From 29325dbb1fed9b472690b8541ef038f138070aea Mon Sep 17 00:00:00 2001 From: dos-reis Date: Sun, 27 Jun 2010 12:31:29 +0000 Subject: * algebra/catdef.spad.pamphlet (LinearlyExplicitRingOver) [leftReducedSystem]: Rename from reducedSystem. --- src/ChangeLog | 5 + src/algebra/catdef.spad.pamphlet | 6 +- src/algebra/strap/INT.lsp | 56 +- src/algebra/strap/POLYCAT-.lsp | 17 +- src/algebra/strap/QFCAT-.lsp | 8 +- src/algebra/strap/SINT.lsp | 60 +- src/share/algebra/browse.daase | 1280 +- src/share/algebra/category.daase | 1556 +- src/share/algebra/compress.daase | 1322 +- src/share/algebra/interp.daase | 9112 +++++----- src/share/algebra/operation.daase | 33307 ++++++++++++++++++------------------ 11 files changed, 23368 insertions(+), 23361 deletions(-) diff --git a/src/ChangeLog b/src/ChangeLog index 0a6758d4..add397e1 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,8 @@ +2010-06-27 Gabriel Dos Reis + + * algebra/catdef.spad.pamphlet (LinearlyExplicitRingOver) + [leftReducedSystem]: Rename from reducedSystem. + 2010-06-26 Gabriel Dos Reis * interp/g-opt.boot ($VMsideEffectFreeOperators): Include %vref diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index aa972025..4b0eb27e 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -1096,12 +1096,12 @@ LeftModule(R:Rng):Category == Join(AbelianGroