + |prefix?| 388 |position| 394 |parts| 427 |new| 432 |more?| + 438 |minIndex| 444 |min| 449 |merge| 455 |members| 468 + |member?| 473 |maxIndex| 479 |max| 484 |match?| 490 + |match| 497 |map!| 504 |map| 510 |lowerCase!| 523 + |lowerCase| 528 |less?| 533 |leftTrim| 539 |latex| 551 + |insert| 556 |indices| 570 |index?| 575 |hash| 581 |first| + 586 |find| 591 |fill!| 597 |every?| 603 |eval| 609 |eq?| + 635 |entry?| 641 |entries| 647 |empty?| 652 |empty| 657 + |elt| 661 |delete| 686 |count| 698 |copyInto!| 710 |copy| + 717 |convert| 722 |construct| 727 |concat| 732 |coerce| + 755 |before?| 765 |any?| 771 >= 777 > 783 = 789 <= 795 < + 801 |#| 807) '((|shallowlyMutable| . 0) (|finiteAggregate| . 0)) (CONS (|makeByteWordVec2| 5 '(0 0 0 0 0 0 0 0 5 0 0 0 1 4 0 1 2 3 4)) @@ -851,8 +870,8 @@ (|Eltable| 11 8) (|Evalable| 8) (|SetCategory|) (|Type|) (|InnerEvalable| 8 8) (|CoercibleTo| 29) - (|ConvertibleTo| 95) (|BasicType|)) - (|makeByteWordVec2| 100 + (|ConvertibleTo| 94) (|BasicType|)) + (|makeByteWordVec2| 99 '(0 11 0 12 2 11 13 0 0 14 0 11 0 21 2 11 0 0 0 22 2 23 0 11 11 24 1 23 0 11 26 1 29 0 28 30 0 33 0 34 1 8 0 0 35 @@ -860,47 +879,46 @@ 28 0 0 0 42 1 23 11 0 44 1 23 13 0 45 1 23 11 0 46 1 0 11 0 47 0 7 0 48 2 11 13 0 0 49 2 11 13 0 0 50 0 7 0 51 - 2 11 0 0 0 52 0 8 0 53 0 54 0 55 2 11 - 13 0 0 57 0 13 0 59 0 13 0 60 2 33 13 - 8 0 64 2 8 13 0 0 68 0 69 0 70 2 69 0 - 2 0 71 1 69 0 0 72 1 11 0 0 78 2 7 0 - 0 0 81 2 11 0 0 0 84 2 11 13 0 0 88 2 - 0 13 0 0 89 2 7 13 0 0 1 1 0 0 0 38 1 - 0 0 0 1 2 0 0 0 8 1 2 0 0 0 33 1 3 0 - 98 0 11 11 1 2 0 13 0 0 66 3 0 13 0 0 - 11 61 2 0 73 0 33 75 2 0 73 0 8 74 1 - 5 13 0 1 2 0 13 97 0 1 1 5 0 0 1 2 0 - 0 97 0 1 1 5 0 0 1 2 0 0 97 0 1 2 0 - 13 0 7 1 3 0 8 0 23 8 1 3 0 8 0 11 8 - 58 2 0 0 96 0 1 0 0 0 1 2 0 0 0 8 79 - 2 0 0 0 33 80 1 0 0 0 1 1 0 0 0 1 3 0 - 0 0 23 0 56 1 7 0 0 1 2 7 0 8 0 1 2 0 - 0 96 0 1 4 7 8 94 0 8 8 1 3 0 8 94 0 - 8 1 2 0 8 94 0 1 3 0 8 0 11 8 1 2 0 8 - 0 11 1 2 0 13 0 0 89 3 7 11 8 0 11 63 - 2 7 11 8 0 1 3 0 11 33 0 11 65 3 0 11 - 0 0 11 62 2 0 11 96 0 1 1 0 91 0 1 2 - 0 0 7 8 9 2 0 13 0 7 1 1 6 11 0 32 2 - 5 0 0 0 1 2 5 0 0 0 1 3 0 0 97 0 0 1 - 1 0 91 0 1 2 7 13 8 0 1 1 6 11 0 47 2 - 5 0 0 0 1 3 0 13 0 0 8 90 3 0 7 0 0 8 - 87 2 0 0 36 0 37 3 0 0 94 0 0 1 2 0 0 - 36 0 1 1 0 0 0 41 1 0 0 0 1 2 0 13 0 - 7 1 2 0 0 0 8 76 2 0 0 0 33 77 1 7 28 - 0 43 3 0 0 8 0 11 1 3 0 0 0 0 11 27 1 - 0 100 0 1 2 0 13 11 0 1 1 7 85 0 86 1 - 6 8 0 1 2 0 99 96 0 1 2 0 0 0 8 1 2 0 - 13 96 0 1 3 9 0 0 91 91 1 3 9 0 0 8 8 - 1 2 9 0 0 93 1 2 9 0 0 92 1 2 0 13 0 - 0 1 2 7 13 8 0 1 1 0 91 0 1 1 0 13 0 - 15 0 0 0 10 2 0 0 0 0 1 2 0 0 0 23 25 - 2 0 8 0 11 67 3 0 8 0 11 8 1 2 0 0 0 - 11 1 2 0 0 0 23 1 2 7 7 8 0 1 2 0 7 - 96 0 1 3 0 0 0 0 11 82 1 0 0 0 20 1 3 - 95 0 1 1 0 0 91 1 2 0 0 0 0 19 1 0 0 - 73 83 2 0 0 8 0 1 2 0 0 0 8 1 1 8 29 - 0 31 1 0 0 8 1 2 7 13 0 0 1 2 0 13 96 - 0 1 2 5 13 0 0 1 2 5 13 0 0 1 2 7 13 - 0 0 17 2 5 13 0 0 1 2 5 13 0 0 18 1 0 - 7 0 16))))) + 2 11 0 0 0 52 0 8 0 53 0 54 0 55 2 7 + 0 0 0 56 2 11 13 0 0 58 0 13 0 60 0 + 13 0 61 2 33 13 8 0 65 2 8 13 0 0 69 + 0 70 0 71 2 70 0 2 0 72 1 70 0 0 73 2 + 11 0 0 0 83 2 11 13 0 0 87 2 0 13 0 0 + 88 2 7 13 0 0 1 1 0 0 0 38 1 0 0 0 1 + 2 0 0 0 8 1 2 0 0 0 33 1 3 0 97 0 11 + 11 1 2 0 13 0 0 67 3 0 13 0 0 11 62 2 + 0 74 0 33 76 2 0 74 0 8 75 1 5 13 0 1 + 2 0 13 96 0 1 1 5 0 0 1 2 0 0 96 0 1 + 1 5 0 0 1 2 0 0 96 0 1 2 0 13 0 7 1 3 + 0 8 0 23 8 1 3 0 8 0 11 8 59 2 0 0 95 + 0 1 0 0 0 1 2 0 0 0 8 79 2 0 0 0 33 + 80 1 0 0 0 1 1 0 0 0 1 3 0 0 0 23 0 + 57 1 7 0 0 1 2 7 0 8 0 1 2 0 0 95 0 1 + 4 7 8 93 0 8 8 1 3 0 8 93 0 8 1 2 0 8 + 93 0 1 3 0 8 0 11 8 1 2 0 8 0 11 1 2 + 0 13 0 0 88 3 7 11 8 0 11 64 2 7 11 8 + 0 1 3 0 11 33 0 11 66 3 0 11 0 0 11 + 63 2 0 11 95 0 1 1 0 90 0 1 2 0 0 7 8 + 9 2 0 13 0 7 1 1 6 11 0 32 2 5 0 0 0 + 1 2 5 0 0 0 1 3 0 0 96 0 0 1 1 0 90 0 + 1 2 7 13 8 0 1 1 6 11 0 47 2 5 0 0 0 + 1 3 0 13 0 0 8 89 3 0 7 0 0 8 86 2 0 + 0 36 0 37 3 0 0 93 0 0 1 2 0 0 36 0 1 + 1 0 0 0 41 1 0 0 0 1 2 0 13 0 7 1 2 0 + 0 0 8 77 2 0 0 0 33 78 1 7 28 0 43 3 + 0 0 8 0 11 1 3 0 0 0 0 11 27 1 0 99 0 + 1 2 0 13 11 0 1 1 7 84 0 85 1 6 8 0 1 + 2 0 98 95 0 1 2 0 0 0 8 1 2 0 13 95 0 + 1 3 9 0 0 90 90 1 3 9 0 0 8 8 1 2 9 0 + 0 92 1 2 9 0 0 91 1 2 0 13 0 0 1 2 7 + 13 8 0 1 1 0 90 0 1 1 0 13 0 15 0 0 0 + 10 2 0 0 0 0 1 2 0 0 0 23 25 2 0 8 0 + 11 68 3 0 8 0 11 8 1 2 0 0 0 11 1 2 0 + 0 0 23 1 2 7 7 8 0 1 2 0 7 95 0 1 3 0 + 0 0 0 11 81 1 0 0 0 20 1 3 94 0 1 1 0 + 0 90 1 2 0 0 0 0 19 1 0 0 74 82 2 0 0 + 8 0 1 2 0 0 0 8 1 1 8 29 0 31 1 0 0 8 + 1 2 7 13 0 0 1 2 0 13 95 0 1 2 5 13 0 + 0 1 2 5 13 0 0 1 2 7 13 0 0 17 2 5 13 + 0 0 1 2 5 13 0 0 18 1 0 7 0 16))))) '|lookupComplete|)) diff --git a/src/algebra/strap/LSAGG-.lsp b/src/algebra/strap/LSAGG-.lsp index d55706bc..c563a160 100644 --- a/src/algebra/strap/LSAGG-.lsp +++ b/src/algebra/strap/LSAGG-.lsp @@ -426,9 +426,9 @@ (DEFUN |LSAGG-;position;MAI;13| (|f| |x| $) (PROG (|k|) (RETURN - (SEQ (SEQ (LETT |k| (SPADCALL |x| (|getShellEntry| $ 33)) - |LSAGG-;position;MAI;13|) - G190 + (SEQ (LETT |k| (SPADCALL |x| (|getShellEntry| $ 33)) + |LSAGG-;position;MAI;13|) + (SEQ G190 (COND ((NULL (COND ((SPADCALL |x| (|getShellEntry| $ 16)) NIL) @@ -438,10 +438,11 @@ (|getShellEntry| $ 18)) |f|))))) (GO G191))) - (SEQ (EXIT (LETT |x| - (SPADCALL |x| (|getShellEntry| $ 17)) + (SEQ (LETT |x| (SPADCALL |x| (|getShellEntry| $ 17)) + |LSAGG-;position;MAI;13|) + (EXIT (LETT |k| (+ |k| 1) |LSAGG-;position;MAI;13|))) - (SETQ |k| (+ |k| 1)) (GO G190) G191 (EXIT NIL)) + NIL (GO G190) G191 (EXIT NIL)) (EXIT (COND ((SPADCALL |x| (|getShellEntry| $ 16)) (- (SPADCALL |x| (|getShellEntry| $ 33)) 1)) @@ -457,19 +458,19 @@ (SPADCALL (SPADCALL |p| (|getShellEntry| $ 17)) (|getShellEntry| $ 18)) (SPADCALL |p| (|getShellEntry| $ 18)) |f|) - (LETT |p| (SPADCALL |p| (|getShellEntry| $ 57)) + (LETT |p| (SPADCALL |p| (|getShellEntry| $ 55)) |LSAGG-;mergeSort|))))) (EXIT (COND ((< |n| 3) |p|) ('T (SEQ (LETT |l| - (LET ((#0=#:G1510 (QUOTIENT2 |n| 2))) + (LET ((#0=#:G1511 (QUOTIENT2 |n| 2))) (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|) #0#)) |LSAGG-;mergeSort|) (LETT |q| (SPADCALL |p| |l| - (|getShellEntry| $ 59)) + (|getShellEntry| $ 57)) |LSAGG-;mergeSort|) (LETT |p| (|LSAGG-;mergeSort| |f| |p| |l| $) |LSAGG-;mergeSort|) @@ -539,7 +540,7 @@ ((NULL (COND ((SPADCALL |x| (|getShellEntry| $ 16)) NIL) ('T - (SPADCALL |r| |a| (|getShellEntry| $ 63))))) + (SPADCALL |r| |a| (|getShellEntry| $ 61))))) (GO G191))) (SEQ (LETT |r| (SPADCALL |r| @@ -594,7 +595,7 @@ (SPADCALL |y| (|getShellEntry| $ 17)) |LSAGG-;map;M3A;19|))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |z| (|getShellEntry| $ 57))))))) + (EXIT (SPADCALL |z| (|getShellEntry| $ 55))))))) (DEFUN |LSAGG-;reverse!;2A;20| (|x| $) (PROG (|z| |y|) @@ -637,7 +638,7 @@ (SEQ (COND ((EQL |k| 1000) (COND - ((SPADCALL |x| (|getShellEntry| $ 69)) + ((SPADCALL |x| (|getShellEntry| $ 67)) (EXIT (|error| "cyclic list")))))) (LETT |y| (SPADCALL @@ -648,7 +649,7 @@ (SPADCALL |x| (|getShellEntry| $ 17)) |LSAGG-;copy;2A;21|))) (SETQ |k| (QSADD1 |k|)) (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |y| (|getShellEntry| $ 57))))))) + (EXIT (SPADCALL |y| (|getShellEntry| $ 55))))))) (DEFUN |LSAGG-;copyInto!;2AIA;22| (|y| |x| |s| $) (PROG (|m| |z|) @@ -660,7 +661,7 @@ ('T (SEQ (LETT |z| (SPADCALL |y| - (LET ((#0=#:G1551 (- |s| |m|))) + (LET ((#0=#:G1552 (- |s| |m|))) (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 39)) @@ -679,7 +680,7 @@ (SEQ (SPADCALL |z| (SPADCALL |x| (|getShellEntry| $ 18)) - (|getShellEntry| $ 71)) + (|getShellEntry| $ 69)) (LETT |x| (SPADCALL |x| (|getShellEntry| $ 17)) @@ -702,13 +703,13 @@ ('T (SEQ (LETT |x| (SPADCALL |x| - (LET ((#0=#:G1557 (- |s| |m|))) + (LET ((#0=#:G1559 (- |s| |m|))) (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|) #0#)) (|getShellEntry| $ 39)) |LSAGG-;position;SA2I;23|) - (SEQ (LETT |k| |s| |LSAGG-;position;SA2I;23|) - G190 + (LETT |k| |s| |LSAGG-;position;SA2I;23|) + (SEQ G190 (COND ((NULL (COND ((SPADCALL |x| @@ -718,15 +719,16 @@ (SPADCALL |w| (SPADCALL |x| (|getShellEntry| $ 18)) - (|getShellEntry| $ 63))))) + (|getShellEntry| $ 61))))) (GO G191))) - (SEQ (EXIT - (LETT |x| - (SPADCALL |x| - (|getShellEntry| $ 17)) + (SEQ (LETT |x| + (SPADCALL |x| + (|getShellEntry| $ 17)) + |LSAGG-;position;SA2I;23|) + (EXIT + (LETT |k| (+ |k| 1) |LSAGG-;position;SA2I;23|))) - (SETQ |k| (+ |k| 1)) (GO G190) G191 - (EXIT NIL)) + NIL (GO G190) G191 (EXIT NIL)) (EXIT (COND ((SPADCALL |x| (|getShellEntry| $ 16)) (- (SPADCALL |x| @@ -750,7 +752,7 @@ (VECTOR $ |p|)) (SPADCALL |p| (|getShellEntry| $ 17)) - (|getShellEntry| $ 75)) + (|getShellEntry| $ 73)) (|getShellEntry| $ 27)) |LSAGG-;removeDuplicates!;2A;24|))) NIL (GO G190) G191 (EXIT NIL)) @@ -760,7 +762,7 @@ (LET (($ (|getShellEntry| $$ 0))) (SPADCALL |#1| (SPADCALL (|getShellEntry| $$ 1) (|getShellEntry| $ 18)) - (|getShellEntry| $ 74)))) + (|getShellEntry| $ 72)))) (DEFUN |LSAGG-;<;2AB;25| (|x| |y| $) (SEQ (SEQ G190 @@ -773,12 +775,12 @@ ((SPADCALL (SPADCALL |x| (|getShellEntry| $ 18)) (SPADCALL |y| (|getShellEntry| $ 18)) - (|getShellEntry| $ 63)) + (|getShellEntry| $ 61)) (RETURN-FROM |LSAGG-;<;2AB;25| (SPADCALL (SPADCALL |x| (|getShellEntry| $ 18)) (SPADCALL |y| (|getShellEntry| $ 18)) - (|getShellEntry| $ 77)))) + (|getShellEntry| $ 75)))) ('T (SEQ (LETT |x| (SPADCALL |x| @@ -797,7 +799,7 @@ (DEFUN |ListAggregate&| (|#1| |#2|) (LET* ((|dv$1| (|devaluate| |#1|)) (|dv$2| (|devaluate| |#2|)) (|dv$| (LIST '|ListAggregate&| |dv$1| |dv$2|)) - ($ (|newShell| 80)) (|pv$| (|buildPredVector| 0 0 NIL))) + ($ (|newShell| 78)) (|pv$| (|buildPredVector| 0 0 NIL))) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 |pv$|) (|stuffDomainSlots| $) @@ -805,20 +807,20 @@ (|setShellEntry| $ 7 |#2|) (COND ((|HasCategory| |#2| '(|SetCategory|)) - (|setShellEntry| $ 64 + (|setShellEntry| $ 62 (CONS (|dispatchFunction| |LSAGG-;reduce;MA3S;17|) $)))) (COND ((|HasCategory| |#2| '(|SetCategory|)) (PROGN - (|setShellEntry| $ 73 + (|setShellEntry| $ 71 (CONS (|dispatchFunction| |LSAGG-;position;SA2I;23|) $)) - (|setShellEntry| $ 76 + (|setShellEntry| $ 74 (CONS (|dispatchFunction| |LSAGG-;removeDuplicates!;2A;24|) $))))) (COND ((|HasCategory| |#2| '(|OrderedSet|)) - (|setShellEntry| $ 78 + (|setShellEntry| $ 76 (CONS (|dispatchFunction| |LSAGG-;<;2AB;25|) $)))) $)) @@ -840,26 +842,25 @@ (113 . |lo|) (118 . |hasHi|) (123 . |hi|) (128 . |maxIndex|) (133 . +) |LSAGG-;delete!;AUsA;11| (|Union| 7 '"failed") |LSAGG-;find;MAU;12| - (|PositiveInteger|) (139 . |One|) |LSAGG-;position;MAI;13| - (143 . |reverse!|) (148 . |quo|) (154 . |split!|) - (160 . |true|) |LSAGG-;sorted?;MAB;15| - |LSAGG-;reduce;MA2S;16| (164 . ~=) (170 . |reduce|) + |LSAGG-;position;MAI;13| (139 . |reverse!|) (144 . |quo|) + (150 . |split!|) (156 . |true|) |LSAGG-;sorted?;MAB;15| + |LSAGG-;reduce;MA2S;16| (160 . ~=) (166 . |reduce|) |LSAGG-;new;NniSA;18| |LSAGG-;map;M3A;19| - |LSAGG-;reverse!;2A;20| (178 . =) (184 . |cyclic?|) - |LSAGG-;copy;2A;21| (189 . |setfirst!|) - |LSAGG-;copyInto!;2AIA;22| (195 . |position|) (202 . =) - (208 . |remove!|) (214 . |removeDuplicates!|) (219 . <) - (225 . <) (|Mapping| 7 7)) - '#(|sorted?| 231 |sort!| 237 |select!| 243 |reverse!| 249 - |removeDuplicates!| 254 |remove!| 259 |reduce| 265 - |position| 286 |new| 299 |merge!| 305 |merge| 312 |map| - 319 |list| 326 |insert!| 331 |find| 345 |delete!| 351 - |copyInto!| 363 |copy| 370 < 375) + |LSAGG-;reverse!;2A;20| (174 . =) (180 . |cyclic?|) + |LSAGG-;copy;2A;21| (185 . |setfirst!|) + |LSAGG-;copyInto!;2AIA;22| (191 . |position|) (198 . =) + (204 . |remove!|) (210 . |removeDuplicates!|) (215 . <) + (221 . <) (|Mapping| 7 7)) + '#(|sorted?| 227 |sort!| 233 |select!| 239 |reverse!| 245 + |removeDuplicates!| 250 |remove!| 255 |reduce| 261 + |position| 282 |new| 295 |merge!| 301 |merge| 308 |map| + 315 |list| 322 |insert!| 327 |find| 341 |delete!| 347 + |copyInto!| 359 |copy| 366 < 371) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 78 + (|makeByteWordVec2| 76 '(1 6 8 0 9 0 6 0 13 2 6 0 7 0 14 1 6 10 0 16 1 6 0 0 17 1 6 7 0 18 3 6 7 19 0 7 20 1 6 0 0 22 3 6 0 11 0 0 23 @@ -868,20 +869,20 @@ 34 2 32 10 0 0 35 0 8 0 36 0 32 0 37 2 32 0 0 0 38 2 6 0 0 8 39 2 6 0 0 0 41 1 45 32 0 46 1 45 10 0 47 1 45 32 - 0 48 1 6 32 0 49 2 32 0 0 0 50 0 54 0 - 55 1 6 0 0 57 2 32 0 0 0 58 2 6 0 0 - 32 59 0 10 0 60 2 7 10 0 0 63 4 0 7 - 19 0 7 7 64 2 8 10 0 0 68 1 6 10 0 69 - 2 6 7 0 7 71 3 0 32 7 0 32 73 2 7 10 - 0 0 74 2 6 0 28 0 75 1 0 0 0 76 2 7 - 10 0 0 77 2 0 10 0 0 78 2 0 10 11 0 - 61 2 0 0 11 0 12 2 0 0 28 0 29 1 0 0 - 0 67 1 0 0 0 76 2 0 0 28 0 43 3 0 7 - 19 0 7 62 4 0 7 19 0 7 7 64 2 0 7 19 - 0 21 2 0 32 28 0 56 3 0 32 7 0 32 73 - 2 0 0 8 7 65 3 0 0 11 0 0 31 3 0 0 11 - 0 0 24 3 0 0 19 0 0 66 1 0 0 7 15 3 0 - 0 7 0 32 40 3 0 0 0 0 32 42 2 0 52 28 - 0 53 2 0 0 0 45 51 2 0 0 0 32 44 3 0 - 0 0 0 32 72 1 0 0 0 70 2 0 10 0 0 78))))) + 0 48 1 6 32 0 49 2 32 0 0 0 50 1 6 0 + 0 55 2 32 0 0 0 56 2 6 0 0 32 57 0 10 + 0 58 2 7 10 0 0 61 4 0 7 19 0 7 7 62 + 2 8 10 0 0 66 1 6 10 0 67 2 6 7 0 7 + 69 3 0 32 7 0 32 71 2 7 10 0 0 72 2 6 + 0 28 0 73 1 0 0 0 74 2 7 10 0 0 75 2 + 0 10 0 0 76 2 0 10 11 0 59 2 0 0 11 0 + 12 2 0 0 28 0 29 1 0 0 0 65 1 0 0 0 + 74 2 0 0 28 0 43 3 0 7 19 0 7 60 4 0 + 7 19 0 7 7 62 2 0 7 19 0 21 2 0 32 28 + 0 54 3 0 32 7 0 32 71 2 0 0 8 7 63 3 + 0 0 11 0 0 31 3 0 0 11 0 0 24 3 0 0 + 19 0 0 64 1 0 0 7 15 3 0 0 7 0 32 40 + 3 0 0 0 0 32 42 2 0 52 28 0 53 2 0 0 + 0 45 51 2 0 0 0 32 44 3 0 0 0 0 32 70 + 1 0 0 0 68 2 0 10 0 0 76))))) '|lookupComplete|)) diff --git a/src/algebra/strap/POLYCAT-.lsp b/src/algebra/strap/POLYCAT-.lsp index bf2be180..4ca58e41 100644 --- a/src/algebra/strap/POLYCAT-.lsp +++ b/src/algebra/strap/POLYCAT-.lsp @@ -324,14 +324,14 @@ (CDR |lv|) (CDR |ln|) (|getShellEntry| $ 70))))) (DEFUN |POLYCAT-;retract;SVarSet;9| (|p| $) - (PROG (#0=#:G1478 |q|) + (PROG (|q|) (RETURN (SEQ (LETT |q| - (PROG2 (LETT #0# (SPADCALL |p| (|getShellEntry| $ 53)) - |POLYCAT-;retract;SVarSet;9|) - (CDR #0#) + (LET ((#0=#:G1478 + (SPADCALL |p| (|getShellEntry| $ 53)))) (|check-union| (EQL (CAR #0#) 0) - (|getShellEntry| $ 9) #0#)) + (|getShellEntry| $ 9) #0#) + (CDR #0#)) |POLYCAT-;retract;SVarSet;9|) (EXIT (COND ((SPADCALL (SPADCALL |q| (|getShellEntry| $ 72)) |p| @@ -374,20 +374,19 @@ (SETQ #0# (CDR #0#))))) (DEFUN |POLYCAT-;totalDegree;SNni;13| (|p| $) - (PROG (#0=#:G1492 |d| |u|) + (PROG (|d| |u|) (RETURN (SEQ (COND ((SPADCALL |p| (|getShellEntry| $ 78)) 0) ('T (SEQ (LETT |u| (SPADCALL |p| - (PROG2 (LETT #0# - (SPADCALL |p| - (|getShellEntry| $ 53)) - |POLYCAT-;totalDegree;SNni;13|) - (CDR #0#) + (LET ((#0=#:G1492 + (SPADCALL |p| + (|getShellEntry| $ 53)))) (|check-union| (EQL (CAR #0#) 0) - (|getShellEntry| $ 9) #0#)) + (|getShellEntry| $ 9) #0#) + (CDR #0#)) (|getShellEntry| $ 59)) |POLYCAT-;totalDegree;SNni;13|) (LETT |d| 0 |POLYCAT-;totalDegree;SNni;13|) @@ -414,7 +413,7 @@ (EXIT |d|)))))))) (DEFUN |POLYCAT-;totalDegree;SLNni;14| (|p| |lv| $) - (PROG (#0=#:G1500 |v| |w| |d| |u|) + (PROG (|v| |w| |d| |u|) (RETURN (SEQ (COND ((SPADCALL |p| (|getShellEntry| $ 78)) 0) @@ -422,14 +421,13 @@ (SEQ (LETT |u| (SPADCALL |p| (LETT |v| - (PROG2 - (LETT #0# - (SPADCALL |p| - (|getShellEntry| $ 53)) - |POLYCAT-;totalDegree;SLNni;14|) - (CDR #0#) + (LET + ((#0=#:G1500 + (SPADCALL |p| + (|getShellEntry| $ 53)))) (|check-union| (EQL (CAR #0#) 0) - (|getShellEntry| $ 9) #0#)) + (|getShellEntry| $ 9) #0#) + (CDR #0#)) |POLYCAT-;totalDegree;SLNni;14|) (|getShellEntry| $ 59)) |POLYCAT-;totalDegree;SLNni;14|) @@ -1131,36 +1129,28 @@ (|getShellEntry| $ 204))) (DEFUN |POLYCAT-;primitivePart;2S;36| (|p| $) - (PROG (#0=#:G1658) - (RETURN - (QVELT (SPADCALL - (PROG2 (LETT #0# - (SPADCALL |p| - (SPADCALL |p| - (|getShellEntry| $ 206)) - (|getShellEntry| $ 207)) - |POLYCAT-;primitivePart;2S;36|) - (CDR #0#) - (|check-union| (EQL (CAR #0#) 0) - (|getShellEntry| $ 6) #0#)) - (|getShellEntry| $ 209)) - 1)))) + (QVELT (SPADCALL + (LET ((#0=#:G1658 + (SPADCALL |p| + (SPADCALL |p| (|getShellEntry| $ 206)) + (|getShellEntry| $ 207)))) + (|check-union| (EQL (CAR #0#) 0) (|getShellEntry| $ 6) + #0#) + (CDR #0#)) + (|getShellEntry| $ 209)) + 1)) (DEFUN |POLYCAT-;primitivePart;SVarSetS;37| (|p| |v| $) - (PROG (#0=#:G1664) - (RETURN - (QVELT (SPADCALL - (PROG2 (LETT #0# - (SPADCALL |p| - (SPADCALL |p| |v| - (|getShellEntry| $ 211)) - (|getShellEntry| $ 212)) - |POLYCAT-;primitivePart;SVarSetS;37|) - (CDR #0#) - (|check-union| (EQL (CAR #0#) 0) - (|getShellEntry| $ 6) #0#)) - (|getShellEntry| $ 209)) - 1)))) + (QVELT (SPADCALL + (LET ((#0=#:G1664 + (SPADCALL |p| + (SPADCALL |p| |v| (|getShellEntry| $ 211)) + (|getShellEntry| $ 212)))) + (|check-union| (EQL (CAR #0#) 0) (|getShellEntry| $ 6) + #0#) + (CDR #0#)) + (|getShellEntry| $ 209)) + 1)) (DEFUN |POLYCAT-;before?;2SB;38| (|p| |q| $) (PROG (|dp| |dq|) diff --git a/src/algebra/strap/URAGG-.lsp b/src/algebra/strap/URAGG-.lsp index 44f85770..68179ede 100644 --- a/src/algebra/strap/URAGG-.lsp +++ b/src/algebra/strap/URAGG-.lsp @@ -228,7 +228,8 @@ (DEFUN |URAGG-;#;ANni;15| (|x| $) (PROG (|k|) (RETURN - (SEQ (SEQ (LETT |k| 0 |URAGG-;#;ANni;15|) G190 + (SEQ (LETT |k| 0 |URAGG-;#;ANni;15|) + (SEQ G190 (COND ((NULL (NOT (SPADCALL |x| (|getShellEntry| $ 20)))) (GO G191))) @@ -237,10 +238,10 @@ (COND ((SPADCALL |x| (|getShellEntry| $ 48)) (EXIT (|error| "cyclic list")))))) - (EXIT (LETT |x| - (SPADCALL |x| (|getShellEntry| $ 14)) - |URAGG-;#;ANni;15|))) - (SETQ |k| (QSADD1 |k|)) (GO G190) G191 (EXIT NIL)) + (LETT |x| (SPADCALL |x| (|getShellEntry| $ 14)) + |URAGG-;#;ANni;15|) + (EXIT (LETT |k| (+ |k| 1) |URAGG-;#;ANni;15|))) + NIL (GO G190) G191 (EXIT NIL)) (EXIT |k|))))) (DEFUN |URAGG-;tail;2A;16| (|x| $) @@ -282,7 +283,7 @@ ((NULL (NOT (SPADCALL |y| (|getShellEntry| $ 20)))) (GO G191))) (SEQ (COND - ((SPADCALL |x| |y| (|getShellEntry| $ 51)) + ((SPADCALL |x| |y| (|getShellEntry| $ 54)) (RETURN-FROM |URAGG-;findCycle| |x|))) (LETT |x| (SPADCALL |x| (|getShellEntry| $ 14)) |URAGG-;findCycle|) @@ -292,7 +293,7 @@ ((SPADCALL |y| (|getShellEntry| $ 20)) (RETURN-FROM |URAGG-;findCycle| |y|))) (COND - ((SPADCALL |x| |y| (|getShellEntry| $ 51)) + ((SPADCALL |x| |y| (|getShellEntry| $ 54)) (RETURN-FROM |URAGG-;findCycle| |y|))) (EXIT (LETT |y| (SPADCALL |y| (|getShellEntry| $ 14)) @@ -306,7 +307,7 @@ (SEQ (COND ((SPADCALL (LETT |y| - (LETT |x| (SPADCALL |x| (|getShellEntry| $ 52)) + (LETT |x| (SPADCALL |x| (|getShellEntry| $ 55)) |URAGG-;cycleTail;2A;18|) |URAGG-;cycleTail;2A;18|) (|getShellEntry| $ 20)) @@ -317,7 +318,7 @@ (SEQ G190 (COND ((NULL (NOT (SPADCALL |x| |z| - (|getShellEntry| $ 51)))) + (|getShellEntry| $ 54)))) (GO G191))) (SEQ (LETT |y| |z| |URAGG-;cycleTail;2A;18|) (EXIT (LETT |z| @@ -328,7 +329,7 @@ (EXIT |y|)))))))) (DEFUN |URAGG-;cycleEntry;2A;19| (|x| $) - (PROG (|l| |z| |k| |y|) + (PROG (|z| |l| |k| |y|) (RETURN (SEQ (COND ((SPADCALL |x| (|getShellEntry| $ 20)) |x|) @@ -340,15 +341,19 @@ ('T (SEQ (LETT |z| (SPADCALL |y| (|getShellEntry| $ 14)) |URAGG-;cycleEntry;2A;19|) - (SEQ (LETT |l| 1 |URAGG-;cycleEntry;2A;19|) G190 + (LETT |l| 1 |URAGG-;cycleEntry;2A;19|) + (SEQ G190 (COND ((NULL (NOT (SPADCALL |y| |z| - (|getShellEntry| $ 51)))) + (|getShellEntry| $ 54)))) (GO G191))) - (LETT |z| (SPADCALL |z| (|getShellEntry| $ 14)) - |URAGG-;cycleEntry;2A;19|) - (SETQ |l| (QSADD1 |l|)) (GO G190) G191 - (EXIT NIL)) + (SEQ (LETT |z| + (SPADCALL |z| + (|getShellEntry| $ 14)) + |URAGG-;cycleEntry;2A;19|) + (EXIT (LETT |l| (+ |l| 1) + |URAGG-;cycleEntry;2A;19|))) + NIL (GO G190) G191 (EXIT NIL)) (LETT |y| |x| |URAGG-;cycleEntry;2A;19|) (SEQ (LETT |k| 1 |URAGG-;cycleEntry;2A;19|) G190 (COND ((QSGREATERP |k| |l|) (GO G191))) @@ -359,7 +364,7 @@ (SEQ G190 (COND ((NULL (NOT (SPADCALL |x| |y| - (|getShellEntry| $ 51)))) + (|getShellEntry| $ 54)))) (GO G191))) (SEQ (LETT |x| (SPADCALL |x| @@ -373,7 +378,7 @@ (EXIT |x|)))))))) (DEFUN |URAGG-;cycleLength;ANni;20| (|x| $) - (PROG (|k| |y|) + (PROG (|y| |k|) (RETURN (SEQ (COND ((OR (SPADCALL |x| (|getShellEntry| $ 20)) @@ -385,15 +390,19 @@ ('T (SEQ (LETT |y| (SPADCALL |x| (|getShellEntry| $ 14)) |URAGG-;cycleLength;ANni;20|) - (SEQ (LETT |k| 1 |URAGG-;cycleLength;ANni;20|) G190 + (LETT |k| 1 |URAGG-;cycleLength;ANni;20|) + (SEQ G190 (COND ((NULL (NOT (SPADCALL |x| |y| - (|getShellEntry| $ 51)))) + (|getShellEntry| $ 54)))) (GO G191))) - (LETT |y| (SPADCALL |y| (|getShellEntry| $ 14)) - |URAGG-;cycleLength;ANni;20|) - (SETQ |k| (QSADD1 |k|)) (GO G190) G191 - (EXIT NIL)) + (SEQ (LETT |y| + (SPADCALL |y| + (|getShellEntry| $ 14)) + |URAGG-;cycleLength;ANni;20|) + (EXIT (LETT |k| (+ |k| 1) + |URAGG-;cycleLength;ANni;20|))) + NIL (GO G190) G191 (EXIT NIL)) (EXIT |k|)))))))) (DEFUN |URAGG-;rest;ANniA;21| (|x| |n| $) @@ -415,24 +424,24 @@ (DEFUN |URAGG-;last;ANniA;22| (|x| |n| $) (PROG (|m|) (RETURN - (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 57)) + (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 60)) |URAGG-;last;ANniA;22|) (EXIT (COND ((> |n| |m|) (|error| "index out of range")) ('T (SPADCALL (SPADCALL |x| - (LET ((#0=#:G1500 (- |m| |n|))) + (LET ((#0=#:G1502 (- |m| |n|))) (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 59)) - (|getShellEntry| $ 60))))))))) + (|getShellEntry| $ 62)) + (|getShellEntry| $ 63))))))))) (DEFUN |URAGG-;=;2AB;23| (|x| |y| $) (PROG (|k|) (RETURN (SEQ (COND - ((SPADCALL |x| |y| (|getShellEntry| $ 51)) T) + ((SPADCALL |x| |y| (|getShellEntry| $ 54)) T) ('T (SEQ (SEQ (LETT |k| 0 |URAGG-;=;2AB;23|) G190 (COND @@ -457,7 +466,7 @@ (|getShellEntry| $ 8)) (SPADCALL |y| (|getShellEntry| $ 8)) - (|getShellEntry| $ 63)) + (|getShellEntry| $ 66)) (RETURN-FROM |URAGG-;=;2AB;23| NIL)) ('T @@ -486,7 +495,7 @@ ((NULL (NOT (SPADCALL |v| (|getShellEntry| $ 20)))) (GO G191))) (SEQ (EXIT (COND - ((SPADCALL |u| |v| (|getShellEntry| $ 65)) + ((SPADCALL |u| |v| (|getShellEntry| $ 68)) (RETURN-FROM |URAGG-;node?;2AB;24| T)) ('T (SEQ (COND @@ -501,20 +510,20 @@ (|getShellEntry| $ 14)) |URAGG-;node?;2AB;24|))))))) (SETQ |k| (QSADD1 |k|)) (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |u| |v| (|getShellEntry| $ 65))))))) + (EXIT (SPADCALL |u| |v| (|getShellEntry| $ 68))))))) (DEFUN |URAGG-;setelt;Afirst2S;25| (|x| T3 |a| $) - (SPADCALL |x| |a| (|getShellEntry| $ 67))) + (SPADCALL |x| |a| (|getShellEntry| $ 70))) (DEFUN |URAGG-;setelt;Alast2S;26| (|x| T4 |a| $) - (SPADCALL |x| |a| (|getShellEntry| $ 69))) + (SPADCALL |x| |a| (|getShellEntry| $ 72))) (DEFUN |URAGG-;setelt;Arest2A;27| (|x| T5 |a| $) - (SPADCALL |x| |a| (|getShellEntry| $ 71))) + (SPADCALL |x| |a| (|getShellEntry| $ 74))) (DEFUN |URAGG-;concat;3A;28| (|x| |y| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 60)) |y| - (|getShellEntry| $ 73))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 63)) |y| + (|getShellEntry| $ 76))) (DEFUN |URAGG-;setlast!;A2S;29| (|x| |s| $) (SEQ (COND @@ -522,17 +531,17 @@ (|error| "setlast: empty list")) ('T (SEQ (SPADCALL (SPADCALL |x| (|getShellEntry| $ 24)) |s| - (|getShellEntry| $ 67)) + (|getShellEntry| $ 70)) (EXIT |s|)))))) (DEFUN |URAGG-;setchildren!;ALA;30| (|u| |lv| $) (COND ((EQL (LENGTH |lv|) 1) - (SPADCALL |u| (|SPADfirst| |lv|) (|getShellEntry| $ 71))) + (SPADCALL |u| (|SPADfirst| |lv|) (|getShellEntry| $ 74))) ('T (|error| "wrong number of children specified")))) (DEFUN |URAGG-;setvalue!;A2S;31| (|u| |s| $) - (SPADCALL |u| |s| (|getShellEntry| $ 67))) + (SPADCALL |u| |s| (|getShellEntry| $ 70))) (DEFUN |URAGG-;split!;AIA;32| (|p| |n| $) (PROG (|q|) @@ -542,15 +551,15 @@ ('T (SEQ (LETT |p| (SPADCALL |p| - (LET ((#0=#:G1526 (- |n| 1))) + (LET ((#0=#:G1528 (- |n| 1))) (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 59)) + (|getShellEntry| $ 62)) |URAGG-;split!;AIA;32|) (LETT |q| (SPADCALL |p| (|getShellEntry| $ 14)) |URAGG-;split!;AIA;32|) - (SPADCALL |p| (SPADCALL (|getShellEntry| $ 81)) - (|getShellEntry| $ 71)) + (SPADCALL |p| (SPADCALL (|getShellEntry| $ 84)) + (|getShellEntry| $ 74)) (EXIT |q|)))))))) (DEFUN |URAGG-;cycleSplit!;2A;33| (|x| $) @@ -558,10 +567,10 @@ (RETURN (SEQ (COND ((OR (SPADCALL - (LETT |y| (SPADCALL |x| (|getShellEntry| $ 52)) + (LETT |y| (SPADCALL |x| (|getShellEntry| $ 55)) |URAGG-;cycleSplit!;2A;33|) (|getShellEntry| $ 20)) - (SPADCALL |x| |y| (|getShellEntry| $ 51))) + (SPADCALL |x| |y| (|getShellEntry| $ 54))) |y|) ('T (SEQ (LETT |z| (SPADCALL |x| (|getShellEntry| $ 14)) @@ -569,7 +578,7 @@ (SEQ G190 (COND ((NULL (NOT (SPADCALL |z| |y| - (|getShellEntry| $ 51)))) + (|getShellEntry| $ 54)))) (GO G191))) (SEQ (LETT |x| |z| |URAGG-;cycleSplit!;2A;33|) (EXIT (LETT |z| @@ -577,14 +586,14 @@ (|getShellEntry| $ 14)) |URAGG-;cycleSplit!;2A;33|))) NIL (GO G190) G191 (EXIT NIL)) - (SPADCALL |x| (SPADCALL (|getShellEntry| $ 81)) - (|getShellEntry| $ 71)) + (SPADCALL |x| (SPADCALL (|getShellEntry| $ 84)) + (|getShellEntry| $ 74)) (EXIT |y|)))))))) (DEFUN |UnaryRecursiveAggregate&| (|#1| |#2|) (LET* ((|dv$1| (|devaluate| |#1|)) (|dv$2| (|devaluate| |#2|)) (|dv$| (LIST '|UnaryRecursiveAggregate&| |dv$1| |dv$2|)) - ($ (|newShell| 85)) + ($ (|newShell| 88)) (|pv$| (|buildPredVector| 0 0 (LIST (|HasAttribute| |#1| '|shallowlyMutable|))))) (|setShellEntry| $ 0 |dv$|) @@ -594,35 +603,35 @@ (|setShellEntry| $ 7 |#2|) (COND ((|HasAttribute| |#1| '|finiteAggregate|) - (|setShellEntry| $ 61 + (|setShellEntry| $ 64 (CONS (|dispatchFunction| |URAGG-;last;ANniA;22|) $)))) (COND ((|HasCategory| |#2| '(|SetCategory|)) (PROGN - (|setShellEntry| $ 64 + (|setShellEntry| $ 67 (CONS (|dispatchFunction| |URAGG-;=;2AB;23|) $)) - (|setShellEntry| $ 66 + (|setShellEntry| $ 69 (CONS (|dispatchFunction| |URAGG-;node?;2AB;24|) $))))) (COND ((|testBitVector| |pv$| 1) (PROGN - (|setShellEntry| $ 68 + (|setShellEntry| $ 71 (CONS (|dispatchFunction| |URAGG-;setelt;Afirst2S;25|) $)) - (|setShellEntry| $ 70 + (|setShellEntry| $ 73 (CONS (|dispatchFunction| |URAGG-;setelt;Alast2S;26|) $)) - (|setShellEntry| $ 72 + (|setShellEntry| $ 75 (CONS (|dispatchFunction| |URAGG-;setelt;Arest2A;27|) $)) - (|setShellEntry| $ 74 + (|setShellEntry| $ 77 (CONS (|dispatchFunction| |URAGG-;concat;3A;28|) $)) - (|setShellEntry| $ 75 - (CONS (|dispatchFunction| |URAGG-;setlast!;A2S;29|) $)) (|setShellEntry| $ 78 + (CONS (|dispatchFunction| |URAGG-;setlast!;A2S;29|) $)) + (|setShellEntry| $ 81 (CONS (|dispatchFunction| |URAGG-;setchildren!;ALA;30|) $)) - (|setShellEntry| $ 79 - (CONS (|dispatchFunction| |URAGG-;setvalue!;A2S;31|) $)) (|setShellEntry| $ 82 + (CONS (|dispatchFunction| |URAGG-;setvalue!;A2S;31|) $)) + (|setShellEntry| $ 85 (CONS (|dispatchFunction| |URAGG-;split!;AIA;32|) $)) - (|setShellEntry| $ 83 + (|setShellEntry| $ 86 (CONS (|dispatchFunction| |URAGG-;cycleSplit!;2A;33|) $))))) $)) @@ -641,57 +650,58 @@ (53 . |Zero|) (57 . >) (63 . |One|) (67 . |One|) (71 . -) |URAGG-;less?;ANniB;12| (77 . |zero?|) |URAGG-;more?;ANniB;13| |URAGG-;size?;ANniB;14| (82 . =) - (88 . |cyclic?|) |URAGG-;#;ANni;15| |URAGG-;tail;2A;16| - (93 . |eq?|) (99 . |cycleEntry|) |URAGG-;cycleTail;2A;18| + (88 . |cyclic?|) (|PositiveInteger|) (93 . |One|) (97 . +) + |URAGG-;#;ANni;15| |URAGG-;tail;2A;16| (103 . |eq?|) + (109 . |cycleEntry|) |URAGG-;cycleTail;2A;18| |URAGG-;cycleEntry;2A;19| |URAGG-;cycleLength;ANni;20| - |URAGG-;rest;ANniA;21| (104 . |#|) (109 . >) - (115 . |rest|) (121 . |copy|) (126 . |last|) - (132 . |true|) (136 . ~=) (142 . =) (148 . =) - (154 . |node?|) (160 . |setfirst!|) (166 . |setelt|) - (173 . |setlast!|) (179 . |setelt|) (186 . |setrest!|) - (192 . |setelt|) (199 . |concat!|) (205 . |concat|) - (211 . |setlast!|) (217 . |#|) (222 . |first|) - (227 . |setchildren!|) (233 . |setvalue!|) (239 . <) - (245 . |empty|) (249 . |split!|) (255 . |cycleSplit!|) + |URAGG-;rest;ANniA;21| (114 . |#|) (119 . >) + (125 . |rest|) (131 . |copy|) (136 . |last|) + (142 . |true|) (146 . ~=) (152 . =) (158 . =) + (164 . |node?|) (170 . |setfirst!|) (176 . |setelt|) + (183 . |setlast!|) (189 . |setelt|) (196 . |setrest!|) + (202 . |setelt|) (209 . |concat!|) (215 . |concat|) + (221 . |setlast!|) (227 . |#|) (232 . |first|) + (237 . |setchildren!|) (243 . |setvalue!|) (249 . <) + (255 . |empty|) (259 . |split!|) (265 . |cycleSplit!|) '"value") - '#(|value| 260 |third| 265 |tail| 270 |split!| 275 |size?| - 281 |setvalue!| 287 |setlast!| 293 |setelt| 299 - |setchildren!| 320 |second| 326 |rest| 331 |nodes| 337 - |node?| 342 |more?| 348 |less?| 354 |leaf?| 360 |last| 365 - |elt| 376 |cyclic?| 394 |cycleTail| 399 |cycleSplit!| 404 - |cycleLength| 409 |cycleEntry| 414 |concat| 419 |children| - 425 = 430 |#| 436) + '#(|value| 270 |third| 275 |tail| 280 |split!| 285 |size?| + 291 |setvalue!| 297 |setlast!| 303 |setelt| 309 + |setchildren!| 330 |second| 336 |rest| 341 |nodes| 347 + |node?| 352 |more?| 358 |less?| 364 |leaf?| 370 |last| 375 + |elt| 386 |cyclic?| 404 |cycleTail| 409 |cycleSplit!| 414 + |cycleLength| 419 |cycleEntry| 424 |concat| 429 |children| + 435 = 440 |#| 446) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 83 + (|makeByteWordVec2| 86 '(1 6 7 0 8 1 6 7 0 11 1 6 0 0 14 1 6 19 0 20 0 19 0 21 1 19 0 0 22 1 6 0 0 24 0 26 0 27 2 26 0 6 0 28 1 26 0 0 29 0 35 0 36 0 37 0 38 2 37 19 0 0 39 0 35 0 40 0 37 0 41 2 37 0 0 0 42 1 37 19 0 44 2 35 19 0 0 47 1 6 19 0 48 - 2 6 19 0 0 51 1 6 0 0 52 1 6 35 0 57 - 2 35 19 0 0 58 2 6 0 0 35 59 1 6 0 0 - 60 2 0 0 0 35 61 0 19 0 62 2 7 19 0 0 - 63 2 0 19 0 0 64 2 6 19 0 0 65 2 0 19 - 0 0 66 2 6 7 0 7 67 3 0 7 0 9 7 68 2 - 6 7 0 7 69 3 0 7 0 12 7 70 2 6 0 0 0 - 71 3 0 0 0 15 0 72 2 6 0 0 0 73 2 0 0 - 0 0 74 2 0 7 0 7 75 1 26 35 0 76 1 26 - 6 0 77 2 0 0 0 30 78 2 0 7 0 7 79 2 - 37 19 0 0 80 0 6 0 81 2 0 0 0 37 82 1 - 0 0 0 83 1 0 7 0 34 1 0 7 0 18 1 0 0 - 0 50 2 0 0 0 37 82 2 0 19 0 35 46 2 0 - 7 0 7 79 2 0 7 0 7 75 3 0 7 0 12 7 70 - 3 0 0 0 15 0 72 3 0 7 0 9 7 68 2 0 0 - 0 30 78 1 0 7 0 17 2 0 0 0 35 56 1 0 - 30 0 31 2 0 19 0 0 66 2 0 19 0 35 45 - 2 0 19 0 35 43 1 0 19 0 33 2 0 0 0 35 - 61 1 0 7 0 25 2 0 7 0 12 13 2 0 0 0 - 15 16 2 0 7 0 9 10 1 0 19 0 23 1 0 0 - 0 53 1 0 0 0 83 1 0 35 0 55 1 0 0 0 - 54 2 0 0 0 0 74 1 0 30 0 32 2 0 19 0 - 0 64 1 0 35 0 49))))) + 0 49 0 50 2 35 0 0 0 51 2 6 19 0 0 54 + 1 6 0 0 55 1 6 35 0 60 2 35 19 0 0 61 + 2 6 0 0 35 62 1 6 0 0 63 2 0 0 0 35 + 64 0 19 0 65 2 7 19 0 0 66 2 0 19 0 0 + 67 2 6 19 0 0 68 2 0 19 0 0 69 2 6 7 + 0 7 70 3 0 7 0 9 7 71 2 6 7 0 7 72 3 + 0 7 0 12 7 73 2 6 0 0 0 74 3 0 0 0 15 + 0 75 2 6 0 0 0 76 2 0 0 0 0 77 2 0 7 + 0 7 78 1 26 35 0 79 1 26 6 0 80 2 0 0 + 0 30 81 2 0 7 0 7 82 2 37 19 0 0 83 0 + 6 0 84 2 0 0 0 37 85 1 0 0 0 86 1 0 7 + 0 34 1 0 7 0 18 1 0 0 0 53 2 0 0 0 37 + 85 2 0 19 0 35 46 2 0 7 0 7 82 2 0 7 + 0 7 78 3 0 7 0 12 7 73 3 0 0 0 15 0 + 75 3 0 7 0 9 7 71 2 0 0 0 30 81 1 0 7 + 0 17 2 0 0 0 35 59 1 0 30 0 31 2 0 19 + 0 0 69 2 0 19 0 35 45 2 0 19 0 35 43 + 1 0 19 0 33 2 0 0 0 35 64 1 0 7 0 25 + 2 0 7 0 12 13 2 0 0 0 15 16 2 0 7 0 9 + 10 1 0 19 0 23 1 0 0 0 56 1 0 0 0 86 + 1 0 35 0 58 1 0 0 0 57 2 0 0 0 0 77 1 + 0 30 0 32 2 0 19 0 0 67 1 0 35 0 52))))) '|lookupComplete|)) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index e506770d..c32617a5 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2266184 . 3485354329) +(2266184 . 3485439394) (-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 -2968) +(-32 R -3014) ((|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 -2968 UP UPUP -2949) +(-40 -3014 UP UPUP -2291) ((|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))) (-3684 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-3684 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-3684 (-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)))) (-3684 (|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 -2968) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-3749 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-3749 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-3749 (-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)))) (-3749 (|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 -3014) ((|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)) -((-3684 (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|))))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|))))))) +((-3749 (-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#2|))))))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2968) +(-54 |Base| R -3014) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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))) (-3684 (-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 -1800) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3749 (-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 -1770) ((|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 -1800) +(-62 -1770) ((|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 -1800) +(-63 -1770) ((|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 -1800) +(-64 -1770) ((|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 -1800) +(-65 -1770) ((|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 -1800) +(-66 -1770) ((|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 -1800) +(-67 -1770) ((|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 -1800) +(-68 -1770) ((|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 -1800) +(-69 -1770) ((|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 -1800) +(-70 -1770) ((|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 -1800) +(-71 -1770) ((|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 -1800) +(-72 -1770) ((|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 -1800) +(-73 -1770) ((|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 -1800) +(-74 -1770) ((|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 -1800) +(-77 -1770) ((|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 -1800) +(-78 -1770) ((|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 -1800) +(-79 -1770) ((|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 -1800) +(-80 -1770) ((|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 -1800) +(-81 -1770) ((|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 -1800) +(-82 -1770) ((|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 -1800) +(-83 -1770) ((|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 -1800) +(-84 -1770) ((|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 -1800) +(-85 -1770) ((|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 -1800) +(-86 -1770) ((|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 -1800) +(-87 -1770) ((|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 -1800) +(-88 -1770) ((|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 -1800) +(-89 -1770) ((|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))) (-3684 (-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))) (-3749 (-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))) (-3684 (-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))) (-3749 (-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))) (-3684 (|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)))) (-3684 (-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))) (-3749 (|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)))) (-3749 (-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 -2968 UP) +(-116 -3014 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))) (-3684 (|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)))) (-3684 (-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))) (-3749 (|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)))) (-3749 (-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))) (-3684 (-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))) (-3749 (-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))) (-3684 (-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))) (-3749 (-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))) (-3684 (-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))) (-3749 (-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)) -((-3684 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-3684 (-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)))) (-3684 (|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)))))) +((-3749 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-3749 (-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)))) (-3749 (|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4454 "*") . T)) NIL -(-136 |minix| -2795 S T$) +(-136 |minix| -2819 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2795 R) +(-137 |minix| -2819 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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)) -((-3684 (-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)))))) +((-3749 (-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 -2968 UP UPUP) +(-149 -3014 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 -2968) +(-159 R -3014) ((|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 -3684 (|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)) (-3419 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-4445 -3749 (|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)) (-3486 . 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 -3684 (|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)) (-3419 . 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))) (-3749 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-3749 (-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))))) (-3749 (|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)))) (-3749 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-3749 (|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))) (-3749 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-3749 (-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))))) (-3749 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3749 (-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| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -2968) +(-190 R -3014) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -2968 UP UPUP R) +(-217 -3014 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 -2968 FP) +(-218 -3014 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))) (-3684 (|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)))) (-3684 (-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))) (-3749 (|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)))) (-3749 (-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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -2968) +(-221 R -3014) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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))) (-3684 (-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))) (-3749 (-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 -2968) +(-226 R -3014) ((|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}."))) -((-3412 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3478 . 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))) (-3684 (-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))) (-3749 (-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 -2795 R) +(-239 S -2819 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 -2795 R) +(-240 -2819 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 -2795 A B) +(-241 -2819 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 -2795 R) +(-242 -2819 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 . 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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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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)))) (-3749 (-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))))) (-3749 (|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)))) (-3749 (|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|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)))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3749 (|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)))) (-3749 (|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)))) (-3749 (-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 -2968) +(-279 R -3014) ((|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 -2968) +(-280 R -3014) ((|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| -2216 -1323 |exactQuo|) +(-293 S R |Mod| -2723 -4356 |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 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#2|)))))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#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 -2968 S) +(-301 -3014 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 -2968) +(-302 E -3014) ((|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 -2968) +(-314 -3014) ((|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))) (-3684 (|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)))) (-3684 (|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))) (-3749 (|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)))) (-3749 (|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 -3684 (-3163 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-3684 (-3163 (|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)))) (-3749 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-3749 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-3749 (-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 -3014) ((|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))) (-3684 (|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|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 -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (-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 -1725) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (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))) (-3749 (|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))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3749 (|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 -2869) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3749 (-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 -1363) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1598) (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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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 -2968) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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 -3014) ((|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 -2968) +(-333 -3014) ((|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 -2968 UP UPUP R) +(-339 S -3014 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 -2968 UP UPUP R) +(-340 -3014 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 -2968 UP UPUP R) +(-341 -3014 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 -2968 UP UPUP) +(-346 S -3014 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 -2968 UP UPUP) +(-347 -3014 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)) -((-3684 (|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)))) +((-3749 (|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)) -((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3749 (|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)) -((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3749 (|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 -2968) +(-355 R UP -3014) ((|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)) -((-3684 (|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)))) +((-3749 (|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)) -((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3749 (|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)) -((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3749 (|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)) -((-3684 (|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)))) +((-3749 (|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)) -((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) -(-361 -2968 GF) +((-3749 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +(-361 -3014 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 -2968 FP FPP) +(-363 -3014 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)) -((-3684 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3749 (|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) (-3412 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-4435 . T) (-4443 . T) (-3478 . 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 -2968 UP UPUP R) +(-398 -3014 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 -1800 |returnType| -4170 |symbols|) +(-404 -1770 |returnType| -4198 |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 -2968 UP) +(-405 -3014 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\"."))) -((-3412 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3478 . 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))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-3684 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-3684 (-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)))) (-3684 (-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))))) (-3684 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-3684 (|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)))) (-3684 (-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))) (-3749 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-3749 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-3749 (-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)))) (-3749 (-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))))) (-3749 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-3749 (|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)))) (-3749 (-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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1604,11 +1604,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-419 R -2968 UP A) +(-419 R -3014 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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 -2968 UP A |ibasis|) +(-420 R -3014 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))) (-3684 (|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|))) (-3684 (|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))) (-3749 (|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|))) (-3749 (|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4452 . T) (-4442 . T) (-4453 . T)) NIL -(-432 R -2968) +(-432 R -3014) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1664,7 +1664,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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 -2968) +(-434 R -3014) ((|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 -3684 (|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 -3749 (|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 -2968) +(-437 R -3014) ((|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 -2968) +(-438 R -3014) ((|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 -2968) +(-439 R -3014) ((|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 -2968 UP) +(-441 R -3014 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 -2968) +(-449 R UP -3014) ((|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))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-3684 (|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)))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-3749 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3749 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3749 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-3749 (|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)))) (-3749 (|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)))) (-3749 (-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| -2968 R) +(-477 |lv| -3014 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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((-4453 . T)) -((-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#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 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#2|)))))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#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 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#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 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#2|)))))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#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.")) 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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))))) (-3749 (|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))) (-3684 (-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 -2968 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3749 (-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 -3014 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))) (-3684 (|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)))) (-3684 (-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))) (-3749 (|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)))) (-3749 (-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 -2968 UP |AlExt| |AlPol|) +(-500 -3014 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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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))) (-3684 (-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))) (-3749 (-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 -2968) +(-505 R UP -3014) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1968,7 +1968,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-510 -2968 |Expon| |VarSet| |DPoly|) +(-510 -3014 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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)) -((-3684 (|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)))) +((-3749 (|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))) (-3684 (-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))) (-3749 (-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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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))) (-3684 (-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))) (-3749 (-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 -2968 |Par|) +(-538 K -3014 |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 -2968 |Par|) +(-544 K -3014 |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 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) -(-557 R -2968) +((-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#2|)))))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +(-557 R -3014) ((|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 -2968 UP UPUP R) +(-558 R0 -3014 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."))) -((-3412 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3478 . 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 -2968) +(-563 R -3014) ((|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 -2968 L) +(-566 R -3014 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 -2968 UP UPUP R) +(-568 -3014 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 -2968 UP) +(-569 -3014 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 -2968 L) +(-572 R -3014 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 -2968) +(-573 R -3014) ((|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 -2968 UP) +(-574 -3014 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 -2968) +(-576 -3014) ((|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."))) -((-3412 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3478 . 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 -2968) +(-579 R -3014) ((|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 -2968 UP) +(-580 -3014 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 -2968) +(-581 R -3014) ((|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 -2968) +(-589 R -3014) ((|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 -2968) +(-590 E -3014) ((|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 -2968) +(-592 -3014) ((|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)) -((-3684 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-3684 (|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)))) (-3684 (|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)))))) +((-3749 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-3749 (|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)))) (-3749 (|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))) (-3684 (|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 -2838) (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))) (-3749 (|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 -2869) (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 -2968 FG) +(-606 R -3014 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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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 -3684 (-3163 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) -((-3684 (|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|)))) (-3684 (-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 -3749 (-3212 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-3749 (|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|)))) (-3749 (-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 (|:| -4111 (-1168)) (|:| -3116 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 |#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 (|:| -4111 (-1168)) (|:| -3116 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 |#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 (|:| -4144 (-1168)) (|:| -3165 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 |#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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-621 -2968 UP) +(-621 -3014 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -2968) +(-628 R -3014) ((|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 -2968) +(-636 R -3014) ((|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| -2968) +(-637 |lv| -3014) ((|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 (|:| -4111 (-1168)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -3116) (QUOTE (-52))))))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 (-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 (|:| -4111 (-1168)) (|:| -3116 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1168)) (|:| -3116 (-52))) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -3165) (QUOTE (-52))))))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 (-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 (|:| -4144 (-1168)) (|:| -3165 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 (-1168)) (|:| -3165 (-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 -3684 (-3163 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) -((-3684 (|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|)))) (-3684 (-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 -3749 (-3212 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-3749 (|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|)))) (-3749 (-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 -((-3152 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) +((-3201 (|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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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))) (-3684 (-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))) (-3749 (-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 -2968 L) +(-658 R -3014 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 -2968 UP) +(-663 -3014 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 -2406) +(-664 A -4005) ((|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 -2968) +(-673 -3014) ((|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 -2968 |Row| |Col| M) +(-674 -3014 |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)))) (-3684 (-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))) (-3684 (|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)))) (-3749 (-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))) (-3749 (|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 -((-3684 (-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))) (-3684 (-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|))))) +((-3749 (-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))) (-3749 (-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)) -((-3684 (-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))) (-3684 (-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|))))) +((-3749 (-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))) (-3749 (-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 -2968 FLAF FLAS) +(-698 S -3014 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)) (-3419 . 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))) (-3684 (|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))) (-3684 (|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))))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-3684 (-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))) (-3684 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-3684 (-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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-3684 (-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)) (-3486 . 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))) (-3749 (|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))) (-3749 (|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))))) (-3749 (|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)))) (-3749 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-3749 (-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))) (-3749 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-3749 (-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)))) (-3749 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-3749 (-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 -2968 PG) +(-704 OV E -3014 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}"))) -((-3412 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-3478 . 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 -3347 I) +(-712 S -3414 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| -2216 -1323 |exactQuo|) +(-717 R |Mod| -2723 -4356 |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))) (-3684 (|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)))) (-3684 (|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))))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3749 (|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)))) (-3749 (|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))))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|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)))) (-3749 (-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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-721 R |Mod| -2216 -1323 |exactQuo|) +(-721 R |Mod| -2723 -4356 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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 -2968) +(-724 -3014) ((|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 -2968 UP) +(-733 -3014 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))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-3684 (|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)))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (-3749 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3749 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3749 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-3749 (|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)))) (-3749 (|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)))) (-3749 (-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 -2968) +(-771 -3014) ((|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 -2968) +(-772 P -3014) ((|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 -2968) +(-774 UP -3014) ((|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 -2968) +(-778 R -3014) ((|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 -2968 |ExtF| |SUEx| |ExtP| |n|) +(-783 -3014 |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)))) (-3201 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-3201 (|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)))) (-3201 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (-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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-804 -3684 R OS S) +(-804 -3749 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-805 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|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|))) (-3684 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (|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|))) (-3749 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3749 (|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 -2968 L) +(-807 R -3014 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 -2968) +(-808 R -3014) ((|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 -2968) +(-810 R -3014) ((|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 -2968 UP UPUP R) +(-812 -3014 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 -2968 UP L LQ) +(-813 -3014 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 -2968 UP L LQ) +(-815 -3014 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 -2968 UP) +(-816 -3014 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 -2968 L UP A LO) +(-817 -3014 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 -2968 UP) +(-818 -3014 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 -2968 LO) +(-819 -3014 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 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 . 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(((-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))) (-3684 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-3684 (|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))) (-3749 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-3749 (|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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4449 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-3684 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-3684 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-3749 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-3749 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-850) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-851 -2795 S) +(-851 -2819 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| -3502) +(-860 R |sigma| -3578) ((|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| -3502) +(-861 |x| R |sigma| -3578) ((|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))) (-3684 (|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)))) (-3684 (-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))) (-3749 (|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)))) (-3749 (-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))) (-3684 (|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)))) (-3684 (-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))) (-3749 (|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)))) (-3749 (-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)))) (-3684 (-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)))) (-3749 (-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 (-3152 (|HasCategory| |#2| (QUOTE (-1058)))) (-3152 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-3152 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) +((-12 (-3201 (|HasCategory| |#2| (QUOTE (-1058)))) (-3201 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-3201 (|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 -3347) +(-897 R -3414) ((|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 -2968) +(-903 UP -3014) ((|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))) (-3684 (-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))) (-3749 (-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.")) (|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)) -((-3684 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) +((-3749 (|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 -2968 UP UPUP R) +(-918 R0 -3014 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 -2968) +(-925 -3014) ((|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 -2968 P) +(-929 -3014 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-930 |xx| -2968) +(-930 |xx| -3014) ((|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 -2968) +(-936 R -3014) ((|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 -2968) +(-939 S R -3014) ((|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 -2968 -3347) +(-944 R -3014 -3414) ((|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 -3347) +(-945 -3414) ((|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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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 -2968) +(-957 E V R P -3014) ((|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|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)))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-960 E V R P -2968) +((|HasCategory| |#1| (QUOTE (-916))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3749 (|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)))) (-3749 (|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)))) (-3749 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-960 E V R P -3014) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-458)))) @@ -3791,12 +3791,12 @@ NIL (-965 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4453 . T) (-4452 . T)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3684 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-3749 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-966) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -2968) +(-967 -3014) ((|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3684 (|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))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3749 (|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)))) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 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(|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-3684 (-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))))) +((-3749 (-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)))) (-3749 (-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)))) (-3749 (-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)))) (-3749 (-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)))) (-3749 (-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 -2968) +(-994 K R UP -3014) ((|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))) (-3684 (|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)))) (-3684 (|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))) (-3749 (|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)))) (-3749 (|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))) (-3684 (-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))) (-3749 (-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 -2968 UP UPUP |radicnd| |n|) +(-1012 -3014 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))) (-3684 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-3684 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-3684 (-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)))) (-3684 (|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))) (-3749 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-3749 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-3749 (-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)))) (-3749 (|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))) (-3684 (|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)))) (-3684 (-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))) (-3749 (|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)))) (-3749 (-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 -2968) +(-1022 R -3014) ((|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 -2968) +(-1023 R -3014) ((|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 -2968 UP) +(-1024 -3014 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 -2968 UP) +(-1025 -3014 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)) -((-3684 (|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 -2968 L) +((-3749 (|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 -3014 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 -2968 |Expon| |VarSet| |FPol| |LFPol|) +(-1043 -3014 |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 (|:| -4111 (-1186)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -3116) (QUOTE (-52))))))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -3165) (QUOTE (-52))))))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1045) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4164,7 +4164,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4449 . T)) NIL -(-1059 |xx| -2968) +(-1059 |xx| -3014) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4183,7 +4183,7 @@ NIL (-1063 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|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))) (-3684 (-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)))) (-3684 (|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))) (-3749 (-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)))) (-3749 (|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 (|:| -4111 (-1186)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -3116) (QUOTE (-52))))))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -3165) (QUOTE (-52))))))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-3749 (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 (-1186)) (|:| -3165 (-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 -2968) +(-1085 |Base| R -3014) ((|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 -2968) +(-1086 |Base| R -3014) ((|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))) (-3684 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-3684 (-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)))) (-3684 (|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))) (-3749 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-3749 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-3749 (-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)))) (-3749 (|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|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)))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3749 (|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)))) (-3749 (|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)))) (-3749 (-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)) -((-3684 (-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|))))) +((-3749 (-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))))) (-3749 (|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 -2968) +(-1125 R -3014) ((|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3684 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3684 (|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)))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-916))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-3749 (|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)))) (-3749 (|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)))) (-3749 (-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))) (-3684 (|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))) (-3749 (|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 -2968) +(-1137 UP -3014) ((|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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4452 . T) (-4453 . T)) -((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-3684 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-3749 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) (-1151 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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)))) (-3684 (-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))) (-3684 (|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)))) (-3749 (-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))) (-3749 (|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))) (-3684 (-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))) (-3749 (-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 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#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 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109)))) +((-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#2|)))))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#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 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#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))) (-3684 (-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))) (-3749 (-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 "*") -3684 (-3163 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-3163 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4445 -3684 (-3163 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-3163 (|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)))) (-3749 (|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))))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3749 (|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)))) (-3749 (-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))) (-3684 (|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|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 -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (-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 -1725) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (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))) (-3749 (|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))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3749 (|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 -2869) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3749 (-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 -1363) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1598) (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))) (-3684 (|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 -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (-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 -1725) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-3749 (|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 -2869) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-3749 (-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 -1363) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1598) (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 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3116) (|devaluate| |#2|)))))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3684 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4144) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3165) (|devaluate| |#2|)))))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-3749 (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4144 |#1|) (|:| -3165 |#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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4453 . T) (-4452 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3684 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-3749 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1214 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4792,7 +4792,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1216 R -2968) +(-1216 R -3014) ((|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 -2968) +(-1218 R -3014) ((|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))) (-3684 (|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))) (-3749 (|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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(LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3749 (-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)))) (-3749 (-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))) (-3684 (|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)))) (-3684 (|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))))) (-3684 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3684 (|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)))) (-3684 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-3749 (|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)))) (-3749 (|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))))) (-3749 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3749 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3749 (|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)))) (-3749 (-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 -2838) (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 -2869) (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))) (-3684 (|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|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 -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (-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 -1725) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (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))) (-3749 (|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))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3749 (|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 -2869) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3749 (-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 -1363) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1598) (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))) (-3684 (|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))) (-3684 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3684 (|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 -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3684 (-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 -1725) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (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))) (-3749 (|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))) (-3749 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-3749 (|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 -2869) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-3749 (-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 -1363) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1598) (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))) (-3684 (|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))) (-3749 (|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 -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1725) (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 -1598) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1363) (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))) (-3684 (|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 -2838) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-3684 (-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 -1725) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1624) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-3749 (|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 -2869) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-3749 (-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 -1363) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1598) (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 -2968 UP L UTS) +(-1271 -3014 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)) -((-3684 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3684 (-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)))) (-3684 (|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|))))) +((-3749 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-3749 (-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)))) (-3749 (|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 -2968) +(-1286 K R UP -3014) ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-1295 S -2968) +(-1295 S -3014) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1296 -2968) +(-1296 -3014) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 9f1265e3..adffd603 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(189904 . 3485354335) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) #0#) |has| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (-313 (-2 (|:| -4111 |#1|) (|:| -3116 |#2|))))) -((((-570)) . T) (($) -3684 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) +(189904 . 3485439400) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) #0#) |has| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (-313 (-2 (|:| -4144 |#1|) (|:| -3165 |#2|))))) +((((-570)) . T) (($) -3749 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -3749 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-570)) . T)) -((($ $) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) +((($ $) -3749 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T)) -((($) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) +((($) -3749 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) (|has| |#1| (-916)) ((((-868)) . T)) ((((-868)) . T)) @@ -24,19 +24,19 @@ ((((-227)) . T) (((-868)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T)) -(-3684 (|has| |#1| (-21)) (|has| |#1| (-854))) -((($ $) . T) ((#0=(-413 (-570)) #0#) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -(-3684 (|has| |#1| (-826)) (|has| |#1| (-856))) +(-3749 (|has| |#1| (-21)) (|has| |#1| (-854))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -3749 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +(-3749 (|has| |#1| (-826)) (|has| |#1| (-856))) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . T)) ((((-868)) . 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T) (($) -3749 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -3749 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -3749 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((|#2|) -3749 (|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))) -(-3684 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-3684 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-3749 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-3749 (|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 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))) . 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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))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (($) . 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T)) (((|#1| (-980)) . T)) ((((-570)) . T) ((|#2|) . T)) @@ -352,7 +352,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1161)) -((((-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))) . T)) +((((-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))) . T)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -364,27 +364,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) -((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -3749 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . 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T)) -((($) -3684 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -3749 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((((-868)) . T)) (|has| (-1262 |#2| |#3| |#4|) (-148)) @@ -395,16 +395,16 @@ ((((-868)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3684 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-3749 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) . T)) ((((-570) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) (((|#1|) . 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T)) (((#0=(-705) (-1182 #0#)) . T)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . 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) (($) -3684 (|has| |#1| (-174)) (|has| |#1| (-562)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -3749 (|has| |#1| (-174)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) . T)) ((((-868)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((($) . T)) -((($ $) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -3684 (|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)) (|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 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))) . T)) +((((-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) -((((-394) (-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))) . T)) +((((-394) (-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#2| (-1161)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|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)) $) . T) (((-570) |#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#2| (-854)) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) -(-3684 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-3749 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-174)) ((|#4|) . T) (((-570)) . T)) (((|#2|) |has| |#2| (-174))) @@ -1010,7 +1010,7 @@ (((|#1|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-413 (-570))) . T)) -((($) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) (|has| |#1| (-834)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (|has| |#1| (-1109)) @@ -1021,13 +1021,13 @@ (((|#4|) |has| |#4| (-1109))) (((|#3|) |has| |#3| (-1109))) (|has| |#3| (-373)) -((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) +((((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3749 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) ((((-868)) . T)) ((((-868)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-368)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3749 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |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)) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) -((($ $) -3684 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($ $) -3749 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) ((($) . T) (((-570)) . 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T)) -(-3684 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +(-3749 (|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)))) -(-3684 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) +(-3749 (|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)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|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 (-2827 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-242 (-2857 |#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)) -(-3684 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3749 (|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 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) -((((-570)) -3684 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) +((((-570)) -3749 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -3749 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . 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 (|:| -4111 |#1|) (|:| -3116 |#2|))) |has| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (-313 (-2 (|:| -4111 |#1|) (|:| -3116 |#2|))))) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))) |has| (-2 (|:| -4111 (-1168)) (|:| -3116 |#1|)) (-313 (-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) |has| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (-313 (-2 (|:| -4144 |#1|) (|:| -3165 |#2|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))) |has| (-2 (|:| -4144 (-1168)) (|:| -3165 |#1|)) (-313 (-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))))) ((((-868)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1156,10 +1156,10 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) ((((-570)) . T) (($) . 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T)) (((|#1|) |has| |#1| (-313 |#1|))) @@ -1262,11 +1262,11 @@ (|has| |#1| (-373)) ((((-1186) $) |has| |#1| (-520 (-1186) $)) (($ $) |has| |#1| (-313 $)) ((|#1| |#1|) |has| |#1| (-313 |#1|)) (((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|))) ((((-1186)) |has| |#1| (-907 (-1186)))) -(-3684 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) +(-3749 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-394) |#1|) . T)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-1109)) (((|#2|) . T) (((-868)) . T)) ((((-868)) . T)) @@ -1274,8 +1274,8 @@ ((((-917 |#1|)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . 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T)) (|has| |#1| (-1212)) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) @@ -1305,8 +1305,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (|has| |#1| (-368)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) . T) ((#0=(-413 (-570)) #0#) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -3749 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -1321,29 +1321,29 @@ (((|#1| |#2|) . T)) (|has| |#1| (-854)) (|has| |#1| (-854)) -((($) . T) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) -(-3684 (|has| |#1| (-174)) (|has| |#1| (-562))) +((($) . T) (((-413 (-570))) -3749 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) ((((-413 (-570))) . T) (((-413 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1182 |#1|)) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1543,8 +1543,8 @@ (((|#1|) . T) (((-570)) . T) (($) . T)) (((|#2|) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))) . T)) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))) . T)) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#2|) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . 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T)) -(-3684 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) -(-3684 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) +(-3749 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) +(-3749 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) (((|#4|) . T)) (|has| |#1| (-146)) ((((-1168) |#1|) . T)) @@ -1628,24 +1628,24 @@ (((|#3|) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) . T)) +((((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -3684 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -3749 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -3749 (|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)) @@ -1737,13 +1737,13 @@ (((|#1|) |has| |#1| (-174))) (|has| |#1| (-290 |#1| |#1|)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) -(((|#3|) -3684 (|has| |#3| (-174)) (|has| |#3| (-368)))) -((($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -(-3684 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-916))) -((($) -3684 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . 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T)) -(-3684 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-854)) (|has| |#1| (-854)) (|has| |#1| (-854)) @@ -1761,14 +1761,14 @@ ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . 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T)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-1058))) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) |has| (-2 (|:| -4111 |#1|) (|:| -3116 |#2|)) (-313 (-2 (|:| -4111 |#1|) (|:| -3116 |#2|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) |has| (-2 (|:| -4144 |#1|) (|:| -3165 |#2|)) (-313 (-2 (|:| -4144 |#1|) (|:| -3165 |#2|))))) (|has| |#1| (-368)) (((|#1|) |has| |#1| (-174))) (((|#1| |#1|) . T)) @@ -2151,7 +2151,7 @@ (((|#1|) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-650 $)) . T) (((-1168)) . T) (((-1186)) . T) (((-570)) . T) (((-227)) . T) (((-868)) . 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T)) +((((-2 (|:| -4144 (-1168)) (|:| -3165 (-52)))) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -2204,17 +2204,17 @@ ((((-705)) . T) (((-413 (-570))) . T) (((-570)) . T)) (((|#1| |#1|) |has| |#1| (-174))) (((|#2|) . T)) -((($) . T) (((-570)) . T) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-570)) . T) (((-413 (-570))) -3749 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-570) |#1|) . 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T)) @@ -2490,10 +2490,10 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -3749 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) @@ -2503,10 +2503,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-368))) -((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -3684 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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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)) (($) |has| |#1| (-562))) -((((-413 (-570))) -3684 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) +((((-413 (-570))) -3749 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -3749 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) (|has| |#1| (-368)) -((($) |has| |#1| (-854)) (((-570)) -3684 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) |has| |#1| (-854)) (((-570)) -3749 (|has| |#1| (-21)) (|has| |#1| (-854)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-148)) @@ -2592,17 +2592,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2| |#3|) . T)) -(-3684 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-3749 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1| (-537 |#2|)) . T)) (((|#1| (-777)) . T)) (((|#1| (-537 (-1097 (-1186)))) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (|has| |#2| (-916)) -(-3684 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-3749 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-868)) . T)) -(((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)))) -(((|#2|) -3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2|) -3749 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -3749 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((($ $) . T) ((#0=(-1262 |#2| |#3| |#4|) #0#) . T) ((#1=(-413 (-570)) #1#) |has| #0# (-38 (-413 (-570))))) ((((-917 |#1|)) . T)) (-12 (|has| |#1| (-368)) (|has| |#2| (-826))) @@ -2610,14 +2610,14 @@ ((((-868)) . T)) ((($) . 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T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) -(-3684 (|has| |#1| (-294)) (|has| |#1| (-368))) +(-3749 (|has| |#1| (-294)) (|has| |#1| (-368))) ((((-145)) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (|has| |#1| (-854)) @@ -2699,7 +2699,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-189)) . T) (((-868)) . T)) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -2712,7 +2712,7 @@ ((((-868)) . T)) ((((-1168)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -((((-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))) . T)) +((((-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))) . T)) (|has| |#1| (-856)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) @@ -2724,16 +2724,16 @@ (((|#2|) . T)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T) (((-618 $)) . T)) -(-3684 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-3684 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-3749 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-3749 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-1186) (-52)) . T)) -(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3749 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3684 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-3684 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3749 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3749 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-916)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (|has| |#1| (-916)) @@ -2750,12 +2750,12 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#1| (-826)) (((#0=(-917 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((((-413 |#2|)) . T)) (|has| |#1| (-854)) -((((-1213 |#1|)) . T) (((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-1213 |#1|)) . T) (((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) . T) ((#1=(-570) #1#) . T) (($ $) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-1058)) (((-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) @@ -2771,29 +2771,29 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) -((((-2 (|:| -4111 (-1186)) (|:| -3116 (-52)))) . T)) +(-3749 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3749 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3749 (|has| |#1| (-146)) (|has| |#1| (-373))) +((((-2 (|:| -4144 (-1186)) (|:| -3165 (-52)))) . T)) ((((-570) |#3|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -4111 (-1186)) (|:| -3116 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -4144 (-1186)) (|:| -3165 #0#))) . T)) (|has| |#1| (-354)) ((((-570)) . T)) ((((-868)) . T)) (((|#1|) . T)) (((#0=(-1263 |#1| |#2| |#3| |#4|) $) |has| #0# (-290 #0# #0#))) (|has| |#1| (-368)) -(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -3684 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -3684 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -3749 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -3749 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -3749 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((#0=(-1091) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-354))) (((#0=(-413 (-570)) #0#) . T) ((#1=(-705) #1#) . T) (($ $) . T)) ((((-320 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) ((((-868)) . T)) (|has| |#1| (-1109)) (((|#1|) . T)) -(((|#1|) -3684 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) -(((|#1|) -3684 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -3749 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -3749 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) ((((-585)) . T)) @@ -2818,7 +2818,7 @@ (((|#1|) . T)) ((((-570)) . T)) (((|#2|) . T) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (($) . T) (((-570)) . T)) -(-3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3749 (|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)) ((($) . T)) @@ -2862,7 +2862,7 @@ (|has| |#2| (-1031)) ((($) . T)) (|has| |#1| (-916)) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2871,10 +2871,10 @@ (|has| |#1| (-368)) ((((-917 |#1|)) . T)) ((($) . T) (((-570)) . T) ((|#1|) . T) (((-413 (-570))) . T)) -((($) -3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) |has| |#1| (-854)) (((-570)) -3684 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) -3749 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) |has| |#1| (-854)) (((-570)) -3749 (|has| |#1| (-21)) (|has| |#1| (-854)))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) -(-3684 (|has| |#1| (-373)) (|has| |#1| (-856))) +(-3749 (|has| |#1| (-373)) (|has| |#1| (-856))) (((|#1|) . T)) ((((-777)) . T)) ((((-868)) . T)) @@ -2885,17 +2885,17 @@ ((((-570)) . T) (($) . T)) ((((-570)) . T) (($) . T)) ((((-777) |#1|) . T)) -(((|#2| (-242 (-2827 |#1|) (-777))) . T)) +(((|#2| (-242 (-2857 |#1|) (-777))) . T)) (((|#1| (-537 |#3|)) . T)) ((((-413 (-570))) . T)) -(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3749 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-1168)) . T) (((-868)) . T)) -(((#0=(-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) #0#) |has| (-2 (|:| -4111 (-1186)) (|:| -3116 (-52))) (-313 (-2 (|:| -4111 (-1186)) (|:| -3116 (-52)))))) +(((#0=(-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) #0#) |has| (-2 (|:| -4144 (-1186)) (|:| -3165 (-52))) (-313 (-2 (|:| -4144 (-1186)) (|:| -3165 (-52)))))) ((((-1168)) . T)) (|has| |#1| (-916)) (|has| |#2| (-368)) (((|#1|) . T) (($) . T) (((-570)) . T)) -(-3684 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3749 (|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)) @@ -2912,11 +2912,11 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-3684 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (-12 (|has| |#1| (-551)) (|has| |#1| (-834))) ((((-868)) . T)) -((((-1186)) -3684 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) +((((-1186)) -3749 (-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)) @@ -2928,7 +2928,7 @@ (((|#2|) |has| |#1| (-368))) (((|#2|) |has| |#1| (-368))) ((((-570)) . T) (($) . T)) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2957,11 +2957,11 @@ (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#2|) |has| |#1| (-368))) ((((-384)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-384)))) (((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-570))))) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . T)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-562))) (((|#3|) . T)) ((((-1168)) . T) (((-512)) . T) (((-227)) . T) (((-570)) . T)) (((|#1|) . T)) @@ -2969,23 +2969,23 @@ (|has| |#1| (-562)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) -(-3684 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3749 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#2|) . T)) (((|#2|) . T)) -(-3684 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) -((((-2 (|:| -4111 (-1168)) (|:| -3116 |#1|))) . T)) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +(-3749 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) +((((-2 (|:| -4144 (-1168)) (|:| -3165 |#1|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-413 (-570)))) -(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3749 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) ((((-1168) |#1|) . T)) (|has| |#1| (-148)) -(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3749 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) -(-3684 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-3749 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) (|has| |#1| (-148)) ((((-587 |#1|)) . T)) @@ -2999,7 +2999,7 @@ ((((-413 (-570))) |has| |#2| (-1047 (-570))) (((-570)) |has| |#2| (-1047 (-570))) (((-1186)) |has| |#2| (-1047 (-1186))) ((|#2|) . T)) (((#0=(-413 |#2|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-3684 (|has| |#1| (-146)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-146)) (|has| |#1| (-354))) (|has| |#1| (-148)) ((((-868)) . T)) ((($) . T)) @@ -3025,7 +3025,7 @@ ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3047,7 +3047,7 @@ ((((-570)) . T)) ((((-868)) . T)) ((((-570)) . T)) -(-3684 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-3749 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -3059,10 +3059,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) $) . T) (((-650 (-570)) $) . T)) -(-3684 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121)) (|has| |#1| (-1109))) +(-3749 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121)) (|has| |#1| (-1109))) (|has| |#1| (-1161)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) @@ -3079,9 +3079,9 @@ (((|#1|) |has| |#1| (-313 |#1|))) ((((-570) |#1|) . T) (((-1244 (-570)) $) . T)) ((((-1186) |#1|) . T)) -(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -3749 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T)) -(((|#1|) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) +(((|#1|) -3749 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) ((((-570)) . T) (((-413 (-570))) . T)) (((|#1|) . T)) (|has| |#1| (-562)) @@ -3090,14 +3090,14 @@ ((((-384)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-562)) (|has| |#1| (-1109)) ((((-786 |#1| (-870 |#2|))) |has| (-786 |#1| (-870 |#2|)) (-313 (-786 |#1| (-870 |#2|))))) -(-3684 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-3749 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3109,13 +3109,13 @@ (|has| |#2| (-368)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((((-2 (|:| -4111 (-1168)) (|:| -3116 (-52)))) . T)) +((((-2 (|:| -4144 (-1168)) (|:| -3165 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-570)) . 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T)) -(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -3684 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -3749 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) @@ -3157,21 +3157,21 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) -3684 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) -((($ $) -3684 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . 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T)) -((($) -3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -3749 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) (((-1186) $) . T)) (|has| |#2| (-916)) ((((-1269 |#1| |#2| |#3|)) . T)) @@ -3667,7 +3667,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-174))) ((((-705)) . T)) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-1191)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1191)) . T)) @@ -3684,13 +3684,13 @@ ((((-1191)) . T)) ((((-1191)) . T)) ((((-1191)) . T)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1191)) . T)) ((((-1191)) . 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T)) ((((-570)) . T)) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3684 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-3749 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) -(-3684 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-3749 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-368)) @@ -3745,7 +3745,7 @@ (((|#1| |#2|) . T)) ((((-570)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-570)) . T)) -(-3684 (|has| |#1| (-354)) (|has| |#1| (-373))) +(-3749 (|has| |#1| (-354)) (|has| |#1| (-373))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-413 (-570))) . T) (($) . T) (((-570)) . T)) @@ -3757,7 +3757,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-570) $) . T) (((-650 (-570)) $) . T)) ((($) . T) (((-413 (-570))) . T)) (|has| |#1| (-916)) @@ -3769,14 +3769,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-570)) . T)) ((((-1191)) . T)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-3684 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-3749 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#2|) . T)) -(-3684 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-3749 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -3684 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) +((((-868)) -3749 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) ((((-413 |#2|) |#3|) . T)) ((((-413 (-570))) . T) (($) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -3790,19 +3790,19 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((#0=(-570) #0#) . T)) ((($) . T) (((-413 (-570))) . T)) -(-3684 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-3684 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-3749 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-3749 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) (|has| |#4| (-799)) -(-3684 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-3749 (|has| |#4| (-799)) (|has| |#4| (-854))) (|has| |#4| (-854)) (|has| |#3| (-799)) ((((-1191)) . T)) -(-3684 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-3749 (|has| |#3| (-799)) (|has| |#3| (-854))) (|has| |#3| (-854)) ((((-570)) . T)) (((|#2|) . T)) -((((-1186)) -3684 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) +((((-1186)) -3749 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-777) |#1|))) (|has| |#1| (-907 (-1186))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3817,11 +3817,11 @@ ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-1149 |#1| |#2|)) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2|) . T) (((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) -((((-2 (|:| -4111 (-1186)) (|:| -3116 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) +((((-2 (|:| -4144 (-1186)) (|:| -3165 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1031)) -(((|#2|) . T) (((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4144 |#1|) (|:| -3165 |#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)) @@ -3838,15 +3838,15 @@ ((((-1184 |#1| |#2| |#3|)) . T)) ((((-1184 |#1| |#2| |#3|)) . T) (((-1177 |#1| |#2| |#3|)) . T)) ((((-868)) . T)) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3749 (|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) (($) -3684 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -3684 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) -(((|#2|) . T) (($) -3684 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -3684 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) +(((|#3|) . T) ((|#2|) . T) (($) -3749 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -3749 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) +(((|#2|) . T) (($) -3749 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -3749 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -3860,7 +3860,7 @@ ((((-189)) . T) (((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-130)) . T) (((-868)) . T)) ((((-570) |#1|) . T) (((-1244 (-570)) $) . T)) ((((-130)) . T)) @@ -3869,13 +3869,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-368)) (|has| |#2| (-290 |#2| |#2|))) (($ $) . T) (((-570) |#1|) . T)) ((($ $) . T) (((-413 (-570)) |#1|) . T)) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) -(-3684 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) +(-3749 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-537 |#2|)) . T)) -((((-2 (|:| -4111 (-1186)) (|:| -3116 (-52)))) . T)) +((((-2 (|:| -4144 (-1186)) (|:| -3165 (-52)))) . T)) ((((-570) (-130)) . T)) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) @@ -3890,8 +3890,8 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) -(-3684 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-3684 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-3749 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-3749 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((($) . T)) (((|#2| (-537 (-870 |#1|))) . T)) ((((-1191)) . T)) @@ -3906,13 +3906,13 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-868)) -3684 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -3749 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#2| (-777)) . T)) (((|#1| |#2|) . T)) ((((-1168) |#1|) . T)) ((((-413 |#2|)) . T)) -((((-2 (|:| -4111 |#1|) (|:| -3116 |#2|))) . T)) +((((-2 (|:| -4144 |#1|) (|:| -3165 |#2|))) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) ((($) . T) ((|#2|) . T)) @@ -3923,14 +3923,14 @@ ((((-570)) . T) (($) . T)) (((|#2| $) |has| |#2| (-290 |#2| |#2|))) (((|#1| (-650 |#1|)) |has| |#1| (-854))) -(-3684 (|has| |#1| (-235)) (|has| |#1| (-354))) -(-3684 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-235)) (|has| |#1| (-354))) +(-3749 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1273 |#1|)) . T) (((-570)) . T) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) (|has| |#1| (-1109)) (((|#1|) . T)) -((((-1273 |#1|)) . T) (((-570)) . T) (($) -3684 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -3684 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) +((((-1273 |#1|)) . T) (((-570)) . T) (($) -3749 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -3749 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) ((((-413 (-570))) . T) (($) . T)) -((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -3684 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -3684 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -3749 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -3749 (|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)))) @@ -3946,11 +3946,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1149 |#1| |#2|) #0#) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#1|) . 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185936) ((-608 . -290) 185888) ((-611 . -619) 185855) ((-394 . -102) T) ((-1129 . -144) T) ((-127 . -619) 185787) ((-880 . -1109) T) ((-664 . -417) 185771) ((-720 . -619) 185753) ((-251 . -619) 185720) ((-189 . -619) 185702) ((-163 . -619) 185684) ((-158 . -619) 185666) ((-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) 185634) ((-911 . -102) T) ((-737 . -1047) 185510) ((-1184 . -1227) T) ((-537 . -132) T) ((-1183 . -1227) T) ((-1096 . -417) 185494) ((-1009 . -495) 185478) ((-118 . -406) 185455) ((-1177 . -1227) T) ((-788 . -417) 185439) ((-786 . -417) 185423) ((-950 . -34) T) ((-700 . -1161) NIL) ((-254 . -654) 185258) ((-253 . -654) 185080) ((-823 . -927) 185059) ((-460 . -417) 185043) ((-608 . -19) 185027) ((-1155 . -1220) 184996) ((-1177 . -893) NIL) ((-1177 . -891) 184948) ((-608 . -610) 184925) ((-1213 . -619) 184857) ((-1185 . -619) 184839) ((-62 . -401) T) ((-1183 . -1047) 184774) ((-1177 . -1047) 184740) ((-700 . -38) 184690) ((-40 . -652) 184620) ((-480 . -290) 184578) ((-1233 . -619) 184560) ((-737 . -382) 184544) ((-844 . -619) 184526) ((-664 . -1067) T) ((-1261 . -1011) 184492) ((-1240 . -1011) 184458) ((-252 . -1227) T) ((-1097 . -622) 184442) ((-1072 . -1203) 184417) ((-1085 . -622) 184394) ((-878 . -620) 184201) ((-878 . -619) 184183) ((-1199 . -495) 184120) ((-424 . -1031) 184098) ((-48 . -313) 184085) ((-1072 . -107) 184031) ((-485 . -495) 183968) ((-526 . -1227) T) ((-1177 . -343) 183920) ((-1150 . -495) 183891) ((-1177 . -382) 183843) ((-1096 . -1067) T) ((-443 . -102) T) ((-185 . -1109) T) ((-254 . -34) T) ((-253 . -34) T) ((-788 . -1067) T) ((-786 . -1067) T) ((-737 . -907) 183820) ((-460 . -1067) T) ((-59 . -495) 183804) ((-1043 . -1065) 183778) ((-525 . -495) 183762) ((-522 . -495) 183746) ((-503 . -495) 183730) ((-502 . -495) 183714) ((-247 . -520) 183647) ((-1043 . -111) 183614) ((-1184 . -907) 183527) ((-1183 . -907) 183433) 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T) ((-1013 . -891) 180601) ((-1013 . -893) 180583) ((-1221 . -723) 180480) ((-629 . -233) 180464) ((-627 . -21) T) ((-293 . -562) T) ((-627 . -25) T) ((-1207 . -1109) T) ((-717 . -723) 180429) ((-242 . -382) 180398) ((-1013 . -1047) 180358) ((-384 . -1058) T) ((-225 . -1067) T) ((-118 . -233) 180335) ((-59 . -290) 180287) ((-153 . -23) T) ((-522 . -290) 180239) ((-331 . -520) 180172) ((-502 . -290) 180124) ((-384 . -245) T) ((-384 . -235) T) ((-842 . -1058) T) ((-833 . -1058) T) ((-718 . -956) 180093) ((-707 . -856) T) ((-480 . -619) 180075) ((-1263 . -1060) 179980) ((-586 . -652) 179952) ((-570 . -652) 179924) ((-501 . -652) 179874) ((-833 . -235) 179853) ((-135 . -856) T) ((-1263 . -646) 179745) ((-664 . -1109) T) ((-1199 . -610) 179724) ((-556 . -1203) 179703) ((-341 . -1109) T) ((-323 . -368) 179682) ((-413 . -148) 179661) ((-413 . -146) 179640) ((-971 . -1121) 179539) ((-242 . -907) 179471) ((-821 . -1121) 179381) ((-660 . -858) 179365) ((-485 . -610) 179344) ((-556 . -107) 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174871) ((-227 . -732) T) ((-522 . -620) 174832) ((-522 . -619) 174744) ((-503 . -619) 174676) ((-502 . -620) 174637) ((-502 . -619) 174549) ((-1089 . -368) 174500) ((-40 . -417) 174477) ((-77 . -1227) T) ((-877 . -916) NIL) ((-364 . -333) 174461) ((-364 . -368) T) ((-358 . -333) 174445) ((-358 . -368) T) ((-350 . -333) 174429) ((-350 . -368) T) ((-320 . -288) 174408) ((-108 . -368) T) ((-70 . -1227) T) ((-1241 . -343) 174360) ((-877 . -654) 174305) ((-1241 . -382) 174257) ((-971 . -132) 174112) ((-821 . -132) 173982) ((-965 . -657) 173966) ((-1096 . -174) 173877) ((-965 . -378) 173861) ((-1071 . -800) T) ((-1071 . -797) T) ((-878 . -622) 173759) ((-788 . -174) 173650) ((-786 . -174) 173561) ((-822 . -47) 173523) ((-1071 . -732) T) ((-331 . -495) 173507) ((-959 . -732) T) ((-1290 . -313) 173445) ((-460 . -174) 173356) ((-247 . -290) 173308) ((-1269 . -907) 173221) ((-1262 . -907) 173127) ((-1261 . -1065) 172962) ((-487 . -732) T) ((-1241 . -907) 172795) ((-1240 . -1065) 172603) ((-1221 . -294) 172582) ((-1196 . -1227) T) ((-1193 . -373) T) ((-1192 . -373) T) ((-1155 . -152) 172566) ((-1129 . -102) T) ((-1127 . -1109) T) ((-1089 . -23) T) ((-1089 . -1121) T) ((-1084 . -102) T) ((-1066 . -619) 172533) ((-934 . -962) T) ((-743 . -313) 172471) ((-75 . -1227) T) ((-670 . -387) 172443) ((-171 . -916) 172396) ((-30 . -962) T) ((-112 . -850) T) ((-1 . -619) 172378) ((-1012 . -415) 172350) ((-129 . -657) 172332) ((-50 . -626) 172316) ((-700 . -652) 172251) ((-601 . -907) 172164) ((-444 . -102) T) ((-129 . -378) 172146) ((-142 . -313) NIL) ((-878 . -1058) T) ((-839 . -856) 172125) ((-81 . -1227) T) ((-717 . -294) T) ((-40 . -1067) T) ((-587 . -174) T) ((-524 . -174) T) ((-517 . -619) 172107) ((-171 . -654) 172017) ((-513 . -619) 171999) ((-356 . -148) 171981) ((-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) 171960) ((-1261 . -111) 171781) ((-1240 . -111) 171570) 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. -562) 165500) ((-254 . -1047) 165327) ((-253 . -1047) 165154) ((-127 . -120) 165138) ((-917 . -1065) 165103) ((-718 . -102) T) ((-705 . -1067) T) ((-603 . -622) 165084) ((-591 . -622) 165065) ((-542 . -624) 164968) ((-348 . -174) T) ((-88 . -619) 164950) ((-153 . -21) T) ((-153 . -25) T) ((-917 . -111) 164906) ((-40 . -723) 164851) ((-876 . -1109) T) ((-670 . -622) 164828) ((-651 . -622) 164809) ((-360 . -622) 164746) ((-357 . -622) 164683) ((-553 . -1109) T) ((-349 . -622) 164620) ((-331 . -620) 164581) ((-331 . -619) 164493) ((-267 . -622) 164246) ((-249 . -622) 164031) ((-1240 . -798) 163984) ((-1240 . -801) 163937) ((-254 . -382) 163906) ((-253 . -382) 163875) ((-660 . -38) 163845) ((-614 . -34) T) ((-488 . -1121) 163755) ((-481 . -34) T) ((-1122 . -132) 163625) ((-971 . -25) 163436) ((-917 . -622) 163386) ((-880 . -619) 163368) ((-971 . -21) 163323) ((-821 . -21) 163233) ((-821 . -25) 163084) ((-1233 . -373) T) ((-629 . -1067) T) ((-1188 . -562) 163063) ((-1182 . -47) 163040) 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. -25) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1036 . -152) 130846) ((-878 . -826) 130825) ((-878 . -927) T) ((-718 . -290) 130752) ((-602 . -21) T) ((-344 . -652) 130711) ((-602 . -25) T) ((-601 . -21) T) ((-176 . -652) 130628) ((-40 . -732) T) ((-224 . -520) 130561) ((-601 . -25) T) ((-482 . -152) 130545) ((-469 . -152) 130529) ((-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) 130513) ((-1297 . -1060) 130497) ((-1299 . -646) 130467) ((-1166 . -1109) 130445) ((-877 . -1231) T) ((-1297 . -646) 130415) ((-660 . -619) 130397) ((-877 . -562) T) ((-700 . -373) NIL) ((-44 . -1060) 130381) ((-1306 . -622) 130363) ((-1300 . -1109) T) ((-676 . -102) T) ((-364 . -1284) 130347) ((-358 . -1284) 130331) ((-44 . -646) 130315) ((-350 . -1284) 130299) ((-554 . -102) T) ((-526 . -856) 130278) ((-1055 . -1109) T) ((-823 . -458) 130257) ((-153 . -1060) 130241) ((-1055 . -1080) 130170) 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. -1060) 114029) ((-45 . -102) T) ((-823 . -102) T) ((-1188 . -646) 113926) ((-1250 . -25) T) ((-1250 . -21) T) ((-861 . -25) T) ((-44 . -372) 113910) ((-861 . -21) T) ((-737 . -458) 113861) ((-1300 . -619) 113843) ((-1289 . -1060) 113813) ((-1063 . -313) 113751) ((-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) 113721) ((-627 . -1109) T) ((-705 . -893) 113703) ((-1277 . -1227) T) ((-229 . -313) 113641) ((-145 . -373) T) ((-1055 . -620) 113583) ((-1055 . -619) 113526) ((-317 . -916) NIL) ((-1235 . -850) T) ((-705 . -1047) 113471) ((-717 . -927) T) ((-480 . -1231) 113450) ((-1183 . -458) 113429) ((-1177 . -458) 113408) ((-334 . -102) T) ((-878 . -1121) T) ((-323 . -652) 113290) ((-320 . -654) 113111) ((-317 . -654) 113040) ((-480 . -562) 112991) ((-344 . -520) 112957) ((-556 . -152) 112907) ((-40 . -311) T) ((-849 . -619) 112889) ((-707 . -294) T) ((-878 . 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107574) ((-1300 . -1065) 107558) ((-821 . -417) 107527) ((-103 . -120) 107511) ((-130 . -1109) T) ((-52 . -1109) T) ((-933 . -619) 107493) ((-877 . -1001) 107470) ((-829 . -102) T) ((-1300 . -111) 107449) ((-659 . -38) 107419) ((-577 . -856) T) ((-360 . -1121) T) ((-357 . -1121) T) ((-349 . -1121) T) ((-267 . -1121) T) ((-249 . -1121) T) ((-629 . -311) 107398) ((-1159 . -313) 107202) ((-670 . -23) T) ((-530 . -1092) T) ((-315 . -1109) T) ((-488 . -233) 107171) ((-153 . -1067) T) ((-360 . -23) T) ((-357 . -23) T) ((-349 . -23) T) ((-118 . -311) T) ((-267 . -23) T) ((-249 . -23) T) ((-1012 . -1058) T) ((-718 . -916) 107150) ((-1166 . -622) 107127) ((-1012 . -235) 107099) ((-1012 . -245) T) ((-118 . -1031) NIL) ((-917 . -1121) T) ((-1262 . -458) 107078) ((-1241 . -458) 107057) ((-529 . -619) 106989) ((-718 . -654) 106914) ((-413 . -1065) 106866) ((-510 . -619) 106848) ((-917 . -23) T) ((-493 . -313) NIL) ((-1300 . -622) 106804) ((-480 . -132) T) ((-219 . -313) NIL) ((-413 . -111) 106742) 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. -1237) 105518) ((-521 . -25) T) ((-501 . -306) T) ((-517 . -23) T) ((-516 . -25) T) ((-514 . -25) T) ((-513 . -23) T) ((-424 . -1060) 105492) ((-413 . -1058) T) ((-323 . -1067) T) ((-700 . -311) T) ((-424 . -646) 105466) ((-108 . -854) T) ((-718 . -732) T) ((-413 . -245) T) ((-413 . -235) 105445) ((-493 . -38) 105395) ((-219 . -38) 105345) ((-480 . -499) 105311) ((-1234 . -373) T) ((-1168 . -1153) T) ((-1110 . -102) T) ((-707 . -619) 105293) ((-707 . -620) 105208) ((-720 . -21) T) ((-720 . -25) T) ((-1144 . -102) T) ((-488 . -652) 104958) ((-135 . -619) 104940) ((-117 . -619) 104922) ((-158 . -25) T) ((-1299 . -1109) T) ((-878 . -645) 104870) ((-1297 . -1109) T) ((-970 . -102) T) ((-741 . -102) T) ((-721 . -102) T) ((-459 . -102) T) ((-822 . -458) 104821) ((-44 . -1109) T) ((-1097 . -856) T) ((-1072 . -313) 104672) ((-670 . -132) T) ((-1063 . -652) 104641) ((-676 . -723) 104625) ((-293 . -1067) T) ((-360 . -132) T) ((-357 . -132) T) ((-349 . -132) T) ((-267 . -132) T) ((-249 . -132) 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T) ((-1290 . -1227) T) ((-1122 . -417) 102460) ((-612 . -102) T) ((-1086 . -1227) T) ((-1012 . -373) NIL) ((-677 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1188 . -652) 102370) ((-743 . -1227) T) ((-737 . -1060) 102213) ((-44 . -767) T) ((-737 . -646) 102062) ((-599 . -102) T) ((-77 . -402) T) ((-77 . -401) T) ((-659 . -662) 102046) ((-142 . -1227) T) ((-877 . -148) T) ((-877 . -146) NIL) ((-1226 . -93) T) ((-356 . -1058) T) ((-70 . -388) T) ((-70 . -401) T) ((-1175 . -102) T) ((-676 . -520) 101979) ((-1289 . -652) 101924) ((-695 . -313) 101862) ((-970 . -38) 101759) ((-1190 . -619) 101741) ((-741 . -38) 101711) ((-556 . -313) 101515) ((-1184 . -1060) 101398) ((-320 . -1227) T) ((-356 . -235) T) ((-356 . -245) T) ((-317 . -1227) T) ((-293 . -1109) T) ((-1183 . -1060) 101233) ((-1177 . -1060) 101023) ((-1135 . -1060) 100906) ((-1184 . -646) 100803) ((-1183 . -646) 100644) ((-717 . -1231) T) ((-1177 . -646) 100440) ((-1166 . -657) 100424) ((-1135 . -646) 100321) ((-1221 . -562) 100300) ((-825 . -391) 100284) ((-717 . -562) T) ((-320 . -891) 100268) ((-320 . -893) 100193) ((-137 . -1227) T) ((-317 . -891) 100154) ((-317 . -893) NIL) ((-805 . -313) 100119) ((-323 . -723) 99960) ((-392 . -391) 99944) ((-328 . -327) 99921) ((-491 . -102) T) ((-480 . -25) T) ((-480 . -21) T) ((-424 . -38) 99895) ((-320 . -1047) 99558) ((-227 . -1212) T) ((-227 . -1215) T) ((-3 . -619) 99540) ((-317 . -1047) 99470) ((-2 . -1109) T) ((-2 . |RecordCategory|) T) ((-839 . -619) 99452) ((-1122 . -1067) 99382) ((-586 . -927) T) ((-570 . -826) T) ((-570 . -927) T) ((-501 . -927) T) ((-137 . -1047) 99366) ((-227 . -95) T) ((-171 . -148) 99345) ((-75 . -447) T) ((0 . -619) 99327) ((-75 . -401) T) ((-171 . -146) 99278) ((-227 . -35) T) ((-49 . -619) 99260) ((-483 . -1067) T) ((-493 . -233) 99242) ((-490 . -977) 99226) ((-488 . -854) 99205) ((-219 . -233) 99187) ((-81 . -447) T) ((-81 . -401) T) ((-1155 . -34) T) ((-821 . -174) 99166) 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-38) 98282) ((-267 . -645) 98230) ((-249 . -645) 98178) ((-707 . -1065) 98165) ((-601 . -1255) 98142) ((-1135 . -288) 98108) ((-323 . -174) 98039) ((-364 . -1109) T) ((-358 . -1109) T) ((-350 . -1109) T) ((-506 . -19) 98021) ((-1129 . -1047) 98003) ((-1111 . -152) 97987) ((-108 . -1109) T) ((-117 . -1065) 97974) ((-717 . -368) T) ((-506 . -610) 97949) ((-707 . -111) 97934) ((-442 . -102) T) ((-882 . -1272) T) ((-252 . -102) T) ((-45 . -1158) 97884) ((-117 . -111) 97869) ((-1302 . -619) 97836) ((-641 . -726) T) ((-613 . -726) T) ((-1302 . -496) 97818) ((-1279 . -619) 97800) ((-1235 . -619) 97782) ((-1233 . -856) T) ((-1221 . -1121) T) ((-821 . -520) 97715) ((-1044 . -1227) T) ((-242 . -1060) 97612) ((-1221 . -23) T) ((-1182 . -458) 97543) ((-950 . -152) 97527) ((-1177 . -313) 97412) ((-1176 . -1109) T) ((-242 . -646) 97354) ((-1168 . -1109) T) ((-1151 . -654) 97328) ((-1135 . -313) 97315) ((-531 . -102) T) ((-526 . -102) 97265) ((-1134 . -458) 97216) ((-1096 . -562) 97147) ((-1096 . -1231) 97126) ((-788 . -1231) 97105) ((-786 . -1231) 97084) ((-62 . -1227) T) ((-483 . -619) 97036) ((-483 . -620) 96958) ((-1089 . -723) 96826) ((-1003 . -1109) T) ((-788 . -562) 96737) ((-786 . -562) 96668) ((-488 . -417) 96637) ((-629 . -927) 96616) ((-460 . -1231) 96595) ((-737 . -313) 96582) ((-707 . -622) 96554) ((-404 . -619) 96536) ((-681 . -520) 96469) ((-670 . -25) T) ((-670 . -21) T) ((-460 . -562) 96400) ((-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) 96382) ((-117 . -622) 96354) ((-1013 . -1060) 96304) ((-1013 . -646) 96254) ((-950 . -989) 96238) ((-921 . -646) 96190) ((-921 . -1060) 96142) ((-917 . -21) T) ((-917 . -25) T) ((-878 . -856) 96093) ((-872 . -654) 96053) ((-717 . -1121) T) ((-717 . -23) T) ((-707 . -1058) T) ((-293 . -174) T) ((-707 . -235) T) ((-315 . 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88701) ((-483 . -1065) 88666) ((-664 . -132) T) ((-627 . -622) 88635) ((-1122 . -520) 88568) ((-341 . -132) T) ((-171 . -408) 88547) ((-488 . -723) 88489) ((-821 . -290) 88466) ((-483 . -111) 88422) ((-659 . -1067) T) ((-822 . -1060) 88265) ((-1288 . -1092) T) ((-1250 . -458) 88196) ((-822 . -646) 88045) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87987) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87920) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-1008 . -1227) 87889) ((-45 . -1109) T) ((-390 . -723) 87859) ((-823 . -1109) T) ((-482 . -520) 87792) ((-469 . -520) 87725) ((-1302 . -622) 87707) ((-459 . -372) 87677) ((-45 . -616) 87656) ((-320 . -306) T) ((-483 . -622) 87606) ((-1241 . -313) 87491) ((-676 . -619) 87453) ((-59 . -856) 87432) ((-1013 . -406) 87414) ((-554 . -619) 87396) ((-805 . -652) 87355) ((-821 . -610) 87332) ((-522 . -856) 87311) ((-502 . -856) 87290) ((-40 . -1231) T) ((-1008 . 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-313) 81749) ((-970 . -417) 81733) ((-705 . -1231) T) ((-638 . -290) 81686) ((-1096 . -645) 81634) ((-788 . -645) 81582) ((-786 . -645) 81530) ((-348 . -132) T) ((-293 . -619) 81512) ((-912 . -1109) T) ((-705 . -562) T) ((-130 . -622) 81494) ((-876 . -1121) T) ((-460 . -645) 81442) ((-912 . -910) 81426) ((-384 . -458) T) ((-493 . -1109) T) ((-950 . -313) 81364) ((-707 . -654) 81351) ((-555 . -850) T) ((-219 . -1109) T) ((-320 . -927) 81330) ((-317 . -927) T) ((-317 . -826) NIL) ((-396 . -726) T) ((-876 . -23) T) ((-117 . -654) 81317) ((-480 . -146) 81296) ((-424 . -417) 81280) ((-480 . -148) 81259) ((-110 . -495) 81241) ((-315 . -622) 81222) ((-2 . -619) 81204) ((-188 . -102) T) ((-1168 . -19) 81186) ((-1168 . -610) 81161) ((-664 . -21) T) ((-664 . -25) T) ((-599 . -1153) T) ((-1122 . -290) 81138) ((-341 . -25) T) ((-341 . -21) T) ((-242 . -652) 80888) ((-501 . -368) T) ((-1292 . -38) 80858) ((-1182 . -1060) 80681) ((-1151 . -1227) T) ((-1134 . -1060) 80524) ((-860 . -1060) 80508) 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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 6f2ef46d..983c4b93 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3485354327) +(30 . 3485439393) (4455 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -484,668 +484,665 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |sqfree| |readLine!| |clipParametric| - |pointColorDefault| |monicRightDivide| |mkAnswer| |subtractIfCan| - |pointColor| |stoseIntegralLastSubResultant| |addPoint2| |sdf2lst| - |set| |merge| |diag| |normalizedDivide| |uniform01| |powern| - |expenseOfEvaluation| |doubleDisc| |iisin| |setsubMatrix!| - |virtualDegree| |factorFraction| |componentUpperBound| |viewDefaults| - |hermite| |whatInfinity| |rationalPoint?| |collect| |musserTrials| - |wholePart| |myDegree| |slex| |f02wef| |RemainderList| |superscript| - |surface| |s17dcf| |latex| |elaborateFile| |Vectorise| |lists| - |rootRadius| |numberOfFractionalTerms| |cyclotomicFactorization| - |internalSubQuasiComponent?| |bernoulli| |categoryFrame| |setRow!| - |laguerreL| |cartesian| |f02bbf| |coerceP| |factorGroebnerBasis| - |splitLinear| |OMcloseConn| |subTriSet?| |complexNormalize| - |numberOfPrimitivePoly| |quote| |octon| |front| |OMgetEndBind| - |sturmVariationsOf| |distFact| |fractionPart| |laplace| |signature| - |zoom| |realElementary| |monomials| |curve?| |henselFact| - |traceMatrix| |nonQsign| |infinityNorm| |weighted| |d02cjf| - |viewDeltaYDefault| |monomialIntPoly| |asinhIfCan| |bigEndian| |tanNa| - |cylindrical| |rightMinimalPolynomial| |fortranLiteral| |search| - |nextPrime| |expr| |stoseInvertible?reg| |algintegrate| |predicates| - |subSet| |fullDisplay| |Lazard| - |generalizedContinuumHypothesisAssumed| |listYoungTableaus| - |cyclotomic| |hostPlatform| |setEpilogue!| |e01sbf| |groebner?| - |trapezoidalo| |polyPart| |backOldPos| |outputList| |chvar| - |commaSeparate| |factorList| |univariatePolynomialsGcds| - |closedCurve?| |kroneckerDelta| |mathieu12| |leftUnit| |OMgetEndError| - |generalizedInverse| |parts| |inputOutputBinaryFile| |show| - |difference| |lastSubResultant| |removeSuperfluousCases| |startTable!| - |replaceKthElement| |rootBound| |bitCoef| |rename!| |dimension| - |getZechTable| |seriesToOutputForm| |mainKernel| |complete| |ldf2lst| - |variable| |compBound| |setleaves!| |deref| |distribute| |primitive?| - |oneDimensionalArray| |datalist| |firstSubsetGray| |trace| |iiasec| - |f02adf| |palgRDE0| |iterators| |minset| |intermediateResultsIF| - |linearAssociatedExp| |f02ajf| |f01bsf| |associator| - |regularRepresentation| |subst| |mathieu23| |completeEchelonBasis| - |iisech| |removeRoughlyRedundantFactorsInPol| |iterationVar| - |createPrimitivePoly| |LyndonWordsList| |systemCommand| - |OMencodingUnknown| |transcendentalDecompose| |fortranComplex| - |removeSinhSq| |leftExactQuotient| |char| |checkPrecision| - |palginfieldint| |OMUnknownCD?| |duplicates?| |karatsubaDivide| - |associates?| |OMconnOutDevice| |mergeFactors| |bombieriNorm| - |linearPolynomials| |collectQuasiMonic| |bitior| |rowEch| |iFTable| - |dimensionOfIrreducibleRepresentation| |solveInField| |linGenPos| - |localReal?| |precision| |irreducible?| |removeSinSq| |e02daf| - |points| |double?| |s17dhf| |makeFloatFunction| |getPickedPoints| - |FormatArabic| |normal| |UpTriBddDenomInv| |contract| - |internalInfRittWu?| |reducedQPowers| |outputGeneral| |imagI| - |insertionSort!| |readUInt32!| |acscIfCan| |multiple?| |cond| - |normalElement| |ip4Address| |cSinh| |concat| |squareFreePart| - |integerBound| |delete!| |lintgcd| |f04asf| |simplifyPower| |edf2efi| - |sech| |operators| |heapSort| |inspect| |maxRowIndex| |objects| - |subPolSet?| |simplifyExp| |expintfldpoly| |OMputObject| |triangulate| - |hasSolution?| |csch| |f07fef| |listOfLists| |rootOfIrreduciblePoly| - |jacobi| |base| |changeBase| |float| |cycleTail| |maximumExponent| - |primitiveElement| |tubePlot| |firstUncouplingMatrix| |OMgetType| - |asinh| |f07adf| |loopPoints| |Nul| |cCsch| |setAdaptive3D| - |diagonals| |pomopo!| |dominantTerm| |lazyGintegrate| |acosh| - |nullary?| |leftAlternative?| |OMsupportsCD?| |prinpolINFO| |s17aef| - |kind| |nthCoef| |critMonD1| |basisOfLeftAnnihilator| |getIdentifier| - |getOperator| |arg1| |showTheIFTable| |f01rcf| |atanh| |represents| - |halfExtendedResultant1| |leftQuotient| |ref| |head| |rotatex| |op| - |preprocess| |approximants| |clipPointsDefault| |aromberg| |arg2| - |clearTheSymbolTable| |conjugate| |acoth| |range| - |removeSuperfluousQuasiComponents| |cCsc| |diagonalMatrix| |leftTrace| - |leftGcd| |elliptic?| |d01alf| |safetyMargin| |unitNormal| - |rightFactorCandidate| |asech| |generateIrredPoly| |numer| |epilogue| - |cotIfCan| |mightHaveRoots| |charClass| |spherical| |OMputApp| - |conditions| |nlde| |ridHack1| |OMputAttr| |empty| |box| |variables| - |denom| |OMgetEndAttr| |bumptab| |cup| |iiGamma| |solid| - |explimitedint| |nextsousResultant2| |groebnerFactorize| |match| - |options| |multiple| |sizeLess?| |shuffle| |numberOfNormalPoly| - |harmonic| |zeroVector| |e01sef| |gbasis| |stoseInvertible?sqfreg| - |writeLine!| |applyQuote| |invertIfCan| |palglimint| |f01qdf| - |totalfract| |pi| |errorInfo| |tree| |iidsum| |OMreadFile| - |setRealSteps| |any| |exprToXXP| |OMgetObject| |nullity| |f02axf| - |infinity| |rdregime| |rootOf| |union| |resultant| |exptMod| - |viewDeltaXDefault| |binding| |GospersMethod| |string| - |primeFrobenius| |viewZoomDefault| |OMlistSymbols| |tanIfCan| - |discreteLog| |tab1| |cycle| |listBranches| |bipolarCylindrical| - |column| |ruleset| |s14abf| |bivariateSLPEBR| |extract!| |bag| - |previous| |setClipValue| |trailingCoefficient| |selectPDERoutines| - |repeating?| |minimize| |birth| |imagk| |totalDegree| |kernel| - |leftFactor| |stoseInternalLastSubResultant| - |rightCharacteristicPolynomial| |e02bbf| |mulmod| |iitanh| - |leftCharacteristicPolynomial| |palglimint0| |innerSolve| |cfirst| - |list| |complexNumeric| |halfExtendedResultant2| |bat1| |cPower| - |normal01| |makeFR| |submod| |permanent| |suchThat| |mapMatrixIfCan| - |e04dgf| |multiEuclideanTree| |readByte!| |draw| - |mainCharacterization| |before?| |youngGroup| |integrate| |csubst| - |OMputAtp| |toseLastSubResultant| |radPoly| |consnewpol| - |validExponential| |complexElementary| |purelyAlgebraic?| |ode| - |iicsch| |sinhIfCan| |extendedEuclidean| |leftPower| |vconcat| - |torsionIfCan| |extendIfCan| |identity| |innerSolve1| |lfextendedint| - |nextItem| |subMatrix| |setref| - |solveLinearPolynomialEquationByRecursion| - |ScanFloatIgnoreSpacesIfCan| |sequences| |patternVariable| - |primPartElseUnitCanonical!| |lazyPquo| |constantKernel| |curryLeft| - |removeRedundantFactorsInContents| |quadratic| |asecIfCan| - |minimalPolynomial| |f04mbf| |ODESolve| |exponential| |univcase| - |quoByVar| |makeObject| |simpleBounds?| |simplifyLog| |ef2edf| - |enterPointData| |OMputEndBVar| |numberOfComputedEntries| - |returnTypeOf| |showAllElements| |center| |logIfCan| - |tubePointsDefault| |coef| |simplify| |constant?| |quotedOperators| - |unmakeSUP| |inR?| |stack| |topFortranOutputStack| |solveid| - |dequeue!| |subNodeOf?| |cot2tan| |label| |exprHasWeightCosWXorSinWX| - |digits| |iicos| |att2Result| |quasiComponent| |constantLeft| - |makeMulti| |csch2sinh| |fullPartialFraction| |setvalue!| |name| - |d01gbf| |OMgetEndApp| |antiCommutator| |discriminant| |s20adf| - |typeForm| |constantToUnaryFunction| |supersub| |closed?| - |coercePreimagesImages| |endOfFile?| |body| |hexDigit?| - |chineseRemainder| |readUInt16!| |slash| |OMbindTCP| |cAcosh| - |nthRoot| |monicDecomposeIfCan| |mapDown!| |wordInStrongGenerators| - |quadratic?| |interpret| |pdct| |light| |lastSubResultantElseSplit| - |fTable| |nextSubsetGray| |pol| |quasiMonic?| |coerceImages| - |subCase?| |sequence| |algebraicDecompose| |repSq| |selectsecond| - |aQuartic| |createMultiplicationTable| |setLength!| |extractProperty| - |dihedral| |setVariableOrder| |addPoint| |extend| |getCode| - |pmintegrate| |Ci| |dequeue| |remainder| |point| |s21bdf| |length| - |stiffnessAndStabilityOfODEIF| |nextPrimitiveNormalPoly| - |linearMatrix| |f07aef| |palgLODE0| |cAsin| |roman| - |symmetricRemainder| |cyclicSubmodule| |coord| |scripts| - |createNormalElement| |iiabs| |squareFreePrim| - |getSyntaxFormsFromFile| |cAsech| |exQuo| |characteristic| |option| - |asechIfCan| |semiResultantEuclidean2| |sinhcosh| |leadingSupport| - |showTheSymbolTable| |basisOfLeftNucleus| |insertRoot!| |tubePoints| - |elRow1!| SEGMENT |bindings| |sign| |series| |cTan| - |zeroSetSplitIntoTriangularSystems| |bitTruth| |zCoord| |port| - |binary| |hspace| |df2fi| |createLowComplexityTable| |prod| - |stopTable!| |conditionP| |definingEquations| - |basisOfRightAnnihilator| |complexNumericIfCan| |low| |clikeUniv| - |gensym| |bandedJacobian| |testDim| |stronglyReduced?| |f02agf| - |showClipRegion| |swapRows!| |leaf?| |t| |leastMonomial| |minordet| - |invertibleElseSplit?| |fortranTypeOf| |divideIfCan!| |setErrorBound| - |substitute| |wholeRagits| |f01mcf| |list?| |df2st| |duplicates| - |makeEq| |s13adf| |OMopenFile| |outputMeasure| |min| - |numericalOptimization| |pureLex| |leastPower| |completeHermite| - |lyndon| |rdHack1| |atrapezoidal| |infRittWu?| |fixPredicate| - |mapExpon| |reducedDiscriminant| |inconsistent?| |extractClosed| - |leftRecip| |headReduced?| |imagJ| |viewWriteDefault| - |binaryTournament| |elaborate| |accuracyIF| |identification| - |viewPhiDefault| |eigenvectors| |fibonacci| |nthr| |univariate?| - |baseRDEsys| |createThreeSpace| |zeroSquareMatrix| |cSin| - |expandTrigProducts| |certainlySubVariety?| |digit?| |scalarMatrix| - |euclideanSize| |eulerPhi| |unknown| |apply| |completeHensel| |d02bbf| - |leadingExponent| |any?| |functionIsContinuousAtEndPoints| - |firstNumer| |key?| |internalIntegrate0| |isAtom| |associative?| - |relerror| |first| |s13aaf| |radicalSolve| |separate| |shiftLeft| - |rightRank| |OMencodingBinary| |integralCoordinates| |fortranInteger| - |currentSubProgram| |xor| |imag| |d01anf| |rk4f| |rest| - |constantOperator| |binaryFunction| |getMultiplicationMatrix| - |nthExponent| |quasiAlgebraicSet| |directProduct| |rst| |vspace| - |case| |chebyshevT| |elementary| |prem| |perfectNthPower?| - |algebraicCoefficients?| |cCosh| |trigs| |index?| |rowEchelonLocal| - |LazardQuotient| |d01fcf| |Zero| |LyndonBasis| |setelt!| |UP2ifCan| - |taylorQuoByVar| |keys| |comp| |true| |extendedint| |sech2cosh| - |enterInCache| |void| |evenInfiniteProduct| |One| |top| |denominator| - |middle| |cExp| |nil?| |multMonom| |pade| |capacity| |fixedPoint| - |pointData| |leftRank| |digit| |continue| |c06fpf| |redpps| |reduced?| - |addMatch| |quasiRegular| |legendre| |crushedSet| |mainSquareFreePart| - |sort| |plusInfinity| |edf2ef| |rarrow| |revert| |functorData| |shape| - |expandLog| |adaptive3D?| |multinomial| |bits| |compose| - |minusInfinity| |setnext!| |setMaxPoints3D| |setEmpty!| - |radicalOfLeftTraceForm| |e04fdf| |leftTraceMatrix| |makeSeries| - |closedCurve| |critM| |complexIntegrate| |mainVariable?| |reorder| - |pquo| |id| |algDsolve| |times!| |scan| |repeatUntilLoop| - |setLegalFortranSourceExtensions| |polygon?| |mainVariables| |nodeOf?| - |bezoutResultant| |ratDenom| |setAttributeButtonStep| |bat| |elt| - |minPoints3D| |OMputEndError| |lo| |rowEchLocal| |OMconnectTCP| |cLog| - |argumentListOf| |isOr| |random| |wordsForStrongGenerators| - |antisymmetricTensors| |monicModulo| |sqfrFactor| |primaryDecomp| - |next| |iibinom| |recip| |chiSquare| |positiveSolve| |rubiksGroup| - |mix| |has?| |leftRankPolynomial| |decrease| |divide| |external?| - |startStats!| |drawToScale| |f01qef| |rectangularMatrix| |eq?| - |e02dcf| |possiblyNewVariety?| |mathieu24| |indiceSubResultant| - |eigenvalues| |terms| |transform| |laplacian| |divisorCascade| - |OMencodingXML| |infix| |enqueue!| |reducedSystem| |stronglyReduce| - |sub| |cschIfCan| |iiasinh| |subHeight| |imaginary| - |associatedEquations| |commutative?| |printStats!| - |createNormalPrimitivePoly| |rk4qc| |s17dlf| - |subResultantGcdEuclidean| |decomposeFunc| |open?| |scopes| - |bezoutMatrix| |tubeRadiusDefault| |someBasis| - |lastSubResultantEuclidean| |insert| |replace| |iiacos| - |roughSubIdeal?| |generic| |ratDsolve| |iiasech| |ramifiedAtInfinity?| - |isExpt| |composite| |palgint0| |c06eaf| |leader| |reduceLODE| - |OMputBVar| |mkPrim| |OMgetInteger| |returns| |sts2stst| |groebgen| - |explicitEntries?| |besselK| |normalize| |stoseInvertibleSetreg| - |incrementKthElement| |meshFun2Var| |lowerCase| |factorOfDegree| - |rewriteIdealWithRemainder| |setFieldInfo| |cdr| |sample| - |setScreenResolution3D| |distance| |explicitlyEmpty?| |thenBranch| - |internalZeroSetSplit| |categoryMode| |besselI| |plus!| |determinant| - |jordanAdmissible?| |Aleph| |rationalIfCan| |clip| |compound?| - |removeRoughlyRedundantFactorsInContents| |lprop| |writeUInt8!| - |minColIndex| |droot| |derivative| |axes| |physicalLength!| - |selectODEIVPRoutines| |pointColorPalette| |back| - |fortranDoubleComplex| |viewThetaDefault| |f02xef| |rischDE| - |collectUnder| |shanksDiscLogAlgorithm| |leadingIndex| |reduction| - |asimpson| |factorset| |iiperm| |simpsono| |makeSketch| |newTypeLists| - |symbolTable| |ipow| |internalIntegrate| |OMUnknownSymbol?| |uniform| - |primeFactor| |dfRange| |sin?| |realSolve| |findConstructor| - |normalized?| |taylorIfCan| |cTanh| |getDatabase| |anfactor| - |cycleRagits| |mainCoefficients| |whileLoop| |iiacsch| - |pushFortranOutputStack| |anticoord| |torsion?| |s19adf| - |structuralConstants| |integralLastSubResultant| |checkForZero| |bit?| - |credPol| |untab| |popFortranOutputStack| |dflist| |width| - |symmetricDifference| |lagrange| |approxSqrt| |super| |dual| |hessian| - |redPo| |outputAsFortran| |ParCondList| |sec2cos| |supDimElseRittWu?| - |setTex!| |tab| |elseBranch| |signatureAst| |fintegrate| Y |lookup| - |initiallyReduced?| |graphs| |nor| |genericLeftMinimalPolynomial| - |coerceS| |interactiveEnv| |bsolve| |Hausdorff| |iicsc| |binomThmExpt| - |cycles| |ranges| |maxrow| |internalLastSubResultant| |permutations| - |s17dgf| |shufflein| |graphState| |swap!| |splitNodeOf!| - |resetVariableOrder| |identityMatrix| |expressIdealMember| |region| - |limitedIntegrate| |newReduc| |gradient| |clearCache| - |numberOfOperations| |c05pbf| |knownInfBasis| |lift| |table| |arity| - |wordInGenerators| |compdegd| |realEigenvectors| |whitePoint| - |argscript| |euler| |disjunction| |f02aaf| |reduce| |new| |pushdown| - |argumentList!| |integralDerivationMatrix| |obj| |readInt32!| - |integralBasisAtInfinity| |gcdprim| |gcdcofact| |BasicMethod| - |ScanRoman| |rischDEsys| |d03edf| |cache| |patternMatch| - |subresultantSequence| |lookupFunction| |nextPartition| - |iflist2Result| |cyclic?| |li| |d01akf| |hex| |deepExpand| - |factorSquareFreeByRecursion| |cot2trig| |c06gcf| |c06gqf| |cAsinh| - |maxColIndex| |viewpoint| |iExquo| |selectOrPolynomials| - |singleFactorBound| |pseudoDivide| |sumOfSquares| |OMunhandledSymbol| - |lowerCase!| |nary?| |fractionFreeGauss!| |factor| - |parabolicCylindrical| |seed| |sinh2csch| |karatsubaOnce| - |viewPosDefault| |generalTwoFactor| |iCompose| |roughBase?| |tanAn| - |changeNameToObjf| |noValueMode| |remove!| |pointLists| |pow| - |generalInfiniteProduct| |innerint| |startTableInvSet!| |curryRight| - |bipolar| |readable?| |vector| |subspace| |symmetricGroup| - |extractIndex| |OMgetAttr| |numberOfComposites| |trunc| |tableau| - |hclf| |maxPoints3D| |moebius| |differentiate| |innerEigenvectors| - |quasiMonicPolynomials| |invmultisect| |ceiling| |subResultantGcd| - |isImplies| |predicate| |lowerBound| |oblateSpheroidal| |secIfCan| - |fracPart| |airyBi| |factorials| |normalizeAtInfinity| |reify| - |typeLists| |rational?| |diff| |s21bbf| |toseInvertibleSet| |powerSum| - |constantIfCan| |ord| |size| |decreasePrecision| |weierstrass| |left| - ** |indices| |monomial| |endSubProgram| |dom| |test| |isPower| - |insertTop!| |fixedPointExquo| |getMultiplicationTable| |nextColeman| - |byte| |setPosition| |processTemplate| |right| |multivariate| - |printInfo!| |plotPolar| |univariatePolynomials| |resultantEuclidean| - |acosIfCan| |cCos| |symFunc| |escape| |edf2df| |elliptic| |linear| - 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|addBadValue| |graeffe| |nsqfree| |thetaCoord| |qelt| |explogs2trigs| - |retractable?| |singularitiesOf| |antiCommutative?| |normInvertible?| - |SturmHabichtSequence| |qsetelt| |reverse!| |hasoln| |e02gaf| - |string?| |part?| |selectNonFiniteRoutines| |genericPosition| - |inGroundField?| |imagE| |indiceSubResultantEuclidean| |type| - |safeFloor| |s18adf| |exactQuotient!| |resultantEuclideannaif| |rem| - |xRange| |e02bdf| |coefficients| |sorted?| |generators| |writeInt8!| - |mainVariable| |variable?| |critpOrder| |stFuncN| |quo| |yRange| - |solveLinearPolynomialEquation| |initial| |space| |isTimes| |rroot| - |zeroDim?| |cons| |degreeSubResultant| |chebyshevU| |infiniteProduct| - |zRange| |pole?| |domainTemplate| |create| |dmpToHdmp| |null?| |dim| - |map!| |palgintegrate| |meshPar2Var| |interval| |div| |evaluate| - |factorSFBRlcUnit| |resultantReduit| |computeBasis| |normalise| - |bezoutDiscriminant| |qsetelt!| |failed?| |ReduceOrder| |exquo| - |adaptive?| |useEisensteinCriterion?| |vark| |log2| |setClosed| - 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|mainValue| |cAcoth| |overbar| |minus!| |stoseInvertibleSet| - |linearPart| |userOrdered?| |write| |listRepresentation| |abs| |inc| - |aspFilename| |eval| |radix| |computeCycleEntry| |FormatRoman| - |zeroMatrix| |hdmpToP| |setelt| |save| |abelianGroup| |intensity| - |nonLinearPart| |ScanArabic| |principalAncestors| |asinIfCan| |sn| - |viewport3D| |hostByteOrder| |youngDiagram| |rootProduct| |randnum| - |sumOfDivisors| |pile| |number?| |rightExactQuotient| |minPoints| - |besselJ| |expenseOfEvaluationIF| |intcompBasis| |connectTo| |ode1| - |copy| |entry?| |fixedDivisor| |cAtanh| |geometric| |sh| |error| - |prolateSpheroidal| |rotatey| |screenResolution| |compiledFunction| - |changeWeightLevel| |se2rfi| |squareFreeFactors| EQ |imagi| - |alternatingGroup| |LazardQuotient2| |atoms| |drawStyle| |rCoord| - |OMputInteger| |pToDmp| |infLex?| |rightPower| |normDeriv2| - |setchildren!| |purelyAlgebraicLeadingMonomial?| |partialDenominators| - |leviCivitaSymbol| |prepareDecompose| |roughBasicSet| - 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|parent| |genericLeftDiscriminant| |linearlyDependentOverZ?| - |jacobian| |tanh2coth| |useNagFunctions| |setValue!| |SturmHabicht| - |dualSignature| |redPol| |exprHasLogarithmicWeights| - |indicialEquations| |oddintegers| |copies| |defineProperty| - |idealSimplify| |print| |makeSin| |eulerE| |sup| |properties| - |intChoose| |rational| |fillPascalTriangle| |fortranLinkerArgs| - |infix?| |drawComplex| |integralAtInfinity?| |resolve| |cAcsc| - |translate| |s14aaf| |exponential1| |subscriptedVariables| |mask| - |row| |declare| |symbolTableOf| |htrigs| |alphabetic?| |complexForm| - |f02bjf| |logical?| |pToHdmp| |decimal| |reverseLex| - |selectPolynomials| |appendPoint| |unitVector| |ratpart| - |sturmSequence| |rationalPower| |e04naf| |invertibleSet| - |cyclicEntries| |routines| |lazyIntegrate| |direction| |twist| - |linearDependence| |controlPanel| |hasHi| |acotIfCan| |f02aff| - |tanh2trigh| |HermiteIntegrate| |semicolonSeparate| GE - |lineColorDefault| |cAsec| |setOrder| |eigenvector| |child?| |order| - 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|nrows| |bfEntry| |support| |complexEigenvectors| |realEigenvalues| - |read!| |brillhartTrials| |opeval| |setLabelValue| |dAndcExp| |f01ref| - |taylorRep| |ncols| |result| |OMputEndAtp| UTS2UP |select!| - |OMgetFloat| |isConnected?| |iisec| |forLoop| |notelem| |cAtan| - |minrank| |unit?| |monicCompleteDecompose| |lazyEvaluate| - |readLineIfCan!| |bernoulliB| |coefficient| |isMult| |leadingTerm| - |complexEigenvalues| |sylvesterSequence| |karatsuba| |fixedPoints| - |screenResolution3D| |goodnessOfFit| |mainPrimitivePart| |f04mcf| - |eigenMatrix| |tower| |removeZero| |basisOfRightNucleus| |lex| - |intPatternMatch| |e02agf| |repeating| |color| - |stoseInvertibleSetsqfreg| |extractIfCan| |increment| |listLoops| - |primintegrate| |computeCycleLength| |trim| |updatF| |digamma| |mat| - |inHallBasis?| |mesh| |triangularSystems| |blankSeparate| |conjugates| - |exactQuotient| |taylor| |setleft!| |comment| |fractRadix| - |removeRedundantFactors| |debug3D| |minimumDegree| |solveRetract| - |positiveRemainder| |upperCase!| |logGamma| |matrixGcd| - |differentialVariables| |laurent| |heap| |unvectorise| - |perfectNthRoot| |insert!| |groebnerIdeal| |normalForm| |getRef| - |normalizedAssociate| |setButtonValue| |tan2trig| |leadingBasisTerm| - |puiseux| |lepol| |normFactors| |showTheRoutinesTable| |tube| - |squareFree| |matrix| |cyclicEqual?| |cyclic| |index| |s17ahf| - |OMgetVariable| |numerators| |genericRightMinimalPolynomial| - |semiResultantEuclideannaif| |lambda| |close!| |e02zaf| |max| - |closeComponent| |unitNormalize| |meshPar1Var| |lazyPseudoQuotient| - |yCoordinates| |normalizeIfCan| |lexGroebner| |printTypes| |inv| - |leadingCoefficientRicDE| |dn| |getlo| |separateFactors| |polyred| - |fortranReal| |splitConstant| |byteBuffer| |swap| |ground?| - |setfirst!| |qroot| |newSubProgram| |components| |changeThreshhold| - |pdf2ef| |completeEval| |prindINFO| |less?| |vertConcat| |parametric?| - |pair| |equality| |getProperty| |module| |content| |s01eaf| - |rewriteSetWithReduction| |ground| |stoseInvertible?| - |partialNumerators| |exp1| |quoted?| |createRandomElement| - 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|selectMultiDimensionalRoutines| |ldf2vmf| |in?| |bothWays| - |variationOfParameters| |removeRoughlyRedundantFactorsInPols| |root?| - |iroot| |balancedBinaryTree| |showRegion| |resetAttributeButtons| - |vedf2vef| |s18aff| |contains?| |factorSquareFree| |perspective| - |numberOfVariables| |prefixRagits| |lllip| |listexp| |stFunc2| FG2F - |nonSingularModel| |leastAffineMultiple| |pair?| |complex?| - |irreducibleRepresentation| |numFunEvals3D| |bivariatePolynomials| - |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| |OMputEndBind| |middle| |bottom!| |member?| + |wrregime| |multiEuclideanTree| |clipWithRanges| + |subresultantSequence| |measure| |cExp| |ddFact| |set| |pleskenSplit| + |e02ahf| |pointSizeDefault| |readByte!| |lookupFunction| |e02def| + |toseInvertible?| |inverseColeman| |nil?| |lexTriangular| |property| + |interReduce| |mainCharacterization| |setIntersection| |nextPartition| + |monomial?| |iiexp| |multMonom| |setPoly| |collectUpper| + |scanOneDimSubspaces| |before?| |iflist2Result| |s21baf| |unit| + |polynomialZeros| |pade| |unknownEndian| |e01saf| |maxdeg| + |youngGroup| |parent| |cyclic?| |doubleComplex?| |lists| |capacity| + |badNum| |s15aef| |traverse| |finite?| |integrate| + |genericLeftDiscriminant| |d01akf| |llprop| |fixedPoint| |getCurve| + |exportedOperators| |alphanumeric| |cosIfCan| |signature| |csubst| + |hex| |linearlyDependentOverZ?| |curveColor| |minPol| |pointData| + |ratPoly| |branchPointAtInfinity?| |removeDuplicates!| |coerceP| + |OMputAtp| |deepExpand| |jacobian| |isobaric?| |leftRank| |ocf2ocdf| + |nextsubResultant2| |search| |phiCoord| |continuedFraction| |expr| + |factorGroebnerBasis| |toseLastSubResultant| + |factorSquareFreeByRecursion| |tanh2coth| |tValues| |digit| + |OMputEndApp| |OMread| |dihedralGroup| |currentScope| |radPoly| + |useNagFunctions| |cot2trig| |sayLength| |outputList| |c06fpf| + |viewWriteAvailable| |weakBiRank| |changeMeasure| |minPoly| + |consnewpol| |c06gcf| |setValue!| |iitan| |solve1| |show| |redpps| + |f04adf| |getVariableOrder| |nextPrimitivePoly| |validExponential| + |c06gqf| |SturmHabicht| |node?| |OMsend| |reduced?| |convergents| + |selectFiniteRoutines| |c05adf| |variable| |complexElementary| + |dualSignature| |cAsinh| |quotient| |primintfldpoly| |trace| + |addMatch| |readBytes!| |upperBound| |boundOfCauchy| |iterators| + |listYoungTableaus| |purelyAlgebraic?| |redPol| |maxColIndex| + |printStatement| |factorList| |rightExtendedGcd| |quasiRegular| + |position!| |atanIfCan| |datalist| |areEquivalent?| |cyclotomic| + |systemCommand| |ode| |exprHasLogarithmicWeights| |viewpoint| |d02kef| + |char| |univariatePolynomialsGcds| |subst| |checkPrecision| + |perfectSqrt| |legendre| |hconcat| |hasPredicate?| |expint| |iicsch| + |iExquo| |indicialEquations| |belong?| |bitior| |crushedSet| + |initiallyReduce| |swapColumns!| |permutationGroup| |move| |sinhIfCan| + |selectOrPolynomials| |oddintegers| |critMTonD1| |socf2socdf| + |mainSquareFreePart| |e04mbf| |imagK| |reducedContinuedFraction| + |extendedEuclidean| |precision| |normal| |copies| |singleFactorBound| + |purelyTranscendental?| |edf2ef| |redmat| |s20acf| |binomial| |refine| + |cond| |defineProperty| |pseudoDivide| |concat| |rur| |s18acf| + |rarrow| |writable?| |zeroSetSplit| |internalDecompose| |leftGcd| + |sech| |sumOfSquares| |idealSimplify| |transcendent?| + |selectIntegrationRoutines| |revert| |isOpen?| |cosSinInfo| + |transcendenceDegree| |elliptic?| |csch| |operation| |makeSin| + |OMunhandledSymbol| |palgLODE| |functorData| |f2df| |objects| |float| + |quickSort| |characteristicSerie| |contractSolve| |d01alf| |asinh| + |eulerE| |lowerCase!| |fortranLiteralLine| |base| |specialTrigs| + |ptFunc| |paraboloidal| |bernoulli| |safetyMargin| |acosh| |nary?| + |sup| |inputOutputBinaryFile| |logpart| |kind| |entry?| |duplicates| + |central?| |categoryFrame| |pushNewContour| |removeZeroes| + |unitNormal| |arg1| |hostPlatform| |atanh| |fractionFreeGauss!| + |intChoose| |e02akf| |difference| |makeEq| |op| |fixedDivisor| + |basisOfCentroid| |arg2| |f01qcf| |setEpilogue!| + |selectMultiDimensionalRoutines| |rightFactorCandidate| |acoth| + |parabolicCylindrical| |rational| |numericIfCan| |cAtanh| |s13adf| + |imports| |randomR| |ldf2vmf| |generateIrredPoly| |asech| + |rangePascalTriangle| |numer| |OMopenFile| |geometric| |splitLinear| + |fi2df| |complexSolve| |in?| |extendedResultant| |conditions| + |epilogue| |realSolve| |variables| |denom| |algebraic?| + |findConstructor| |outputMeasure| |sh| |bothWays| |choosemon| + |OMcloseConn| |totalGroebner| |match| |options| |multiple| |cotIfCan| + |singularAtInfinity?| |box| |readIfCan!| |prolateSpheroidal| + |numericalOptimization| |factorsOfCyclicGroupSize| |zag| + |variationOfParameters| |applyQuote| |mightHaveRoots| |c06frf| + |normalized?| |host| |pi| |tree| |rotatey| |pureLex| + |removeRoughlyRedundantFactorsInPols| |charClass| |applyRules| + |taylorIfCan| |extension| |infinity| |leastPower| |screenResolution| + |union| |homogeneous?| |setlast!| |any| |root?| |spherical| |string| + |inverseIntegralMatrix| |cTanh| |omError| |compiledFunction| + |completeHermite| |idealiserMatrix| |d03eef| |iroot| |OMputApp| + |ruleset| |getDatabase| |putGraph| |trapezoidal| |lyndon| + |changeWeightLevel| |invmod| |charthRoot| |balancedBinaryTree| |nlde| + |anfactor| |powers| |kernel| |previous| |se2rfi| |rdHack1| |e04jaf| + |mapSolve| |showRegion| |ridHack1| |cycleRagits| |concat!| |padecf| + |expandPower| |list| |complexNumeric| |atrapezoidal| + |squareFreeFactors| |isAbsolutelyIrreducible?| |create3Space| + |resetAttributeButtons| |e01sbf| |OMputAttr| |suchThat| + |mainCoefficients| |var2StepsDefault| |iiacosh| |divergence| |draw| + |imagi| |infRittWu?| |leftOne| |root| |vedf2vef| |groebner?| |empty| + |whileLoop| |leftMinimalPolynomial| |prinshINFO| + |discriminantEuclidean| |alternatingGroup| |fixPredicate| |An| + |semiDegreeSubResultantEuclidean| |OMgetEndAttr| |iiacsch| + |particularSolution| |OMmakeConn| |diophantineSystem| |getZechTable| + |mapExpon| |LazardQuotient2| |schwerpunkt| |linearAssociatedOrder| + |genericRightMinimalPolynomial| |bumptab| |anticoord| |e04ycf| + |reciprocalPolynomial| |pack!| |realElementary| |atoms| + |reducedDiscriminant| |symmetricSquare| |outputBinaryFile| + |semiResultantEuclideannaif| |cup| |leftLcm| |torsion?| + |cyclotomicDecomposition| |mindegTerm| |makeObject| + |toseSquareFreePart| |inconsistent?| |drawStyle| |sin2csc| |monomials| + |close!| |integralMatrixAtInfinity| |iiGamma| |s19adf| |center| + |allRootsOf| |currentCategoryFrame| |coef| |rCoord| |extractClosed| + |zeroDimPrimary?| |pushuconst| |e02zaf| |stack| |solid| |cycleElt| + |hMonic| |structuralConstants| |OMgetError| |label| |leftRecip| + |OMputInteger| |nthExpon| |makingStats?| |max| |explimitedint| + |integralLastSubResultant| |externalList| |squareFreeLexTriangular| + |point?| |name| |pToDmp| |headReduced?| |constantOpIfCan| + |stripCommentsAndBlanks| |closeComponent| |nextsousResultant2| + |checkForZero| |stopMusserTrials| |just| |rightFactorIfCan| |body| + |imagJ| |infLex?| |changeName| |component| |unitNormalize| + |rangeIsFinite| |groebnerFactorize| |typeForm| |bit?| |stirling2| + |highCommonTerms| |interpret| |rightPower| |viewWriteDefault| |maxint| + |LowTriBddDenomInv| |meshPar1Var| |sizeLess?| |credPol| + |chainSubResultants| |extractBottom!| |meatAxe| |binaryTournament| + |normDeriv2| |rightMult| |e01sff| |lazyPseudoQuotient| |shuffle| + |unravel| |untab| |createZechTable| |setFormula!| |elaborate| + |setchildren!| |characteristicPolynomial| |expIfCan| |yCoordinates| + |numberOfNormalPoly| |dflist| |bringDown| |splitSquarefree| + |internal?| |accuracyIF| |purelyAlgebraicLeadingMonomial?| |solid?| + |nativeModuleExtension| |normalizeIfCan| |harmonic| |point| |length| + |symmetricDifference| |status| |Si| |makeResult| |partialDenominators| + |identification| |outputSpacing| |readInt16!| |lexGroebner| + |setprevious!| |option| |zeroVector| |scripts| |lagrange| |d02ejf| + |implies| |leviCivitaSymbol| |alternative?| |viewPhiDefault| + |nilFactor| SEGMENT |printTypes| |e01sef| |approxSqrt| |s15adf| + |iiasin| |monic?| |port| |eigenvectors| |prepareDecompose| + |leftRemainder| |minRowIndex| |leadingCoefficientRicDE| |gbasis| + |series| |dual| |integralBasis| |prime| |resetBadValues| |fibonacci| + |roughBasicSet| |separateDegrees| |countRealRootsMultiple| |dn| + |stoseInvertible?sqfreg| |hessian| |f04maf| |restorePrecision| + |monicLeftDivide| |t| |nthr| |numberOfImproperPartitions| |unary?| + |rightDiscriminant| |getlo| |writeLine!| |redPo| |elements| + |genericLeftNorm| |palgint| |lfunc| |univariate?| |maxIndex| + |lifting1| |separateFactors| |invertIfCan| |ParCondList| + |cyclicParents| |createPrimitiveElement| |simpson| |e02adf| + |baseRDEsys| |basisOfCommutingElements| |evenlambert| |polyred| + |palglimint| |min| |subSet| |sec2cos| |monicRightFactorIfCan| + |zeroDimensional?| |LagrangeInterpolation| |f04qaf| |createThreeSpace| + |finiteBasis| |OMgetEndAtp| |fortranReal| |fullDisplay| |f01qdf| + |supDimElseRittWu?| |colorDef| |insertBottom!| |nextIrreduciblePoly| + |zeroSquareMatrix| |polygon| |putProperties| |multiEuclidean| + |splitConstant| |totalfract| |rootNormalize| |setTex!| |dmpToP| + |semiIndiceSubResultantEuclidean| |unknown| |apply| |alphanumeric?| + |cSin| |lieAlgebra?| |figureUnits| |byteBuffer| |seriesToOutputForm| + |errorInfo| |ramified?| |tab| |alternating| |top!| |first| |moduleSum| + |expandTrigProducts| |arrayStack| |janko2| |swap| |mainKernel| + |iidsum| |absolutelyIrreducible?| |elseBranch| |xor| |imag| |LiePoly| + |divideIfCan| |rest| |certainlySubVariety?| |viewSizeDefault| + |leftDiscriminant| |safeCeiling| |setfirst!| |directProduct| + |OMreadFile| |case| |singRicDE| |signatureAst| |odd?| + |stopTableInvSet!| |digit?| |returnType!| |cAcos| |axesColorDefault| + |qroot| |setRealSteps| |Zero| |OMgetBVar| |fintegrate| |contours| + |pseudoQuotient| |mapCoef| |comp| |keys| |true| |scalarMatrix| + |noncommutativeJordanAlgebra?| |diagonal| |newSubProgram| |void| + |hcrf| |exprToXXP| |lookup| |One| |top| |tableForDiscreteLogarithm| + |tablePow| |euclideanSize| |acoshIfCan| |drawComplexVectorField| + |one?| |components| |continue| |OMgetObject| |primlimitedint| + |initiallyReduced?| |branchIfCan| |triangSolve| |associatorDependence| + |eulerPhi| |iidprod| |OMclose| |changeThreshhold| |sort| + |plusInfinity| |nullity| |dimensionsOf| |graphs| |weight| + |setPredicates| |completeHensel| |monicDivide| |rightAlternative?| + |setMinPoints3D| |pdf2ef| |minusInfinity| |f02axf| |nor| |headAst| + |iiacsc| |setScreenResolution| |d02bbf| |floor| |asinhIfCan| + |symmetricProduct| |cothIfCan| |completeEval| + |genericRightDiscriminant| |rdregime| |genericLeftMinimalPolynomial| + |primextendedint| |unitCanonical| |id| |bigEndian| |leadingExponent| + |bubbleSort!| |commutativeEquality| |c06gsf| |prindINFO| |prinb| + |coerceS| |rootOf| |elt| |twoFactor| |eof?| |lo| |any?| |readInt8!| + |s17def| |OMputString| |less?| |random| |resultant| |interactiveEnv| + |d03faf| |palgextint| |getBadValues| |next| + |functionIsContinuousAtEndPoints| |antisymmetric?| |rightRecip| + |overset?| |vertConcat| |exptMod| |varselect| |bsolve| |iiatan| + |measure2Result| |increasePrecision| |firstNumer| |writeByte!| + |fractRagits| |parametric?| |viewDeltaXDefault| |sincos| |Hausdorff| + |inf| |leftMult| |key?| |polyRDE| |rightNorm| |adjoint| |equality| + |binding| |iicsc| |univariateSolve| |clearFortranOutputStack| + |graphImage| |internalIntegrate0| |groebSolve| |argument| |coefChoose| + |getProperty| |GospersMethod| |binomThmExpt| |divideExponents| + |exists?| |s17agf| |isAtom| |triangular?| |find| |iomode| |module| + |primeFrobenius| |insert| |cycles| |interpolate| |legendreP| + |supRittWu?| |ignore?| |associative?| |totalDifferential| |mapmult| + |content| |viewZoomDefault| |ranges| |outputAsTex| + |pmComplexintegrate| |polygamma| |leader| |relerror| + |recoverAfterFail| |complement| |d01bbf| |s01eaf| |trapezoidalo| + |OMlistSymbols| |partialQuotients| |maxrow| |lfinfieldint| |prime?| + |Lazard| |wreath| |s13aaf| |e01bgf| |OMopenString| + |rewriteSetWithReduction| |f01brf| |internalLastSubResultant| + |rightZero| |d02gaf| |generalizedContinuumHypothesisAssumed| + |roughUnitIdeal?| |radicalSolve| |s14baf| |even?| |complete| + |stoseInvertible?| |maxRowIndex| |littleEndian| |permutations| |smith| + |linearDependenceOverZ| |leftNorm| |separate| |uncouplingMatrices| + |empty?| |partialNumerators| |ldf2lst| |subPolSet?| |critT| |s17dgf| + |OMgetEndBVar| |removeRedundantFactorsInPols| |totolex| |shiftLeft| + |copyInto!| |decompose| |exp1| |simplifyExp| |shufflein| + |diagonalProduct| |f02akf| |pushup| |leftScalarTimes!| |graphStates| + |quoted?| |expintfldpoly| |symbolTable| |factorsOfDegree| |graphState| + |radicalSimplify| |mainMonomials| |symmetricRemainder| |setStatus| + |unparse| UP2UTS |createRandomElement| |OMputObject| |swap!| + |var1StepsDefault| |cAcot| |mpsode| |pr2dmp| |cyclicSubmodule| + |unaryFunction| |primitivePart| |initializeGroupForWordProblem| + |triangulate| |pushFortranOutputStack| |countable?| |splitNodeOf!| + |exteriorDifferential| |optpair| |coord| |medialSet| |atanhIfCan| + |tanSum| |commonDenominator| |hasSolution?| |popFortranOutputStack| + |iicot| |cAcsch| |width| |createNormalElement| |euclideanNormalForm| + |every?| |s17acf| |super| |tubeRadius| |f07fef| |normalize| + |outputAsFortran| |evaluateInverse| |matrixConcat3D| |mainExpression| + |iiabs| |conjunction| |setTopPredicate| |nullSpace| |nthFactor| Y + |listOfLists| |environment| |stoseInvertibleSetreg| |neglist| + |radicalEigenvector| |ideal| |squareFreePrim| |getMatch| |ListOfTerms| + |leftRegularRepresentation| |rootOfIrreduciblePoly| |outputFixed| + |incrementKthElement| |callForm?| |getProperties| + |getSyntaxFormsFromFile| |reseed| |rightLcm| |jacobi| |elaboration| + |meshFun2Var| |genus| |HenselLift| |genericRightTraceForm| |cAsech| + |f04arf| |algebraicVariables| |sparsityIF| |changeBase| |lowerCase| + |noKaratsuba| |clearCache| |inputBinaryFile| |symmetricPower| |irCtor| + |exQuo| |lift| |table| |e01baf| |midpoints| |modTree| |cycleTail| + |factorOfDegree| |OMParseError?| |modulus| |companionBlocks| + |cardinality| |characteristic| |reduce| |new| |rischNormalize| + LODO2FUN |makeVariable| |obj| |maximumExponent| |iiatanh| + |rewriteIdealWithRemainder| F2FG |asechIfCan| |normalDeriv| |irDef| + |optAttributes| |setFieldInfo| |primitiveElement| |cache| + |removeCoshSq| |var2Steps| |integralMatrix| |iipow| |li| + |semiResultantEuclidean2| |derivationCoordinates| |commutator| |elem?| + |tubePlot| |gethi| |cdr| |OMputFloat| |largest| + |solveLinearPolynomialEquationByFractions| |sinhcosh| + |mainDefiningPolynomial| |bumprow| |trigs2explogs| + |firstUncouplingMatrix| |linkToFortran| |sample| |leftZero| |rombergo| + |leadingSupport| |c05nbf| |infieldIntegrate| |univariatePolynomial| + |factor| |OMgetType| |minimumExponent| |setScreenResolution3D| + |bfKeys| |divisor| |midpoint| |showTheSymbolTable| |groebner| + |subQuasiComponent?| |eigenMatrix| |f07adf| |distance| |getOperands| + |mappingMode| |gcdPrimitive| |basisOfLeftNucleus| |goto| |var1Steps| + |computePowers| |removeZero| |explicitlyEmpty?| |loopPoints| |vector| + |setrest!| |qfactor| |polCase| |insertRoot!| |coleman| |tRange| + |unrankImproperPartitions0| |basisOfRightNucleus| |Nul| |thenBranch| + |gderiv| |differentiate| |elRow2!| |SturmHabichtMultiple| |tubePoints| + |fglmIfCan| |palgextint0| |partition| |lex| |predicate| |cCsch| + |SFunction| |internalZeroSetSplit| |genericRightTrace| + |outputAsScript| |elRow1!| |lexico| |errorKind| |atom?| + |intPatternMatch| |rootSplit| |setAdaptive3D| |iiacot| |categoryMode| + |bindings| |vectorise| |iicoth| |size| |monomial| |left| ** |octon| + |rewriteSetByReducingWithParticularGenerators| |cubic| |e02agf| |dom| + |test| |diagonals| |exprHasAlgebraicWeight| |besselI| |assign| + |showAll?| |byte| |multivariate| |mainValue| |sign| |right| |front| + |blue| |primitivePart!| |repeating| |pomopo!| |morphism| |plus!| + |gcdcofactprim| |e02dff| |cAcoth| |cTan| |romberg| |probablyZeroDim?| + |color| |retractIfCan| |polyPart| |dominantTerm| + |constantCoefficientRicDE| |determinant| |tanQ| |getGraph| |close| + |overbar| |zeroSetSplitIntoTriangularSystems| |diagonal?| + |stopTableGcd!| |linear| |stoseInvertibleSetsqfreg| |lazyGintegrate| + |recolor| |jordanAdmissible?| |cosh2sech| |dimensions| |bitTruth| + |minus!| |problemPoints| |numberOfComponents| |extractIfCan| |sqrt| + |nullary?| |Aleph| |powerAssociative?| |createGenericMatrix| + |nextLatticePermutation| |leadingIdeal| |leaves| |display| |zCoord| + |stoseInvertibleSet| |plot| |polynomial| |increment| |real| |title| + |ravel| |leftAlternative?| |rationalIfCan| |numberOfChildren| + |shellSort| |updatD| |linearPart| |units| |freeOf?| |binary| |prefix| + |mvar| |listLoops| |clip| |OMsupportsCD?| |exprToGenUPS| |horizConcat| + |reshape| |fortranCompilerName| |hspace| |userOrdered?| + |inverseLaplace| |more?| |parameters| |primintegrate| |prinpolINFO| + |mapdiv| |compound?| |s17aff| |clearTable!| |summation| |df2fi| + |listRepresentation| |int| |tanNa| |leftDivide| |computeCycleLength| + |e| |s17aef| |po| |removeRoughlyRedundantFactorsInContents| + |lazyPremWithDefault| |laurentRep| |node| |cylindrical| + |createLowComplexityTable| |abs| |divisors| |s19abf| |trim| |nthCoef| + |rootKerSimp| |lprop| |makeop| |multiplyExponents| + |functionIsOscillatory| |aspFilename| |prod| |generalPosition| |input| + |updatF| |map| |hypergeometric0F1| |critMonD1| |directSum| + |writeUInt8!| |deepestTail| |brace| |kernels| |code| |tanintegrate| + |radix| |stopTable!| |library| |pushdterm| |digamma| + |basisOfLeftAnnihilator| |moebiusMu| |cyclicGroup| |minColIndex| + |limitPlus| |update| |eq| |operator| |basisOfCenter| + |computeCycleEntry| |conditionP| |fortran| |showSummary| |zero?| |mat| + |viewDeltaYDefault| |getIdentifier| |droot| |quatern| + |unrankImproperPartitions1| |connect| |iter| |FormatRoman| |optimize| + |definingEquations| |coshIfCan| |solve| |inHallBasis?| + |monomialIntPoly| |getOperator| |derivative| |d01amf| |f04jgf| + |product| |basisOfRightAnnihilator| |zeroMatrix| |rightQuotient| + |mathieu11| |mesh| |comparison| |showTheIFTable| |assert| |axes| + |updateStatus!| |rationalFunction| |complexNumericIfCan| |hdmpToP| + |e02ajf| |showArrayValues| |triangularSystems| |convert| |f01rcf| + |weights| |physicalLength!| |setColumn!| |increase| |yellow| + |abelianGroup| |low| |lfextlimint| |showAttributes| |blankSeparate| + |level| |permutation| |represents| |c06ecf| |selectODEIVPRoutines| + |skewSFunction| |position| |intensity| |clikeUniv| |df2mf| + |OMputError| |conjugates| |halfExtendedResultant1| |pointColorPalette| + |OMsetEncoding| |showFortranOutputStack| |makeTerm| |nonLinearPart| + |gensym| |setright!| |block| |exactQuotient| |leftQuotient| |back| + |eyeDistance| |btwFact| |deepestInitial| |bandedJacobian| |ScanArabic| + |subResultantsChain| |removeIrreducibleRedundantFactors| |setleft!| + |compile| |ref| |fortranDoubleComplex| |upDateBranches| |systemSizeIF| + |degree| |exp| |principalAncestors| |testDim| |numberOfFactors| + |explicitlyFinite?| |fractRadix| |head| |stFunc1| |viewThetaDefault| + |factors| |parametersOf| |equation| |createLowComplexityNormalBasis| + |asinIfCan| |stronglyReduced?| |s19aaf| |numeric| + |removeRedundantFactors| |rotatex| |f02xef| |children| |flagFactor| + |nextSublist| |radical| |f02agf| |viewport3D| |addmod| + |getExplanations| |debug3D| |preprocess| |basis| |rischDE| + |fortranCharacter| |prevPrime| |hostByteOrder| |showClipRegion| + |createNormalPoly| |xCoord| |minimumDegree| |approximants| + |collectUnder| |findCycle| |algint| |generalLambert| |swapRows!| + |script| |youngDiagram| |rightDivide| |setMinPoints| |solveRetract| + |clipPointsDefault| |shanksDiscLogAlgorithm| |BumInSepFFE| |reflect| + |removeSquaresIfCan| |rootProduct| |printInfo| |leaf?| |nullary| + |leftExtendedGcd| |positiveRemainder| |aromberg| + |rightRegularRepresentation| |leadingIndex| |yCoord| |makeViewport2D| + |randnum| |leastMonomial| |qualifier| |rquo| |upperCase!| + |clearTheSymbolTable| |reduction| |rspace| |startTableGcd!| |tan2cot| + |sumOfDivisors| |minordet| |tex| |critB| |aQuadratic| |logGamma| + |conjugate| |asimpson| |selectSumOfSquaresRoutines| |nextNormalPoly| + |ricDsolve| |nothing| |pile| |invertibleElseSplit?| |stirling1| + |besselY| |matrixGcd| |range| |factorset| |negative?| + |clearTheIFTable| |padicallyExpand| |number?| |fortranTypeOf| + |inverseIntegralMatrixAtInfinity| |sumSquares| |differentialVariables| + |removeSuperfluousQuasiComponents| |iiperm| |checkRur| |e01bhf| + |OMgetSymbol| |divideIfCan!| |rightExactQuotient| |c06gbf| + |principalIdeal| |heap| |cCsc| |encodingDirectory| |simpsono| + |mapBivariate| |scale| |setErrorBound| |rightMinimalPolynomial| + |s21bcf| |minPoints| |irreducibleFactors| |qelt| |unvectorise| + |diagonalMatrix| |makeSketch| |sort!| |c06fuf| |tanhIfCan| |qsetelt| + |type| |fortranLiteral| |lfintegrate| |substitute| |besselJ| |lquo| + |rem| |perfectNthRoot| |leftTrace| |const| |newTypeLists| |newLine| + |OMputSymbol| |expenseOfEvaluationIF| |f02aef| |setMaxPoints| + |wholeRagits| |quo| |xRange| |insert!| |noLinearFactor?| |initial| + |ipow| |parseString| |ParCond| |cons| |flexible?| |intcompBasis| + |f01mcf| |positive?| |yRange| |groebnerIdeal| |iterationVar| + |shallowExpand| |testModulus| |internalIntegrate| |hasTopPredicate?| + |dim| |connectTo| |bivariate?| |stoseSquareFreePart| |list?| |div| + |zRange| |normalForm| |createPrimitivePoly| |OMUnknownSymbol?| |fmecg| + |deleteProperty!| |modifyPoint| |df2st| |map!| |linears| |ode1| + |possiblyInfinite?| |exquo| |getRef| |LyndonWordsList| |uniform| + |viewport2D| |zerosOf| |integerIfCan| |reindex| |qsetelt!| + |cycleLength| ~= |normalizedAssociate| |OMencodingUnknown| + |primeFactor| |aCubic| |relationsIdeal| |ScanFloatIgnoreSpaces| + |setvalue!| |size?| |entries| |#| |setButtonValue| + |transcendentalDecompose| |dfRange| |e01bef| |s18dcf| + |OMsupportsSymbol?| |d01gbf| |showTheFTable| |zero| ~ |outputArgs| + |coerce| |tan2trig| |fortranComplex| |sin?| |reopen!| + |factorPolynomial| |check| |source| |OMgetEndApp| |primlimintfrac| + |LyndonCoordinates| |leadingBasisTerm| |construct| |removeSinhSq| + |complementaryBasis| |monomRDE| |antiCommutator| |And| |inRadical?| + |mergeDifference| |lepol| |leftExactQuotient| |genericRightNorm| + |f01qef| |ellipticCylindrical| |f02abf| |/\\| |discriminant| + |OMputEndObject| |Or| |headReduce| |acsch| |normFactors| + |palginfieldint| |rectangularMatrix| |clipSurface| + |listConjugateBases| |multisect| |s20adf| |sylvesterMatrix| |Not| + |dictionary| |\\/| |showTheRoutinesTable| |OMUnknownCD?| |eq?| + |listOfMonoms| |nand| |cSec| |constantToUnaryFunction| |tube| + |duplicates?| |e02dcf| |augment| |s17ajf| |numberOfCycles| |target| + |supersub| |insertTop!| |numberOfMonomials| |squareFree| + |karatsubaDivide| |possiblyNewVariety?| |aLinear| |s18def| |infinite?| + |closed?| |printHeader| |fixedPointExquo| |cyclicEqual?| |associates?| + |exponent| |mathieu24| |gcdPolynomial| |interpretString| + |coercePreimagesImages| |getMultiplicationTable| |isNot| |cyclic| + |OMconnOutDevice| |d01apf| |indiceSubResultant| |setRow!| |endOfFile?| + |nextColeman| |delay| |diag| |s17ahf| |mergeFactors| |eigenvalues| + |principal?| |rightRemainder| |hasoln| |laguerreL| |second| + |hexDigit?| |open| |setPosition| |psolve| |normalizedDivide| + |OMgetVariable| |bombieriNorm| |PDESolve| |terms| |minGbasis| |e02gaf| + |third| |chineseRemainder| |processTemplate| |useEisensteinCriterion| + |uniform01| |numerators| |linearPolynomials| |transform| + |quadraticForm| |string?| |coth2tanh| |readUInt16!| |coordinates| + |printInfo!| |powern| |collectQuasiMonic| |laplacian| |constDsolve| + |arbitrary| |part?| |slash| |polyRicDE| |plotPolar| |localUnquote| + |expenseOfEvaluation| |divisorCascade| |rowEch| |dark| |reset| + |modularFactor| |selectNonFiniteRoutines| |compBound| |bright| + |operations| |OMbindTCP| |univariatePolynomials| |laurentIfCan| + |c06ekf| |doubleDisc| F |iFTable| |c02aff| |OMencodingXML| + |fprindINFO| |genericPosition| |setleaves!| |cAcosh| |shrinkable| + |resultantEuclidean| |iisin| |truncate| + |dimensionOfIrreducibleRepresentation| |OMReadError?| |infix| |write| + |numericalIntegration| |inGroundField?| |inc| |deref| |eval| |nthRoot| + |jokerMode| |acosIfCan| |mappingAst| |setsubMatrix!| |setelt| |save| + |solveInField| |enqueue!| |nodes| |imagE| |norm| |distribute| + |monicDecomposeIfCan| |signAround| |cCos| |linearAssociatedLog| + |virtualDegree| |linGenPos| |reducedSystem| |isPlus| |overlap| + |indiceSubResultantEuclidean| |mapDown!| |setProperties| |sn| + |symFunc| |fortranDouble| |factorFraction| |copy| |localReal?| + |maxrank| |stronglyReduce| |safeFloor| |members| |error| + |wordInStrongGenerators| |escape| |setDifference| + |componentUpperBound| |patternMatchTimes| |irreducible?| |sub| + |rename| EQ |s18adf| |integer?| |quadratic?| |edf2df| |jordanAlgebra?| + |xn| |viewDefaults| |closedCurve?| |removeSinSq| |infieldint| + |cschIfCan| |B1solve| |exactQuotient!| |kroneckerDelta| |pdct| + |elliptic| |degreePartition| |s19acf| |hermite| |e02daf| |iiasinh| + |lazyResidueClass| |resultantEuclideannaif| |multiplyCoefficients| + |light| |roughEqualIdeals?| |relativeApprox| |f04axf| |whatInfinity| + |points| |numberOfHues| |subHeight| |makeCrit| |e02bdf| |match?| + |lastSubResultantElseSplit| |critBonD| |OMreceive| |rationalPoint?| + |findBinding| |autoCoerce| |double?| |imaginary| |curveColorPalette| + |kmax| |coefficients| |fTable| |denominators| |pointPlot| + |generalizedEigenvector| |collect| |s17dhf| |associatedEquations| + |shade| |sorted?| |car| |setImagSteps| |nextSubsetGray| |infinityNorm| + |expPot| |musserTrials| |perfectSquare?| |makeFloatFunction| + |commutative?| |definingPolynomial| |OMlistCDs| |generators| |pol| + |flexibleArray| |symbol?| |wholePart| |solveLinearlyOverQ| + |getPickedPoints| |removeDuplicates| |printStats!| |writeInt8!| + |deleteRoutine!| |isAnd| |quasiMonic?| |weighted| |child| + |makeGraphImage| |myDegree| |createNormalPrimitivePoly| |FormatArabic| + |entry| |writeBytes!| |denomRicDE| |mainVariable| |d02cjf| + |coerceImages| |stosePrepareSubResAlgo| |extensionDegree| |slex| + |curve| |UpTriBddDenomInv| |rk4qc| |prepareSubResAlgo| |variable?| + |isOp| |subCase?| |cRationalPower| |d02bhf| |f02wef| + |splitDenominator| |write!| |contract| |critpOrder| |s17dlf| |null| + |sinIfCan| |sequence| |OMputBind| |degreeSubResultantEuclidean| + |factor1| |RemainderList| |corrPoly| |internalInfRittWu?| |subset?| + |subResultantGcdEuclidean| |stFuncN| |not| |algebraicDecompose| + |hermiteH| |initTable!| |superscript| |square?| |reducedQPowers| + |solveLinearPolynomialEquation| |decomposeFunc| |split| |extractPoint| + |and| |repSq| |goodPoint| |postfix| |bfEntry| |surface| |categories| + |space| |outputGeneral| |open?| |mirror| |scripted?| |or| |delete| + |selectsecond| |localAbs| |superHeight| |s17dcf| |support| |imagI| + |scopes| |calcRanges| |polarCoordinates| |isTimes| |aQuartic| + |rightTraceMatrix| |d01asf| |complexEigenvectors| |latex| + |insertionSort!| |bezoutMatrix| |lyndon?| |paren| |rroot| |cartesian| + |createMultiplicationTable| |isList| |numerator| |elaborateFile| + |realEigenvalues| |backOldPos| |readUInt32!| + |semiResultantReduitEuclidean| |tubeRadiusDefault| |zeroDim?| |split!| + |f02bbf| |setLength!| |rightRankPolynomial| |palgRDE| |read!| + |Vectorise| |chvar| |acscIfCan| |someBasis| |cscIfCan| + |degreeSubResultant| |semiSubResultantGcdEuclidean1| |extractProperty| + |addMatchRestricted| |stoseLastSubResultant| |brillhartTrials| + |randomLC| |multiple?| |lastSubResultantEuclidean| |cycleSplit!| + |isQuotient| |chebyshevU| |dihedral| |doubleResultant| |cos2sec| + |opeval| |normalElement| |separant| |replace| |infiniteProduct| + |LiePolyIfCan| |setVariableOrder| |representationType| |queue| + |setLabelValue| |ip4Address| |rootSimp| |iiacos| |pole?| |oddlambert| + |addPoint| |LyndonWordsList1| |deriv| |dAndcExp| |cSinh| + |roughSubIdeal?| |squareMatrix| |domainTemplate| |primes| |depth| + |extend| |rationalPoints| |qqq| |f01ref| |squareFreePart| |generic| + |leftFactorIfCan| |create| |enumerate| |cn| |getCode| |d02gbf| + |OMgetString| |taylorRep| |integerBound| |copy!| |ratDsolve| |round| + |height| |dmpToHdmp| |pmintegrate| |identitySquareMatrix| + |trivialIdeal?| |OMputEndAtp| |delete!| |iiasech| |edf2fi| |e04ucf| + |null?| |dec| |Ci| |rightUnits| |cyclePartition| UTS2UP |lintgcd| + |ramifiedAtInfinity?| |OMgetBind| |palgintegrate| |insertMatch| + |dequeue| |getButtonValue| |alphabetic| |select!| |f04asf| |f04atf| + |isExpt| |meshPar2Var| |orbit| |log10| |remainder| |scaleRoots| + |s17adf| |OMgetFloat| |simplifyPower| |Is| |composite| |interval| + |permutationRepresentation| |bitand| |s21bdf| |saturate| + |sumOfKthPowerDivisors| |isConnected?| |edf2efi| |palgint0| |e04gcf| + |element?| |evaluate| |stiffnessAndStabilityOfODEIF| |ksec| + |removeConstantTerm| |iisec| |operators| |c06eaf| |d01ajf| + |modularGcdPrimitive| |factorSFBRlcUnit| |nextPrimitiveNormalPoly| + |reducedForm| |definingInequation| |forLoop| |heapSort| |reduceLODE| + |regime| |rightScalarTimes!| |resultantReduit| |linearMatrix| + |seriesSolve| |d02raf| |notelem| |inspect| |OMputBVar| |OMreadStr| + |computeBasis| |halfExtendedSubResultantGcd2| |debug| |f07aef| + |failed| |badValues| |dot| |cAtan| |lSpaceBasis| |mkPrim| |normalise| + |transpose| |substring?| D |palgLODE0| |orthonormalBasis| |poisson| + |minrank| |OMgetInteger| |rotate!| |bezoutDiscriminant| |e02bef| + |cAsin| |hdmpToDmp| |prologue| |unit?| |returns| |integral?| |charpol| + |failed?| |suffix?| |curve?| |roman| |PollardSmallFactor| + |primextintfrac| |monicCompleteDecompose| |OMgetApp| |sts2stst| + |extendedIntegrate| |ReduceOrder| |henselFact| |nil| |lazyEvaluate| + |indicialEquation| |removeCosSq| |tail| |log| |groebgen| |univariate| + |prefix?| |iteratedInitials| |adaptive?| |sechIfCan| |leftPower| + |basisOfLeftNucloid| |lifting| |readLineIfCan!| |init| |factorial| + |explicitEntries?| |useEisensteinCriterion?| |clearDenominator| + |subTriSet?| |vconcat| |macroExpand| |rotatez| |internalSubPolSet?| + |bernoulliB| |associatedSystem| |resultantReduitEuclidean| |besselK| + |vark| |varList| |complexNormalize| |cyclotomicFactorization| + |torsionIfCan| |exponents| |approximate| |mathieu22| |mathieu12| + |coefficient| |tracePowMod| |log2| |extendIfCan| + |internalSubQuasiComponent?| |complex| |SturmHabichtCoefficients| + |setPrologue!| |leftUnit| |isMult| |semiDiscriminantEuclidean| |shape| + |OMgetAtp| |setClosed| |identity| |attributeData| + |tryFunctionalDecomposition| |leadingTerm| |brillhartIrreducible?| + |expandLog| |iisqrt3| |intersect| |innerSolve1| |print| + |lieAdmissible?| |oddInfiniteProduct| |complexEigenvalues| + |properties| |multiset| |adaptive3D?| |putProperty| |e02baf| |infix?| + |lfextendedint| |resolve| |sylvesterSequence| |translate| |hexDigit| + |multinomial| |mask| |csc2sin| |cycleEntry| |declare| |traceMatrix| + |nextItem| |fillPascalTriangle| |seed| |karatsuba| |bits| + |fortranCarriageReturn| |normal?| |upperCase| |subMatrix| |nonQsign| + |fortranLinkerArgs| |sinh2csch| |fixedPoints| |compose| |addPointLast| + |linSolve| |rewriteIdealWithHeadRemainder| |setref| |drawComplex| + |karatsubaOnce| |screenResolution3D| |setnext!| |mindeg| + |solveLinearPolynomialEquationByRecursion| |integralAtInfinity?| + |viewPosDefault| |goodnessOfFit| |setMaxPoints3D| GE |getOrder| + |binarySearchTree| |wholeRadix| |cAcsc| |ScanFloatIgnoreSpacesIfCan| + |generalTwoFactor| |nextPrime| |mainPrimitivePart| + |genericLeftTraceForm| |setEmpty!| GT |fortranLogical| |putColorInfo| + |iCompose| |sequences| |s14aaf| |stoseInvertible?reg| |f04mcf| + |radicalOfLeftTraceForm| |say| |limitedint| LE |bracket| + |subResultantChain| |delta| |patternVariable| |roughBase?| + |exponential1| |e04fdf| |quartic| LT |squareFreePolynomial| + |makeYoungTableau| |primPartElseUnitCanonical!| |subscriptedVariables| + |tanAn| |qinterval| |polar| |leftTraceMatrix| |exprex| + |makeViewport3D| |plus| |lazyPquo| |changeNameToObjf| |row| + |elColumn2!| |extractTop!| |makeSeries| |printCode| |resize| + |constantKernel| |noValueMode| |symbolTableOf| |exprToUPS| + |createIrreduciblePoly| |shift| |closedCurve| |lowerPolynomial| + |coerceL| |curryLeft| |remove!| |htrigs| |crest| |remove| |critM| + |d01gaf| |rightGcd| |coerceListOfPairs| |s18aff| + |removeRedundantFactorsInContents| |alphabetic?| |pointLists| + |binaryTree| |complexIntegrate| |radicalEigenvalues| |outputFloating| + |radicalEigenvectors| |contains?| |times| |quadratic| |pow| + |complexForm| |integers| |last| |commaSeparate| |over| |mainVariable?| + |useSingleFactorBound?| |qPot| |generator| |factorSquareFree| + |algintegrate| |mantissa| |asecIfCan| |f02bjf| + |generalInfiniteProduct| |semiSubResultantGcdEuclidean2| |assoc| + |reorder| |changeVar| |inrootof| |semiLastSubResultantEuclidean| + |perspective| |innerint| |minimalPolynomial| |logical?| |predicates| + |cyclicCopy| |s18aef| |pquo| |iiacoth| |hyperelliptic| + |numberOfVariables| |f04mbf| BY |pToHdmp| |startTableInvSet!| + |pseudoRemainder| |basisOfNucleus| |condition| |algDsolve| |merge!| + |lazyPseudoDivide| |monom| |prefixRagits| |ODESolve| |decimal| + |curryRight| |nextNormalPrimitivePoly| |times!| |presub| |cSech| + |kovacic| |lllip| |exponential| |bipolar| |reverseLex| |c06fqf| + |jacobiIdentity?| |scan| |complexExpand| |Ei| |listexp| |univcase| + |readable?| |selectPolynomials| |f02fjf| |erf| |basisOfMiddleNucleus| + |repeatUntilLoop| |idealiser| |toScale| |output| |common| |stFunc2| + |quoByVar| |appendPoint| |subspace| |lazyPseudoRemainder| + |setLegalFortranSourceExtensions| |mapUnivariateIfCan| |parabolic| + |deepCopy| FG2F |simpleBounds?| |symmetricGroup| |unitVector| + |hitherPlane| |constant| |UnVectorise| |polygon?| |s17akf| |integral| + |constructor| |nonSingularModel| |simplifyLog| |ratpart| + |extractIndex| |compactFraction| |dilog| |mainVariables| NOT |real?| + |startPolynomial| |quotientByP| |leastAffineMultiple| |incr| |ef2edf| + |OMgetAttr| |sturmSequence| |complexRoots| |sin| |function| |d01aqf| + |nodeOf?| OR |ffactor| |froot| |hi| |pair?| |enterPointData| + |numberOfComposites| |rationalPower| |mapUnivariate| |cos| + |bezoutResultant| |trace2PowMod| |lazyVariations| AND |iprint| + |rightTrim| |complex?| |OMputEndBVar| |e04naf| |trunc| |sPol| |tan| + |ratDenom| |acschIfCan| |leftTrim| |basicSet| |cross| + |irreducibleRepresentation| |numberOfComputedEntries| |invertibleSet| + |tableau| |getGoodPrime| |cot| |setAttributeButtonStep| |iilog| + |presuper| |setOfMinN| |numFunEvals3D| |returnTypeOf| |hclf| + |cyclicEntries| |semiResultantEuclidean1| |sec| |integralRepresents| + |bat| |complexZeros| |halfExtendedSubResultantGcd1| + |bivariatePolynomials| |showAllElements| |maxPoints3D| |routines| + |pastel| |csc| |symbol| |f2st| |minPoints3D| |rootPower| |lyndonIfCan| + |logIfCan| |moebius| |lazyIntegrate| |autoReduced?| |asin| + |expression| |denomLODE| |OMputEndError| |lazyIrreducibleFactors| + |monomRDEsys| |tubePointsDefault| |innerEigenvectors| |direction| + |partitions| |acos| |zeroDimPrime?| |integer| |rowEchLocal| |destruct| + |rk4a| |setAdaptive| |simplify| |twist| |quasiMonicPolynomials| + |numberOfPrimitivePoly| |mdeg| |atan| |lastSubResultant| + |OMconnectTCP| |symmetricTensors| |getConstant| |baseRDE| |constant?| + |linearDependence| |invmultisect| |symbolIfCan| |quote| |acot| |cLog| + |moreAlgebraic?| |clearTheFTable| |constantRight| |quotedOperators| + |ceiling| |controlPanel| |float?| |asec| |argumentListOf| |typeList| * + |doubleRank| |raisePolynomial| |lhs| |unmakeSUP| |hasHi| + |subResultantGcd| |genericLeftTrace| |acsc| |colorFunction| + |removeSuperfluousCases| |lcm| |isOr| |bytes| |wronskianMatrix| |rhs| + |inR?| |isImplies| |acotIfCan| |acothIfCan| |sinh| |lflimitedint| + |wordsForStrongGenerators| |powmod| |linearlyDependent?| |generate| + |topFortranOutputStack| |f02aff| |lowerBound| |dmp2rfi| |lowerCase?| + |cosh| |append| |equiv| |antisymmetricTensors| |hash| = |green| + |currentEnv| |oblateSpheroidal| |solveid| |tanh2trigh| |pattern| + |coth2trigh| |tanh| |count| |imagj| |gcd| |monicModulo| |f04faf| + |maxPoints| |incrementBy| |dequeue!| |HermiteIntegrate| |secIfCan| + |dioSolve| |sqfrFactor| |coth| |totalLex| |false| |lp| |is?| < + |symmetric?| |expand| |category| |fracPart| |subNodeOf?| + |semicolonSeparate| |ptree| |nthFlag| |balancedFactorisation| + |factorAndSplit| |rightUnit| |primaryDecomp| |flatten| |sqfree| > + |filterWhile| |domain| |cot2tan| |airyBi| |lineColorDefault| + |loadNativeModule| |pop!| |iibinom| |scalarTypeOf| |linear?| + |readLine!| <= |high| |filterUntil| |factorials| |package| + |exprHasWeightCosWXorSinWX| |cAsec| |message| |makeprod| + |clipParametric| |sizeMultiplication| |showScalarValues| |recip| + |sizePascalTriangle| >= |select| |digits| |normalizeAtInfinity| + |setOrder| |realZeros| |universe| |rootBound| |chiSquare| |makeSUP| + |plenaryPower| |pointColorDefault| |double| |iicos| |reify| + |eigenvector| |moduloP| |parts| |bitCoef| |hue| |positiveSolve| + |monicRightDivide| |algebraicOf| |coHeight| |att2Result| |child?| + |typeLists| |e02aef| |mapUp!| |combineFeatureCompatibility| + |mapExponents| |rubiksGroup| |mkAnswer| + |quasiComponent| |rational?| + |order| |f01rdf| |subtractIfCan| |parents| |toroidal| |e02ddf| |mix| + |partialFraction| - |constantLeft| |diff| |chiSquare1| |mkIntegral| + |has?| |generalizedContinuumHypothesisAssumed?| |pointColor| + |getMeasure| |outputForm| / |makeMulti| |s21bbf| |OMconnInDevice| + |rule| |rootDirectory| |leftRankPolynomial| |KrullNumber| |composites| + RF2UTS |makeRecord| |csch2sinh| |makeCos| |toseInvertibleSet| + |generalizedEigenvectors| |decrease| |upperCase?| |irVar| + |outerProduct| |indicialEquationAtInfinity| |fullPartialFraction| + |powerSum| |doubleFloatFormat| |Beta| |finiteBound| |divide| |e01bff| + |addBadValue| |declare!| |constantIfCan| |OMputVariable| + |OMgetEndObject| |distdfact| |external?| |graeffe| + |standardBasisOfCyclicSubmodule| |tanIfCan| |ord| |generic?| + |OMgetEndBind| |localIntegralBasis| GF2FG |startStats!| |nsqfree| + |invertible?| |discreteLog| |realRoots| |decreasePrecision| + |doublyTransitive?| |sturmVariationsOf| |drawToScale| |power!| + |thetaCoord| |inverse| |rules| |tab1| |physicalLength| |weierstrass| + |rightTrace| |explogs2trigs| |modifyPointData| |cycle| |indices| + |solveLinear| |shallowCopy| |rightRank| |reduceByQuasiMonic| + |stoseIntegralLastSubResultant| |step| |retractable?| |initials| + |listBranches| |rowEchelon| |endSubProgram| |unitsColorDefault| + |rootsOf| |OMencodingBinary| |singularitiesOf| |addPoint2| + |headRemainder| |bipolarCylindrical| |df2ef| |isPower| + |pascalTriangle| |integralCoordinates| |addiag| |antiCommutative?| + |graphCurves| |column| |segment| |distFact| |OMserve| |fortranInteger| + |squareTop| |conical| |normInvertible?| |s14abf| |f02awf| + |resetVariableOrder| |getStream| |fractionPart| |currentSubProgram| + |quasiRegular?| |irForm| |SturmHabichtSequence| |bivariateSLPEBR| + |identityMatrix| |padicFraction| |zeroOf| |d01anf| |resetNew| |build| + |reverse!| |extract!| |numberOfDivisors| |expressIdealMember| + |usingTable?| |rk4f| |power| |bag| |shiftRight| |region| |unexpand| + |constantOperator| |reduceBasisAtInfinity| |cCoth| + |extendedSubResultantGcd| |setClipValue| |limitedIntegrate| + |coordinate| |character?| |key| |useSingleFactorBound| + |binaryFunction| |iicosh| |matrixDimensions| |trailingCoefficient| + |newReduc| |red| |npcoef| |getMultiplicationMatrix| + |monomialIntegrate| |resultantnaif| |value| |outlineRender| + |selectPDERoutines| |gradient| |mainContent| |filename| |nthExponent| + |expt| |iisinh| |rotate| |repeating?| |biRank| |numberOfOperations| + |firstDenom| |optional| |algSplitSimple| |quasiAlgebraicSet| + |basisOfRightNucloid| |rightOne| |minimize| |sortConstraints| |c05pbf| + |pdf2df| |formula| |parse| |rst| |satisfy?| |normalDenom| |schema| + |birth| |knownInfBasis| |factorSquareFreePolynomial| |subscript| + |stop| |vspace| |push!| |expextendedint| |approxNthRoot| + |numberOfIrreduciblePoly| |imagk| |arity| |mr| |arguments| + |expintegrate| |chebyshevT| |setStatus!| |push| |overlabel| |lighting| + |totalDegree| |quadraticNorm| |wordInGenerators| |frobenius| + |elementary| |cap| |style| |iisqrt2| |stiffnessAndStabilityFactor| + |leftFactor| |compdegd| |algebraicSort| |drawCurves| |nrows| |result| + |prem| |subNode?| |fill!| |isEquiv| |clipBoolean| |rootRadius| + |stoseInternalLastSubResultant| |realEigenvectors| |mainMonomial| + |tryFunctionalDecomposition?| |ncols| |euclideanGroebner| + |perfectNthPower?| |limit| |magnitude| |antiAssociative?| + |rightCharacteristicPolynomial| |whitePoint| |completeSmith| + |numberOfFractionalTerms| |primitive?| |radicalRoots| + |algebraicCoefficients?| |characteristicSet| |OMputEndAttr| |OMwrite| + |tower| |buildSyntax| |e02bbf| |mapGen| |argscript| + |oneDimensionalArray| |lazyPrem| |cCosh| + |rewriteIdealWithQuasiMonicGenerators| |irreducibleFactor| + |numFunEvals| |Frobenius| |mulmod| |conditionsForIdempotents| |euler| + |sncndn| |firstSubsetGray| |lllp| |trigs| |eisensteinIrreducible?| + |curry| |createPrimitiveNormalPoly| |taylor| |iitanh| |comment| |cCot| + |disjunction| |iiasec| |beauzamyBound| |modularGcd| |index?| + |nthFractionalTerm| |laguerre| |mesh?| |laurent| + |leftCharacteristicPolynomial| |f02aaf| |selectOptimizationRoutines| + |f02adf| |Gamma| |createMultiplicationMatrix| |rowEchelonLocal| |frst| + |orbits| |shiftRoots| |puiseux| |option?| |palglimint0| |pushdown| + |generalSqFr| |palgRDE0| |matrix| |index| |gramschmidt| + |LazardQuotient| |adaptive| |primPartElseUnitCanonical| + |showIntensityFunctions| |innerSolve| |s13acf| |argumentList!| + |bandedHessian| |minset| |laplace| |d01fcf| |selectfirst| |computeInt| + |voidMode| |trueEqual| |inv| |lambda| |cfirst| + |integralDerivationMatrix| |bitLength| |intermediateResultsIF| + |tensorProduct| |zoom| |call| |LyndonBasis| |printingInfo?| |ground?| + |readUInt8!| |Lazard2| |startTable!| |halfExtendedResultant2| + |readInt32!| |c06ebf| |linearAssociatedExp| |bumptab1| |pair| + |sdf2lst| |ground| |setelt!| |f01maf| |pushucoef| |rk4| |nthRootIfCan| + |replaceKthElement| |bat1| |integralBasisAtInfinity| |bounds| + |singular?| |f02ajf| |directory| |rootPoly| |UP2ifCan| |setCondition!| + |rationalApproximation| |ode2| |leadingMonomial| |merge| |cPower| + |gcdprim| |OMencodingSGML| |e01daf| |f01bsf| |sum| + |functionIsFracPolynomial?| |exponentialOrder| |taylorQuoByVar| + |reverse| |lazy?| |topPredicate| |leadingCoefficient| |normal01| + |gcdcofact| |minIndex| |associator| |withPredicates| |rename!| + |extendedint| |c02agf| |ran| |countRealRoots| |mkcomm| + |primitiveMonomials| |makeFR| |BasicMethod| |makeUnit| + |regularRepresentation| |airyAi| |retract| |dimension| |f07fdf| + |sech2cosh| |complexLimit| |optional?| |setUnion| |reductum| + |branchPoint?| |submod| |ScanRoman| |OMgetEndError| |internalAugment| + |mathieu23| |mainForm| |enterInCache| |selectAndPolynomials| + |extractSplittingLeaf| |leftUnits| |generalizedInverse| |permanent| + |rischDEsys| |RittWuCompare| |messagePrint| |completeEchelonBasis| + |rank| |closed| |evenInfiniteProduct| |e02bcf| |subresultantVector| + |setProperty| |mapMatrixIfCan| |d03edf| |strongGenerators| |iisech| + |recur| |packageCall| |denominator| |conjug| |factorByRecursion| + |iifact| |e04dgf| |patternMatch| |unprotectedRemoveRedundantFactors| + |lambert| |removeRoughlyRedundantFactorsInPol| |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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T) ((-233 |#1|) . T) ((-235) -3749 (|has| |#1| (-354)) (|has| |#1| (-235))) ((-245) -3749 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-288) |has| |#1| (-1212)) ((-290 |#1| $) |has| |#1| (-290 |#1| |#1|)) ((-294) -3749 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-311) -3749 (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-313 |#1|) |has| |#1| (-313 |#1|)) ((-368) -3749 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-408) |has| |#1| (-354)) ((-373) -3749 (|has| |#1| (-373)) (|has| |#1| (-354))) ((-354) |has| |#1| (-354)) ((-375 |#1| #1#) . T) ((-415 |#1| #1#) . T) ((-343 |#1|) . T) ((-382 |#1|) . T) ((-406 |#1|) . T) ((-417 |#1|) . 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T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-893 (-384)) |has| |#1| (-893 (-384))) ((-893 (-570)) |has| |#1| (-893 (-570))) ((-891 |#1|) . T) ((-916) -12 (|has| |#1| (-311)) (|has| |#1| (-916))) ((-927) -3749 (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-1011) -12 (|has| |#1| (-1011)) (|has| |#1| (-1212))) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1060 #0#) -3749 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1060 |#1|) . T) ((-1060 $) . T) ((-1065 #0#) -3749 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1065 |#1|) . T) ((-1065 $) . T) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1161) |has| |#1| (-354)) ((-1212) |has| |#1| (-1212)) ((-1215) |has| |#1| (-1212)) ((-1227) . 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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) -3684 (|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|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -3684 (|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)) -3684 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -3684 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -3684 (|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)) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -3684 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -3684 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -3684 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -3684 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -3684 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -3684 (|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|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -3684 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -3684 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -3684 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) -((-2077 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-2315 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-2536 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) -(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -2077 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -2315 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -2536 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) -((-2536 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-2315 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-2077 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) -(-10 -7 (-15 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(($ $ (-650 (-1186))) NIL (-12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) (($ $ (-1186) (-777)) NIL (-12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) (($ $ (-650 (-1186)) (-650 (-777))) NIL (-12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) (($ $ (-1 |#2| |#2|) (-777)) NIL (|has| |#2| (-1058))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1058)))) (-3905 (((-112) $ $) NIL (-3684 (|has| |#2| (-799)) (|has| |#2| (-854))))) (-3877 (((-112) $ $) NIL (-3684 (|has| |#2| (-799)) (|has| |#2| (-854))))) (-3833 (((-112) $ $) 27 (|has| |#2| (-1109)))) (-3891 (((-112) $ $) NIL (-3684 (|has| |#2| (-799)) (|has| |#2| (-854))))) (-3862 (((-112) $ $) 66 (-3684 (|has| |#2| (-799)) (|has| |#2| (-854))))) (-3964 (($ $ |#2|) NIL (|has| |#2| (-368)))) (-3953 (($ $ $) NIL (|has| |#2| (-1058))) (($ $) NIL (|has| |#2| (-1058)))) (-3943 (($ $ $) 34 (|has| |#2| (-25)))) (** (($ $ (-777)) NIL (|has| |#2| (-732))) (($ $ (-928)) NIL (|has| |#2| (-732)))) (* (($ (-570) $) NIL (|has| |#2| (-1058))) (($ 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(|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) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-23) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-25) -3749 (|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) -3749 (|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|) -3749 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -3749 (|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)) -3749 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -3749 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -3749 (|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)) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -3749 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -3749 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -3749 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -3749 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -3749 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -3749 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -3749 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -3749 (|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|) -3749 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -3749 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -3749 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -3749 (|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))) +((-3693 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-2295 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-2536 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) +(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -3693 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -2295 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -2536 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) +((-2536 (*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)))) (-2295 (*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)))) (-3693 (*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) -3684 (|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) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -3684 (|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) -3684 (|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 $) -3684 (|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 $) -3684 (|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 $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1231) |has| |#1| (-916))) -((-2818 (((-112) $ $) 19 (|has| |#1| (-1109)))) (-4012 ((|#1| $) 55)) (-2027 ((|#1| $) 45)) (-2558 (((-112) $ (-777)) 8)) (-2183 (($) 7 T CONST)) (-3247 (($ $) 61)) (-2751 (($ $) 49)) (-3090 ((|#1| |#1| $) 47)) (-4138 ((|#1| $) 46)) (-1427 (((-650 |#1|) $) 31 (|has| $ (-6 -4452)))) (-3594 (((-112) $ (-777)) 9)) (-3858 (((-650 |#1|) $) 30 (|has| $ (-6 -4452)))) (-2661 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-2796 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4453)))) (-2536 (($ (-1 |#1| |#1|) $) 36)) (-4323 (((-112) $ (-777)) 10)) (-1853 (((-777) $) 62)) (-1349 (((-1168) $) 22 (|has| |#1| (-1109)))) (-1534 ((|#1| $) 40)) (-2423 ((|#1| |#1| $) 53)) (-4010 ((|#1| |#1| $) 52)) (-4269 (($ |#1| $) 41)) (-3266 (((-777) $) 56)) (-3832 (((-1129) $) 21 (|has| |#1| (-1109)))) (-1372 ((|#1| $) 63)) (-3147 ((|#1| $) 51)) (-3998 ((|#1| $) 50)) (-1685 ((|#1| $) 42)) (-2626 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4452)))) (-2986 (($ $ (-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))))) (-2118 (((-112) $ $) 14)) (-2130 ((|#1| |#1| $) 59)) (-2620 (((-112) $) 11)) (-1622 (($) 12)) (-1786 ((|#1| $) 60)) (-1849 (($) 58) (($ (-650 |#1|)) 57)) (-3250 (((-777) $) 44)) (-3848 (((-777) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4452))) (((-777) |#1| $) 29 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3016 (($ $) 13)) (-2838 (((-868) $) 18 (|has| |#1| (-619 (-868))))) (-3738 ((|#1| $) 54)) (-1723 (((-112) $ $) 23 (|has| |#1| (-1109)))) (-1686 (($ (-650 |#1|)) 43)) (-2208 ((|#1| $) 64)) (-1970 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4452)))) (-3833 (((-112) $ $) 20 (|has| |#1| (-1109)))) (-2827 (((-777) $) 6 (|has| $ (-6 -4452))))) +((-2299 (*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)))) (-2753 (*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)))) (-3995 (*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)))) (-3995 (*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)))) (-2650 (*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)))) (-2603 (*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))))) (-2023 (*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)))) (-2603 (*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))))) (-2023 (*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)))) (-1386 (*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)))) (-2134 (*1 *2 *1) (-12 (-4 *1 (-256 *3 *4 *2 *5)) (-4 *3 (-1058)) (-4 *4 (-856)) (-4 *5 (-799)) (-4 *2 (-269 *4)))) (-2803 (*1 *1 *1) (-12 (-4 *1 (-256 *2 *3 *4 *5)) (-4 *2 (-1058)) (-4 *3 (-856)) (-4 *4 (-269 *3)) (-4 *5 (-799)))) (-3285 (*1 *1 *1) (-12 (-4 *1 (-256 *2 *3 *4 *5)) (-4 *2 (-1058)) (-4 *3 (-856)) (-4 *4 (-269 *3)) (-4 *5 (-799)))) (-2299 (*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 -2299 ((-1 $ (-777)) |t#2|)) (-15 -2753 ((-650 |t#2|) $)) (-15 -3995 ((-777) $ |t#2|)) (-15 -3995 ((-777) $)) (-15 -2650 ((-777) $ |t#2|)) (-15 -2603 ((-650 (-777)) $)) (-15 -2023 ((-777) $)) (-15 -2603 ((-650 (-777)) $ |t#2|)) (-15 -2023 ((-777) $ |t#2|)) (-15 -1386 ((-112) $)) (-15 -2134 (|t#3| $)) (-15 -2803 ($ $)) (-15 -3285 ($ $)) (IF (|has| |t#1| (-235)) (PROGN (-6 (-520 |t#2| |t#1|)) (-6 (-520 |t#2| $)) (-6 (-313 $)) (-15 -2299 ((-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 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-413 (-570)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #0#) -3749 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 |#1|) . T) ((-622 |#2|) . T) ((-622 |#3|) . T) ((-622 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-619 (-868)) . T) ((-174) -3749 (|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) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -3749 (|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) -3749 (|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 $) -3749 (|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 $) -3749 (|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 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1231) |has| |#1| (-916))) +((-2847 (((-112) $ $) 19 (|has| |#1| (-1109)))) (-1947 ((|#1| $) 55)) (-1999 ((|#1| $) 45)) (-2855 (((-112) $ (-777)) 8)) (-2333 (($) 7 T CONST)) (-3420 (($ $) 61)) (-4125 (($ $) 49)) (-4191 ((|#1| |#1| $) 47)) (-3940 ((|#1| $) 46)) (-3976 (((-650 |#1|) $) 31 (|has| $ (-6 -4452)))) (-2497 (((-112) $ (-777)) 9)) (-3069 (((-650 |#1|) $) 30 (|has| $ (-6 -4452)))) (-1314 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-2833 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4453)))) (-2536 (($ (-1 |#1| |#1|) $) 36)) (-2065 (((-112) $ (-777)) 10)) (-1831 (((-777) $) 62)) (-3240 (((-1168) $) 22 (|has| |#1| (-1109)))) (-3398 ((|#1| $) 40)) (-2927 ((|#1| |#1| $) 53)) (-1923 ((|#1| |#1| $) 52)) (-2801 (($ |#1| $) 41)) (-3326 (((-777) $) 56)) (-3891 (((-1129) $) 21 (|has| |#1| (-1109)))) (-2421 ((|#1| $) 63)) (-3600 ((|#1| $) 51)) (-1802 ((|#1| $) 50)) (-4126 ((|#1| $) 42)) (-2231 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4452)))) (-3034 (($ $ (-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))))) (-2914 (((-112) $ $) 14)) (-3043 ((|#1| |#1| $) 59)) (-2171 (((-112) $) 11)) (-1698 (($) 12)) (-3908 ((|#1| $) 60)) (-3347 (($) 58) (($ (-650 |#1|)) 57)) (-3307 (((-777) $) 44)) (-3901 (((-777) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4452))) (((-777) |#1| $) 29 (-12 (|has| |#1| (-1109)) (|has| $ (-6 -4452))))) (-3064 (($ $) 13)) (-2869 (((-868) $) 18 (|has| |#1| (-619 (-868))))) (-1313 ((|#1| $) 54)) (-1344 (((-112) $ $) 23 (|has| |#1| (-1109)))) (-4132 (($ (-650 |#1|)) 43)) (-2636 ((|#1| $) 64)) (-2061 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4452)))) (-3892 (((-112) $ $) 20 (|has| |#1| (-1109)))) (-2857 (((-777) $) 6 (|has| $ (-6 -4452))))) (((-257 |#1|) (-141) (-1227)) (T -257)) -((-1849 (*1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-1849 (*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-257 *3)))) (-3266 (*1 *2 *1) (-12 (-4 *1 (-257 *3)) (-4 *3 (-1227)) (-5 *2 (-777)))) (-4012 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-3738 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2423 (*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-4010 (*1 *2 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-3147 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-3998 (*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227)))) (-2751 (*1 *1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227))))) -(-13 (-1130 |t#1|) (-1004 |t#1|) (-10 -8 (-15 -1849 ($)) (-15 -1849 ($ (-650 |t#1|))) (-15 -3266 ((-777) $)) (-15 -4012 (|t#1| $)) (-15 -3738 (|t#1| $)) (-15 -2423 (|t#1| |t#1| $)) (-15 -4010 (|t#1| |t#1| $)) (-15 -3147 (|t#1| $)) (-15 -3998 (|t#1| $)) (-15 -2751 ($ $)))) -(((-34) . 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T) ((-23) . T) ((-47 |#1| #0=(-777)) . T) ((-25) . T) ((-38 #1=(-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-413 (-570)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #1#) -3684 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 #2=(-1091)) . T) ((-622 |#1|) . T) ((-622 $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-619 (-868)) . 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T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #1#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #1#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #1#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-732) . T) ((-907 #2#) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-893 (-384)) -12 (|has| (-1091) (-893 (-384))) (|has| |#1| (-893 (-384)))) ((-893 (-570)) -12 (|has| (-1091) (-893 (-570))) (|has| |#1| (-893 (-570)))) ((-956 |#1| #0# #2#) . T) ((-916) |has| |#1| (-916)) ((-927) |has| |#1| (-368)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 #2#) . T) ((-1047 |#1|) . T) ((-1060 #1#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-1065 #1#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -3684 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1161) |has| |#1| (-1161)) ((-1227) . T) ((-1231) |has| |#1| (-916))) -((-1624 (((-650 (-1091)) $) 34)) (-4388 (($ $) 31)) (-2418 (($ |#2| |#3|) NIL) (($ $ (-1091) |#3|) 28) (($ $ (-650 (-1091)) (-650 |#3|)) 27)) (-4347 (($ $) 14)) (-4360 ((|#2| $) 12)) (-3954 ((|#3| $) 10))) -(((-1254 |#1| |#2| |#3|) (-10 -8 (-15 -1624 ((-650 (-1091)) |#1|)) (-15 -2418 (|#1| |#1| (-650 (-1091)) (-650 |#3|))) (-15 -2418 (|#1| |#1| (-1091) |#3|)) (-15 -4388 (|#1| |#1|)) (-15 -2418 (|#1| |#2| |#3|)) (-15 -3954 (|#3| |#1|)) (-15 -4347 (|#1| |#1|)) (-15 -4360 (|#2| |#1|))) (-1255 |#2| |#3|) (-1058) (-798)) (T -1254)) -NIL -(-10 -8 (-15 -1624 ((-650 (-1091)) |#1|)) (-15 -2418 (|#1| |#1| (-650 (-1091)) (-650 |#3|))) (-15 -2418 (|#1| |#1| (-1091) |#3|)) (-15 -4388 (|#1| |#1|)) (-15 -2418 (|#1| |#2| |#3|)) (-15 -3954 (|#3| |#1|)) (-15 -4347 (|#1| |#1|)) (-15 -4360 (|#2| |#1|))) -((-2818 (((-112) $ $) 7)) (-2523 (((-112) $) 17)) (-1624 (((-650 (-1091)) $) 86)) (-1444 (((-1186) $) 116)) (-1607 (((-2 (|:| -4074 $) (|:| -4439 $) (|:| |associate| $)) 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|commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-368)) (PROGN (-6 (-311)) (-6 -4448) (-15 -2057 (|t#1| (-413 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-413 (-570)))) (-15 -1363 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-777)) . T) ((-25) . T) ((-38 #1=(-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-413 (-570)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #1#) -3749 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 #2=(-1091)) . T) ((-622 |#1|) . T) ((-622 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-619 (-868)) . T) ((-174) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| (-1091) (-620 (-542))) (|has| |#1| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| (-1091) (-620 (-899 (-384)))) (|has| |#1| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| (-1091) (-620 (-899 (-570)))) (|has| |#1| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) . T) ((-290 (-413 $) (-413 $)) |has| |#1| (-562)) ((-290 |#1| |#1|) . T) ((-290 $ $) . T) ((-294) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-311) |has| |#1| (-368)) ((-313 $) . T) ((-330 |#1| #0#) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -3749 (|has| |#1| (-916)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-520 #2# |#1|) . T) ((-520 #2# $) . T) ((-520 $ $) . T) ((-562) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-652 #1#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #1#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #1#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #1#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-732) . T) ((-907 #2#) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-893 (-384)) -12 (|has| (-1091) (-893 (-384))) (|has| |#1| (-893 (-384)))) ((-893 (-570)) -12 (|has| (-1091) (-893 (-570))) (|has| |#1| (-893 (-570)))) ((-956 |#1| #0# #2#) . T) ((-916) |has| |#1| (-916)) ((-927) |has| |#1| (-368)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 #2#) . T) ((-1047 |#1|) . T) ((-1060 #1#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-1065 #1#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -3749 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1161) |has| |#1| (-1161)) ((-1227) . 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2955146) (-1233 2953451 2953961 2954068 "UINT32" 2954179 T UINT32 (NIL) -8 NIL NIL 2954264) (-1232 2952569 2953079 2953186 "UINT16" 2953297 T UINT16 (NIL) -8 NIL NIL 2953382) (-1231 2950872 2951829 2951859 "UFD" 2952071 T UFD (NIL) -9 NIL 2952185 NIL) (-1230 2950666 2950712 2950807 "UFD-" 2950812 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2949748 2949931 2950147 "UDVO" 2950472 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2947564 2947973 2948444 "UDPO" 2949312 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2947497 2947502 2947532 "TYPE" 2947537 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2947257 2947452 2947483 "TYPEAST" 2947488 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2946228 2946430 2946670 "TWOFACT" 2947051 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2945251 2945637 2945872 "TUPLE" 2946028 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2942942 2943461 2944000 "TUBETOOL" 2944734 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2941791 2941996 2942237 "TUBE" 2942735 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2936520 2940763 2941046 "TS" 2941543 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2925160 2929279 2929376 "TSETCAT" 2934645 NIL TSETCAT (NIL T T T T) -9 NIL 2936176 NIL) (-1219 2919892 2921492 2923383 "TSETCAT-" 2923388 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2914531 2915378 2916307 "TRMANIP" 2919028 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2913972 2914035 2914198 "TRIMAT" 2914463 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2911838 2912075 2912432 "TRIGMNIP" 2913721 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2911358 2911471 2911501 "TRIGCAT" 2911714 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911027 2911106 2911247 "TRIGCAT-" 2911252 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2907872 2909885 2910166 "TREE" 2910781 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2907146 2907674 2907704 "TRANFUN" 2907739 T TRANFUN (NIL) -9 NIL 2907805 NIL) (-1211 2906425 2906616 2906896 "TRANFUN-" 2906901 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2906229 2906261 2906322 "TOPSP" 2906386 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2905577 2905692 2905846 "TOOLSIGN" 2906110 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2904211 2904754 2904993 "TEXTFILE" 2905360 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2902123 2902664 2903093 "TEX" 2903804 T TEX (NIL) -8 NIL NIL NIL) (-1206 2901904 2901935 2902007 "TEX1" 2902086 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2901552 2901615 2901705 "TEMUTL" 2901836 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2899706 2899986 2900311 "TBCMPPK" 2901275 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2891483 2897866 2897922 "TBAGG" 2898322 NIL TBAGG (NIL T T) -9 NIL 2898533 NIL) (-1202 2886553 2888041 2889795 "TBAGG-" 2889800 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2885937 2886044 2886189 "TANEXP" 2886442 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2885448 2885712 2885802 "TALGOP" 2885882 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2878838 2885305 2885398 "TABLE" 2885403 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2878250 2878349 2878487 "TABLEAU" 2878735 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2872858 2874078 2875326 "TABLBUMP" 2877036 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872080 2872227 2872408 "SYSTEM" 2872699 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2868539 2869238 2870021 "SYSSOLP" 2871331 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2868337 2868494 2868525 "SYSPTR" 2868530 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2867373 2867878 2867997 "SYSNNI" 2868183 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868268) (-1192 2866672 2867131 2867210 "SYSINT" 2867270 NIL SYSINT (NIL NIL) -8 NIL NIL 2867315) (-1191 2863004 2863950 2864660 "SYNTAX" 2865984 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2860162 2860764 2861396 "SYMTAB" 2862394 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2855411 2856313 2857296 "SYMS" 2859201 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2852646 2854869 2855099 "SYMPOLY" 2855216 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2852163 2852238 2852361 "SYMFUNC" 2852558 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2848183 2849475 2850288 "SYMBOL" 2851372 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2841722 2843411 2845131 "SWITCH" 2846485 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2834956 2840543 2840846 "SUTS" 2841477 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827022 2834203 2834476 "SUPXS" 2834741 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2818781 2826640 2826766 "SUP" 2826931 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2817940 2818067 2818284 "SUPFRACF" 2818649 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2817561 2817620 2817733 "SUP2" 2817875 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816009 2816283 2816639 "SUMRF" 2817260 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2815344 2815410 2815602 "SUMFS" 2815930 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2799311 2814521 2814772 "SULS" 2815151 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2798913 2799133 2799203 "SUCHTAST" 2799263 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2798208 2798438 2798578 "SUCH" 2798821 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792075 2793114 2794073 "SUBSPACE" 2797296 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2791505 2791595 2791759 "SUBRESP" 2791963 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2784873 2786170 2787481 "STTF" 2790241 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779046 2780166 2781313 "STTFNC" 2783773 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2770359 2772228 2774022 "STTAYLOR" 2777287 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2763489 2770223 2770306 "STRTBL" 2770311 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2758853 2763444 2763475 "STRING" 2763480 T STRING (NIL) -8 NIL NIL NIL) (-1167 2753682 2758196 2758226 "STRICAT" 2758285 T STRICAT (NIL) -9 NIL 2758347 NIL) (-1166 2746435 2751301 2751912 "STREAM" 2753106 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2745945 2746022 2746166 "STREAM3" 2746352 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2744927 2745110 2745345 "STREAM2" 2745758 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2744615 2744667 2744760 "STREAM1" 2744869 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2743631 2743812 2744043 "STINPROD" 2744431 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2743183 2743393 2743423 "STEP" 2743503 T STEP (NIL) -9 NIL 2743581 NIL) (-1160 2742370 2742672 2742820 "STEPAST" 2743057 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2735802 2742269 2742346 "STBL" 2742351 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2730897 2734993 2735036 "STAGG" 2735189 NIL STAGG (NIL T) -9 NIL 2735278 NIL) (-1157 2728599 2729201 2730073 "STAGG-" 2730078 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2726746 2728369 2728461 "STACK" 2728542 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2719441 2724887 2725343 "SREGSET" 2726376 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2711866 2713235 2714748 "SRDCMPK" 2718047 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2704751 2709276 2709306 "SRAGG" 2710609 T SRAGG (NIL) -9 NIL 2711217 NIL) (-1152 2703768 2704023 2704402 "SRAGG-" 2704407 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2698228 2702715 2703136 "SQMATRIX" 2703394 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2691913 2694946 2695673 "SPLTREE" 2697573 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2687876 2688569 2689215 "SPLNODE" 2691339 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2686923 2687156 2687186 "SPFCAT" 2687630 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2685660 2685870 2686134 "SPECOUT" 2686681 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2676770 2678642 2678672 "SPADXPT" 2683348 T SPADXPT (NIL) -9 NIL 2685512 NIL) (-1145 2676531 2676571 2676640 "SPADPRSR" 2676723 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2674580 2676486 2676517 "SPADAST" 2676522 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2666525 2668298 2668341 "SPACEC" 2672714 NIL SPACEC (NIL T) -9 NIL 2674530 NIL) (-1142 2664655 2666457 2666506 "SPACE3" 2666511 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2663407 2663578 2663869 "SORTPAK" 2664460 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2661499 2661802 2662214 "SOLVETRA" 2663071 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2660549 2660771 2661032 "SOLVESER" 2661272 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2655853 2656741 2657736 "SOLVERAD" 2659601 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2651668 2652277 2653006 "SOLVEFOR" 2655220 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2645938 2651017 2651114 "SNTSCAT" 2651119 NIL SNTSCAT (NIL T T T T) -9 NIL 2651189 NIL) (-1135 2640044 2644261 2644652 "SMTS" 2645628 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2634729 2639932 2640009 "SMP" 2640014 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2632888 2633189 2633587 "SMITH" 2634426 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2625601 2629797 2629900 "SMATCAT" 2631251 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631801 NIL) (-1131 2622541 2623364 2624542 "SMATCAT-" 2624547 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2620207 2621777 2621820 "SKAGG" 2622081 NIL SKAGG (NIL T) -9 NIL 2622216 NIL) (-1129 2616533 2619680 2619864 "SINT" 2620016 T SINT (NIL) -8 NIL NIL 2620178) (-1128 2616305 2616343 2616409 "SIMPAN" 2616489 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2615584 2615840 2615980 "SIG" 2616187 T SIG (NIL) -8 NIL NIL NIL) (-1126 2614422 2614643 2614918 "SIGNRF" 2615343 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2613255 2613406 2613690 "SIGNEF" 2614251 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2612561 2612838 2612962 "SIGAST" 2613153 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2610251 2610705 2611211 "SHP" 2612102 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2604103 2610152 2610228 "SHDP" 2610233 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2603676 2603868 2603898 "SGROUP" 2603991 T SGROUP (NIL) -9 NIL 2604053 NIL) (-1120 2603534 2603560 2603633 "SGROUP-" 2603638 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2600325 2601023 2601746 "SGCF" 2602833 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2594693 2599772 2599869 "SFRTCAT" 2599874 NIL SFRTCAT (NIL T T T T) -9 NIL 2599913 NIL) (-1117 2588114 2589132 2590268 "SFRGCD" 2593676 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2581240 2582313 2583499 "SFQCMPK" 2587047 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2580860 2580949 2581060 "SFORT" 2581181 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2579978 2580700 2580821 "SEXOF" 2580826 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2579085 2579859 2579927 "SEX" 2579932 T SEX (NIL) -8 NIL NIL NIL) (-1112 2574866 2575581 2575676 "SEXCAT" 2578298 NIL SEXCAT (NIL T T T T T) -9 NIL 2578858 NIL) (-1111 2572019 2574800 2574848 "SET" 2574853 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570243 2570732 2571037 "SETMN" 2571760 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2569739 2569891 2569921 "SETCAT" 2570097 T SETCAT (NIL) -9 NIL 2570207 NIL) (-1108 2569431 2569509 2569639 "SETCAT-" 2569644 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2565792 2567892 2567935 "SETAGG" 2568805 NIL SETAGG (NIL T) -9 NIL 2569145 NIL) (-1106 2565250 2565366 2565603 "SETAGG-" 2565608 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2564693 2564946 2565047 "SEQAST" 2565171 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2563892 2564186 2564247 "SEGXCAT" 2564533 NIL SEGXCAT (NIL T T) -9 NIL 2564653 NIL) (-1103 2562898 2563558 2563740 "SEG" 2563745 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2561877 2562091 2562134 "SEGCAT" 2562656 NIL SEGCAT (NIL T) -9 NIL 2562877 NIL) (-1101 2560809 2561240 2561448 "SEGBIND" 2561704 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2560430 2560489 2560602 "SEGBIND2" 2560744 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560003 2560231 2560308 "SEGAST" 2560375 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559222 2559348 2559552 "SEG2" 2559847 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2558632 2559157 2559204 "SDVAR" 2559209 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551159 2558402 2558532 "SDPOL" 2558537 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2549752 2550018 2550337 "SCPKG" 2550874 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2548916 2549088 2549280 "SCOPE" 2549582 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548136 2548270 2548449 "SCACHE" 2548771 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2547782 2547968 2547998 "SASTCAT" 2548003 T SASTCAT (NIL) -9 NIL 2548016 NIL) (-1091 2547269 2547617 2547693 "SAOS" 2547728 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2546834 2546869 2547042 "SAERFFC" 2547228 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2540773 2546731 2546811 "SAE" 2546816 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2540366 2540401 2540560 "SAEFACT" 2540732 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2538687 2539001 2539402 "RURPK" 2540032 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2537324 2537630 2537935 "RULESET" 2538521 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2534547 2535077 2535535 "RULE" 2537005 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534159 2534341 2534424 "RULECOLD" 2534499 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2533949 2533977 2534048 "RTVALUE" 2534110 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2533420 2533666 2533760 "RSTRCAST" 2533877 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528268 2529063 2529983 "RSETGCD" 2532619 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2517498 2522577 2522674 "RSETCAT" 2526793 NIL RSETCAT (NIL T T T T) -9 NIL 2527890 NIL) (-1079 2515425 2515964 2516788 "RSETCAT-" 2516793 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2507811 2509187 2510707 "RSDCMPK" 2514024 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505790 2506257 2506331 "RRCC" 2507417 NIL RRCC (NIL T T) -9 NIL 2507761 NIL) (-1076 2505141 2505315 2505594 "RRCC-" 2505599 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2504584 2504837 2504938 "RPTAST" 2505062 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2478430 2487789 2487856 "RPOLCAT" 2498522 NIL RPOLCAT (NIL T T T) -9 NIL 2501682 NIL) (-1073 2469928 2472268 2475390 "RPOLCAT-" 2475395 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2460859 2468139 2468621 "ROUTINE" 2469468 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2457657 2460485 2460625 "ROMAN" 2460741 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2455901 2456517 2456777 "ROIRC" 2457462 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452133 2454417 2454447 "RNS" 2454751 T RNS (NIL) -9 NIL 2455025 NIL) (-1068 2450642 2451025 2451559 "RNS-" 2451634 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450045 2450453 2450483 "RNG" 2450488 T RNG (NIL) -9 NIL 2450509 NIL) (-1066 2449048 2449410 2449612 "RNGBIND" 2449896 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2448447 2448835 2448878 "RMODULE" 2448883 NIL RMODULE (NIL T) -9 NIL 2448910 NIL) (-1064 2447283 2447377 2447713 "RMCAT2" 2448348 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444133 2446629 2446926 "RMATRIX" 2447045 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2436960 2439220 2439335 "RMATCAT" 2442694 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443676 NIL) (-1061 2436335 2436482 2436789 "RMATCAT-" 2436794 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2435736 2435957 2436000 "RLINSET" 2436194 NIL RLINSET (NIL T) -9 NIL 2436285 NIL) (-1059 2435303 2435378 2435506 "RINTERP" 2435655 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2434361 2434915 2434945 "RING" 2435001 T RING (NIL) -9 NIL 2435093 NIL) (-1057 2434153 2434197 2434294 "RING-" 2434299 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2432994 2433231 2433489 "RIDIST" 2433917 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2424283 2432462 2432668 "RGCHAIN" 2432842 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2423633 2424039 2424080 "RGBCSPC" 2424138 NIL RGBCSPC (NIL T) -9 NIL 2424190 NIL) (-1053 2422791 2423172 2423213 "RGBCMDL" 2423445 NIL RGBCMDL (NIL T) -9 NIL 2423559 NIL) (-1052 2419785 2420399 2421069 "RF" 2422155 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2419431 2419494 2419597 "RFFACTOR" 2419716 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419156 2419191 2419288 "RFFACT" 2419390 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2417273 2417637 2418019 "RFDIST" 2418796 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2416726 2416818 2416981 "RETSOL" 2417175 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2416362 2416442 2416485 "RETRACT" 2416618 NIL RETRACT (NIL T) -9 NIL 2416705 NIL) (-1046 2416211 2416236 2416323 "RETRACT-" 2416328 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2415813 2416033 2416103 "RETAST" 2416163 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2408551 2415466 2415593 "RESULT" 2415708 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407142 2407820 2408019 "RESRING" 2408454 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2406778 2406827 2406925 "RESLATC" 2407079 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2406483 2406518 2406625 "REPSQ" 2406737 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2403905 2404485 2405087 "REP" 2405903 T REP (NIL) -7 NIL NIL NIL) (-1039 2403602 2403637 2403748 "REPDB" 2403864 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2397502 2398891 2400114 "REP2" 2402414 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2393879 2394560 2395368 "REP1" 2396729 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2386575 2392020 2392476 "REGSET" 2393509 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2385340 2385723 2385973 "REF" 2386360 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2384717 2384820 2384987 "REDORDER" 2385224 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2380685 2383930 2384157 "RECLOS" 2384545 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2379737 2379918 2380133 "REALSOLV" 2380492 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2379583 2379624 2379654 "REAL" 2379659 T REAL (NIL) -9 NIL 2379694 NIL) (-1030 2376066 2376868 2377752 "REAL0Q" 2378748 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2371667 2372655 2373716 "REAL0" 2375047 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371138 2371384 2371478 "RDUCEAST" 2371595 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2370543 2370615 2370822 "RDIV" 2371060 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2369611 2369785 2369998 "RDIST" 2370365 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368208 2368495 2368867 "RDETRS" 2369319 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366020 2366474 2367012 "RDETR" 2367750 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2364645 2364923 2365320 "RDEEFS" 2365736 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363154 2363460 2363885 "RDEEF" 2364333 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357215 2360135 2360165 "RCFIELD" 2361460 T RCFIELD (NIL) -9 NIL 2362191 NIL) (-1020 2355279 2355783 2356479 "RCFIELD-" 2356554 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2351548 2353380 2353423 "RCAGG" 2354507 NIL RCAGG (NIL T) -9 NIL 2354972 NIL) (-1018 2351176 2351270 2351433 "RCAGG-" 2351438 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2350511 2350623 2350788 "RATRET" 2351060 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350064 2350131 2350252 "RATFACT" 2350439 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2349372 2349492 2349644 "RANDSRC" 2349934 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349106 2349150 2349223 "RADUTIL" 2349321 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2342220 2347937 2348248 "RADIX" 2348829 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2333839 2342062 2342192 "RADFF" 2342197 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2333486 2333561 2333591 "RADCAT" 2333751 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2333268 2333316 2333416 "RADCAT-" 2333421 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2331366 2333038 2333130 "QUEUE" 2333211 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2327903 2331299 2331347 "QUAT" 2331352 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2327534 2327577 2327708 "QUATCT2" 2327854 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2320945 2324290 2324332 "QUATCAT" 2325123 NIL QUATCAT (NIL T) -9 NIL 2325889 NIL) (-1005 2317084 2318121 2319511 "QUATCAT-" 2319607 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2314549 2316160 2316203 "QUAGG" 2316584 NIL QUAGG (NIL T) -9 NIL 2316759 NIL) (-1003 2314151 2314371 2314441 "QQUTAST" 2314501 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313164 2313664 2313829 "QFORM" 2314032 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304157 2309396 2309438 "QFCAT" 2310106 NIL QFCAT (NIL T) -9 NIL 2311107 NIL) (-1000 2299724 2300925 2302519 "QFCAT-" 2302615 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2299358 2299401 2299530 "QFCAT2" 2299675 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2298818 2298928 2299058 "QEQUAT" 2299248 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2291964 2293037 2294221 "QCMPACK" 2297751 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2289513 2289961 2290389 "QALGSET" 2291619 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2288758 2288932 2289164 "QALGSET2" 2289333 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2287448 2287672 2287989 "PWFFINTB" 2288531 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2285630 2285798 2286152 "PUSHVAR" 2287262 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2281548 2282602 2282643 "PTRANFN" 2284527 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2279950 2280241 2280563 "PTPACK" 2281259 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2279582 2279639 2279748 "PTFUNC2" 2279887 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274027 2278424 2278465 "PTCAT" 2278761 NIL PTCAT (NIL T) -9 NIL 2278914 NIL) (-988 2273685 2273720 2273844 "PSQFR" 2273986 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272280 2272578 2272912 "PSEUDLIN" 2273383 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259043 2261414 2263738 "PSETPK" 2270040 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252061 2254801 2254897 "PSETCAT" 2257918 NIL PSETCAT (NIL T T T T) -9 NIL 2258732 NIL) (-984 2249897 2250531 2251352 "PSETCAT-" 2251357 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2249246 2249411 2249439 "PSCURVE" 2249707 T PSCURVE (NIL) -9 NIL 2249874 NIL) (-982 2245244 2246760 2246825 "PSCAT" 2247669 NIL PSCAT (NIL T T T) -9 NIL 2247909 NIL) (-981 2244307 2244523 2244923 "PSCAT-" 2244928 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2242666 2243376 2243639 "PRTITION" 2244064 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2242141 2242387 2242479 "PRTDAST" 2242594 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2231231 2233445 2235633 "PRS" 2240003 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2229042 2230581 2230621 "PRQAGG" 2230804 NIL PRQAGG (NIL T) -9 NIL 2230906 NIL) (-976 2228378 2228683 2228711 "PROPLOG" 2228850 T PROPLOG (NIL) -9 NIL 2228965 NIL) (-975 2227982 2228039 2228162 "PROPFUN2" 2228301 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2227297 2227418 2227590 "PROPFUN1" 2227843 NIL 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NIL 2045337 NIL) (-890 2043178 2043573 2043996 "PARTPERM" 2044593 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2042799 2042862 2042964 "PARSURF" 2043109 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042431 2042488 2042597 "PARSU2" 2042736 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042195 2042235 2042302 "PARSER" 2042384 T PARSER (NIL) -7 NIL NIL NIL) (-886 2041816 2041879 2041981 "PARSCURV" 2042126 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041448 2041505 2041614 "PARSC2" 2041753 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041087 2041145 2041242 "PARPCURV" 2041384 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2040719 2040776 2040885 "PARPC2" 2041024 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2039780 2040092 2040274 "PARAMAST" 2040557 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039300 2039386 2039505 "PAN2EXPR" 2039681 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038077 2038421 2038649 "PALETTE" 2039092 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036470 2037082 2037442 "PAIR" 2037763 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030338 2035727 2035922 "PADICRC" 2036324 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023565 2029682 2029867 "PADICRAT" 2030185 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2021880 2023502 2023547 "PADIC" 2023552 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2018990 2020554 2020594 "PADICCT" 2021175 NIL PADICCT (NIL NIL) -9 NIL 2021457 NIL) (-874 2017947 2018147 2018415 "PADEPAC" 2018777 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-873 2017159 2017292 2017498 "PADE" 2017809 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-872 2015546 2016367 2016647 "OWP" 2016963 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-871 2015039 2015252 2015349 "OVERSET" 2015469 T OVERSET (NIL) -8 NIL NIL NIL) (-870 2014085 2014644 2014816 "OVAR" 2014907 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-869 2013349 2013470 2013631 "OUT" 2013944 T OUT (NIL) -7 NIL NIL NIL) (-868 2002221 2004458 2006658 "OUTFORM" 2011169 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 2001557 2001818 2001945 "OUTBFILE" 2002114 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 2000864 2001029 2001057 "OUTBCON" 2001375 T OUTBCON (NIL) -9 NIL 2001541 NIL) (-865 2000465 2000577 2000734 "OUTBCON-" 2000739 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1999845 2000194 2000283 "OSI" 2000396 T OSI (NIL) -8 NIL NIL NIL) (-863 1999375 1999713 1999741 "OSGROUP" 1999746 T OSGROUP (NIL) -9 NIL 1999768 NIL) (-862 1998120 1998347 1998632 "ORTHPOL" 1999122 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-861 1995671 1997955 1998076 "OREUP" 1998081 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993074 1995362 1995489 "ORESUP" 1995613 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990602 1991102 1991663 "OREPCTO" 1992563 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984288 1986489 1986530 "OREPCAT" 1988878 NIL OREPCAT (NIL T) -9 NIL 1989982 NIL) (-857 1981435 1982217 1983275 "OREPCAT-" 1983280 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980586 1980884 1980912 "ORDSET" 1981221 T ORDSET (NIL) -9 NIL 1981385 NIL) (-855 1980017 1980165 1980389 "ORDSET-" 1980394 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978582 1979373 1979401 "ORDRING" 1979603 T ORDRING (NIL) -9 NIL 1979728 NIL) (-853 1978227 1978321 1978465 "ORDRING-" 1978470 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977607 1978070 1978098 "ORDMON" 1978103 T ORDMON (NIL) -9 NIL 1978124 NIL) (-851 1976769 1976916 1977111 "ORDFUNS" 1977456 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976107 1976526 1976554 "ORDFIN" 1976619 T ORDFIN (NIL) -9 NIL 1976693 NIL) (-849 1972666 1974693 1975102 "ORDCOMP" 1975731 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1971932 1972059 1972245 "ORDCOMP2" 1972526 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968513 1969423 1970237 "OPTPROB" 1971138 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965315 1965954 1966658 "OPTPACK" 1967829 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963002 1963768 1963796 "OPTCAT" 1964615 T OPTCAT (NIL) -9 NIL 1965265 NIL) (-844 1962386 1962679 1962784 "OPSIG" 1962917 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962154 1962193 1962259 "OPQUERY" 1962340 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959285 1960465 1960969 "OP" 1961683 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958659 1958885 1958926 "OPERCAT" 1959138 NIL OPERCAT (NIL T) -9 NIL 1959235 NIL) (-840 1958414 1958470 1958587 "OPERCAT-" 1958592 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955227 1957211 1957580 "ONECOMP" 1958078 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954532 1954647 1954821 "ONECOMP2" 1955099 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953951 1954057 1954187 "OMSERVER" 1954422 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1950813 1953391 1953431 "OMSAGG" 1953492 NIL OMSAGG (NIL T) -9 NIL 1953556 NIL) (-835 1949436 1949699 1949981 "OMPKG" 1950551 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1948866 1948969 1948997 "OM" 1949296 T OM (NIL) -9 NIL NIL NIL) (-833 1947413 1948415 1948584 "OMLO" 1948747 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946373 1946520 1946740 "OMEXPR" 1947239 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945664 1945919 1946055 "OMERR" 1946257 T OMERR (NIL) -8 NIL NIL NIL) (-830 1944815 1945085 1945245 "OMERRK" 1945524 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944266 1944492 1944600 "OMENC" 1944727 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938161 1939346 1940517 "OMDEV" 1943115 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937230 1937401 1937595 "OMCONN" 1937987 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1935751 1936727 1936755 "OINTDOM" 1936760 T OINTDOM (NIL) -9 NIL 1936781 NIL) (-825 1933089 1934439 1934776 "OFMONOID" 1935446 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932500 1933026 1933071 "ODVAR" 1933076 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1929923 1932245 1932400 "ODR" 1932405 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922504 1929699 1929825 "ODPOL" 1929830 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916326 1922376 1922481 "ODP" 1922486 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915092 1915307 1915582 "ODETOOLS" 1916100 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912059 1912717 1913433 "ODESYS" 1914425 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1906941 1907849 1908874 "ODERTRIC" 1911134 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906367 1906449 1906643 "ODERED" 1906853 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903255 1903803 1904480 "ODERAT" 1905790 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900214 1900679 1901276 "ODEPRRIC" 1902784 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898157 1898753 1899239 "ODEPROB" 1899748 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894677 1895162 1895809 "ODEPRIM" 1897636 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1893926 1894028 1894288 "ODEPAL" 1894569 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890088 1890879 1891743 "ODEPACK" 1893082 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889149 1889256 1889478 "ODEINT" 1889977 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883250 1884675 1886122 "ODEIFTBL" 1887722 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878648 1879434 1880386 "ODEEF" 1882409 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1877997 1878086 1878309 "ODECONST" 1878553 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876122 1876783 1876811 "ODECAT" 1877416 T ODECAT (NIL) -9 NIL 1877947 NIL) (-805 1872977 1875827 1875949 "OCT" 1876032 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872615 1872658 1872785 "OCTCT2" 1872928 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867226 1869661 1869701 "OC" 1870798 NIL OC (NIL T) -9 NIL 1871656 NIL) (-802 1864453 1865201 1866191 "OC-" 1866285 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1863805 1864273 1864301 "OCAMON" 1864306 T OCAMON (NIL) -9 NIL 1864327 NIL) (-800 1863336 1863677 1863705 "OASGP" 1863710 T OASGP (NIL) -9 NIL 1863730 NIL) (-799 1862597 1863086 1863114 "OAMONS" 1863154 T OAMONS (NIL) -9 NIL 1863197 NIL) (-798 1862011 1862444 1862472 "OAMON" 1862477 T OAMON (NIL) -9 NIL 1862497 NIL) (-797 1861269 1861787 1861815 "OAGROUP" 1861820 T OAGROUP (NIL) -9 NIL 1861840 NIL) (-796 1860959 1861009 1861097 "NUMTUBE" 1861213 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854532 1856050 1857586 "NUMQUAD" 1859443 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850288 1851276 1852301 "NUMODE" 1853527 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847643 1848523 1848551 "NUMINT" 1849474 T NUMINT (NIL) -9 NIL 1850238 NIL) (-792 1846591 1846788 1847006 "NUMFMT" 1847445 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1832950 1835895 1838427 "NUMERIC" 1844098 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827320 1832399 1832494 "NTSCAT" 1832499 NIL NTSCAT (NIL T T T T) -9 NIL 1832538 NIL) (-789 1826514 1826679 1826872 "NTPOLFN" 1827159 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814591 1823339 1824151 "NSUP" 1825735 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814223 1814280 1814389 "NSUP2" 1814528 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804449 1813997 1814130 "NSMP" 1814135 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1802881 1803182 1803539 "NREP" 1804137 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801472 1801724 1802082 "NPCOEF" 1802624 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800538 1800653 1800869 "NORMRETR" 1801353 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798579 1798869 1799278 "NORMPK" 1800246 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798264 1798292 1798416 "NORMMA" 1798545 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798064 1798221 1798250 "NONE" 1798255 T NONE (NIL) -8 NIL NIL NIL) (-779 1797853 1797882 1797951 "NONE1" 1798028 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797350 1797412 1797591 "NODE1" 1797785 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795631 1796482 1796737 "NNI" 1797084 T NNI (NIL) -8 NIL NIL 1797319) (-776 1794051 1794364 1794728 "NLINSOL" 1795299 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790292 1791287 1792186 "NIPROB" 1793172 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789049 1789283 1789585 "NFINTBAS" 1790054 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788223 1788699 1788740 "NETCLT" 1788912 NIL NETCLT (NIL T) -9 NIL 1788994 NIL) (-772 1786931 1787162 1787443 "NCODIV" 1787991 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786693 1786730 1786805 "NCNTFRAC" 1786888 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1784873 1785237 1785657 "NCEP" 1786318 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1783724 1784497 1784525 "NASRING" 1784635 T NASRING (NIL) -9 NIL 1784715 NIL) (-768 1783519 1783563 1783657 "NASRING-" 1783662 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782626 1783151 1783179 "NARNG" 1783296 T NARNG (NIL) -9 NIL 1783387 NIL) (-766 1782318 1782385 1782519 "NARNG-" 1782524 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781197 1781404 1781639 "NAGSP" 1782103 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772469 1774153 1775826 "NAGS" 1779544 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771017 1771325 1771656 "NAGF07" 1772158 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765555 1766846 1768153 "NAGF04" 1769730 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758523 1760137 1761770 "NAGF02" 1763942 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1753747 1754847 1755964 "NAGF01" 1757426 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747375 1748941 1750526 "NAGE04" 1752182 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738544 1740665 1742795 "NAGE02" 1745265 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734497 1735444 1736408 "NAGE01" 1737600 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732292 1732826 1733384 "NAGD03" 1733959 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724042 1725970 1727924 "NAGD02" 1730358 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1717853 1719278 1720718 "NAGD01" 1722622 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714062 1714884 1715721 "NAGC06" 1717036 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712527 1712859 1713215 "NAGC05" 1713726 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1711903 1712022 1712166 "NAGC02" 1712403 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1710862 1711445 1711485 "NAALG" 1711564 NIL NAALG (NIL T) -9 NIL 1711625 NIL) (-749 1710697 1710726 1710816 "NAALG-" 1710821 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704647 1705755 1706942 "MULTSQFR" 1709593 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1703966 1704041 1704225 "MULTFACT" 1704559 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696690 1700603 1700656 "MTSCAT" 1701726 NIL MTSCAT (NIL T T) -9 NIL 1702241 NIL) (-745 1696402 1696456 1696548 "MTHING" 1696630 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696194 1696227 1696287 "MSYSCMD" 1696362 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692276 1694949 1695269 "MSET" 1695907 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689345 1691837 1691878 "MSETAGG" 1691883 NIL MSETAGG (NIL T) -9 NIL 1691917 NIL) (-741 1685187 1686724 1687469 "MRING" 1688645 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1684753 1684820 1684951 "MRF2" 1685114 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684371 1684406 1684550 "MRATFAC" 1684712 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1681983 1682278 1682709 "MPRFF" 1684076 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676280 1681837 1681934 "MPOLY" 1681939 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1675770 1675805 1676013 "MPCPF" 1676239 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675284 1675327 1675511 "MPC3" 1675721 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674479 1674560 1674781 "MPC2" 1675199 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1672780 1673117 1673507 "MONOTOOL" 1674139 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672005 1672322 1672350 "MONOID" 1672569 T MONOID (NIL) -9 NIL 1672716 NIL) (-731 1671551 1671670 1671851 "MONOID-" 1671856 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662026 1667977 1668036 "MONOGEN" 1668710 NIL MONOGEN (NIL T T) -9 NIL 1669166 NIL) (-729 1659244 1659979 1660979 "MONOGEN-" 1661098 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658077 1658523 1658551 "MONADWU" 1658943 T MONADWU (NIL) -9 NIL 1659181 NIL) (-727 1657449 1657608 1657856 "MONADWU-" 1657861 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1656808 1657052 1657080 "MONAD" 1657287 T MONAD (NIL) -9 NIL 1657399 NIL) (-725 1656493 1656571 1656703 "MONAD-" 1656708 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1654782 1655406 1655685 "MOEBIUS" 1656246 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654060 1654464 1654504 "MODULE" 1654509 NIL MODULE (NIL T) -9 NIL 1654548 NIL) (-722 1653628 1653724 1653914 "MODULE-" 1653919 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651308 1651992 1652319 "MODRING" 1653452 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648252 1649413 1649934 "MODOP" 1650837 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1646840 1647319 1647596 "MODMONOM" 1648115 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1636884 1645131 1645545 "MODMON" 1646477 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634040 1635728 1636004 "MODFIELD" 1636759 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633017 1633321 1633511 "MMLFORM" 1633870 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632543 1632586 1632765 "MMAP" 1632968 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630622 1631389 1631430 "MLO" 1631853 NIL MLO (NIL T) -9 NIL 1632095 NIL) (-713 1627988 1628504 1629106 "MLIFT" 1630103 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627379 1627463 1627617 "MKUCFUNC" 1627899 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1626978 1627048 1627171 "MKRECORD" 1627302 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626025 1626187 1626415 "MKFUNC" 1626789 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625413 1625517 1625673 "MKFLCFN" 1625908 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624690 1624792 1624977 "MKBCFUNC" 1625306 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621397 1624244 1624380 "MINT" 1624574 T MINT (NIL) -8 NIL NIL NIL) (-706 1620209 1620452 1620729 "MHROWRED" 1621152 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615589 1618744 1619149 "MFLOAT" 1619824 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1614946 1615022 1615193 "MFINFACT" 1615501 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611261 1612109 1612993 "MESH" 1614082 T MESH (NIL) -7 NIL NIL NIL) (-702 1609651 1609963 1610316 "MDDFACT" 1610948 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606446 1608810 1608851 "MDAGG" 1609106 NIL MDAGG (NIL T) -9 NIL 1609249 NIL) (-700 1596186 1605739 1605946 "MCMPLX" 1606259 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595323 1595469 1595670 "MCDEN" 1596035 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593213 1593483 1593863 "MCALCFN" 1595053 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592138 1592378 1592611 "MAYBE" 1593019 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1589750 1590273 1590835 "MATSTOR" 1591609 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1585707 1589122 1589370 "MATRIX" 1589535 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581473 1582180 1582916 "MATLIN" 1585064 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571579 1574765 1574842 "MATCAT" 1579722 NIL MATCAT (NIL T T T) -9 NIL 1581139 NIL) (-692 1567935 1568956 1570312 "MATCAT-" 1570317 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566529 1566682 1567015 "MATCAT2" 1567770 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564641 1564965 1565349 "MAPPKG3" 1566204 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563622 1563795 1564017 "MAPPKG2" 1564465 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562121 1562405 1562732 "MAPPKG1" 1563328 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561200 1561527 1561704 "MAPPAST" 1561964 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1560811 1560869 1560992 "MAPHACK3" 1561136 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560403 1560464 1560578 "MAPHACK2" 1560743 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1559841 1559944 1560086 "MAPHACK1" 1560294 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1557920 1558541 1558845 "MAGMA" 1559569 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557399 1557644 1557735 "MACROAST" 1557849 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1553817 1555638 1556099 "M3D" 1556971 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1547892 1552156 1552197 "LZSTAGG" 1552979 NIL LZSTAGG (NIL T) -9 NIL 1553274 NIL) (-679 1543850 1545023 1546480 "LZSTAGG-" 1546485 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1540937 1541741 1542228 "LWORD" 1543395 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540513 1540741 1540816 "LSTAST" 1540882 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1533679 1540284 1540418 "LSQM" 1540423 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1532903 1533042 1533270 "LSPP" 1533534 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1530715 1531016 1531472 "LSMP" 1532592 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527494 1528168 1528898 "LSMP1" 1530017 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521340 1526631 1526672 "LSAGG" 1526734 NIL LSAGG (NIL T) -9 NIL 1526812 NIL) (-671 1518035 1518959 1520172 "LSAGG-" 1520177 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515634 1517179 1517428 "LPOLY" 1517830 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515216 1515301 1515424 "LPEFRAC" 1515543 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513537 1514310 1514563 "LO" 1515048 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513189 1513301 1513329 "LOGIC" 1513440 T LOGIC (NIL) -9 NIL 1513521 NIL) (-666 1513051 1513074 1513145 "LOGIC-" 1513150 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512244 1512384 1512577 "LODOOPS" 1512907 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1509667 1512160 1512226 "LODO" 1512231 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508205 1508440 1508793 "LODOF" 1509414 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504409 1506840 1506881 "LODOCAT" 1507319 NIL LODOCAT (NIL T) -9 NIL 1507530 NIL) (-661 1504142 1504200 1504327 "LODOCAT-" 1504332 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501462 1503983 1504101 "LODO2" 1504106 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1498897 1501399 1501444 "LODO1" 1501449 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1497778 1497943 1498248 "LODEEF" 1498720 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493081 1495972 1496013 "LNAGG" 1496875 NIL LNAGG (NIL T) -9 NIL 1497310 NIL) (-656 1492228 1492442 1492784 "LNAGG-" 1492789 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488364 1489153 1489792 "LMOPS" 1491643 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1487767 1488155 1488196 "LMODULE" 1488201 NIL LMODULE (NIL T) -9 NIL 1488227 NIL) (-653 1484965 1487412 1487535 "LMDICT" 1487677 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484371 1484592 1484633 "LLINSET" 1484824 NIL LLINSET (NIL T) -9 NIL 1484915 NIL) (-651 1484070 1484279 1484339 "LITERAL" 1484344 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477233 1483004 1483308 "LIST" 1483799 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1476758 1476832 1476971 "LIST3" 1477153 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1475765 1475943 1476171 "LIST2" 1476576 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1473899 1474211 1474610 "LIST2MAP" 1475412 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473495 1473732 1473773 "LINSET" 1473778 NIL LINSET (NIL T) -9 NIL 1473812 NIL) (-645 1472156 1472826 1472867 "LINEXP" 1473122 NIL LINEXP (NIL T) -9 NIL 1473271 NIL) (-644 1470803 1471063 1471360 "LINDEP" 1471908 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467570 1468289 1469066 "LIMITRF" 1470058 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1465873 1466169 1466578 "LIMITPS" 1467265 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460301 1465384 1465612 "LIE" 1465694 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459249 1459718 1459758 "LIECAT" 1459898 NIL LIECAT (NIL T) -9 NIL 1460049 NIL) (-639 1459090 1459117 1459205 "LIECAT-" 1459210 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451677 1458630 1458786 "LIB" 1458954 T LIB (NIL) -8 NIL NIL NIL) (-637 1447312 1448195 1449130 "LGROBP" 1450794 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445310 1445584 1445934 "LF" 1447033 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444150 1444842 1444870 "LFCAT" 1445077 T LFCAT (NIL) -9 NIL 1445216 NIL) (-634 1441052 1441682 1442370 "LEXTRIPK" 1443514 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1437796 1438622 1439125 "LEXP" 1440632 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437272 1437517 1437609 "LETAST" 1437724 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435670 1435983 1436384 "LEADCDET" 1436954 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1434860 1434934 1435163 "LAZM3PK" 1435591 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429777 1432937 1433475 "LAUPOL" 1434372 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429356 1429400 1429561 "LAPLACE" 1429727 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427295 1428457 1428708 "LA" 1429189 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426289 1426873 1426914 "LALG" 1426976 NIL LALG (NIL T) -9 NIL 1427035 NIL) (-625 1426003 1426062 1426198 "LALG-" 1426203 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1425838 1425862 1425903 "KVTFROM" 1425965 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424761 1425205 1425390 "KTVLOGIC" 1425673 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424596 1424620 1424661 "KRCFROM" 1424723 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423500 1423687 1423986 "KOVACIC" 1424396 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423335 1423359 1423400 "KONVERT" 1423462 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423170 1423194 1423235 "KOERCE" 1423297 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421001 1421763 1422140 "KERNEL" 1422826 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420497 1420578 1420710 "KERNEL2" 1420915 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414267 1419036 1419090 "KDAGG" 1419467 NIL KDAGG (NIL T T) -9 NIL 1419673 NIL) (-615 1413796 1413920 1414125 "KDAGG-" 1414130 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1406944 1413457 1413612 "KAFILE" 1413674 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401372 1406455 1406683 "JORDAN" 1406765 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400751 1401021 1401142 "JOINAST" 1401271 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400597 1400656 1400711 "JAVACODE" 1400716 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1396849 1398802 1398856 "IXAGG" 1399785 NIL IXAGG (NIL T T) -9 NIL 1400244 NIL) (-609 1395768 1396074 1396493 "IXAGG-" 1396498 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391298 1395690 1395749 "IVECTOR" 1395754 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390064 1390301 1390567 "ITUPLE" 1391065 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388566 1388743 1389038 "ITRIGMNP" 1389886 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387311 1387515 1387798 "ITFUN3" 1388342 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1386943 1387000 1387109 "ITFUN2" 1387248 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386102 1386423 1386597 "ITFORM" 1386789 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384063 1385122 1385400 "ITAYLOR" 1385857 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373008 1378200 1379363 "ISUPS" 1382933 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372112 1372252 1372488 "ISUMP" 1372855 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367487 1372057 1372098 "ISTRING" 1372103 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1366963 1367208 1367300 "ISAST" 1367415 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366172 1366254 1366470 "IRURPK" 1366877 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365108 1365309 1365549 "IRSN" 1365952 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363179 1363534 1363963 "IRRF2F" 1364746 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1362926 1362964 1363040 "IRREDFFX" 1363135 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361541 1361800 1362099 "IROOT" 1362659 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358145 1359225 1359917 "IR" 1360881 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357350 1357638 1357789 "IRFORM" 1358014 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1354963 1355458 1356024 "IR2" 1356828 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354063 1354176 1354390 "IR2F" 1354846 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1353854 1353888 1353948 "IPRNTPK" 1354023 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350435 1353743 1353812 "IPF" 1353817 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348762 1350360 1350417 "IPADIC" 1350422 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348074 1348322 1348452 "IP4ADDR" 1348652 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347448 1347703 1347835 "IOMODE" 1347962 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346521 1347045 1347172 "IOBFILE" 1347341 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346009 1346425 1346453 "IOBCON" 1346458 T IOBCON (NIL) -9 NIL 1346479 NIL) (-581 1345520 1345578 1345761 "INVLAPLA" 1345945 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335168 1337522 1339908 "INTTR" 1343184 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331503 1332245 1333110 "INTTOOLS" 1334353 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331089 1331180 1331297 "INTSLPE" 1331406 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329042 1331012 1331071 "INTRVL" 1331076 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326644 1327156 1327731 "INTRF" 1328527 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326055 1326152 1326294 "INTRET" 1326542 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324052 1324441 1324911 "INTRAT" 1325663 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321315 1321898 1322517 "INTPM" 1323537 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318060 1318659 1319397 "INTPAF" 1320701 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313239 1314201 1315252 "INTPACK" 1317029 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310187 1313036 1313145 "INT" 1313150 T INT (NIL) -8 NIL NIL NIL) (-569 1309439 1309591 1309799 "INTHERTR" 1310029 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1308878 1308958 1309146 "INTHERAL" 1309353 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306724 1307167 1307624 "INTHEORY" 1308441 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298130 1299751 1301523 "INTG0" 1305076 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278703 1283493 1288303 "INTFTBL" 1293340 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1277952 1278090 1278263 "INTFACT" 1278562 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275379 1275825 1276382 "INTEF" 1277506 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273746 1274485 1274513 "INTDOM" 1274814 T INTDOM (NIL) -9 NIL 1275021 NIL) (-561 1273115 1273289 1273531 "INTDOM-" 1273536 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269503 1271431 1271485 "INTCAT" 1272284 NIL INTCAT (NIL T) -9 NIL 1272605 NIL) (-559 1268975 1269078 1269206 "INTBIT" 1269395 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267674 1267828 1268135 "INTALG" 1268820 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267157 1267247 1267404 "INTAF" 1267578 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260500 1266967 1267107 "INTABL" 1267112 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1259833 1260299 1260364 "INT8" 1260398 T INT8 (NIL) -8 NIL NIL 1260443) (-554 1259165 1259631 1259696 "INT64" 1259730 T INT64 (NIL) -8 NIL NIL 1259775) (-553 1258497 1258963 1259028 "INT32" 1259062 T INT32 (NIL) -8 NIL NIL 1259107) (-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 -3030 (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 (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 3228419 3228424 3228429 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3228404 3228409 3228414 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3228389 3228394 3228399 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3228374 3228379 3228384 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1306 3227517 3228249 3228326 "ZMOD" 3228331 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1305 3226627 3226791 3227000 "ZLINDEP" 3227349 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1304 3215927 3217695 3219667 "ZDSOLVE" 3224757 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1303 3215173 3215314 3215503 "YSTREAM" 3215773 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1302 3214601 3214847 3214960 "YDIAGRAM" 3215082 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1301 3212375 3213902 3214106 "XRPOLY" 3214444 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3208928 3210246 3210821 "XPR" 3211847 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3206649 3208259 3208463 "XPOLY" 3208759 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3204302 3205670 3205725 "XPOLYC" 3206013 NIL XPOLYC (NIL T T) -9 NIL 3206126 NIL) (-1297 3200678 3202819 3203207 "XPBWPOLY" 3203960 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3196373 3198668 3198710 "XF" 3199331 NIL XF (NIL T) -9 NIL 3199731 NIL) (-1295 3195994 3196082 3196251 "XF-" 3196256 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191190 3192479 3192534 "XFALG" 3194706 NIL XFALG (NIL T T) -9 NIL 3195495 NIL) (-1293 3190323 3190427 3190632 "XEXPPKG" 3191082 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3188432 3190173 3190269 "XDPOLY" 3190274 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3187239 3187839 3187882 "XALG" 3187887 NIL XALG (NIL T) -9 NIL 3187998 NIL) (-1290 3180681 3185216 3185710 "WUTSET" 3186831 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3178937 3179733 3180056 "WP" 3180492 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3178539 3178759 3178829 "WHILEAST" 3178889 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178011 3178256 3178350 "WHEREAST" 3178467 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3176897 3177095 3177390 "WFFINTBS" 3177808 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3174801 3175228 3175690 "WEIER" 3176469 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3173847 3174297 3174339 "VSPACE" 3174475 NIL VSPACE (NIL T) -9 NIL 3174549 NIL) (-1283 3173685 3173712 3173803 "VSPACE-" 3173808 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3173494 3173536 3173604 "VOID" 3173639 T VOID (NIL) -8 NIL NIL NIL) (-1281 3171630 3171989 3172395 "VIEW" 3173110 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168054 3168693 3169430 "VIEWDEF" 3170915 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3157358 3159602 3161775 "VIEW3D" 3165903 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3149609 3151269 3152848 "VIEW2D" 3155801 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3144962 3149379 3149471 "VECTOR" 3149552 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3143539 3143798 3144116 "VECTOR2" 3144692 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3136981 3141290 3141333 "VECTCAT" 3142328 NIL VECTCAT (NIL T) -9 NIL 3142915 NIL) (-1274 3135995 3136249 3136639 "VECTCAT-" 3136644 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3135449 3135646 3135766 "VARIABLE" 3135910 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3135382 3135387 3135417 "UTYPE" 3135422 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3134212 3134366 3134628 "UTSODETL" 3135208 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3131652 3132112 3132636 "UTSODE" 3133753 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3123490 3129278 3129767 "UTS" 3131221 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3114327 3119695 3119738 "UTSCAT" 3120850 NIL UTSCAT (NIL T) -9 NIL 3121608 NIL) (-1267 3111675 3112397 3113386 "UTSCAT-" 3113391 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3111302 3111345 3111478 "UTS2" 3111626 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3105528 3108140 3108183 "URAGG" 3110253 NIL URAGG (NIL T) -9 NIL 3110976 NIL) (-1264 3102467 3103330 3104453 "URAGG-" 3104458 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3098176 3101102 3101567 "UPXSSING" 3102131 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3090242 3097423 3097696 "UPXS" 3097961 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3083315 3090146 3090218 "UPXSCONS" 3090223 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073023 3079817 3079879 "UPXSCCA" 3080453 NIL UPXSCCA (NIL T T) -9 NIL 3080686 NIL) (-1259 3072661 3072746 3072920 "UPXSCCA-" 3072925 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3062221 3068788 3068831 "UPXSCAT" 3069479 NIL UPXSCAT (NIL T) -9 NIL 3070088 NIL) (-1257 3061651 3061730 3061909 "UPXS2" 3062136 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3060305 3060558 3060909 "UPSQFREE" 3061394 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3053778 3056836 3056891 "UPSCAT" 3057971 NIL UPSCAT (NIL T T) -9 NIL 3058736 NIL) (-1254 3052982 3053189 3053516 "UPSCAT-" 3053521 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3038623 3046391 3046434 "UPOLYC" 3048535 NIL UPOLYC (NIL T) -9 NIL 3049756 NIL) (-1252 3029951 3032377 3035524 "UPOLYC-" 3035529 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3029578 3029621 3029754 "UPOLYC2" 3029902 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3021389 3029261 3029390 "UP" 3029497 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3020728 3020835 3020999 "UPMP" 3021278 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3020281 3020362 3020501 "UPDIVP" 3020641 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3018849 3019098 3019414 "UPDECOMP" 3020030 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018080 3018192 3018378 "UPCDEN" 3018733 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3017599 3017668 3017817 "UP2" 3018005 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016066 3016803 3017080 "UNISEG" 3017357 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3015281 3015408 3015613 "UNISEG2" 3015909 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3014341 3014521 3014747 "UNIFACT" 3015097 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2998273 3013518 3013769 "ULS" 3014148 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2986271 2998177 2998249 "ULSCONS" 2998254 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2968279 2980265 2980327 "ULSCCAT" 2980965 NIL ULSCCAT (NIL T T) -9 NIL 2981254 NIL) (-1238 2967329 2967574 2967962 "ULSCCAT-" 2967967 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2956666 2963147 2963190 "ULSCAT" 2964053 NIL ULSCAT (NIL T) -9 NIL 2964784 NIL) (-1236 2956096 2956175 2956354 "ULS2" 2956581 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2955215 2955725 2955832 "UINT8" 2955943 T UINT8 (NIL) -8 NIL NIL 2956028) (-1234 2954333 2954843 2954950 "UINT64" 2955061 T UINT64 (NIL) -8 NIL NIL 2955146) (-1233 2953451 2953961 2954068 "UINT32" 2954179 T UINT32 (NIL) -8 NIL NIL 2954264) (-1232 2952569 2953079 2953186 "UINT16" 2953297 T UINT16 (NIL) -8 NIL NIL 2953382) (-1231 2950872 2951829 2951859 "UFD" 2952071 T UFD (NIL) -9 NIL 2952185 NIL) (-1230 2950666 2950712 2950807 "UFD-" 2950812 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2949748 2949931 2950147 "UDVO" 2950472 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2947564 2947973 2948444 "UDPO" 2949312 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2947497 2947502 2947532 "TYPE" 2947537 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2947257 2947452 2947483 "TYPEAST" 2947488 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2946228 2946430 2946670 "TWOFACT" 2947051 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2945251 2945637 2945872 "TUPLE" 2946028 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2942942 2943461 2944000 "TUBETOOL" 2944734 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2941791 2941996 2942237 "TUBE" 2942735 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2936520 2940763 2941046 "TS" 2941543 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2925160 2929279 2929376 "TSETCAT" 2934645 NIL TSETCAT (NIL T T T T) -9 NIL 2936176 NIL) (-1219 2919892 2921492 2923383 "TSETCAT-" 2923388 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2914531 2915378 2916307 "TRMANIP" 2919028 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2913972 2914035 2914198 "TRIMAT" 2914463 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2911838 2912075 2912432 "TRIGMNIP" 2913721 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2911358 2911471 2911501 "TRIGCAT" 2911714 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911027 2911106 2911247 "TRIGCAT-" 2911252 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2907872 2909885 2910166 "TREE" 2910781 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2907146 2907674 2907704 "TRANFUN" 2907739 T TRANFUN (NIL) -9 NIL 2907805 NIL) (-1211 2906425 2906616 2906896 "TRANFUN-" 2906901 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2906229 2906261 2906322 "TOPSP" 2906386 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2905577 2905692 2905846 "TOOLSIGN" 2906110 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2904211 2904754 2904993 "TEXTFILE" 2905360 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2902123 2902664 2903093 "TEX" 2903804 T TEX (NIL) -8 NIL NIL NIL) (-1206 2901904 2901935 2902007 "TEX1" 2902086 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2901552 2901615 2901705 "TEMUTL" 2901836 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2899706 2899986 2900311 "TBCMPPK" 2901275 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2891483 2897866 2897922 "TBAGG" 2898322 NIL TBAGG (NIL T T) -9 NIL 2898533 NIL) (-1202 2886553 2888041 2889795 "TBAGG-" 2889800 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2885937 2886044 2886189 "TANEXP" 2886442 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2885448 2885712 2885802 "TALGOP" 2885882 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2878838 2885305 2885398 "TABLE" 2885403 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2878250 2878349 2878487 "TABLEAU" 2878735 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2872858 2874078 2875326 "TABLBUMP" 2877036 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872080 2872227 2872408 "SYSTEM" 2872699 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2868539 2869238 2870021 "SYSSOLP" 2871331 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2868337 2868494 2868525 "SYSPTR" 2868530 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2867373 2867878 2867997 "SYSNNI" 2868183 NIL SYSNNI (NIL NIL) -8 NIL NIL 2868268) (-1192 2866672 2867131 2867210 "SYSINT" 2867270 NIL SYSINT (NIL NIL) -8 NIL NIL 2867315) (-1191 2863004 2863950 2864660 "SYNTAX" 2865984 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2860162 2860764 2861396 "SYMTAB" 2862394 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2855411 2856313 2857296 "SYMS" 2859201 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2852646 2854869 2855099 "SYMPOLY" 2855216 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2852163 2852238 2852361 "SYMFUNC" 2852558 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2848183 2849475 2850288 "SYMBOL" 2851372 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2841722 2843411 2845131 "SWITCH" 2846485 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2834956 2840543 2840846 "SUTS" 2841477 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827022 2834203 2834476 "SUPXS" 2834741 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2818781 2826640 2826766 "SUP" 2826931 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2817940 2818067 2818284 "SUPFRACF" 2818649 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2817561 2817620 2817733 "SUP2" 2817875 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816009 2816283 2816639 "SUMRF" 2817260 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2815344 2815410 2815602 "SUMFS" 2815930 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2799311 2814521 2814772 "SULS" 2815151 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2798913 2799133 2799203 "SUCHTAST" 2799263 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2798208 2798438 2798578 "SUCH" 2798821 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792075 2793114 2794073 "SUBSPACE" 2797296 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2791505 2791595 2791759 "SUBRESP" 2791963 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2784873 2786170 2787481 "STTF" 2790241 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779046 2780166 2781313 "STTFNC" 2783773 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2770359 2772228 2774022 "STTAYLOR" 2777287 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2763489 2770223 2770306 "STRTBL" 2770311 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2758853 2763444 2763475 "STRING" 2763480 T STRING (NIL) -8 NIL NIL NIL) (-1167 2753682 2758196 2758226 "STRICAT" 2758285 T STRICAT (NIL) -9 NIL 2758347 NIL) (-1166 2746435 2751301 2751912 "STREAM" 2753106 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2745945 2746022 2746166 "STREAM3" 2746352 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2744927 2745110 2745345 "STREAM2" 2745758 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2744615 2744667 2744760 "STREAM1" 2744869 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2743631 2743812 2744043 "STINPROD" 2744431 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2743183 2743393 2743423 "STEP" 2743503 T STEP (NIL) -9 NIL 2743581 NIL) (-1160 2742370 2742672 2742820 "STEPAST" 2743057 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2735802 2742269 2742346 "STBL" 2742351 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2730897 2734993 2735036 "STAGG" 2735189 NIL STAGG (NIL T) -9 NIL 2735278 NIL) (-1157 2728599 2729201 2730073 "STAGG-" 2730078 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2726746 2728369 2728461 "STACK" 2728542 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2719441 2724887 2725343 "SREGSET" 2726376 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2711866 2713235 2714748 "SRDCMPK" 2718047 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2704751 2709276 2709306 "SRAGG" 2710609 T SRAGG (NIL) -9 NIL 2711217 NIL) (-1152 2703768 2704023 2704402 "SRAGG-" 2704407 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2698228 2702715 2703136 "SQMATRIX" 2703394 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2691913 2694946 2695673 "SPLTREE" 2697573 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2687876 2688569 2689215 "SPLNODE" 2691339 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2686923 2687156 2687186 "SPFCAT" 2687630 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2685660 2685870 2686134 "SPECOUT" 2686681 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2676770 2678642 2678672 "SPADXPT" 2683348 T SPADXPT (NIL) -9 NIL 2685512 NIL) (-1145 2676531 2676571 2676640 "SPADPRSR" 2676723 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2674580 2676486 2676517 "SPADAST" 2676522 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2666525 2668298 2668341 "SPACEC" 2672714 NIL SPACEC (NIL T) -9 NIL 2674530 NIL) (-1142 2664655 2666457 2666506 "SPACE3" 2666511 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2663407 2663578 2663869 "SORTPAK" 2664460 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2661499 2661802 2662214 "SOLVETRA" 2663071 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2660549 2660771 2661032 "SOLVESER" 2661272 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2655853 2656741 2657736 "SOLVERAD" 2659601 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2651668 2652277 2653006 "SOLVEFOR" 2655220 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2645938 2651017 2651114 "SNTSCAT" 2651119 NIL SNTSCAT (NIL T T T T) -9 NIL 2651189 NIL) (-1135 2640044 2644261 2644652 "SMTS" 2645628 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2634729 2639932 2640009 "SMP" 2640014 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2632888 2633189 2633587 "SMITH" 2634426 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2625601 2629797 2629900 "SMATCAT" 2631251 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631801 NIL) (-1131 2622541 2623364 2624542 "SMATCAT-" 2624547 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2620207 2621777 2621820 "SKAGG" 2622081 NIL SKAGG (NIL T) -9 NIL 2622216 NIL) (-1129 2616533 2619680 2619864 "SINT" 2620016 T SINT (NIL) -8 NIL NIL 2620178) (-1128 2616305 2616343 2616409 "SIMPAN" 2616489 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2615584 2615840 2615980 "SIG" 2616187 T SIG (NIL) -8 NIL NIL NIL) (-1126 2614422 2614643 2614918 "SIGNRF" 2615343 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2613255 2613406 2613690 "SIGNEF" 2614251 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2612561 2612838 2612962 "SIGAST" 2613153 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2610251 2610705 2611211 "SHP" 2612102 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2604103 2610152 2610228 "SHDP" 2610233 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2603676 2603868 2603898 "SGROUP" 2603991 T SGROUP (NIL) -9 NIL 2604053 NIL) (-1120 2603534 2603560 2603633 "SGROUP-" 2603638 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2600325 2601023 2601746 "SGCF" 2602833 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2594693 2599772 2599869 "SFRTCAT" 2599874 NIL SFRTCAT (NIL T T T T) -9 NIL 2599913 NIL) (-1117 2588114 2589132 2590268 "SFRGCD" 2593676 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2581240 2582313 2583499 "SFQCMPK" 2587047 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2580860 2580949 2581060 "SFORT" 2581181 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2579978 2580700 2580821 "SEXOF" 2580826 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2579085 2579859 2579927 "SEX" 2579932 T SEX (NIL) -8 NIL NIL NIL) (-1112 2574866 2575581 2575676 "SEXCAT" 2578298 NIL SEXCAT (NIL T T T T T) -9 NIL 2578858 NIL) (-1111 2572019 2574800 2574848 "SET" 2574853 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570243 2570732 2571037 "SETMN" 2571760 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2569739 2569891 2569921 "SETCAT" 2570097 T SETCAT (NIL) -9 NIL 2570207 NIL) (-1108 2569431 2569509 2569639 "SETCAT-" 2569644 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2565792 2567892 2567935 "SETAGG" 2568805 NIL SETAGG (NIL T) -9 NIL 2569145 NIL) (-1106 2565250 2565366 2565603 "SETAGG-" 2565608 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2564693 2564946 2565047 "SEQAST" 2565171 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2563892 2564186 2564247 "SEGXCAT" 2564533 NIL SEGXCAT (NIL T T) -9 NIL 2564653 NIL) (-1103 2562898 2563558 2563740 "SEG" 2563745 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2561877 2562091 2562134 "SEGCAT" 2562656 NIL SEGCAT (NIL T) -9 NIL 2562877 NIL) (-1101 2560809 2561240 2561448 "SEGBIND" 2561704 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2560430 2560489 2560602 "SEGBIND2" 2560744 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560003 2560231 2560308 "SEGAST" 2560375 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559222 2559348 2559552 "SEG2" 2559847 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2558632 2559157 2559204 "SDVAR" 2559209 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551159 2558402 2558532 "SDPOL" 2558537 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2549752 2550018 2550337 "SCPKG" 2550874 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2548916 2549088 2549280 "SCOPE" 2549582 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548136 2548270 2548449 "SCACHE" 2548771 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2547782 2547968 2547998 "SASTCAT" 2548003 T SASTCAT (NIL) -9 NIL 2548016 NIL) (-1091 2547269 2547617 2547693 "SAOS" 2547728 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2546834 2546869 2547042 "SAERFFC" 2547228 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2540773 2546731 2546811 "SAE" 2546816 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2540366 2540401 2540560 "SAEFACT" 2540732 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2538687 2539001 2539402 "RURPK" 2540032 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2537324 2537630 2537935 "RULESET" 2538521 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2534547 2535077 2535535 "RULE" 2537005 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534159 2534341 2534424 "RULECOLD" 2534499 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2533949 2533977 2534048 "RTVALUE" 2534110 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2533420 2533666 2533760 "RSTRCAST" 2533877 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528268 2529063 2529983 "RSETGCD" 2532619 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2517498 2522577 2522674 "RSETCAT" 2526793 NIL RSETCAT (NIL T T T T) -9 NIL 2527890 NIL) (-1079 2515425 2515964 2516788 "RSETCAT-" 2516793 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2507811 2509187 2510707 "RSDCMPK" 2514024 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505790 2506257 2506331 "RRCC" 2507417 NIL RRCC (NIL T T) -9 NIL 2507761 NIL) (-1076 2505141 2505315 2505594 "RRCC-" 2505599 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2504584 2504837 2504938 "RPTAST" 2505062 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2478430 2487789 2487856 "RPOLCAT" 2498522 NIL RPOLCAT (NIL T T T) -9 NIL 2501682 NIL) (-1073 2469928 2472268 2475390 "RPOLCAT-" 2475395 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2460859 2468139 2468621 "ROUTINE" 2469468 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2457657 2460485 2460625 "ROMAN" 2460741 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2455901 2456517 2456777 "ROIRC" 2457462 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452133 2454417 2454447 "RNS" 2454751 T RNS (NIL) -9 NIL 2455025 NIL) (-1068 2450642 2451025 2451559 "RNS-" 2451634 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450045 2450453 2450483 "RNG" 2450488 T RNG (NIL) -9 NIL 2450509 NIL) (-1066 2449048 2449410 2449612 "RNGBIND" 2449896 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2448447 2448835 2448878 "RMODULE" 2448883 NIL RMODULE (NIL T) -9 NIL 2448910 NIL) (-1064 2447283 2447377 2447713 "RMCAT2" 2448348 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444133 2446629 2446926 "RMATRIX" 2447045 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2436960 2439220 2439335 "RMATCAT" 2442694 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443676 NIL) (-1061 2436335 2436482 2436789 "RMATCAT-" 2436794 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2435736 2435957 2436000 "RLINSET" 2436194 NIL RLINSET (NIL T) -9 NIL 2436285 NIL) (-1059 2435303 2435378 2435506 "RINTERP" 2435655 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2434361 2434915 2434945 "RING" 2435001 T RING (NIL) -9 NIL 2435093 NIL) (-1057 2434153 2434197 2434294 "RING-" 2434299 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2432994 2433231 2433489 "RIDIST" 2433917 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2424283 2432462 2432668 "RGCHAIN" 2432842 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2423633 2424039 2424080 "RGBCSPC" 2424138 NIL RGBCSPC (NIL T) -9 NIL 2424190 NIL) (-1053 2422791 2423172 2423213 "RGBCMDL" 2423445 NIL RGBCMDL (NIL T) -9 NIL 2423559 NIL) (-1052 2419785 2420399 2421069 "RF" 2422155 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2419431 2419494 2419597 "RFFACTOR" 2419716 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419156 2419191 2419288 "RFFACT" 2419390 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2417273 2417637 2418019 "RFDIST" 2418796 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2416726 2416818 2416981 "RETSOL" 2417175 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2416362 2416442 2416485 "RETRACT" 2416618 NIL RETRACT (NIL T) -9 NIL 2416705 NIL) (-1046 2416211 2416236 2416323 "RETRACT-" 2416328 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2415813 2416033 2416103 "RETAST" 2416163 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2408551 2415466 2415593 "RESULT" 2415708 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407142 2407820 2408019 "RESRING" 2408454 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2406778 2406827 2406925 "RESLATC" 2407079 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2406483 2406518 2406625 "REPSQ" 2406737 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2403905 2404485 2405087 "REP" 2405903 T REP (NIL) -7 NIL NIL NIL) (-1039 2403602 2403637 2403748 "REPDB" 2403864 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2397502 2398891 2400114 "REP2" 2402414 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2393879 2394560 2395368 "REP1" 2396729 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2386575 2392020 2392476 "REGSET" 2393509 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2385340 2385723 2385973 "REF" 2386360 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2384717 2384820 2384987 "REDORDER" 2385224 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2380685 2383930 2384157 "RECLOS" 2384545 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2379737 2379918 2380133 "REALSOLV" 2380492 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2379583 2379624 2379654 "REAL" 2379659 T REAL (NIL) -9 NIL 2379694 NIL) (-1030 2376066 2376868 2377752 "REAL0Q" 2378748 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2371667 2372655 2373716 "REAL0" 2375047 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371138 2371384 2371478 "RDUCEAST" 2371595 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2370543 2370615 2370822 "RDIV" 2371060 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2369611 2369785 2369998 "RDIST" 2370365 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368208 2368495 2368867 "RDETRS" 2369319 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366020 2366474 2367012 "RDETR" 2367750 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2364645 2364923 2365320 "RDEEFS" 2365736 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363154 2363460 2363885 "RDEEF" 2364333 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357215 2360135 2360165 "RCFIELD" 2361460 T RCFIELD (NIL) -9 NIL 2362191 NIL) (-1020 2355279 2355783 2356479 "RCFIELD-" 2356554 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2351548 2353380 2353423 "RCAGG" 2354507 NIL RCAGG (NIL T) -9 NIL 2354972 NIL) (-1018 2351176 2351270 2351433 "RCAGG-" 2351438 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2350511 2350623 2350788 "RATRET" 2351060 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350064 2350131 2350252 "RATFACT" 2350439 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2349372 2349492 2349644 "RANDSRC" 2349934 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349106 2349150 2349223 "RADUTIL" 2349321 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2342220 2347937 2348248 "RADIX" 2348829 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2333839 2342062 2342192 "RADFF" 2342197 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2333486 2333561 2333591 "RADCAT" 2333751 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2333268 2333316 2333416 "RADCAT-" 2333421 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2331366 2333038 2333130 "QUEUE" 2333211 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2327903 2331299 2331347 "QUAT" 2331352 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2327534 2327577 2327708 "QUATCT2" 2327854 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2320945 2324290 2324332 "QUATCAT" 2325123 NIL QUATCAT (NIL T) -9 NIL 2325889 NIL) (-1005 2317084 2318121 2319511 "QUATCAT-" 2319607 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2314549 2316160 2316203 "QUAGG" 2316584 NIL QUAGG (NIL T) -9 NIL 2316759 NIL) (-1003 2314151 2314371 2314441 "QQUTAST" 2314501 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313164 2313664 2313829 "QFORM" 2314032 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1001 2304157 2309396 2309438 "QFCAT" 2310106 NIL QFCAT (NIL T) -9 NIL 2311107 NIL) (-1000 2299724 2300925 2302519 "QFCAT-" 2302615 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-999 2299358 2299401 2299530 "QFCAT2" 2299675 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2298818 2298928 2299058 "QEQUAT" 2299248 T QEQUAT (NIL) -8 NIL NIL NIL) (-997 2291964 2293037 2294221 "QCMPACK" 2297751 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-996 2289513 2289961 2290389 "QALGSET" 2291619 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-995 2288758 2288932 2289164 "QALGSET2" 2289333 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-994 2287448 2287672 2287989 "PWFFINTB" 2288531 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-993 2285630 2285798 2286152 "PUSHVAR" 2287262 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-992 2281548 2282602 2282643 "PTRANFN" 2284527 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-991 2279950 2280241 2280563 "PTPACK" 2281259 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-990 2279582 2279639 2279748 "PTFUNC2" 2279887 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-989 2274027 2278424 2278465 "PTCAT" 2278761 NIL PTCAT (NIL T) -9 NIL 2278914 NIL) (-988 2273685 2273720 2273844 "PSQFR" 2273986 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-987 2272280 2272578 2272912 "PSEUDLIN" 2273383 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-986 2259043 2261414 2263738 "PSETPK" 2270040 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-985 2252061 2254801 2254897 "PSETCAT" 2257918 NIL PSETCAT (NIL T T T T) -9 NIL 2258732 NIL) (-984 2249897 2250531 2251352 "PSETCAT-" 2251357 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-983 2249246 2249411 2249439 "PSCURVE" 2249707 T PSCURVE (NIL) -9 NIL 2249874 NIL) (-982 2245244 2246760 2246825 "PSCAT" 2247669 NIL PSCAT (NIL T T T) -9 NIL 2247909 NIL) (-981 2244307 2244523 2244923 "PSCAT-" 2244928 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-980 2242666 2243376 2243639 "PRTITION" 2244064 T PRTITION (NIL) -8 NIL NIL NIL) (-979 2242141 2242387 2242479 "PRTDAST" 2242594 T PRTDAST (NIL) -8 NIL NIL NIL) (-978 2231231 2233445 2235633 "PRS" 2240003 NIL PRS (NIL T T) -7 NIL NIL NIL) (-977 2229042 2230581 2230621 "PRQAGG" 2230804 NIL PRQAGG (NIL T) -9 NIL 2230906 NIL) (-976 2228378 2228683 2228711 "PROPLOG" 2228850 T PROPLOG (NIL) -9 NIL 2228965 NIL) (-975 2227982 2228039 2228162 "PROPFUN2" 2228301 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-974 2227297 2227418 2227590 "PROPFUN1" 2227843 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-973 2225478 2226044 2226341 "PROPFRML" 2227033 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-972 2224947 2225054 2225182 "PROPERTY" 2225370 T PROPERTY (NIL) -8 NIL NIL NIL) (-971 2219005 2223113 2223933 "PRODUCT" 2224173 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-970 2216283 2218463 2218697 "PR" 2218816 NIL PR (NIL T T) -8 NIL NIL NIL) (-969 2216079 2216111 2216170 "PRINT" 2216244 T PRINT (NIL) -7 NIL NIL NIL) (-968 2215419 2215536 2215688 "PRIMES" 2215959 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2213484 2213885 2214351 "PRIMELT" 2214998 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2213213 2213262 2213290 "PRIMCAT" 2213414 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2209328 2213151 2213196 "PRIMARR" 2213201 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-964 2208335 2208513 2208741 "PRIMARR2" 2209146 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-963 2207978 2208034 2208145 "PREASSOC" 2208273 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2207453 2207586 2207614 "PPCURVE" 2207819 T PPCURVE (NIL) -9 NIL 2207955 NIL) (-961 2207048 2207248 2207331 "PORTNUM" 2207390 T PORTNUM (NIL) -8 NIL NIL NIL) (-960 2204407 2204806 2205398 "POLYROOT" 2206629 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-959 2198589 2204011 2204171 "POLY" 2204280 NIL POLY (NIL T) -8 NIL NIL NIL) (-958 2197972 2198030 2198264 "POLYLIFT" 2198525 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2194247 2194696 2195325 "POLYCATQ" 2197517 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2180959 2186087 2186152 "POLYCAT" 2189666 NIL POLYCAT (NIL T T T) -9 NIL 2191544 NIL) (-955 2174408 2176270 2178654 "POLYCAT-" 2178659 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2173995 2174063 2174183 "POLY2UP" 2174334 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2173627 2173684 2173793 "POLY2" 2173932 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2172312 2172551 2172827 "POLUTIL" 2173401 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-951 2170667 2170944 2171275 "POLTOPOL" 2172034 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-950 2166132 2170603 2170649 "POINT" 2170654 NIL POINT (NIL T) -8 NIL NIL NIL) (-949 2164319 2164676 2165051 "PNTHEORY" 2165777 T PNTHEORY (NIL) -7 NIL NIL NIL) (-948 2162777 2163074 2163473 "PMTOOLS" 2164017 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-947 2162370 2162448 2162565 "PMSYM" 2162693 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-946 2161878 2161947 2162122 "PMQFCAT" 2162295 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-945 2161233 2161343 2161499 "PMPRED" 2161755 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-944 2160626 2160712 2160874 "PMPREDFS" 2161134 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2159290 2159498 2159876 "PMPLCAT" 2160388 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-942 2158822 2158901 2159053 "PMLSAGG" 2159205 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-941 2158295 2158371 2158553 "PMKERNEL" 2158740 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-940 2157912 2157987 2158100 "PMINS" 2158214 NIL PMINS (NIL T) -7 NIL NIL NIL) (-939 2157354 2157423 2157632 "PMFS" 2157837 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-938 2156582 2156700 2156905 "PMDOWN" 2157231 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-937 2155749 2155907 2156088 "PMASS" 2156421 T PMASS (NIL) -7 NIL NIL NIL) (-936 2155022 2155132 2155295 "PMASSFS" 2155636 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2154677 2154745 2154839 "PLOTTOOL" 2154948 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-934 2149284 2150488 2151636 "PLOT" 2153549 T PLOT (NIL) -8 NIL NIL NIL) (-933 2145088 2146132 2147053 "PLOT3D" 2148383 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2144000 2144177 2144412 "PLOT1" 2144892 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2119391 2124066 2128917 "PLEQN" 2139266 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-930 2118709 2118831 2119011 "PINTERP" 2119256 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-929 2118402 2118449 2118552 "PINTERPA" 2118656 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2117618 2118166 2118253 "PI" 2118293 T PI (NIL) -8 NIL NIL 2118360) (-927 2115915 2116890 2116918 "PID" 2117100 T PID (NIL) -9 NIL 2117234 NIL) (-926 2115666 2115703 2115778 "PICOERCE" 2115872 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2114986 2115125 2115301 "PGROEB" 2115522 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-924 2110573 2111387 2112292 "PGE" 2114101 T PGE (NIL) -7 NIL NIL NIL) (-923 2108696 2108943 2109309 "PGCD" 2110290 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-922 2108034 2108137 2108298 "PFRPAC" 2108580 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-921 2104674 2106582 2106935 "PFR" 2107713 NIL PFR (NIL T) -8 NIL NIL NIL) (-920 2103063 2103307 2103632 "PFOTOOLS" 2104421 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-919 2101596 2101835 2102186 "PFOQ" 2102820 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-918 2100097 2100309 2100665 "PFO" 2101380 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-917 2096650 2099986 2100055 "PF" 2100060 NIL PF (NIL NIL) -8 NIL NIL NIL) (-916 2093984 2095255 2095283 "PFECAT" 2095868 T PFECAT (NIL) -9 NIL 2096252 NIL) (-915 2093429 2093583 2093797 "PFECAT-" 2093802 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2092032 2092284 2092585 "PFBRU" 2093178 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2089898 2090250 2090682 "PFBR" 2091683 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2085944 2087410 2088057 "PERM" 2089284 NIL PERM (NIL T) -8 NIL NIL NIL) (-911 2081178 2082151 2083021 "PERMGRP" 2085107 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2079297 2080257 2080298 "PERMCAT" 2080698 NIL PERMCAT (NIL T) -9 NIL 2080996 NIL) (-909 2078950 2078991 2079115 "PERMAN" 2079250 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2076438 2078615 2078737 "PENDTREE" 2078861 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-907 2074462 2075230 2075271 "PDRING" 2075928 NIL PDRING (NIL T) -9 NIL 2076214 NIL) (-906 2073565 2073783 2074145 "PDRING-" 2074150 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-905 2070780 2071558 2072226 "PDEPROB" 2072917 T PDEPROB (NIL) -8 NIL NIL NIL) (-904 2068325 2068829 2069384 "PDEPACK" 2070245 T PDEPACK (NIL) -7 NIL NIL NIL) (-903 2067237 2067427 2067678 "PDECOMP" 2068124 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-902 2064816 2065659 2065687 "PDECAT" 2066474 T PDECAT (NIL) -9 NIL 2067187 NIL) (-901 2064567 2064600 2064690 "PCOMP" 2064777 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-900 2062745 2063368 2063665 "PBWLB" 2064296 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-899 2055218 2056818 2058156 "PATTERN" 2061428 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-898 2054850 2054907 2055016 "PATTERN2" 2055155 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2052607 2052995 2053452 "PATTERN1" 2054439 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2049975 2050556 2051037 "PATRES" 2052172 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-895 2049539 2049606 2049738 "PATRES2" 2049902 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2047422 2047827 2048234 "PATMATCH" 2049206 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-893 2046932 2047141 2047182 "PATMAB" 2047289 NIL PATMAB (NIL T) -9 NIL 2047372 NIL) (-892 2045450 2045786 2046044 "PATLRES" 2046737 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-891 2044996 2045119 2045160 "PATAB" 2045165 NIL PATAB (NIL T) -9 NIL 2045337 NIL) (-890 2043178 2043573 2043996 "PARTPERM" 2044593 T PARTPERM (NIL) -7 NIL NIL NIL) (-889 2042799 2042862 2042964 "PARSURF" 2043109 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-888 2042431 2042488 2042597 "PARSU2" 2042736 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-887 2042195 2042235 2042302 "PARSER" 2042384 T PARSER (NIL) -7 NIL NIL NIL) (-886 2041816 2041879 2041981 "PARSCURV" 2042126 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-885 2041448 2041505 2041614 "PARSC2" 2041753 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-884 2041087 2041145 2041242 "PARPCURV" 2041384 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-883 2040719 2040776 2040885 "PARPC2" 2041024 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-882 2039780 2040092 2040274 "PARAMAST" 2040557 T PARAMAST (NIL) -8 NIL NIL NIL) (-881 2039300 2039386 2039505 "PAN2EXPR" 2039681 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-880 2038077 2038421 2038649 "PALETTE" 2039092 T PALETTE (NIL) -8 NIL NIL NIL) (-879 2036470 2037082 2037442 "PAIR" 2037763 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-878 2030338 2035727 2035922 "PADICRC" 2036324 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-877 2023565 2029682 2029867 "PADICRAT" 2030185 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-876 2021880 2023502 2023547 "PADIC" 2023552 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-875 2018990 2020554 2020594 "PADICCT" 2021175 NIL PADICCT (NIL NIL) -9 NIL 2021457 NIL) (-874 2017947 2018147 2018415 "PADEPAC" 2018777 NIL PADEPAC (NIL 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(-861 1995671 1997955 1998076 "OREUP" 1998081 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993074 1995362 1995489 "ORESUP" 1995613 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990602 1991102 1991663 "OREPCTO" 1992563 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984288 1986489 1986530 "OREPCAT" 1988878 NIL OREPCAT (NIL T) -9 NIL 1989982 NIL) (-857 1981435 1982217 1983275 "OREPCAT-" 1983280 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980586 1980884 1980912 "ORDSET" 1981221 T ORDSET (NIL) -9 NIL 1981385 NIL) (-855 1980017 1980165 1980389 "ORDSET-" 1980394 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978582 1979373 1979401 "ORDRING" 1979603 T ORDRING (NIL) -9 NIL 1979728 NIL) (-853 1978227 1978321 1978465 "ORDRING-" 1978470 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977607 1978070 1978098 "ORDMON" 1978103 T ORDMON (NIL) -9 NIL 1978124 NIL) (-851 1976769 1976916 1977111 "ORDFUNS" 1977456 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976107 1976526 1976554 "ORDFIN" 1976619 T ORDFIN (NIL) -9 NIL 1976693 NIL) (-849 1972666 1974693 1975102 "ORDCOMP" 1975731 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1971932 1972059 1972245 "ORDCOMP2" 1972526 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968513 1969423 1970237 "OPTPROB" 1971138 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965315 1965954 1966658 "OPTPACK" 1967829 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963002 1963768 1963796 "OPTCAT" 1964615 T OPTCAT (NIL) -9 NIL 1965265 NIL) (-844 1962386 1962679 1962784 "OPSIG" 1962917 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962154 1962193 1962259 "OPQUERY" 1962340 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959285 1960465 1960969 "OP" 1961683 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958659 1958885 1958926 "OPERCAT" 1959138 NIL OPERCAT (NIL T) -9 NIL 1959235 NIL) (-840 1958414 1958470 1958587 "OPERCAT-" 1958592 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955227 1957211 1957580 "ONECOMP" 1958078 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954532 1954647 1954821 "ONECOMP2" 1955099 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953951 1954057 1954187 "OMSERVER" 1954422 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1950813 1953391 1953431 "OMSAGG" 1953492 NIL OMSAGG (NIL T) -9 NIL 1953556 NIL) (-835 1949436 1949699 1949981 "OMPKG" 1950551 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1948866 1948969 1948997 "OM" 1949296 T OM (NIL) -9 NIL NIL NIL) (-833 1947413 1948415 1948584 "OMLO" 1948747 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946373 1946520 1946740 "OMEXPR" 1947239 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945664 1945919 1946055 "OMERR" 1946257 T OMERR (NIL) -8 NIL NIL NIL) (-830 1944815 1945085 1945245 "OMERRK" 1945524 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944266 1944492 1944600 "OMENC" 1944727 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938161 1939346 1940517 "OMDEV" 1943115 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937230 1937401 1937595 "OMCONN" 1937987 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1935751 1936727 1936755 "OINTDOM" 1936760 T OINTDOM (NIL) -9 NIL 1936781 NIL) (-825 1933089 1934439 1934776 "OFMONOID" 1935446 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932500 1933026 1933071 "ODVAR" 1933076 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1929923 1932245 1932400 "ODR" 1932405 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922504 1929699 1929825 "ODPOL" 1929830 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916326 1922376 1922481 "ODP" 1922486 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915092 1915307 1915582 "ODETOOLS" 1916100 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912059 1912717 1913433 "ODESYS" 1914425 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1906941 1907849 1908874 "ODERTRIC" 1911134 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906367 1906449 1906643 "ODERED" 1906853 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903255 1903803 1904480 "ODERAT" 1905790 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900214 1900679 1901276 "ODEPRRIC" 1902784 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898157 1898753 1899239 "ODEPROB" 1899748 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894677 1895162 1895809 "ODEPRIM" 1897636 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1893926 1894028 1894288 "ODEPAL" 1894569 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890088 1890879 1891743 "ODEPACK" 1893082 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889149 1889256 1889478 "ODEINT" 1889977 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883250 1884675 1886122 "ODEIFTBL" 1887722 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878648 1879434 1880386 "ODEEF" 1882409 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1877997 1878086 1878309 "ODECONST" 1878553 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876122 1876783 1876811 "ODECAT" 1877416 T ODECAT (NIL) -9 NIL 1877947 NIL) (-805 1872977 1875827 1875949 "OCT" 1876032 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872615 1872658 1872785 "OCTCT2" 1872928 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867226 1869661 1869701 "OC" 1870798 NIL OC (NIL T) -9 NIL 1871656 NIL) (-802 1864453 1865201 1866191 "OC-" 1866285 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1863805 1864273 1864301 "OCAMON" 1864306 T OCAMON (NIL) -9 NIL 1864327 NIL) (-800 1863336 1863677 1863705 "OASGP" 1863710 T OASGP (NIL) -9 NIL 1863730 NIL) (-799 1862597 1863086 1863114 "OAMONS" 1863154 T OAMONS (NIL) -9 NIL 1863197 NIL) (-798 1862011 1862444 1862472 "OAMON" 1862477 T OAMON (NIL) -9 NIL 1862497 NIL) (-797 1861269 1861787 1861815 "OAGROUP" 1861820 T OAGROUP (NIL) -9 NIL 1861840 NIL) (-796 1860959 1861009 1861097 "NUMTUBE" 1861213 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854532 1856050 1857586 "NUMQUAD" 1859443 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850288 1851276 1852301 "NUMODE" 1853527 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847643 1848523 1848551 "NUMINT" 1849474 T NUMINT (NIL) -9 NIL 1850238 NIL) (-792 1846591 1846788 1847006 "NUMFMT" 1847445 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1832950 1835895 1838427 "NUMERIC" 1844098 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827320 1832399 1832494 "NTSCAT" 1832499 NIL NTSCAT (NIL T T T T) -9 NIL 1832538 NIL) (-789 1826514 1826679 1826872 "NTPOLFN" 1827159 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814591 1823339 1824151 "NSUP" 1825735 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814223 1814280 1814389 "NSUP2" 1814528 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804449 1813997 1814130 "NSMP" 1814135 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1802881 1803182 1803539 "NREP" 1804137 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801472 1801724 1802082 "NPCOEF" 1802624 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800538 1800653 1800869 "NORMRETR" 1801353 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798579 1798869 1799278 "NORMPK" 1800246 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798264 1798292 1798416 "NORMMA" 1798545 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798064 1798221 1798250 "NONE" 1798255 T NONE (NIL) -8 NIL NIL NIL) (-779 1797853 1797882 1797951 "NONE1" 1798028 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797350 1797412 1797591 "NODE1" 1797785 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795631 1796482 1796737 "NNI" 1797084 T NNI (NIL) -8 NIL NIL 1797319) (-776 1794051 1794364 1794728 "NLINSOL" 1795299 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790292 1791287 1792186 "NIPROB" 1793172 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789049 1789283 1789585 "NFINTBAS" 1790054 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788223 1788699 1788740 "NETCLT" 1788912 NIL NETCLT (NIL T) -9 NIL 1788994 NIL) (-772 1786931 1787162 1787443 "NCODIV" 1787991 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786693 1786730 1786805 "NCNTFRAC" 1786888 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1784873 1785237 1785657 "NCEP" 1786318 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1783724 1784497 1784525 "NASRING" 1784635 T NASRING (NIL) -9 NIL 1784715 NIL) (-768 1783519 1783563 1783657 "NASRING-" 1783662 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782626 1783151 1783179 "NARNG" 1783296 T NARNG (NIL) -9 NIL 1783387 NIL) (-766 1782318 1782385 1782519 "NARNG-" 1782524 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781197 1781404 1781639 "NAGSP" 1782103 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772469 1774153 1775826 "NAGS" 1779544 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771017 1771325 1771656 "NAGF07" 1772158 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765555 1766846 1768153 "NAGF04" 1769730 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758523 1760137 1761770 "NAGF02" 1763942 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1753747 1754847 1755964 "NAGF01" 1757426 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747375 1748941 1750526 "NAGE04" 1752182 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738544 1740665 1742795 "NAGE02" 1745265 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734497 1735444 1736408 "NAGE01" 1737600 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732292 1732826 1733384 "NAGD03" 1733959 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724042 1725970 1727924 "NAGD02" 1730358 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1717853 1719278 1720718 "NAGD01" 1722622 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714062 1714884 1715721 "NAGC06" 1717036 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712527 1712859 1713215 "NAGC05" 1713726 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1711903 1712022 1712166 "NAGC02" 1712403 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1710862 1711445 1711485 "NAALG" 1711564 NIL NAALG (NIL T) -9 NIL 1711625 NIL) (-749 1710697 1710726 1710816 "NAALG-" 1710821 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704647 1705755 1706942 "MULTSQFR" 1709593 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1703966 1704041 1704225 "MULTFACT" 1704559 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696690 1700603 1700656 "MTSCAT" 1701726 NIL MTSCAT (NIL T T) -9 NIL 1702241 NIL) (-745 1696402 1696456 1696548 "MTHING" 1696630 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696194 1696227 1696287 "MSYSCMD" 1696362 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692276 1694949 1695269 "MSET" 1695907 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689345 1691837 1691878 "MSETAGG" 1691883 NIL MSETAGG (NIL T) -9 NIL 1691917 NIL) (-741 1685187 1686724 1687469 "MRING" 1688645 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1684753 1684820 1684951 "MRF2" 1685114 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684371 1684406 1684550 "MRATFAC" 1684712 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1681983 1682278 1682709 "MPRFF" 1684076 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676280 1681837 1681934 "MPOLY" 1681939 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1675770 1675805 1676013 "MPCPF" 1676239 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675284 1675327 1675511 "MPC3" 1675721 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674479 1674560 1674781 "MPC2" 1675199 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1672780 1673117 1673507 "MONOTOOL" 1674139 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672005 1672322 1672350 "MONOID" 1672569 T MONOID (NIL) -9 NIL 1672716 NIL) (-731 1671551 1671670 1671851 "MONOID-" 1671856 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662026 1667977 1668036 "MONOGEN" 1668710 NIL MONOGEN (NIL T T) -9 NIL 1669166 NIL) (-729 1659244 1659979 1660979 "MONOGEN-" 1661098 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658077 1658523 1658551 "MONADWU" 1658943 T MONADWU (NIL) -9 NIL 1659181 NIL) (-727 1657449 1657608 1657856 "MONADWU-" 1657861 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1656808 1657052 1657080 "MONAD" 1657287 T MONAD (NIL) -9 NIL 1657399 NIL) (-725 1656493 1656571 1656703 "MONAD-" 1656708 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1654782 1655406 1655685 "MOEBIUS" 1656246 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654060 1654464 1654504 "MODULE" 1654509 NIL MODULE (NIL T) -9 NIL 1654548 NIL) (-722 1653628 1653724 1653914 "MODULE-" 1653919 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651308 1651992 1652319 "MODRING" 1653452 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648252 1649413 1649934 "MODOP" 1650837 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1646840 1647319 1647596 "MODMONOM" 1648115 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1636884 1645131 1645545 "MODMON" 1646477 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634040 1635728 1636004 "MODFIELD" 1636759 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633017 1633321 1633511 "MMLFORM" 1633870 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632543 1632586 1632765 "MMAP" 1632968 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630622 1631389 1631430 "MLO" 1631853 NIL MLO (NIL T) -9 NIL 1632095 NIL) (-713 1627988 1628504 1629106 "MLIFT" 1630103 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627379 1627463 1627617 "MKUCFUNC" 1627899 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1626978 1627048 1627171 "MKRECORD" 1627302 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626025 1626187 1626415 "MKFUNC" 1626789 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625413 1625517 1625673 "MKFLCFN" 1625908 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624690 1624792 1624977 "MKBCFUNC" 1625306 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621397 1624244 1624380 "MINT" 1624574 T MINT (NIL) -8 NIL NIL NIL) (-706 1620209 1620452 1620729 "MHROWRED" 1621152 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615589 1618744 1619149 "MFLOAT" 1619824 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1614946 1615022 1615193 "MFINFACT" 1615501 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611261 1612109 1612993 "MESH" 1614082 T MESH (NIL) -7 NIL NIL NIL) (-702 1609651 1609963 1610316 "MDDFACT" 1610948 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606446 1608810 1608851 "MDAGG" 1609106 NIL MDAGG (NIL T) -9 NIL 1609249 NIL) (-700 1596186 1605739 1605946 "MCMPLX" 1606259 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595323 1595469 1595670 "MCDEN" 1596035 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593213 1593483 1593863 "MCALCFN" 1595053 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592138 1592378 1592611 "MAYBE" 1593019 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1589750 1590273 1590835 "MATSTOR" 1591609 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1585707 1589122 1589370 "MATRIX" 1589535 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581473 1582180 1582916 "MATLIN" 1585064 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571579 1574765 1574842 "MATCAT" 1579722 NIL MATCAT (NIL T T T) -9 NIL 1581139 NIL) (-692 1567935 1568956 1570312 "MATCAT-" 1570317 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566529 1566682 1567015 "MATCAT2" 1567770 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564641 1564965 1565349 "MAPPKG3" 1566204 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563622 1563795 1564017 "MAPPKG2" 1564465 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562121 1562405 1562732 "MAPPKG1" 1563328 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561200 1561527 1561704 "MAPPAST" 1561964 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1560811 1560869 1560992 "MAPHACK3" 1561136 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560403 1560464 1560578 "MAPHACK2" 1560743 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1559841 1559944 1560086 "MAPHACK1" 1560294 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1557920 1558541 1558845 "MAGMA" 1559569 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557399 1557644 1557735 "MACROAST" 1557849 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1553817 1555638 1556099 "M3D" 1556971 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1547892 1552156 1552197 "LZSTAGG" 1552979 NIL LZSTAGG (NIL T) -9 NIL 1553274 NIL) (-679 1543850 1545023 1546480 "LZSTAGG-" 1546485 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1540937 1541741 1542228 "LWORD" 1543395 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540513 1540741 1540816 "LSTAST" 1540882 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1533679 1540284 1540418 "LSQM" 1540423 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1532903 1533042 1533270 "LSPP" 1533534 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1530715 1531016 1531472 "LSMP" 1532592 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527494 1528168 1528898 "LSMP1" 1530017 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521340 1526631 1526672 "LSAGG" 1526734 NIL LSAGG (NIL T) -9 NIL 1526812 NIL) (-671 1518035 1518959 1520172 "LSAGG-" 1520177 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515634 1517179 1517428 "LPOLY" 1517830 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515216 1515301 1515424 "LPEFRAC" 1515543 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513537 1514310 1514563 "LO" 1515048 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513189 1513301 1513329 "LOGIC" 1513440 T LOGIC (NIL) -9 NIL 1513521 NIL) (-666 1513051 1513074 1513145 "LOGIC-" 1513150 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512244 1512384 1512577 "LODOOPS" 1512907 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1509667 1512160 1512226 "LODO" 1512231 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508205 1508440 1508793 "LODOF" 1509414 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504409 1506840 1506881 "LODOCAT" 1507319 NIL LODOCAT (NIL T) -9 NIL 1507530 NIL) (-661 1504142 1504200 1504327 "LODOCAT-" 1504332 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501462 1503983 1504101 "LODO2" 1504106 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1498897 1501399 1501444 "LODO1" 1501449 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1497778 1497943 1498248 "LODEEF" 1498720 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493081 1495972 1496013 "LNAGG" 1496875 NIL LNAGG (NIL T) -9 NIL 1497310 NIL) (-656 1492228 1492442 1492784 "LNAGG-" 1492789 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488364 1489153 1489792 "LMOPS" 1491643 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1487767 1488155 1488196 "LMODULE" 1488201 NIL LMODULE (NIL T) -9 NIL 1488227 NIL) (-653 1484965 1487412 1487535 "LMDICT" 1487677 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484371 1484592 1484633 "LLINSET" 1484824 NIL LLINSET (NIL T) -9 NIL 1484915 NIL) (-651 1484070 1484279 1484339 "LITERAL" 1484344 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477233 1483004 1483308 "LIST" 1483799 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1476758 1476832 1476971 "LIST3" 1477153 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1475765 1475943 1476171 "LIST2" 1476576 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1473899 1474211 1474610 "LIST2MAP" 1475412 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473495 1473732 1473773 "LINSET" 1473778 NIL LINSET (NIL T) -9 NIL 1473812 NIL) (-645 1472156 1472826 1472867 "LINEXP" 1473122 NIL LINEXP (NIL T) -9 NIL 1473271 NIL) (-644 1470803 1471063 1471360 "LINDEP" 1471908 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467570 1468289 1469066 "LIMITRF" 1470058 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1465873 1466169 1466578 "LIMITPS" 1467265 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460301 1465384 1465612 "LIE" 1465694 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459249 1459718 1459758 "LIECAT" 1459898 NIL LIECAT (NIL T) -9 NIL 1460049 NIL) (-639 1459090 1459117 1459205 "LIECAT-" 1459210 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451677 1458630 1458786 "LIB" 1458954 T LIB (NIL) -8 NIL NIL NIL) (-637 1447312 1448195 1449130 "LGROBP" 1450794 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445310 1445584 1445934 "LF" 1447033 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444150 1444842 1444870 "LFCAT" 1445077 T LFCAT (NIL) -9 NIL 1445216 NIL) (-634 1441052 1441682 1442370 "LEXTRIPK" 1443514 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1437796 1438622 1439125 "LEXP" 1440632 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437272 1437517 1437609 "LETAST" 1437724 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435670 1435983 1436384 "LEADCDET" 1436954 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1434860 1434934 1435163 "LAZM3PK" 1435591 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429777 1432937 1433475 "LAUPOL" 1434372 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429356 1429400 1429561 "LAPLACE" 1429727 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427295 1428457 1428708 "LA" 1429189 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426289 1426873 1426914 "LALG" 1426976 NIL LALG (NIL T) -9 NIL 1427035 NIL) (-625 1426003 1426062 1426198 "LALG-" 1426203 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1425838 1425862 1425903 "KVTFROM" 1425965 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424761 1425205 1425390 "KTVLOGIC" 1425673 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424596 1424620 1424661 "KRCFROM" 1424723 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423500 1423687 1423986 "KOVACIC" 1424396 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423335 1423359 1423400 "KONVERT" 1423462 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423170 1423194 1423235 "KOERCE" 1423297 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421001 1421763 1422140 "KERNEL" 1422826 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420497 1420578 1420710 "KERNEL2" 1420915 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414267 1419036 1419090 "KDAGG" 1419467 NIL KDAGG (NIL T T) -9 NIL 1419673 NIL) (-615 1413796 1413920 1414125 "KDAGG-" 1414130 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1406944 1413457 1413612 "KAFILE" 1413674 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401372 1406455 1406683 "JORDAN" 1406765 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400751 1401021 1401142 "JOINAST" 1401271 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400597 1400656 1400711 "JAVACODE" 1400716 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1396849 1398802 1398856 "IXAGG" 1399785 NIL IXAGG (NIL T T) -9 NIL 1400244 NIL) (-609 1395768 1396074 1396493 "IXAGG-" 1396498 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391298 1395690 1395749 "IVECTOR" 1395754 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390064 1390301 1390567 "ITUPLE" 1391065 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388566 1388743 1389038 "ITRIGMNP" 1389886 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387311 1387515 1387798 "ITFUN3" 1388342 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1386943 1387000 1387109 "ITFUN2" 1387248 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386102 1386423 1386597 "ITFORM" 1386789 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384063 1385122 1385400 "ITAYLOR" 1385857 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373008 1378200 1379363 "ISUPS" 1382933 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372112 1372252 1372488 "ISUMP" 1372855 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367487 1372057 1372098 "ISTRING" 1372103 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1366963 1367208 1367300 "ISAST" 1367415 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366172 1366254 1366470 "IRURPK" 1366877 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365108 1365309 1365549 "IRSN" 1365952 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363179 1363534 1363963 "IRRF2F" 1364746 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1362926 1362964 1363040 "IRREDFFX" 1363135 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361541 1361800 1362099 "IROOT" 1362659 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358145 1359225 1359917 "IR" 1360881 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357350 1357638 1357789 "IRFORM" 1358014 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1354963 1355458 1356024 "IR2" 1356828 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354063 1354176 1354390 "IR2F" 1354846 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1353854 1353888 1353948 "IPRNTPK" 1354023 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350435 1353743 1353812 "IPF" 1353817 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348762 1350360 1350417 "IPADIC" 1350422 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348074 1348322 1348452 "IP4ADDR" 1348652 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347448 1347703 1347835 "IOMODE" 1347962 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346521 1347045 1347172 "IOBFILE" 1347341 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346009 1346425 1346453 "IOBCON" 1346458 T IOBCON (NIL) -9 NIL 1346479 NIL) (-581 1345520 1345578 1345761 "INVLAPLA" 1345945 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335168 1337522 1339908 "INTTR" 1343184 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331503 1332245 1333110 "INTTOOLS" 1334353 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331089 1331180 1331297 "INTSLPE" 1331406 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329042 1331012 1331071 "INTRVL" 1331076 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326644 1327156 1327731 "INTRF" 1328527 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326055 1326152 1326294 "INTRET" 1326542 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324052 1324441 1324911 "INTRAT" 1325663 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321315 1321898 1322517 "INTPM" 1323537 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318060 1318659 1319397 "INTPAF" 1320701 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313239 1314201 1315252 "INTPACK" 1317029 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310187 1313036 1313145 "INT" 1313150 T INT (NIL) -8 NIL NIL NIL) (-569 1309439 1309591 1309799 "INTHERTR" 1310029 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1308878 1308958 1309146 "INTHERAL" 1309353 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306724 1307167 1307624 "INTHEORY" 1308441 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298130 1299751 1301523 "INTG0" 1305076 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278703 1283493 1288303 "INTFTBL" 1293340 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1277952 1278090 1278263 "INTFACT" 1278562 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275379 1275825 1276382 "INTEF" 1277506 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273746 1274485 1274513 "INTDOM" 1274814 T INTDOM (NIL) -9 NIL 1275021 NIL) (-561 1273115 1273289 1273531 "INTDOM-" 1273536 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269503 1271431 1271485 "INTCAT" 1272284 NIL INTCAT (NIL T) -9 NIL 1272605 NIL) (-559 1268975 1269078 1269206 "INTBIT" 1269395 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267674 1267828 1268135 "INTALG" 1268820 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267157 1267247 1267404 "INTAF" 1267578 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260500 1266967 1267107 "INTABL" 1267112 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1259833 1260299 1260364 "INT8" 1260398 T INT8 (NIL) -8 NIL NIL 1260443) (-554 1259165 1259631 1259696 "INT64" 1259730 T INT64 (NIL) -8 NIL NIL 1259775) (-553 1258497 1258963 1259028 "INT32" 1259062 T INT32 (NIL) -8 NIL NIL 1259107) (-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 -3079 (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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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 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(-828))))) +(((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-928)) (-5 *1 (-792))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-551)))) +(((*1 *2 *3) + (-12 (-4 *1 (-347 *4 *3 *5)) (-4 *4 (-1231)) (-4 *3 (-1253 *4)) + (-4 *5 (-1253 (-413 *3))) (-5 *2 (-112)))) ((*1 *2 *3) - (-12 (-5 *3 (-618 *1)) (-4 *1 (-1058)) (-4 *1 (-306)) - (-5 *2 (-1182 *1))))) + (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) + (-4 *5 (-1253 (-413 *4))) (-5 *2 (-112))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-798)))) ((*1 *1 *1) (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1058)) (-14 *3 (-650 (-1186))))) @@ -277,10 +242,10 @@ (-12 (-4 *1 (-387 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-1109)))) ((*1 *1 *1) (-12 (-14 *2 (-650 (-1186))) (-4 *3 (-174)) - (-4 *5 (-240 (-2827 *2) (-777))) + (-4 *5 (-240 (-2857 *2) (-777))) (-14 *6 - (-1 (-112) (-2 (|:| -4286 *4) (|:| -3201 *5)) - (-2 (|:| -4286 *4) (|:| -3201 *5)))) + (-1 (-112) (-2 (|:| -4298 *4) (|:| -2940 *5)) + (-2 (|:| -4298 *4) (|:| -2940 *5)))) (-5 *1 (-467 *2 *3 *4 *5 *6 *7)) (-4 *4 (-856)) (-4 *7 (-956 *3 *5 (-870 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-515 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-856)))) @@ -296,30 +261,44 @@ (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-1300 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-852))))) -(((*1 *1) (-5 *1 (-1094)))) -(((*1 *2 *1) - (-12 (-5 *2 (-176 (-413 (-570)))) (-5 *1 (-118 *3)) (-14 *3 (-570)))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *3 (-1166 *2)) (-4 *2 (-311)) (-5 *1 (-176 *2)))) - ((*1 *1 *2) (-12 (-5 *2 (-413 *3)) (-4 *3 (-311)) (-5 *1 (-176 *3)))) - ((*1 *2 *3) - (-12 (-5 *2 (-176 (-570))) (-5 *1 (-771 *3)) (-4 *3 (-410)))) - ((*1 *2 *1) - (-12 (-5 *2 (-176 (-413 (-570)))) (-5 *1 (-877 *3)) (-14 *3 (-570)))) - ((*1 *2 *1) - (-12 (-14 *3 (-570)) (-5 *2 (-176 (-413 (-570)))) - (-5 *1 (-878 *3 *4)) (-4 *4 (-875 *3))))) -(((*1 *1 *1) (-12 (-4 *1 (-286 *2)) (-4 *2 (-1227)) (-4 *2 (-1109)))) - ((*1 *1 *1) (-12 (-4 *1 (-701 *2)) (-4 *2 (-1109))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-135)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-839 *3)) (-4 *3 (-1109)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-849 *3)) (-4 *3 (-1109))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1298 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058)) - (-5 *2 (-825 *3)))) +(((*1 *1 *1 *1) + (-12 (-5 *1 (-650 *2)) (-4 *2 (-1109)) (-4 *2 (-1227))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *4 (-298 (-839 *3))) + (-4 *5 (-13 (-458) (-1047 (-570)) (-645 (-570)))) + (-5 *2 (-839 *3)) (-5 *1 (-642 *5 *3)) + (-4 *3 (-13 (-27) (-1212) (-436 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-298 (-839 (-959 *5)))) (-4 *5 (-458)) + (-5 *2 (-839 (-413 (-959 *5)))) (-5 *1 (-643 *5)) + (-5 *3 (-413 (-959 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-298 (-413 (-959 *5)))) (-5 *3 (-413 (-959 *5))) + (-4 *5 (-458)) (-5 *2 (-839 *3)) (-5 *1 (-643 *5))))) +(((*1 *2 *2) + (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1212)))))) +(((*1 *2 *3 *4 *4 *5) + (-12 (-5 *3 (-1168)) (-5 *4 (-570)) (-5 *5 (-695 (-227))) + (-5 *2 (-1044)) (-5 *1 (-763))))) +(((*1 *2) + (-12 (-14 *4 (-777)) (-4 *5 (-1227)) (-5 *2 (-135)) + (-5 *1 (-239 *3 *4 *5)) (-4 *3 (-240 *4 *5)))) + ((*1 *2) + (-12 (-4 *4 (-368)) (-5 *2 (-135)) (-5 *1 (-332 *3 *4)) + (-4 *3 (-333 *4)))) + ((*1 *2) + (-12 (-5 *2 (-777)) (-5 *1 (-396 *3 *4 *5)) (-14 *3 *2) (-14 *4 *2) + (-4 *5 (-174)))) ((*1 *2 *1) - (-12 (-4 *2 (-852)) (-5 *1 (-1300 *3 *2)) (-4 *3 (-1058))))) + (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-570)) + (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-650 *6)) (-4 *6 (-856)) (-4 *4 (-368)) (-4 *5 (-799)) + (-5 *2 (-570)) (-5 *1 (-510 *4 *5 *6 *7)) (-4 *7 (-956 *4 *5 *6)))) + ((*1 *2 *1) (-12 (-4 *1 (-989 *3)) (-4 *3 (-1058)) (-5 *2 (-928)))) + ((*1 *2) (-12 (-4 *1 (-1284 *3)) (-4 *3 (-368)) (-5 *2 (-135))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) (-12 (-5 *2 (-959 (-384))) (-5 *1 (-344 *3 *4 *5)) @@ -375,11 +354,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -1598 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-320 (-227))) - (|:| -1598 (-650 (-1103 (-849 (-227))))) + (|:| -2744 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-775)))) ((*1 *2 *1) @@ -395,13 +374,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-320 (-227))) (|:| -3392 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -3458 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-650 (-320 (-227)))) - (|:| -3392 (-650 (-227))))))) + (|:| -3458 (-650 (-227))))))) (-5 *1 (-847)))) ((*1 *2 *1) (-12 @@ -420,26 +399,26 @@ (-4 *4 (-799)) (-4 *5 (-856)) (-4 *1 (-985 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1047 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) - (-3684 + (-3749 (-12 (-5 *2 (-959 *3)) - (-12 (-3152 (-4 *3 (-38 (-413 (-570))))) - (-3152 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) + (-12 (-3201 (-4 *3 (-38 (-413 (-570))))) + (-3201 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-3152 (-4 *3 (-551))) (-3152 (-4 *3 (-38 (-413 (-570))))) + (-12 (-3201 (-4 *3 (-551))) (-3201 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-3152 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) + (-12 (-3201 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))))) ((*1 *1 *2) - (-3684 + (-3749 (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) - (-12 (-3152 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) + (-12 (-3201 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) @@ -449,89 +428,63 @@ (-12 (-5 *2 (-959 (-413 (-570)))) (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-650 (-1277 *5))) (-5 *4 (-570)) (-5 *2 (-1277 *5)) - (-5 *1 (-1038 *5)) (-4 *5 (-368)) (-4 *5 (-373)) (-4 *5 (-1058))))) -(((*1 *2 *2) - (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) - (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-986 *3 *4 *5 *6))))) -(((*1 *2) (-12 (-5 *2 (-928)) (-5 *1 (-1280)))) - ((*1 *2 *2) (-12 (-5 *2 (-928)) (-5 *1 (-1280))))) -(((*1 *2 *3 *4) +(((*1 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) + ((*1 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) + ((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-437 *3 *2)) (-4 *2 (-436 *3)))) + ((*1 *1 *1) (-4 *1 (-1148)))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1277 *1)) (-4 *1 (-375 *4 *5)) (-4 *4 (-174)) + (-4 *5 (-1253 *4)) (-5 *2 (-695 *4)))) + ((*1 *2 *1) + (-12 (-4 *1 (-415 *3 *4)) (-4 *3 (-174)) (-4 *4 (-1253 *3)) + (-5 *2 (-695 *3))))) +(((*1 *1) + (-12 (-5 *1 (-655 *2 *3 *4)) (-4 *2 (-1109)) (-4 *3 (-23)) + (-14 *4 *3)))) +(((*1 *2 *3) (-12 (-5 *2 (-424 *3)) (-5 *1 (-564 *3)) (-4 *3 (-551))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-650 - (-2 (|:| |eqzro| (-650 *8)) (|:| |neqzro| (-650 *8)) - (|:| |wcond| (-650 (-959 *5))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1277 (-413 (-959 *5)))) - (|:| -3296 (-650 (-1277 (-413 (-959 *5)))))))))) - (-5 *4 (-1168)) (-4 *5 (-13 (-311) (-148))) (-4 *8 (-956 *5 *7 *6)) - (-4 *6 (-13 (-856) (-620 (-1186)))) (-4 *7 (-799)) (-5 *2 (-570)) - (-5 *1 (-931 *5 *6 *7 *8))))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-159 *3 *2)) (-4 *2 (-436 *3))))) -(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-780)) (-5 *1 (-115)))) - ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1168)) (-5 *3 (-780)) (-5 *1 (-115))))) + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *2) + (|:| |xpnt| (-570))))) + (-4 *2 (-562)) (-5 *1 (-424 *2)))) + ((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |contp| (-570)) + (|:| -2660 (-650 (-2 (|:| |irr| *4) (|:| -3634 (-570))))))) + (-4 *4 (-1253 (-570))) (-5 *2 (-424 *4)) (-5 *1 (-448 *4))))) (((*1 *2 *1) (-12 (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-650 *1)) (-4 *1 (-956 *3 *4 *5))))) -(((*1 *2) - (|partial| -12 (-4 *3 (-562)) (-4 *3 (-174)) - (-5 *2 (-2 (|:| |particular| *1) (|:| -3296 (-650 *1)))) - (-4 *1 (-372 *3)))) - ((*1 *2) - (|partial| -12 - (-5 *2 - (-2 (|:| |particular| (-459 *3 *4 *5 *6)) - (|:| -3296 (-650 (-459 *3 *4 *5 *6))))) - (-5 *1 (-459 *3 *4 *5 *6)) (-4 *3 (-174)) (-14 *4 (-928)) - (-14 *5 (-650 (-1186))) (-14 *6 (-1277 (-695 *3)))))) -(((*1 *1 *1 *1) - (-12 (-5 *1 (-650 *2)) (-4 *2 (-1109)) (-4 *2 (-1227))))) (((*1 *1 *1 *1) (-5 *1 (-163))) ((*1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-163))))) -(((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| |var| (-650 (-1186))) (|:| |pred| (-52)))) - (-5 *1 (-899 *3)) (-4 *3 (-1109))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-227)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-227)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-384)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-384))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *3 (-777)) (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *2 *3 *3 *4) - (-12 (-5 *4 (-777)) (-4 *3 (-562)) (-5 *1 (-978 *3 *2)) - (-4 *2 (-1253 *3))))) -(((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-501))))) (((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) - (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) - (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) - (|:| |abserr| (-227)) (|:| |relerr| (-227)))) - (-5 *2 - (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) - (|:| |expense| (-384)) (|:| |accuracy| (-384)) - (|:| |intermediateResults| (-384)))) - (-5 *1 (-809))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-1058)) (-5 *1 (-450 *3 *2)) (-4 *2 (-1253 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) (-5 *2 (-112))))) + (-12 (-5 *3 (-1250 *5 *4)) (-4 *4 (-826)) (-14 *5 (-1186)) + (-5 *2 (-570)) (-5 *1 (-1123 *4 *5))))) (((*1 *2 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1182 *4)) (-5 *1 (-362 *4)) - (-4 *4 (-354))))) + (-12 (-5 *3 (-570)) (-4 *4 (-799)) (-4 *5 (-856)) (-4 *2 (-1058)) + (-5 *1 (-325 *4 *5 *2 *6)) (-4 *6 (-956 *2 *4 *5))))) +(((*1 *2 *3 *4 *5 *4) + (-12 (-5 *3 (-695 (-227))) (-5 *4 (-570)) (-5 *5 (-112)) + (-5 *2 (-1044)) (-5 *1 (-751))))) +(((*1 *2 *3 *3) + (|partial| -12 (-4 *4 (-13 (-368) (-148) (-1047 (-570)))) + (-4 *5 (-1253 *4)) + (-5 *2 (-2 (|:| -3730 (-413 *5)) (|:| |coeff| (-413 *5)))) + (-5 *1 (-574 *4 *5)) (-5 *3 (-413 *5))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-1021)) (-5 *2 (-868))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-650 (-52))) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-767)))) +(((*1 *2 *1) + (-12 (-4 *1 (-610 *2 *3)) (-4 *3 (-1227)) (-4 *2 (-1109)) + (-4 *2 (-856))))) (((*1 *2 *2) - (-12 (-4 *3 (-354)) (-4 *4 (-333 *3)) (-4 *5 (-1253 *4)) - (-5 *1 (-783 *3 *4 *5 *2 *6)) (-4 *2 (-1253 *5)) (-14 *6 (-928)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-777)) (-4 *1 (-1296 *3)) (-4 *3 (-368)) (-4 *3 (-373)))) - ((*1 *1 *1) (-12 (-4 *1 (-1296 *2)) (-4 *2 (-368)) (-4 *2 (-373))))) + (-12 (-5 *2 (-650 *3)) (-4 *3 (-1253 (-570))) (-5 *1 (-492 *3))))) +(((*1 *2) (-12 (-5 *2 (-384)) (-5 *1 (-1049))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-798)) (-4 *2 (-1058)))) ((*1 *2 *1) (-12 (-4 *2 (-1058)) (-5 *1 (-50 *2 *3)) (-14 *3 (-650 (-1186))))) @@ -541,10 +494,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-387 *2 *3)) (-4 *3 (-1109)) (-4 *2 (-1058)))) ((*1 *2 *1) - (-12 (-14 *3 (-650 (-1186))) (-4 *5 (-240 (-2827 *3) (-777))) + (-12 (-14 *3 (-650 (-1186))) (-4 *5 (-240 (-2857 *3) (-777))) (-14 *6 - (-1 (-112) (-2 (|:| -4286 *4) (|:| -3201 *5)) - (-2 (|:| -4286 *4) (|:| -3201 *5)))) + (-1 (-112) (-2 (|:| -4298 *4) (|:| -2940 *5)) + (-2 (|:| -4298 *4) (|:| -2940 *5)))) (-4 *2 (-174)) (-5 *1 (-467 *3 *2 *4 *5 *6 *7)) (-4 *4 (-856)) (-4 *7 (-956 *2 *5 (-870 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-515 *2 *3)) (-4 *3 (-856)) (-4 *2 (-1109)))) @@ -561,26 +514,27 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1074 *3 *4 *2)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *2 (-856))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-1191))) (-5 *1 (-1191)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-512)) (-5 *3 (-650 (-1191))) (-5 *1 (-1191))))) +(((*1 *2 *1) + (-12 (-5 *2 (-2 (|:| |var| (-650 (-1186))) (|:| |pred| (-52)))) + (-5 *1 (-899 *3)) (-4 *3 (-1109))))) +(((*1 *2 *1) (-12 (-4 *1 (-680 *3)) (-4 *3 (-1227)) (-5 *2 (-112))))) (((*1 *1 *1) (-12 (-4 *1 (-378 *2)) (-4 *2 (-1227)))) ((*1 *2 *2) (-12 (-4 *3 (-1058)) (-5 *1 (-450 *3 *2)) (-4 *2 (-1253 *3)))) ((*1 *1 *1) (-12 (-5 *1 (-655 *2 *3 *4)) (-4 *2 (-1109)) (-4 *3 (-23)) (-14 *4 *3)))) -(((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-371 *3 *4)) - (-4 *3 (-372 *4)))) - ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *3 (-650 (-266))) (-5 *1 (-264))))) +(((*1 *1 *1) (-12 (-5 *1 (-601 *2)) (-4 *2 (-1058))))) +(((*1 *2 *1) + (-12 (-5 *2 (-413 (-570))) (-5 *1 (-323 *3 *4 *5)) (-4 *3 (-368)) + (-14 *4 (-1186)) (-14 *5 *3)))) (((*1 *2 *3) - (-12 (-5 *3 (-695 (-320 (-227)))) - (-5 *2 - (-2 (|:| |stiffnessFactor| (-384)) (|:| |stabilityFactor| (-384)))) - (-5 *1 (-207))))) + (-12 + (-5 *3 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (-5 *2 (-112)) (-5 *1 (-304))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-1103 *3)) (-4 *3 (-956 *7 *6 *4)) (-4 *6 (-799)) (-4 *4 (-856)) (-4 *7 (-562)) @@ -615,44 +569,38 @@ (-12 (-5 *4 (-1101 (-413 (-959 *5)))) (-5 *3 (-413 (-959 *5))) (-4 *5 (-13 (-562) (-1047 (-570)))) (-5 *2 (-3 *3 (-320 *5))) (-5 *1 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(-12 (-5 *2 (-650 (-959 *4))) (-5 *3 (-650 (-1186))) (-4 *4 (-458)) - (-5 *1 (-925 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-458)) (-4 *4 (-799)) (-4 *5 (-856)) - (-4 *6 (-1074 *3 *4 *5)) (-5 *1 (-630 *3 *4 *5 *6 *7 *2)) - (-4 *7 (-1080 *3 *4 *5 *6)) (-4 *2 (-1118 *3 *4 *5 *6))))) -(((*1 *2 *1) - (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) - (-4 *5 (-1253 (-413 *4))) - (-5 *2 (-2 (|:| |num| (-1277 *4)) (|:| |den| *4)))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-1058))))) -(((*1 *2 *3 *3 *3 *4 *5 *6) - (-12 (-5 *3 (-320 (-570))) (-5 *4 (-1 (-227) (-227))) - (-5 *5 (-1103 (-227))) (-5 *6 (-650 (-266))) (-5 *2 (-1142 (-227))) - (-5 *1 (-703))))) -(((*1 *1 *1) (-12 (-5 *1 (-424 *2)) (-4 *2 (-562))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-650 (-777))) (-5 *3 (-112)) (-5 *1 (-1174 *4 *5)) - (-14 *4 (-928)) (-4 *5 (-1058))))) -(((*1 *1) - (-12 (-4 *1 (-410)) (-3152 (|has| *1 (-6 -4443))) - (-3152 (|has| *1 (-6 -4435))))) - ((*1 *2 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 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*3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-112)) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) + ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-266)))) + ((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-473)))) + ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-473))))) +(((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-777)) (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) + (-4 *4 (-799)) (-4 *5 (-856)) (-4 *3 (-562))))) +(((*1 *2 *2) (-12 (-5 *2 (-650 (-695 (-320 (-570))))) (-5 *1 (-1040))))) (((*1 *1 *2) (-12 (-5 *2 (-928)) (-4 *1 (-373)))) ((*1 *2 *3 *3) (-12 (-5 *3 (-928)) (-5 *2 (-1277 *4)) (-5 *1 (-534 *4)) @@ -891,12 +838,8 @@ ((*1 *2 *1) (-12 (-4 *2 (-856)) (-5 *1 (-719 *2 *3 *4)) (-4 *3 (-1109)) (-14 *4 - (-1 (-112) (-2 (|:| -4286 *2) (|:| -3201 *3)) - (-2 (|:| -4286 *2) (|:| -3201 *3))))))) -(((*1 *2 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1188 (-413 (-570)))) (-5 *1 (-192))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1213 *3)) (-4 *3 (-1109))))) + (-1 (-112) (-2 (|:| -4298 *2) (|:| -2940 *3)) + (-2 (|:| -4298 *2) (|:| -2940 *3))))))) (((*1 *1 *2) (-12 (-5 *2 (-650 (-650 *3))) (-4 *3 (-1058)) (-4 *1 (-693 *3 *4 *5)) (-4 *4 (-378 *3)) (-4 *5 (-378 *3)))) @@ -908,48 +851,61 @@ (-12 (-5 *2 (-650 (-650 *5))) (-4 *5 (-1058)) (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5))))) -(((*1 *2 *3) (-12 (-5 *2 (-424 *3)) (-5 *1 (-564 *3)) (-4 *3 (-551)))) - ((*1 *2 *3) - (-12 (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-311)) (-5 *2 (-424 *3)) - (-5 *1 (-748 *4 *5 *6 *3)) (-4 *3 (-956 *6 *4 *5)))) - ((*1 *2 *3) - (-12 (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-311)) - (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-424 (-1182 *7))) - (-5 *1 (-748 *4 *5 *6 *7)) (-5 *3 (-1182 *7)))) - ((*1 *2 *1) - (-12 (-4 *3 (-458)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 (-424 *1)) (-4 *1 (-956 *3 *4 *5)))) - ((*1 *2 *3) - (-12 (-4 *4 (-856)) (-4 *5 (-799)) (-4 *6 (-458)) (-5 *2 (-424 *3)) - (-5 *1 (-988 *4 *5 *6 *3)) (-4 *3 (-956 *6 *5 *4)))) - ((*1 *2 *3) - (-12 (-4 *4 (-799)) (-4 *5 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+ (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-650 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-566 *7 *3 *8)) (-4 *8 (-1109))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-266))) (-5 *4 (-1186)) (-5 *2 (-112)) + (-5 *1 (-266))))) (((*1 *2 *3) (-12 (-5 *3 (-1186)) (-4 *4 (-13 (-458) (-1047 (-570)) (-645 (-570)))) (-5 *2 (-52)) @@ -984,105 +940,32 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-413 (-570))) (-4 *4 (-1058)) (-4 *1 (-1260 *4 *3)) (-4 *3 (-1237 *4))))) -(((*1 *1 *1) - (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1058)) (-14 *3 (-650 (-1186))))) - ((*1 *1 *1) - (-12 (-5 *1 (-225 *2 *3)) (-4 *2 (-13 (-1058) (-856))) - (-14 *3 (-650 (-1186)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1212)))))) -(((*1 *2 *3 *3 *2) (-12 (-5 *2 (-384)) (-5 *3 (-1168)) (-5 *1 (-97)))) - ((*1 *2 *3 *2) (-12 (-5 *2 (-384)) (-5 *3 (-1168)) (-5 *1 (-97))))) (((*1 *2 *2 *3) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *2 (-1074 *4 *5 *6)) (-5 *1 (-782 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(-286 *2)) (-4 *2 (-1227)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -4111 - (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -1598 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (|:| -3116 - (-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"))) - (|:| -1598 - (-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 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(-12 (-4 *1 (-793)) (-5 *2 (-1044)) - (-5 *3 - (-2 (|:| |fn| (-320 (-227))) - (|:| -1598 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))))) - ((*1 *2 *3 *2) - (-12 (-4 *1 (-793)) (-5 *2 (-1044)) - (-5 *3 - (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -1598 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227))))))) -(((*1 *2 *3 *4 *4 *2 *2 *2 *2) - (-12 (-5 *2 (-570)) - (-5 *3 - (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-777)) (|:| |poli| *4) - (|:| |polj| *4))) - (-4 *6 (-799)) (-4 *4 (-956 *5 *6 *7)) (-4 *5 (-458)) (-4 *7 (-856)) - (-5 *1 (-455 *5 *6 *7 *4))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-570)) (-5 *1 (-424 *2)) (-4 *2 (-562))))) (((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -2908 (-570)) (|:| -2859 (-650 *3)))) - (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) -(((*1 *1) (-5 *1 (-55)))) -(((*1 *2 *2) - (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1212)))))) + (-12 (-5 *3 (-298 (-959 (-570)))) + (-5 *2 + (-2 (|:| |varOrder| (-650 (-1186))) + (|:| |inhom| (-3 (-650 (-1277 (-777))) "failed")) + (|:| |hom| (-650 (-1277 (-777)))))) + (-5 *1 (-238))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1253 *5)) (-4 *5 (-368)) + (-4 *7 (-1253 (-413 *6))) + (-5 *2 (-2 (|:| |answer| *3) (|:| -1550 *3))) + (-5 *1 (-568 *5 *6 *7 *3)) (-4 *3 (-347 *5 *6 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1253 *5)) (-4 *5 (-368)) + (-5 *2 + (-2 (|:| |answer| (-413 *6)) (|:| -1550 (-413 *6)) + (|:| |specpart| (-413 *6)) (|:| |polypart| *6))) + (-5 *1 (-569 *5 *6)) (-5 *3 (-413 *6))))) +(((*1 *2 *1) (-12 (-4 *1 (-1004 *2)) (-4 *2 (-1227))))) (((*1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-536 *3)) (-4 *3 (-13 (-732) (-25)))))) -(((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4452)) (-4 *1 (-495 *3)) (-4 *3 (-1227)) - (-4 *3 (-1109)) (-5 *2 (-777)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4452)) (-4 *1 (-495 *4)) - (-4 *4 (-1227)) (-5 *2 (-777))))) -(((*1 *2 *2) - (-12 (-5 *2 (-650 *6)) (-4 *6 (-956 *3 *4 *5)) (-4 *3 (-458)) - (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-455 *3 *4 *5 *6))))) +(((*1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-473)))) + ((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-473)))) + ((*1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-934))))) +(((*1 *2 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-762))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-1058)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856))))) (((*1 *1 *2) (-12 (-5 *2 (-650 *1)) (-4 *1 (-458)))) ((*1 *1 *1 *1) (-4 *1 (-458))) ((*1 *2 *3) @@ -3311,16 +2823,13 @@ ((*1 *2 *2 *1) (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) (-4 *4 (-856)) (-4 *2 (-458))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) -(((*1 *1 *2 *3 *4) - (-12 (-14 *5 (-650 (-1186))) (-4 *2 (-174)) - (-4 *4 (-240 (-2827 *5) (-777))) - (-14 *6 - (-1 (-112) (-2 (|:| -4286 *3) (|:| -3201 *4)) - (-2 (|:| -4286 *3) (|:| -3201 *4)))) - (-5 *1 (-467 *5 *2 *3 *4 *6 *7)) (-4 *3 (-856)) - (-4 *7 (-956 *2 *4 (-870 *5)))))) -(((*1 *2 *1) (-12 (-5 *2 (-591)) (-5 *1 (-284))))) +(((*1 *2 *1) (-12 (-4 *1 (-803 *2)) (-4 *2 (-174))))) +(((*1 *2 *3 *1) + (-12 (|has| *1 (-6 -4452)) (-4 *1 (-495 *3)) (-4 *3 (-1227)) + (-4 *3 (-1109)) (-5 *2 (-777)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4452)) (-4 *1 (-495 *4)) + (-4 *4 (-1227)) (-5 *2 (-777))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -3340,57 +2849,25 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-368) (-1212) (-1011)))))) +(((*1 *2 *2) + (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1212)))))) (((*1 *2 *1) (-12 (-4 *3 (-1109)) (-4 *4 (-13 (-1058) (-893 *3) (-620 *2))) (-5 *2 (-899 *3)) (-5 *1 (-1085 *3 *4 *5)) (-4 *5 (-13 (-436 *4) (-893 *3) (-620 *2)))))) -(((*1 *2 *3 *4 *4 *5 *6) - (-12 (-5 *3 (-650 (-650 (-950 (-227))))) (-5 *4 (-880)) - (-5 *5 (-928)) (-5 *6 (-650 (-266))) (-5 *2 (-474)) (-5 *1 (-1281)))) - ((*1 *2 *3) - (-12 (-5 *3 (-650 (-650 (-950 (-227))))) (-5 *2 (-474)) - (-5 *1 (-1281)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-650 (-650 (-950 (-227))))) (-5 *4 (-650 (-266))) - (-5 *2 (-474)) (-5 *1 (-1281))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-985 *4 *5 *6 *3)) (-4 *4 (-1058)) (-4 *5 (-799)) - (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-4 *4 (-562)) - (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1220 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-799)) - (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-650 *6))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-777)) (-5 *3 (-950 *4)) (-4 *1 (-1143 *4)) - (-4 *4 (-1058)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-777)) (-5 *4 (-950 (-227))) (-5 *2 (-1282)) - (-5 *1 (-1279))))) -(((*1 *1) (-5 *1 (-295)))) (((*1 *2 *2) - (|partial| -12 (-4 *3 (-368)) (-4 *4 (-378 *3)) (-4 *5 (-378 *3)) - (-5 *1 (-527 *3 *4 *5 *2)) (-4 *2 (-693 *3 *4 *5)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-562)) (-4 *5 (-378 *4)) (-4 *6 (-378 *4)) - (-4 *7 (-1001 *4)) (-4 *2 (-693 *7 *8 *9)) - (-5 *1 (-528 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-693 *4 *5 *6)) - (-4 *8 (-378 *7)) (-4 *9 (-378 *7)))) - ((*1 *1 *1) - (|partial| -12 (-4 *1 (-693 *2 *3 *4)) (-4 *2 (-1058)) - (-4 *3 (-378 *2)) (-4 *4 (-378 *2)) (-4 *2 (-368)))) - ((*1 *2 *2) - (|partial| -12 (-4 *3 (-368)) (-4 *3 (-174)) (-4 *4 (-378 *3)) - (-4 *5 (-378 *3)) (-5 *1 (-694 *3 *4 *5 *2)) - (-4 *2 (-693 *3 *4 *5)))) - ((*1 *1 *1) - (|partial| -12 (-5 *1 (-695 *2)) (-4 *2 (-368)) (-4 *2 (-1058)))) - ((*1 *1 *1) - (|partial| -12 (-4 *1 (-1132 *2 *3 *4 *5)) (-4 *3 (-1058)) - (-4 *4 (-240 *2 *3)) (-4 *5 (-240 *2 *3)) (-4 *3 (-368)))) - ((*1 *2 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-856)) (-5 *1 (-1197 *3))))) + (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1212)))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *5 (-1277 (-650 *3))) (-4 *4 (-311)) + (-5 *2 (-650 *3)) (-5 *1 (-461 *4 *3)) (-4 *3 (-1253 *4))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) + (-4 *3 (-13 (-368) (-1212) (-1011)))))) +(((*1 *1) (-5 *1 (-295)))) +(((*1 *1) (-5 *1 (-158))) + ((*1 *2 *1) (-12 (-4 *1 (-1053 *2)) (-4 *2 (-23))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112)))) ((*1 *1 *2 *2) (-12 (-5 *1 (-298 *2)) (-4 *2 (-1227)))) ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-440)))) @@ -3398,20 +2875,14 @@ ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1035 *3)) (-4 *3 (-1227))))) (((*1 *2 *1) (-12 (-4 *1 (-1109)) (-5 *2 (-1129))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1080 *4 *5 *6 *3)) (-4 *4 (-458)) (-4 *5 (-799)) - (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *3 (-1074 *4 *5 *6)) - (-5 *2 (-650 (-2 (|:| |val| (-112)) (|:| -4228 *1)))) - (-4 *1 (-1080 *4 *5 *6 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-650 (-695 *5))) (-5 *4 (-1277 *5)) (-4 *5 (-311)) - (-4 *5 (-1058)) (-5 *2 (-695 *5)) (-5 *1 (-1038 *5))))) -(((*1 *2 *3 *4 *4 *4 *3 *4 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-757))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-695 *4)) (-5 *3 (-928)) (|has| *4 (-6 (-4454 "*"))) + (-4 *4 (-1058)) (-5 *1 (-1037 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-650 (-695 *4))) (-5 *3 (-928)) + (|has| *4 (-6 (-4454 "*"))) (-4 *4 (-1058)) (-5 *1 (-1037 *4))))) +(((*1 *1 *1 *1) (-4 *1 (-976)))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-650 *2)) (-4 *2 (-1227))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -3431,38 +2902,26 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-650 *2)) (-4 *2 (-1227))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) (((*1 *2 *3) - (-12 (-5 *3 (-659 (-413 *2))) (-4 *2 (-1253 *4)) (-5 *1 (-816 *4 *2)) - (-4 *4 (-13 (-368) (-148) (-1047 (-570)) (-1047 (-413 (-570))))))) + (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) + (-4 *6 (-799)) (-5 *2 (-413 (-959 *4))) (-5 *1 (-931 *4 *5 *6 *3)) + (-4 *3 (-956 *4 *6 *5)))) ((*1 *2 *3) - (-12 (-5 *3 (-660 *2 (-413 *2))) (-4 *2 (-1253 *4)) - (-5 *1 (-816 *4 *2)) - (-4 *4 (-13 (-368) (-148) (-1047 (-570)) (-1047 (-413 (-570)))))))) -(((*1 *2 *3) - (-12 (-5 *3 (-413 *5)) (-4 *5 (-1253 *4)) (-4 *4 (-562)) - (-4 *4 (-1058)) (-4 *2 (-1268 *4)) (-5 *1 (-1271 *4 *5 *6 *2)) - (-4 *6 (-662 *5))))) -(((*1 *2 *1 *3 *3 *4) - (-12 (-5 *3 (-1 (-868) (-868) (-868))) (-5 *4 (-570)) (-5 *2 (-868)) - (-5 *1 (-655 *5 *6 *7)) (-4 *5 (-1109)) (-4 *6 (-23)) (-14 *7 *6))) - ((*1 *2 *1 *2) - (-12 (-5 *2 (-868)) (-5 *1 (-860 *3 *4 *5)) (-4 *3 (-1058)) - (-14 *4 (-99 *3)) (-14 *5 (-1 *3 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-227)) (-5 *1 (-868)))) - ((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-868)))) - ((*1 *1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-868)))) - ((*1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868)))) - ((*1 *2 *1 *2) - (-12 (-5 *2 (-868)) (-5 *1 (-1182 *3)) (-4 *3 (-1058))))) -(((*1 *1 *2 *3) - (-12 (-5 *3 (-424 *2)) (-4 *2 (-311)) (-5 *1 (-921 *2)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-413 (-959 *5))) (-5 *4 (-1186)) - (-4 *5 (-13 (-311) (-148))) (-5 *2 (-52)) (-5 *1 (-922 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-424 (-959 *6))) (-5 *5 (-1186)) (-5 *3 (-959 *6)) - (-4 *6 (-13 (-311) (-148))) (-5 *2 (-52)) (-5 *1 (-922 *6))))) + (-12 (-5 *3 (-695 *7)) (-4 *7 (-956 *4 *6 *5)) + (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) + (-4 *6 (-799)) (-5 *2 (-695 (-413 (-959 *4)))) + (-5 *1 (-931 *4 *5 *6 *7)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 *7)) (-4 *7 (-956 *4 *6 *5)) + (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) + (-4 *6 (-799)) (-5 *2 (-650 (-413 (-959 *4)))) + (-5 *1 (-931 *4 *5 *6 *7))))) +(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1160))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-761))))) +(((*1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-397))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-777)) (-5 *2 (-1277 (-650 (-570)))) (-5 *1 (-486)))) ((*1 *1 *2 *3) @@ -3470,17 +2929,21 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1227)) (-5 *1 (-1166 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1227)) (-5 *1 (-1166 *3))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-384)) (-5 *1 (-207)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-650 (-384))) (-5 *2 (-384)) (-5 *1 (-207))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1070 (-1033 *4) (-1182 (-1033 *4)))) (-5 *3 (-868)) - (-5 *1 (-1033 *4)) (-4 *4 (-13 (-854) (-368) (-1031)))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-928)) (-4 *1 (-750 *3)) (-4 *3 (-174))))) -(((*1 *2) (-12 (-5 *2 (-777)) (-5 *1 (-451 *3)) (-4 *3 (-1058))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1277 *5)) (-4 *5 (-645 *4)) (-4 *4 (-562)) + (-5 *2 (-112)) (-5 *1 (-644 *4 *5))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-551)))) (((*1 *2 *1) - (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2024 "void"))) - (-5 *1 (-443))))) + (-12 (-5 *2 (-650 (-650 (-777)))) (-5 *1 (-911 *3)) (-4 *3 (-1109))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-650 *3)) + (-4 *3 (-13 (-27) (-1212) (-436 *6))) + (-4 *6 (-13 (-458) (-148) (-1047 (-570)) (-645 (-570)))) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-650 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-563 *6 *3))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -3500,30 +2963,12 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-458) (-148))) (-5 *2 (-424 *3)) - (-5 *1 (-100 *4 *3)) (-4 *3 (-1253 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-650 *3)) (-4 *3 (-1253 *5)) (-4 *5 (-13 (-458) (-148))) - (-5 *2 (-424 *3)) (-5 *1 (-100 *5 *3))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-306)) (-5 *3 (-1186)) (-5 *2 (-112)))) - ((*1 *2 *1 *3) (-12 (-4 *1 (-306)) (-5 *3 (-115)) (-5 *2 (-112)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1186)) (-5 *2 (-112)) (-5 *1 (-618 *4)) - (-4 *4 (-1109)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-115)) (-5 *2 (-112)) (-5 *1 (-618 *4)) (-4 *4 (-1109)))) - ((*1 *2 *1 *3) (-12 (-4 *1 (-841 *3)) (-4 *3 (-1109)) (-5 *2 (-112)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1109)) (-5 *2 (-112)) (-5 *1 (-894 *5 *3 *4)) - (-4 *3 (-893 *5)) (-4 *4 (-620 (-899 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-650 *6)) (-4 *6 (-893 *5)) (-4 *5 (-1109)) - (-5 *2 (-112)) (-5 *1 (-894 *5 *6 *4)) (-4 *4 (-620 (-899 *5)))))) -(((*1 *2 *3 *3 *4 *4 *4 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-762))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *1) + (-12 (-5 *2 (-697 (-879 (-973 *3) (-973 *3)))) (-5 *1 (-973 *3)) + (-4 *3 (-1109))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) (((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-138)))) ((*1 *2 *1) (-12 (-5 *2 (-1226)) (-5 *1 (-157)))) ((*1 *2 *1) (-12 (-5 *1 (-298 *2)) (-4 *2 (-1227)))) @@ -3537,16 +2982,30 @@ (-4 *4 (-13 (-1058) (-893 *3) (-620 (-899 *3)))))) ((*1 *2 *1) (-12 (-4 *2 (-1109)) (-5 *1 (-1175 *3 *2)) (-4 *3 (-1109))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-551)))) -(((*1 *2 *1) (-12 (-5 *2 (-215 4 (-130))) (-5 *1 (-585))))) (((*1 *2 *3) - (-12 (-5 *3 (-1182 *6)) (-4 *6 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 (-1182 *7)) (-5 *1 (-325 *4 *5 *6 *7)) - (-4 *7 (-956 *6 *4 *5))))) -(((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-565))))) + (-12 (-5 *3 (-650 *4)) (-4 *4 (-368)) (-5 *2 (-695 *4)) + (-5 *1 (-820 *4 *5)) (-4 *5 (-662 *4)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-650 *5)) (-5 *4 (-777)) (-4 *5 (-368)) + (-5 *2 (-695 *5)) (-5 *1 (-820 *5 *6)) (-4 *6 (-662 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-215 4 (-130))) (-5 *1 (-585))))) +(((*1 *2 *1) + (-12 (-5 *2 (-697 (-879 (-973 *3) (-973 *3)))) (-5 *1 (-973 *3)) + (-4 *3 (-1109))))) (((*1 *1 *2) (-12 (-5 *2 (-650 *1)) (-4 *1 (-458)))) ((*1 *1 *1 *1) (-4 *1 (-458)))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1113)) (-5 *1 (-283))))) +(((*1 *2 *2) + (-12 (-5 *2 (-650 (-2 (|:| |val| (-650 *6)) (|:| -4246 *7)))) + (-4 *6 (-1074 *3 *4 *5)) (-4 *7 (-1080 *3 *4 *5 *6)) (-4 *3 (-458)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-997 *3 *4 *5 *6 *7)))) + ((*1 *2 *2) + (-12 (-5 *2 (-650 (-2 (|:| |val| (-650 *6)) (|:| -4246 *7)))) + (-4 *6 (-1074 *3 *4 *5)) (-4 *7 (-1080 *3 *4 *5 *6)) (-4 *3 (-458)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-1116 *3 *4 *5 *6 *7))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1 (-227) (-227) (-227) (-227))) (-5 *1 (-266)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 (-227) (-227) (-227))) (-5 *1 (-266)))) + ((*1 *1 *2) (-12 (-5 *2 (-1 (-227) (-227))) (-5 *1 (-266))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -3563,29 +3022,20 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-934))))) -(((*1 *2 *3 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1253 *5)) - (-4 *5 (-13 (-368) (-148) (-1047 (-570)))) - (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-413 *6)) (|:| |h| *6) - (|:| |c1| (-413 *6)) (|:| |c2| (-413 *6)) (|:| -1911 *6))) - (-5 *1 (-1025 *5 *6)) (-5 *3 (-413 *6))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-458) (-1047 (-570)))) (-4 *3 (-562)) - (-5 *1 (-41 *3 *2)) (-4 *2 (-436 *3)) - (-4 *2 - (-13 (-368) (-306) - (-10 -8 (-15 -1611 ((-1134 *3 (-618 $)) $)) - (-15 -1625 ((-1134 *3 (-618 $)) $)) - (-15 -2838 ($ (-1134 *3 (-618 $)))))))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3846 (-788 *3)) (|:| |coef1| (-788 *3)))) - (-5 *1 (-788 *3)) (-4 *3 (-562)) (-4 *3 (-1058)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-562)) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 (-2 (|:| -3846 *1) (|:| |coef1| *1))) - (-4 *1 (-1074 *3 *4 *5))))) +(((*1 *2 *1) + (-12 (-5 *2 (-413 (-959 *3))) (-5 *1 (-459 *3 *4 *5 *6)) + (-4 *3 (-562)) (-4 *3 (-174)) (-14 *4 (-928)) + (-14 *5 (-650 (-1186))) (-14 *6 (-1277 (-695 *3)))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-978 *3 *2)) (-4 *2 (-1253 *3)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1253 *2)) (-4 *2 (-1058)) (-4 *2 (-562))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1244 *3)) (-4 *3 (-1227))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1182 *3)) (-4 *3 (-1058)) (-4 *1 (-1253 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-138)))) ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-157)))) ((*1 *2 *1) (-12 (-5 *1 (-298 *2)) (-4 *2 (-1227)))) @@ -3599,22 +3049,13 @@ (-4 *4 (-13 (-1058) (-893 *3) (-620 (-899 *3)))))) ((*1 *2 *1) (-12 (-4 *2 (-1109)) (-5 *1 (-1175 *2 *3)) (-4 *3 (-1109))))) -(((*1 *1 *2) - (-12 (-5 *2 (-650 (-928))) (-5 *1 (-1110 *3 *4)) (-14 *3 (-928)) - (-14 *4 (-928))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-1 (-112) *9)) (-5 *5 (-1 (-112) *9 *9)) - (-4 *9 (-1074 *6 *7 *8)) (-4 *6 (-562)) (-4 *7 (-799)) - (-4 *8 (-856)) (-5 *2 (-2 (|:| |bas| *1) (|:| -2027 (-650 *9)))) - (-5 *3 (-650 *9)) (-4 *1 (-1220 *6 *7 *8 *9)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-1 (-112) *8 *8)) (-4 *8 (-1074 *5 *6 *7)) - (-4 *5 (-562)) (-4 *6 (-799)) (-4 *7 (-856)) - (-5 *2 (-2 (|:| |bas| *1) (|:| -2027 (-650 *8)))) - (-5 *3 (-650 *8)) (-4 *1 (-1220 *5 *6 *7 *8))))) -(((*1 *2 *2 *3 *2) - (-12 (-5 *3 (-777)) (-4 *4 (-354)) (-5 *1 (-218 *4 *2)) - (-4 *2 (-1253 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1182 *6)) (-4 *6 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) + (-5 *2 (-1182 *7)) (-5 *1 (-325 *4 *5 *6 *7)) + (-4 *7 (-956 *6 *4 *5))))) +(((*1 *2 *3) + (-12 (-4 *4 (-562)) (-5 *2 (-777)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-423 *4))))) (((*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-777)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-928)))) ((*1 *1 *1 *1) @@ -3645,10 +3086,10 @@ ((*1 *1 *2 *1) (-12 (-4 *1 (-391 *2)) (-4 *2 (-1109)))) ((*1 *1 *2 *1) (-12 (-14 *3 (-650 (-1186))) (-4 *4 (-174)) - (-4 *6 (-240 (-2827 *3) (-777))) + (-4 *6 (-240 (-2857 *3) (-777))) (-14 *7 - (-1 (-112) (-2 (|:| -4286 *5) (|:| -3201 *6)) - (-2 (|:| -4286 *5) (|:| -3201 *6)))) + (-1 (-112) (-2 (|:| -4298 *5) (|:| -2940 *6)) + (-2 (|:| -4298 *5) (|:| -2940 *6)))) (-5 *1 (-467 *3 *4 *5 *6 *7 *2)) (-4 *5 (-856)) (-4 *2 (-956 *4 *6 (-870 *3))))) ((*1 *1 *1 *2) @@ -3722,13 +3163,15 @@ (-12 (-4 *1 (-1294 *3 *2)) (-4 *3 (-856)) (-4 *2 (-1058)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-1300 *2 *3)) (-4 *2 (-1058)) (-4 *3 (-852))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-4 *5 (-436 *4)) - (-5 *2 (-424 *3)) (-5 *1 (-441 *4 *5 *3)) (-4 *3 (-1253 *5))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-368) (-854))) - (-5 *2 (-2 (|:| |start| *3) (|:| -2859 (-424 *3)))) - (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4)))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-440)) + (-5 *2 + (-650 + (-3 (|:| -1770 (-1186)) + (|:| -4346 (-650 (-3 (|:| S (-1186)) (|:| P (-959 (-570))))))))) + (-5 *1 (-1190))))) +(((*1 *2 *3 *1) + (-12 (-5 *2 (-650 (-1186))) (-5 *1 (-1189)) (-5 *3 (-1186))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -3745,53 +3188,31 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *1 *2 *3) - (-12 (-5 *3 (-1186)) (-5 *1 (-592 *2)) (-4 *2 (-1047 *3)) - (-4 *2 (-368)))) - ((*1 *1 *2 *2) (-12 (-5 *1 (-592 *2)) (-4 *2 (-368)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1186)) (-4 *4 (-562)) (-5 *1 (-636 *4 *2)) - (-4 *2 (-13 (-436 *4) (-1011) (-1212))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1101 *2)) (-4 *2 (-13 (-436 *4) (-1011) (-1212))) - (-4 *4 (-562)) (-5 *1 (-636 *4 *2)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-966)) (-5 *2 (-1186)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-1101 *1)) (-4 *1 (-966))))) -(((*1 *1 *1) - (-12 (-5 *1 (-1174 *2 *3)) (-14 *2 (-928)) (-4 *3 (-1058))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) - ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-266))))) -(((*1 *1 *1) (-4 *1 (-635))) - ((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-636 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011) (-1212)))))) -(((*1 *2 *3 *3 *3) - (|partial| -12 - (-4 *4 (-13 (-148) (-27) (-1047 (-570)) (-1047 (-413 (-570))))) - (-4 *5 (-1253 *4)) (-5 *2 (-1182 (-413 *5))) (-5 *1 (-621 *4 *5)) - (-5 *3 (-413 *5)))) - ((*1 *2 *3 *3 *3 *4) - (|partial| -12 (-5 *4 (-1 (-424 *6) *6)) (-4 *6 (-1253 *5)) - (-4 *5 (-13 (-148) (-27) (-1047 (-570)) (-1047 (-413 (-570))))) - (-5 *2 (-1182 (-413 *6))) (-5 *1 (-621 *5 *6)) (-5 *3 (-413 *6))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-286 *2)) (-4 *2 (-1227)) (-4 *2 (-856)))) - ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-286 *3)) (-4 *3 (-1227)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-977 *2)) (-4 *2 (-856))))) -(((*1 *2) - (|partial| -12 (-4 *4 (-1231)) (-4 *5 (-1253 (-413 *2))) - (-4 *2 (-1253 *4)) (-5 *1 (-346 *3 *4 *2 *5)) - (-4 *3 (-347 *4 *2 *5)))) - ((*1 *2) - (|partial| -12 (-4 *1 (-347 *3 *2 *4)) (-4 *3 (-1231)) - (-4 *4 (-1253 (-413 *2))) (-4 *2 (-1253 *3))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1112 *3 *4 *5 *6 *7)) (-4 *3 (-1109)) (-4 *4 (-1109)) + (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *7 (-1109)) (-5 *2 (-112))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1279))))) +(((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562)) (-4 *2 (-551)))) + ((*1 *1 *1) (-4 *1 (-1069)))) +(((*1 *2 *1) + (-12 (-4 *3 (-1109)) (-4 *4 (-13 (-1058) (-893 *3) (-620 (-899 *3)))) + (-5 *2 (-650 (-1186))) (-5 *1 (-1085 *3 *4 *5)) + (-4 *5 (-13 (-436 *4) (-893 *3) (-620 (-899 *3))))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1109)) (-4 *6 (-1109)) + (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-690 *4 *5 *6)) (-4 *5 (-1109))))) +(((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-565))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-997 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1116 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7))))) +(((*1 *1 *1) + (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -3808,35 +3229,50 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) +(((*1 *1) (-5 *1 (-145))) ((*1 *1 *1) (-5 *1 (-868)))) +(((*1 *2 *1) + (|partial| -12 (-5 *2 (-1186)) (-5 *1 (-618 *3)) (-4 *3 (-1109))))) +(((*1 *2 *3 *3 *2) + (-12 (-5 *2 (-1166 *4)) (-5 *3 (-570)) (-4 *4 (-1058)) + (-5 *1 (-1170 *4)))) + ((*1 *1 *2 *2 *1) + (-12 (-5 *2 (-570)) (-5 *1 (-1269 *3 *4 *5)) (-4 *3 (-1058)) + (-14 *4 (-1186)) (-14 *5 *3)))) (((*1 *2 *3) - (-12 (-5 *3 (-695 (-413 (-959 (-570))))) - (-5 *2 - (-650 - (-2 (|:| |radval| (-320 (-570))) (|:| |radmult| (-570)) - (|:| |radvect| (-650 (-695 (-320 (-570)))))))) - (-5 *1 (-1040))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) -(((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1168)) (-5 *1 (-716))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1282)) (-5 *1 (-1278)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1282)) (-5 *1 (-1279))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1142 (-227))) (-5 *3 (-650 (-266))) (-5 *1 (-1279)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1142 (-227))) (-5 *3 (-1168)) (-5 *1 (-1279)))) - ((*1 *1 *1) (-5 *1 (-1279)))) -(((*1 *2 *3) - (-12 (-5 *2 (-424 (-1182 *1))) (-5 *1 (-320 *4)) (-5 *3 (-1182 *1)) - (-4 *4 (-458)) (-4 *4 (-562)) (-4 *4 (-1109)))) - ((*1 *2 *3) - (-12 (-4 *1 (-916)) (-5 *2 (-424 (-1182 *1))) (-5 *3 (-1182 *1))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 (-868))) (-5 *1 (-868)))) - ((*1 *1 *1) (-5 *1 (-868)))) + (|partial| -12 (-5 *3 (-1277 *5)) (-4 *5 (-645 *4)) (-4 *4 (-562)) + (-5 *2 (-1277 *4)) (-5 *1 (-644 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-283)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899 *3)) (-4 *3 (-1109)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1294 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058)) + (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1300 *3 *4)) (-4 *3 (-1058)) + (-4 *4 (-852))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-368) (-148) (-1047 (-570)))) (-4 *5 (-1253 *4)) + (-5 *2 (-2 (|:| |ans| (-413 *5)) (|:| |nosol| (-112)))) + (-5 *1 (-1024 *4 *5)) (-5 *3 (-413 *5))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1113)) (-5 *1 (-283))))) (((*1 *2 *2 *3) - (-12 (-5 *2 (-650 (-650 (-950 (-227))))) (-5 *3 (-650 (-880))) - (-5 *1 (-474))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-856)) (-5 *1 (-122 *3))))) + (-12 (-5 *2 (-695 *4)) (-5 *3 (-928)) (-4 *4 (-1058)) + (-5 *1 (-1037 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-650 (-695 *4))) (-5 *3 (-928)) (-4 *4 (-1058)) + (-5 *1 (-1037 *4))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-1168)) (-5 *4 (-1129)) (-5 *2 (-112)) (-5 *1 (-827))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-562)) (-4 *2 (-1058)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-978 *3 *2)) (-4 *2 (-1253 *3)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562)))) + ((*1 *2 *3 *3 *1) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *3 (-1074 *4 *5 *6)) + (-5 *2 (-650 (-2 (|:| |val| *3) (|:| -4246 *1)))) + (-4 *1 (-1080 *4 *5 *6 *3))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-227))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -3857,69 +3293,50 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *1 *1 *1) (-5 *1 (-868)))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-650 (-959 *4))) (-5 *3 (-650 (-1186))) (-4 *4 (-458)) - (-5 *1 (-925 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-650 (-413 (-959 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*2 (-1282)) - (-5 *1 (-794))))) -(((*1 *2 *1) (-12 (-4 *1 (-533)) (-5 *2 (-697 (-1235)))))) + (-12 (-5 *2 (-650 (-171 *4))) (-5 *1 (-156 *3 *4)) + (-4 *3 (-1253 (-171 (-570)))) (-4 *4 (-13 (-368) (-854))))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-368) (-854))) (-5 *2 (-650 (-171 *4))) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4))))) + ((*1 *2 *3 *4) + (-12 (-4 *4 (-13 (-368) (-854))) (-5 *2 (-650 (-171 *4))) + (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1198 (-650 *4))) (-4 *4 (-856)) + (-5 *2 (-650 (-650 *4))) (-5 *1 (-1197 *4))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1277 *3)) (-4 *3 (-1253 *4)) (-4 *4 (-1231)) + (-4 *1 (-347 *4 *3 *5)) (-4 *5 (-1253 (-413 *3)))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -4120,27 +3507,24 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *1) (-5 *1 (-603)))) -(((*1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 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(-849 (-227)))) (|:| |abserr| (-227)) + (|:| -2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 @@ -7098,7 +6419,7 @@ (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1598 + (|:| -2744 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -7106,154 +6427,206 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-565))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-959 (-413 (-570)))) (-5 *4 (-1186)) - (-5 *5 (-1103 (-849 (-227)))) (-5 *2 (-650 (-227))) (-5 *1 (-304))))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011)))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-650 (-570))) (-5 *3 (-695 (-570))) (-5 *1 (-1119))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-570)) (-5 *2 (-650 (-2 (|:| -2356 *3) (|:| -3954 *4)))) - (-5 *1 (-702 *3)) 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*5))))))) +(((*1 *1 *2 *3 *3 *3 *3) + (-12 (-5 *2 (-1 (-950 (-227)) (-227))) (-5 *3 (-1103 (-227))) + (-5 *1 (-933)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-950 (-227)) (-227))) (-5 *3 (-1103 (-227))) + (-5 *1 (-933)))) + ((*1 *1 *2 *3 *3 *3) + (-12 (-5 *2 (-1 (-950 (-227)) (-227))) (-5 *3 (-1103 (-227))) + (-5 *1 (-934)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-950 (-227)) (-227))) (-5 *3 (-1103 (-227))) + (-5 *1 (-934))))) +(((*1 *2 *1) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-176 *3)) (-4 *3 (-311))))) +(((*1 *1 *2) + (-12 (-5 *2 - (-2 (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) - (|:| |gd| *5))) - (-4 *1 (-347 *4 *5 *6))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-928)) (-5 *1 (-1041 *2)) - (-4 *2 (-13 (-1109) (-10 -8 (-15 * ($ $ $)))))))) -(((*1 *2 *3 *3) - (-12 (-4 *2 (-562)) (-5 *1 (-978 *2 *3)) (-4 *3 (-1253 *2))))) -(((*1 *2 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1277 *1)) (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) - (-4 *4 (-1253 *3)) (-4 *5 (-1253 (-413 *4)))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1166 *3)) (-4 *3 (-368)) (-4 *3 (-1058)) - (-5 *1 (-1170 *3))))) -(((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-1186))))) + (-650 + (-2 + (|:| -4144 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -3165 + (-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"))) + (|:| -2744 + (-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")))))))) + (-5 *1 (-565))))) (((*1 *2 *1) - (-12 (-4 *1 (-1294 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058)) - (-5 *2 (-112)))) + (-12 (-4 *1 (-330 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-798)) + (-5 *2 (-650 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1300 *3 *4)) (-4 *3 (-1058)) - (-4 *4 (-852))))) -(((*1 *1 *1) - (-12 (-4 *1 (-693 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-378 *2)) - (-4 *4 (-378 *2))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1166 (-1166 *4))) (-5 *2 (-1166 *4)) (-5 *1 (-1170 *4)) - (-4 *4 (-1058))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1182 *1)) (-5 *4 (-1186)) (-4 *1 (-27)) - (-5 *2 (-650 *1)))) - ((*1 *2 *3) (-12 (-5 *3 (-1182 *1)) (-4 *1 (-27)) (-5 *2 (-650 *1)))) - ((*1 *2 *3) (-12 (-5 *3 (-959 *1)) (-4 *1 (-27)) (-5 *2 (-650 *1)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1186)) (-4 *4 (-562)) (-5 *2 (-650 *1)) - (-4 *1 (-29 *4)))) - ((*1 *2 *1) (-12 (-4 *3 (-562)) (-5 *2 (-650 *1)) (-4 *1 (-29 *3))))) -(((*1 *2 *2 *1) - (-12 (-4 *1 (-1220 *3 *4 *5 *2)) (-4 *3 (-562)) (-4 *4 (-799)) - (-4 *5 (-856)) (-4 *2 (-1074 *3 *4 *5))))) + (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-1109)) + (-5 *2 (-650 *3)))) + ((*1 *2 *1) + (-12 (-5 *2 (-1166 *3)) (-5 *1 (-602 *3)) (-4 *3 (-1058)))) + ((*1 *2 *1) + (-12 (-5 *2 (-650 *3)) (-5 *1 (-741 *3 *4)) (-4 *3 (-1058)) + (-4 *4 (-732)))) + ((*1 *2 *1) (-12 (-4 *1 (-858 *3)) (-4 *3 (-1058)) (-5 *2 (-650 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1268 *3)) (-4 *3 (-1058)) (-5 *2 (-1166 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-650 (-487 *4 *5))) (-14 *4 (-650 (-1186))) - (-4 *5 (-458)) (-5 *2 (-650 (-249 *4 *5))) (-5 *1 (-637 *4 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-372 *2)) (-4 *2 (-174))))) -(((*1 *2 *1) - (-12 (-4 *1 (-985 *3 *4 *5 *6)) (-4 *3 (-1058)) (-4 *4 (-799)) - (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) - (-5 *2 (-112))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1188 (-413 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(-776 *4)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-695 *7)) + (-5 *5 + (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -2681 (-650 *6))) + *7 *6)) + (-4 *6 (-368)) (-4 *7 (-662 *6)) + (-5 *2 + (-2 (|:| |particular| (-3 (-1277 *6) "failed")) + (|:| -2681 (-650 (-1277 *6))))) + (-5 *1 (-819 *6 *7)) (-5 *4 (-1277 *6))))) (((*1 *1) (-5 *1 (-334)))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-570)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1227)) @@ -7607,24 +7062,19 @@ ((*1 *2 *1 *3 *2) (-12 (-5 *3 "first") (|has| *1 (-6 -4453)) (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) -(((*1 *2 *3) - (-12 (-5 *3 (-487 *4 *5)) (-14 *4 (-650 (-1186))) (-4 *5 (-1058)) - (-5 *2 (-959 *5)) (-5 *1 (-951 *4 *5))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-1186)) (-5 *4 (-959 (-570))) (-5 *2 (-334)) - (-5 *1 (-336)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-1186)) (-5 *4 (-1101 (-959 (-570)))) (-5 *2 (-334)) - (-5 *1 (-336)))) - ((*1 *1 *2 *2 *2) - (-12 (-5 *2 (-777)) (-5 *1 (-681 *3)) (-4 *3 (-1058)) - (-4 *3 (-1109))))) -(((*1 *2 *3) (-12 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+ (-14 *3 (-1186)) (-14 *4 (-3 (|:| |fst| (-440)) (|:| -1994 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -2544 (-650 (-334))))) (-5 *1 (-404 *3 *4 *5 *6)) (-14 *3 (-1186)) - (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2024 "void"))) + (-14 *4 (-3 (|:| |fst| (-440)) (|:| -1994 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-5 *1 (-404 *3 *4 *5 *6)) - (-14 *3 (-1186)) (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2024 "void"))) + (-14 *3 (-1186)) (-14 *4 (-3 (|:| |fst| (-440)) (|:| -1994 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-5 *1 (-404 *3 *4 *5 *6)) (-14 *3 (-1186)) - (-14 *4 (-3 (|:| |fst| (-440)) (|:| -2024 "void"))) + (-14 *4 (-3 (|:| |fst| (-440)) (|:| -1994 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-335 *4)) (-4 *4 (-13 (-856) (-21))) @@ -8683,7 +8289,7 @@ (-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 (|:| -1777 *3) (|:| -3613 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -1747 *3) (|:| -3677 *4)))) (-4 *3 (-1058)) (-4 *4 (-732)) (-5 *1 (-741 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-570)) (-4 *1 (-769)))) ((*1 *1 *2) @@ -8692,25 +8298,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -1598 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-320 (-227))) - (|:| -1598 (-650 (-1103 (-849 (-227))))) + (|:| -2744 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-320 (-227))) - (|:| -1598 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) + (|:| -2744 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -1598 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-775)))) ((*1 *2 *3) (-12 (-5 *2 (-780)) (-5 *1 (-779 *3)) (-4 *3 (-1227)))) @@ -8728,23 +8334,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-320 (-227))) (|:| -3392 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -3458 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-650 (-320 (-227)))) - (|:| -3392 (-650 (-227))))))) + (|:| -3458 (-650 (-227))))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -3392 (-650 (-227))))) + (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -3458 (-650 (-227))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-320 (-227))) (|:| -3392 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -3458 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (-5 *1 (-847)))) @@ -8845,42 +8451,59 @@ ((*1 *1 *2) (-12 (-5 *2 (-670 *3 *4)) (-4 *3 (-856)) (-4 *4 (-174)) (-5 *1 (-1297 *3 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1212)))))) +(((*1 *2 *3 *3 *4 *5) + (-12 (-5 *3 (-1168)) (-4 *6 (-458)) (-4 *7 (-799)) (-4 *8 (-856)) + (-4 *4 (-1074 *6 *7 *8)) (-5 *2 (-1282)) + (-5 *1 (-782 *6 *7 *8 *4 *5)) (-4 *5 (-1080 *6 *7 *8 *4))))) (((*1 *1 *1) (-4 *1 (-667)))) (((*1 *1 *2 *2) (-12 (-5 *2 (-777)) (-4 *3 (-1058)) (-4 *1 (-693 *3 *4 *5)) (-4 *4 (-378 *3)) (-4 *5 (-378 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-777)) (-4 *1 (-1275 *3)) (-4 *3 (-23)) (-4 *3 (-1227))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-413 (-570))) - (-4 *4 (-13 (-562) (-1047 (-570)) (-645 (-570)))) - (-5 *1 (-280 *4 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *4)))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *4 *4 *3 *3 *3) +(((*1 *1) (-5 *1 (-565)))) +(((*1 *2 *3 *4 *4 *3 *5 *3 *3 *4 *3 *6) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-227)) + (-5 *6 (-3 (|:| |fn| (-394)) (|:| |fp| (-78 FUNCTN)))) + (-5 *2 (-1044)) (-5 *1 (-754))))) +(((*1 *2 *3 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-112)) (-5 *1 (-835))))) +(((*1 *2 *3 *4 *5 *6 *5) + (-12 (-5 *4 (-171 (-227))) (-5 *5 (-570)) (-5 *6 (-1168)) + (-5 *3 (-227)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *3 *4 *4 *3) (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-758))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-1166 *3)) (-4 *3 (-1109)) - (-4 *3 (-1227))))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) - (-4 *2 - (-13 (-368) (-306) - (-10 -8 (-15 -1611 ((-1134 *3 (-618 $)) $)) - (-15 -1625 ((-1134 *3 (-618 $)) $)) - (-15 -2838 ($ (-1134 *3 (-618 $)))))))))) -(((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1282)) (-5 *1 (-1147)))) - ((*1 *2 *3) - (-12 (-5 *3 (-650 (-868))) (-5 *2 (-1282)) (-5 *1 (-1147))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1250 *5 *4)) (-4 *4 (-458)) (-4 *4 (-826)) - (-14 *5 (-1186)) (-5 *2 (-570)) (-5 *1 (-1123 *4 *5))))) -(((*1 *2 *3) - (|partial| -12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-4 *5 (-436 *4)) - (-5 *2 (-424 (-1182 (-413 (-570))))) (-5 *1 (-441 *4 *5 *3)) - (-4 *3 (-1253 *5))))) + (-5 *1 (-757))))) +(((*1 *2 *2) (-12 (-5 *2 (-1103 (-849 (-227)))) (-5 *1 (-309))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-777)) (-4 *6 (-458)) (-4 *7 (-799)) (-4 *8 (-856)) + (-4 *3 (-1074 *6 *7 *8)) + (-5 *2 + (-2 (|:| |done| (-650 *4)) + (|:| |todo| (-650 (-2 (|:| |val| (-650 *3)) (|:| -4246 *4)))))) + (-5 *1 (-1078 *6 *7 *8 *3 *4)) (-4 *4 (-1080 *6 *7 *8 *3)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-4 *3 (-1074 *5 *6 *7)) + (-5 *2 + (-2 (|:| |done| (-650 *4)) + (|:| |todo| (-650 (-2 (|:| |val| (-650 *3)) (|:| -4246 *4)))))) + (-5 *1 (-1078 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-777)) (-4 *6 (-458)) (-4 *7 (-799)) (-4 *8 (-856)) + (-4 *3 (-1074 *6 *7 *8)) + (-5 *2 + (-2 (|:| |done| (-650 *4)) + (|:| |todo| (-650 (-2 (|:| |val| (-650 *3)) (|:| -4246 *4)))))) + (-5 *1 (-1154 *6 *7 *8 *3 *4)) (-4 *4 (-1118 *6 *7 *8 *3)))) + ((*1 *2 *3 *4) + (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) + (-4 *3 (-1074 *5 *6 *7)) + (-5 *2 + (-2 (|:| |done| (-650 *4)) + (|:| |todo| (-650 (-2 (|:| |val| (-650 *3)) (|:| -4246 *4)))))) + (-5 *1 (-1154 *5 *6 *7 *3 *4)) (-4 *4 (-1118 *5 *6 *7 *3))))) +(((*1 *2 *3 *3 *2) (-12 (-5 *2 (-384)) (-5 *3 (-1168)) (-5 *1 (-97)))) + ((*1 *2 *3 *2) (-12 (-5 *2 (-384)) (-5 *3 (-1168)) (-5 *1 (-97))))) (((*1 *2 *1) (-12 (|has| *1 (-6 -4452)) (-4 *1 (-34)) (-5 *2 (-777)))) ((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-252)))) ((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-980)))) @@ -8890,74 +8513,100 @@ ((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-1300 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-852))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-799)) (-4 *4 (-856)) (-4 *5 (-311)) - (-5 *1 (-923 *3 *4 *5 *2)) (-4 *2 (-956 *5 *3 *4)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 (-1182 *6)) (-4 *6 (-956 *5 *3 *4)) (-4 *3 (-799)) - (-4 *4 (-856)) (-4 *5 (-311)) (-5 *1 (-923 *3 *4 *5 *6)))) - ((*1 *2 *3) - (-12 (-5 *3 (-650 *2)) (-4 *2 (-956 *6 *4 *5)) - (-5 *1 (-923 *4 *5 *6 *2)) (-4 *4 (-799)) (-4 *5 (-856)) - (-4 *6 (-311))))) -(((*1 *1 *2 *3 *3 *3 *4) - (-12 (-4 *4 (-368)) (-4 *3 (-1253 *4)) (-4 *5 (-1253 (-413 *3))) - (-4 *1 (-340 *4 *3 *5 *2)) (-4 *2 (-347 *4 *3 *5)))) - ((*1 *1 *2 *2 *3) - (-12 (-5 *3 (-570)) (-4 *2 (-368)) (-4 *4 (-1253 *2)) - (-4 *5 (-1253 (-413 *4))) (-4 *1 (-340 *2 *4 *5 *6)) - (-4 *6 (-347 *2 *4 *5)))) - ((*1 *1 *2 *2) - (-12 (-4 *2 (-368)) (-4 *3 (-1253 *2)) (-4 *4 (-1253 (-413 *3))) - (-4 *1 (-340 *2 *3 *4 *5)) (-4 *5 (-347 *2 *3 *4)))) - ((*1 *1 *2) - (-12 (-4 *3 (-368)) (-4 *4 (-1253 *3)) (-4 *5 (-1253 (-413 *4))) - (-4 *1 (-340 *3 *4 *5 *2)) (-4 *2 (-347 *3 *4 *5)))) - ((*1 *1 *2) - (-12 (-5 *2 (-419 *4 (-413 *4) *5 *6)) (-4 *4 (-1253 *3)) - (-4 *5 (-1253 (-413 *4))) (-4 *6 (-347 *3 *4 *5)) (-4 *3 (-368)) - (-4 *1 (-340 *3 *4 *5 *6))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-384) (-384))) (-5 *4 (-384)) - (-5 *2 - (-2 (|:| -4125 *4) (|:| -3022 *4) (|:| |totalpts| (-570)) - (|:| |success| (-112)))) - (-5 *1 (-795)) (-5 *5 (-570))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1282)) (-5 *1 (-828))))) -(((*1 *2) - (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) - (-4 *5 (-1253 (-413 *4))) (-5 *2 (-695 (-413 *4)))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-650 *6)) (-4 *1 (-985 *3 *4 *5 *6)) (-4 *3 (-1058)) - (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) - (-4 *3 (-562))))) (((*1 *2 *1) - (-12 (-4 *1 (-333 *3)) (-4 *3 (-368)) (-4 *3 (-373)) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1182 *4)) (-4 *4 (-354)) (-5 *2 (-112)) - (-5 *1 (-362 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1277 *4)) (-4 *4 (-354)) (-5 *2 (-112)) - (-5 *1 (-534 *4))))) -(((*1 *2 *2) - (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1212)))))) + (-12 + (-5 *2 + (-650 + (-2 + (|:| -4144 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -3165 + (-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"))) + (|:| -2744 + (-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")))))))) + (-5 *1 (-565)))) + ((*1 *2 *1) + (-12 (-4 *1 (-610 *3 *4)) (-4 *3 (-1109)) (-4 *4 (-1227)) 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-2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-2 @@ -9923,7 +9683,7 @@ (-3 (|:| |str| (-1166 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1598 + (|:| -2744 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -9931,22 +9691,33 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-565))))) -(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-1 (-171 (-227)) (-171 (-227)))) (-5 *4 (-1103 (-227))) - (-5 *2 (-1279)) (-5 *1 (-260))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1132 *3 *4 *2 *5)) (-4 *4 (-1058)) (-4 *5 (-240 *3 *4)) - (-4 *2 (-240 *3 *4))))) -(((*1 *1 *1) - (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) -(((*1 *2 *3) (-12 (-5 *3 (-1277 *1)) (-4 *1 (-372 *2)) (-4 *2 (-174)))) - ((*1 *2) (-12 (-4 *2 (-174)) 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(-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) @@ -9992,12 +9763,12 @@ (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -4228 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -4246 *8))) (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1080 *4 *5 *6 *7)) (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-1168)) (-5 *1 (-1078 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -4228 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-650 *7)) (|:| -4246 *8))) (-4 *7 (-1074 *4 *5 *6)) (-4 *8 (-1118 *4 *5 *6 *7)) (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-1168)) (-5 *1 (-1154 *4 *5 *6 *7 *8)))) @@ -10029,28 +9800,69 @@ (-4 *4 (-13 (-854) (-311) (-148) (-1031))) (-14 *6 (-650 (-1186))) (-5 *2 (-650 (-786 *4 (-870 *6)))) (-5 *1 (-1304 *4 *5 *6)) (-14 *5 (-650 (-1186)))))) -(((*1 *1 *2 *3 *1) - (-12 (-5 *2 (-512)) 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(-1212) (-436 *3))) (-14 *5 (-1186)) + (-14 *6 *4))) + ((*1 *2 *1) + (|partial| -12 (-4 *3 (-13 (-1047 (-570)) (-645 (-570)) (-458))) + (-5 *2 (-849 *4)) (-5 *1 (-1263 *3 *4 *5 *6)) + (-4 *4 (-13 (-27) (-1212) (-436 *3))) (-14 *5 (-1186)) + (-14 *6 *4)))) +(((*1 *2 *1) + (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-378 *3)) + (-4 *5 (-378 *3)) (-5 *2 (-570)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) + (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-570))))) +(((*1 *2 *3) (-12 (-5 *3 (-928)) (-5 *2 (-911 (-570))) (-5 *1 (-924)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 (-570))) (-5 *2 (-911 (-570))) (-5 *1 (-924))))) +(((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) +(((*1 *2 *3) + (-12 (-4 *4 (-562)) (-5 *2 (-650 *3)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-423 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) + ((*1 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) + ((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-437 *3 *2)) (-4 *2 (-436 *3)))) + ((*1 *1 *1) (-4 *1 (-1148)))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1186)) - (-4 *5 (-13 (-458) (-148) (-1047 (-570)) (-645 (-570)))) - (-5 *2 (-592 *3)) (-5 *1 (-563 *5 *3)) - (-4 *3 (-13 (-27) (-1212) (-436 *5)))))) -(((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) -(((*1 *2 *3 *4 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-753))))) + (-12 (-5 *3 (-1182 *2)) (-4 *2 (-956 (-413 (-959 *6)) *5 *4)) + (-5 *1 (-738 *5 *4 *6 *2)) (-4 *5 (-799)) + (-4 *4 (-13 (-856) (-10 -8 (-15 -2601 ((-1186) $))))) + (-4 *6 (-562))))) (((*1 *1 *2) (-12 (-5 *2 (-394)) (-5 *1 (-638))))) (((*1 *2) - (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) - (-4 *5 (-1253 (-413 *4))) (-5 *2 (-695 (-413 *4)))))) + (-12 (-4 *3 (-458)) (-4 *4 (-799)) (-4 *5 (-856)) + (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-1282)) + (-5 *1 (-997 *3 *4 *5 *6 *7)) (-4 *7 (-1080 *3 *4 *5 *6)))) + ((*1 *2) + (-12 (-4 *3 (-458)) (-4 *4 (-799)) (-4 *5 (-856)) + (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-1282)) + (-5 *1 (-1116 *3 *4 *5 *6 *7)) (-4 *7 (-1080 *3 *4 *5 *6))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-413 (-570))) (-5 *4 (-570)) (-5 *2 (-52)) + (-5 *1 (-1014))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 (-1 (-3 (-650 *6) "failed") (-570) *6 *6)) (-4 *6 (-368)) + (-4 *7 (-1253 *6)) + (-5 *2 (-2 (|:| |answer| (-592 (-413 *7))) (|:| |a0| *6))) + (-5 *1 (-580 *6 *7)) (-5 *3 (-413 *7))))) (((*1 *2 *1) (-12 (-5 *2 @@ -10259,7 +10330,7 @@ (-2 (|:| |var| (-1186)) (|:| |arrayIndex| (-650 (-959 (-570)))) (|:| |rand| - (-2 (|:| |ints2Floats?| (-112)) (|:| -1399 (-868)))))) + (-2 (|:| |ints2Floats?| (-112)) (|:| -1393 (-868)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1186)) (|:| |rand| (-868)) (|:| |ints2Floats?| (-112)))) @@ -10267,18 +10338,18 @@ (-2 (|:| |switch| (-1185)) (|:| |thenClause| (-334)) (|:| |elseClause| (-334)))) (|:| |returnBranch| - (-2 (|:| -2620 (-112)) - (|:| -4125 - (-2 (|:| |ints2Floats?| (-112)) (|:| -1399 (-868)))))) + (-2 (|:| -2171 (-112)) + (|:| -4156 + (-2 (|:| |ints2Floats?| (-112)) (|:| -1393 (-868)))))) (|:| |blockBranch| (-650 (-334))) (|:| |commentBranch| (-650 (-1168))) (|:| |callBranch| (-1168)) (|:| |forBranch| - (-2 (|:| -1598 (-1101 (-959 (-570)))) - (|:| |span| (-959 (-570))) (|:| -1812 (-334)))) + (-2 (|:| -2744 (-1101 (-959 (-570)))) + (|:| |span| (-959 (-570))) (|:| -1781 (-334)))) (|:| |labelBranch| (-1129)) - (|:| |loopBranch| (-2 (|:| |switch| (-1185)) (|:| -1812 (-334)))) + (|:| |loopBranch| (-2 (|:| |switch| (-1185)) (|:| -1781 (-334)))) (|:| |commonBranch| - (-2 (|:| -1800 (-1186)) (|:| |contents| (-650 (-1186))))) + (-2 (|:| -1770 (-1186)) (|:| |contents| (-650 (-1186))))) (|:| |printBranch| (-650 (-868))))) (-5 *1 (-334))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-618 *1))) (-4 *1 (-306))))) @@ -10287,26 +10358,25 @@ ((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1109)) (-4 *1 (-1107 *3)))) ((*1 *1) (-12 (-4 *1 (-1107 *2)) (-4 *2 (-1109))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856))))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-866)) (-5 *2 (-697 (-1235))) (-5 *3 (-1235))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-662 *2)) (-4 *2 (-1058)) (-4 *2 (-368)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-368)) (-5 *1 (-665 *4 *2)) + (-4 *2 (-662 *4))))) +(((*1 *2 *3 *2) + (-12 + (-5 *2 + (-650 + (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-777)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *3 (-799)) (-4 *6 (-956 *4 *3 *5)) (-4 *4 (-458)) (-4 *5 (-856)) + (-5 *1 (-455 *4 *3 *5 *6))))) (((*1 *2 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-437 *3 *2)) (-4 *2 (-436 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1148)))) -(((*1 *2 *2 *2 *2) - (-12 (-4 *2 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) - (-5 *1 (-1137 *3 *2)) (-4 *3 (-1253 *2))))) -(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1287))))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-368)) (-4 *3 (-1058)) - (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -3578 *1))) - (-4 *1 (-858 *3))))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-368)) (-4 *3 (-1058)) - (-5 *2 (-2 (|:| -4083 *1) (|:| -1850 *1))) (-4 *1 (-858 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-368)) (-4 *5 (-1058)) - (-5 *2 (-2 (|:| -4083 *3) (|:| -1850 *3))) (-5 *1 (-859 *5 *3)) - (-4 *3 (-858 *5))))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-798)))) @@ -10413,9 +10483,9 @@ (-4 *6 (-368)) (-5 *2 (-592 *6)) (-5 *1 (-590 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -3470 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -3730 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-368)) (-4 *6 (-368)) - (-5 *2 (-2 (|:| -3470 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -3730 *6) (|:| |coeff| *6))) (-5 *1 (-590 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -10534,7 +10604,7 @@ (-4 *8 (-1058)) (-4 *6 (-799)) (-4 *2 (-13 (-1109) - (-10 -8 (-15 -3943 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-777)))))) + (-10 -8 (-15 -3992 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-777)))))) (-5 *1 (-958 *6 *7 *8 *5 *2)) (-4 *5 (-956 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-965 *5)) (-4 *5 (-1227)) @@ -10550,8 +10620,8 @@ (-4 *2 (-956 (-959 *4) *5 *6)) (-4 *5 (-799)) (-4 *6 (-13 (-856) - (-10 -8 (-15 -2596 ((-1186) $)) - (-15 -1444 ((-3 $ "failed") (-1186)))))) + (-10 -8 (-15 -2601 ((-1186) $)) + (-15 -1433 ((-3 $ "failed") (-1186)))))) (-5 *1 (-993 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-562)) (-4 *6 (-562)) @@ -10638,322 +10708,114 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1058)) (-5 *1 (-1300 *3 *4)) (-4 *4 (-852))))) -(((*1 *2 *3) (-12 (-5 *3 (-950 *2)) (-5 *1 (-991 *2)) (-4 *2 (-1058))))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-650 (-2 (|:| |totdeg| (-777)) (|:| -3147 *3)))) + (-5 *4 (-777)) (-4 *3 (-956 *5 *6 *7)) (-4 *5 (-458)) (-4 *6 (-799)) + (-4 *7 (-856)) (-5 *1 (-455 *5 *6 *7 *3))))) (((*1 *2 *1) (|partial| -12 (-5 *2 (-1 (-542) (-650 (-542)))) (-5 *1 (-115)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-542) (-650 (-542)))) (-5 *1 (-115)))) ((*1 *1) (-5 *1 (-584)))) -(((*1 *1 *1 *1 *1) (-4 *1 (-551)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) -(((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-424 *3)) (-4 *3 (-562)))) - ((*1 *2 *3) - (-12 (-5 *3 (-650 (-2 (|:| -2356 *4) (|:| -3954 (-570))))) - (-4 *4 (-1253 (-570))) (-5 *2 (-777)) (-5 *1 (-448 *4))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-650 (-788 *3))) (-5 *1 (-788 *3)) (-4 *3 (-562)) - (-4 *3 (-1058))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-5 *1 (-334))))) -(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) -(((*1 *2 *3 *4 *5 *6) - (|partial| -12 (-5 *4 (-1186)) (-5 *6 (-650 (-618 *3))) - (-5 *5 (-618 *3)) (-4 *3 (-13 (-27) (-1212) (-436 *7))) - (-4 *7 (-13 (-458) (-148) (-1047 (-570)) 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(-15 -2087 ((-1168) $ *3)) (-15 -2475 ((-1282) $)) - (-15 -1404 ((-1282) $))))))) + (-10 -8 (-15 -2057 ((-1168) $ *3)) (-15 -2467 ((-1282) $)) + (-15 -1919 ((-1282) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-998)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-856) - (-10 -8 (-15 -2087 ((-1168) $ (-1186))) (-15 -2475 ((-1282) $)) - (-15 -1404 ((-1282) $))))))) + (-10 -8 (-15 -2057 ((-1168) $ (-1186))) (-15 -2467 ((-1282) $)) + (-15 -1919 ((-1282) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-777)) (-5 *1 (-247 *4)) (-4 *4 (-856)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-247 *3)) (-4 *3 (-856)))) @@ -13538,175 +13577,163 @@ (-12 (-5 *2 "rest") (-4 *1 (-1265 *3)) (-4 *3 (-1227)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-1182 *1)) (-5 *3 (-1186)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-1182 *1)) (-4 *1 (-27)))) + ((*1 *1 *2) (-12 (-5 *2 (-959 *1)) (-4 *1 (-27)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1186)) (-4 *1 (-29 *3)) (-4 *3 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(-181 *4)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-650 *8)) - (-5 *4 - (-650 - (-2 (|:| -3296 (-695 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-695 *7))))) - (-5 *5 (-777)) (-4 *8 (-1253 *7)) (-4 *7 (-1253 *6)) (-4 *6 (-354)) + (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-956 *4 *5 *6)) (-5 *2 (-650 (-650 *7))) + (-5 *1 (-454 *4 *5 *6 *7)) (-5 *3 (-650 *7)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-311) (-148))) (-4 *6 (-799)) + (-4 *7 (-856)) (-4 *8 (-956 *5 *6 *7)) (-5 *2 (-650 (-650 *8))) + (-5 *1 (-454 *5 *6 *7 *8)) (-5 *3 (-650 *8)))) + ((*1 *2 *3) + (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-956 *4 *5 *6)) (-5 *2 (-650 (-650 *7))) + (-5 *1 (-454 *4 *5 *6 *7)) (-5 *3 (-650 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-112)) (-4 *5 (-13 (-311) (-148))) (-4 *6 (-799)) + (-4 *7 (-856)) (-4 *8 (-956 *5 *6 *7)) (-5 *2 (-650 (-650 *8))) + (-5 *1 (-454 *5 *6 *7 *8)) (-5 *3 (-650 *8))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -2744 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) (-5 *2 - (-2 (|:| -3296 (-695 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-695 *7)))) - (-5 *1 (-504 *6 *7 *8)))) - ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) + (-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"))) + (-5 *1 (-194))))) +(((*1 *1 *1) (-12 (-5 *1 (-424 *2)) (-4 *2 (-562))))) +(((*1 *2 *1 *3 *4 *4 *5) + (-12 (-5 *3 (-950 (-227))) (-5 *4 (-880)) (-5 *5 (-928)) + (-5 *2 (-1282)) (-5 *1 (-474)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-950 (-227))) (-5 *2 (-1282)) (-5 *1 (-474)))) + ((*1 *2 *1 *3 *4 *4 *5) + (-12 (-5 *3 (-650 (-950 (-227)))) (-5 *4 (-880)) (-5 *5 (-928)) + (-5 *2 (-1282)) (-5 *1 (-474))))) +(((*1 *2 *3 *3 *2) + (-12 (-5 *2 (-1044)) (-5 *3 (-1186)) (-5 *1 (-194))))) +(((*1 *2 *1 *1 *3 *4) + (-12 (-5 *3 (-1 (-112) *5 *5)) (-5 *4 (-1 (-112) *6 *6)) + (-4 *5 (-13 (-1109) (-34))) (-4 *6 (-13 (-1109) (-34))) + (-5 *2 (-112)) (-5 *1 (-1149 *5 *6))))) +(((*1 *2 *1) (-12 (-4 *1 (-803 *2)) (-4 *2 (-174)))) + ((*1 *2 *1) (-12 (-4 *1 (-1006 *2)) (-4 *2 (-174))))) (((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-31)))) ((*1 *2 *1) (-12 (-5 *2 (-1191)) (-5 *1 (-49)))) ((*1 *2 *1) (-12 (-5 *2 (-650 (-1144))) (-5 *1 (-134)))) @@ -14969,40 +14885,47 @@ ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1028)))) ((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1075)))) ((*1 *2 *1) (-12 (-5 *2 (-650 (-1144))) (-5 *1 (-1105))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1208))))) -(((*1 *1 *2) - (-12 (-5 *2 (-650 (-650 *3))) (-4 *3 (-1109)) (-5 *1 (-912 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-173)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1222 *3)) (-4 *3 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+ (|:| |a0| *7))) + (-5 *1 (-580 *7 *8))))) +(((*1 *1) + (-12 (-4 *1 (-410)) (-3201 (|has| *1 (-6 -4443))) + (-3201 (|has| *1 (-6 -4435))))) + ((*1 *2 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-1109)) (-4 *2 (-856)))) + ((*1 *1) (-4 *1 (-850))) ((*1 *1 *1 *1) (-4 *1 (-856))) + ((*1 *2 *1) (-12 (-4 *1 (-977 *2)) (-4 *2 (-856))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) + (-4 *4 (-1109))))) +(((*1 *2 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-366 *3)) (-4 *3 (-1109)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-570)) (-4 *1 (-391 *4)) (-4 *4 (-1109)) (-5 *2 (-777)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-570)) (-4 *2 (-23)) (-5 *1 (-655 *4 *2 *5)) + (-4 *4 (-1109)) (-14 *5 *2)))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *1 *1) + (|partial| -12 (-4 *1 (-372 *2)) (-4 *2 (-174)) (-4 *2 (-562)))) + ((*1 *1 *1) (|partial| -4 *1 (-728)))) +(((*1 *1 *1 *1) (-5 *1 (-868)))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-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"))) - (|:| -1598 - (-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"))))) - (-5 *2 (-1044)) (-5 *1 (-309))))) + (-12 (-5 *3 (-1277 *1)) (-4 *1 (-372 *4)) (-4 *4 (-174)) + (-5 *2 (-1277 (-695 *4))))) + ((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-1277 (-695 *4))) (-5 *1 (-422 *3 *4)) 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(-4 *2 (-1109)))) ((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1109)) (-5 *1 (-1213 *3)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-650 (-1213 *2))) (-5 *1 (-1213 *2)) (-4 *2 (-1109))))) -(((*1 *2 *1) (-12 (-5 *2 (-650 (-1186))) (-5 *1 (-831))))) (((*1 *2) (-12 (-4 *2 (-13 (-436 *3) (-1011))) (-5 *1 (-279 *3 *2)) (-4 *3 (-562)))) @@ -15976,27 +15724,25 @@ (-12 (-5 *1 (-344 *2 *3 *4)) (-14 *2 (-650 (-1186))) (-14 *3 (-650 (-1186))) (-4 *4 (-393)))) ((*1 *1) (-5 *1 (-483))) ((*1 *1) (-4 *1 (-1212)))) -(((*1 *2 *3) - (-12 (-4 *4 (-799)) - (-4 *5 (-13 (-856) (-10 -8 (-15 -2596 ((-1186) $))))) (-4 *6 (-562)) - (-5 *2 (-2 (|:| -3440 (-959 *6)) (|:| -4024 (-959 *6)))) - (-5 *1 (-738 *4 *5 *6 *3)) (-4 *3 (-956 (-413 (-959 *6)) *4 *5))))) -(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) - (-12 (-5 *3 (-1168)) (-5 *4 (-570)) (-5 *5 (-695 (-227))) - (-5 *2 (-1044)) (-5 *1 (-760))))) -(((*1 *2 *3 *4 *4 *5) - (|partial| -12 (-5 *4 (-618 *3)) (-5 *5 (-650 *3)) - (-4 *3 (-13 (-436 *6) (-27) (-1212))) - (-4 *6 (-13 (-458) (-1047 (-570)) (-148) (-645 (-570)))) - (-5 *2 - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-650 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (-5 *1 (-572 *6 *3 *7)) (-4 *7 (-1109))))) -(((*1 *2 *2) - (|partial| -12 (-4 *3 (-562)) (-4 *3 (-174)) (-4 *4 (-378 *3)) - (-4 *5 (-378 *3)) (-5 *1 (-694 *3 *4 *5 *2)) - (-4 *2 (-693 *3 *4 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-497))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-650 *1)) (-4 *1 (-1074 *4 *5 *6)) (-4 *4 (-1058)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *5 (-856)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1220 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-799)) + (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1220 *4 *5 *6 *3)) (-4 *4 (-562)) (-4 *5 (-799)) + (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112))))) +(((*1 *2 *3 *3 *4 *5 *5 *5 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-1168)) (-5 *5 (-695 (-227))) + (-5 *2 (-1044)) (-5 *1 (-753))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-13 (-854) (-368))) (-5 *2 (-112)) (-5 *1 (-1070 *4 *3)) + (-4 *3 (-1253 *4))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-1186)) (-5 *3 (-650 *1)) (-4 *1 (-436 *4)) (-4 *4 (-1109)))) @@ -16008,29 +15754,36 @@ (-12 (-5 *2 (-1186)) (-4 *1 (-436 *3)) (-4 *3 (-1109)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1186)) (-4 *1 (-436 *3)) (-4 *3 (-1109))))) -(((*1 *2 *1) (-12 (-5 *2 (-1168)) (-5 *1 (-1208)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-1208))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) - (-5 *2 (-650 (-2 (|:| |val| (-112)) (|:| -4228 *4)))) - (-5 *1 (-1117 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-650 *7)) (-5 *3 (-570)) (-4 *7 (-956 *4 *5 *6)) - (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-5 *1 (-455 *4 *5 *6 *7))))) -(((*1 *2 *3 *4 *4 *4 *3 *3 *5 *5 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-227)) - (-5 *2 (-1044)) (-5 *1 (-757))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1186)) (-5 *4 (-959 (-570))) (-5 *2 (-334)) - (-5 *1 (-336))))) -(((*1 *2 *3) (-12 (-5 *2 (-413 (-570))) (-5 *1 (-567)) (-5 *3 (-570))))) -(((*1 *2 *2) (-12 (-5 *2 (-928)) (-5 *1 (-362 *3)) (-4 *3 (-354))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1166 (-650 (-570)))) (-5 *1 (-890)) - (-5 *3 (-650 (-570)))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-311)) (-5 *2 (-112))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *5 (-650 *4)) (-4 *4 (-368)) (-5 *2 (-1277 *4)) + (-5 *1 (-820 *4 *3)) (-4 *3 (-662 *4))))) +(((*1 *1 *1 *1) (-5 *1 (-868)))) +(((*1 *2) + (-12 (-4 *1 (-354)) + (-5 *2 (-650 (-2 (|:| -2340 (-570)) (|:| -2940 (-570)))))))) +(((*1 *2 *3) + (-12 (-4 *1 (-845)) + (-5 *3 + (-2 (|:| |fn| (-320 (-227))) (|:| -3458 (-650 (-227))) + (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) + (|:| |ub| (-650 (-849 (-227)))))) + (-5 *2 (-1044)))) + ((*1 *2 *3) + (-12 (-4 *1 (-845)) + (-5 *3 + (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -3458 (-650 (-227))))) + (-5 *2 (-1044))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) + (-4 *3 (-13 (-368) (-1212) (-1011)))))) +(((*1 *2 *1) (|partial| -12 (-5 *1 (-370 *2)) (-4 *2 (-1109)))) + ((*1 *2 *1) (|partial| -12 (-5 *2 (-1168)) (-5 *1 (-1208))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 *1)) (-4 *1 (-306)))) + ((*1 *1 *1) (-4 *1 (-306))) ((*1 *1 *1) (-5 *1 (-868)))) +(((*1 *2) + (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) + (-4 *5 (-1253 (-413 *4))) (-5 *2 (-112))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) (((*1 *2 *2) (-12 (-4 *3 (-1109)) (-5 *1 (-936 *3 *2)) (-4 *2 (-436 *3)))) ((*1 *2 *3) @@ -16058,47 +15811,26 @@ (-12 (-5 *3 (-650 *5)) (-5 *4 (-650 *2)) (-5 *6 (-1 *2 *5)) (-4 *5 (-1109)) (-4 *2 (-1227)) (-5 *1 (-647 *5 *2)))) ((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1153)) (-5 *3 (-145)) (-5 *2 (-777))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-956 *4 *5 *6)) (-5 *2 (-650 (-650 *7))) - (-5 *1 (-454 *4 *5 *6 *7)) (-5 *3 (-650 *7)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-311) (-148))) (-4 *6 (-799)) - (-4 *7 (-856)) (-4 *8 (-956 *5 *6 *7)) (-5 *2 (-650 (-650 *8))) - (-5 *1 (-454 *5 *6 *7 *8)) (-5 *3 (-650 *8)))) - ((*1 *2 *3) - (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-956 *4 *5 *6)) (-5 *2 (-650 (-650 *7))) - (-5 *1 (-454 *4 *5 *6 *7)) (-5 *3 (-650 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-311) (-148))) (-4 *6 (-799)) - (-4 *7 (-856)) (-4 *8 (-956 *5 *6 *7)) (-5 *2 (-650 (-650 *8))) - (-5 *1 (-454 *5 *6 *7 *8)) (-5 *3 (-650 *8))))) -(((*1 *2 *2 *2 *2 *3) - (-12 (-4 *3 (-562)) (-5 *1 (-978 *3 *2)) (-4 *2 (-1253 *3))))) -(((*1 *2 *3 *4 *5 *6) - (|partial| -12 (-5 *4 (-1 *8 *8)) - (-5 *5 - (-1 (-2 (|:| |ans| *7) (|:| -2430 *7) (|:| |sol?| (-112))) - (-570) *7)) - (-5 *6 (-650 (-413 *8))) (-4 *7 (-368)) (-4 *8 (-1253 *7)) - (-5 *3 (-413 *8)) - (-5 *2 - (-2 - (|:| |answer| - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-650 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (|:| |a0| *7))) - (-5 *1 (-580 *7 *8))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-173))))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-437 *3 *2)) (-4 *2 (-436 *3))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1188 (-413 (-570)))) (-5 *1 (-192))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-650 (-650 (-650 *5)))) (-5 *3 (-1 (-112) *5 *5)) - (-5 *4 (-650 *5)) (-4 *5 (-856)) (-5 *1 (-1197 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-650 (-959 *4))) (-5 *3 (-650 (-1186))) (-4 *4 (-458)) + (-5 *1 (-925 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-827))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-650 (-249 *4 *5))) (-5 *2 (-249 *4 *5)) + (-14 *4 (-650 (-1186))) (-4 *5 (-458)) (-5 *1 (-637 *4 *5))))) +(((*1 *1) (-5 *1 (-584)))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-777)) (-4 *1 (-1294 *3 *4)) (-4 *3 (-856)) + (-4 *4 (-1058)) (-4 *4 (-174)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1294 *2 *3)) (-4 *2 (-856)) (-4 *3 (-1058)) + (-4 *3 (-174))))) +(((*1 *2 *3) (-12 (-5 *3 (-384)) (-5 *2 (-1168)) (-5 *1 (-309))))) +(((*1 *2 *3) (-12 (-5 *3 (-512)) (-5 *2 (-697 (-189))) (-5 *1 (-189))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-1220 *4 *5 *3 *6)) (-4 *4 (-562)) (-4 *5 (-799)) + (-4 *3 (-856)) (-4 *6 (-1074 *4 *5 *3)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-1296 *3)) (-4 *3 (-368)) (-5 *2 (-112))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-1001 *2)) (-4 *4 (-1253 *3)) (-4 *2 (-311)) @@ -16117,7 +15849,7 @@ (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -3392 (-650 (-227))))) + (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -3458 (-650 (-227))))) (-5 *2 (-650 (-1186))) (-5 *1 (-270)))) ((*1 *2 *3) (-12 (-5 *3 (-1182 *7)) (-4 *7 (-956 *6 *4 *5)) (-4 *4 (-799)) @@ -16139,7 +15871,7 @@ (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-368) - (-10 -8 (-15 -2838 ($ *7)) (-15 -1611 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*2 (-227)) (-5 *1 (-309))))) +(((*1 *2 *1) (-12 (-5 *2 (-337)) (-5 *1 (-251))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *5 (-618 *4)) (-5 *6 (-1186)) + (-4 *4 (-13 (-436 *7) (-27) (-1212))) + (-4 *7 (-13 (-458) (-1047 (-570)) (-148) (-645 (-570)))) + (-5 *2 + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2681 (-650 *4)))) + (-5 *1 (-572 *7 *4 *3)) (-4 *3 (-662 *4)) (-4 *3 (-1109))))) +(((*1 *2 *3 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-316)) (-5 *1 (-835))))) +(((*1 *1 *2 *3) + (-12 (-5 *1 (-433 *3 *2)) (-4 *3 (-13 (-174) (-38 (-413 (-570))))) + (-4 *2 (-13 (-856) (-21)))))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-3 (|:| |Null| "null") (|:| |Assignment| "assignment") + (|:| |Conditional| "conditional") (|:| |Return| "return") + (|:| |Block| "block") (|:| |Comment| "comment") + (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") + (|:| |Repeat| "repeat") (|:| |Goto| "goto") + (|:| |Continue| "continue") + (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") + (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print"))) + (-5 *1 (-334))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -16568,61 +16296,38 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*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) - (-12 (-4 *5 (-368)) - (-5 *2 - (-2 (|:| A (-695 *5)) - (|:| |eqs| +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |pde| (-650 (-320 (-227)))) + (|:| |constraints| (-650 - (-2 (|:| C (-695 *5)) (|:| |g| (-1277 *5)) (|:| -2556 *6) - (|:| |rh| *5)))))) - (-5 *1 (-819 *5 *6)) (-5 *3 (-695 *5)) (-5 *4 (-1277 *5)) - (-4 *6 (-662 *5)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-368)) (-4 *6 (-662 *5)) - (-5 *2 (-2 (|:| -4245 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\ No newline at end of file |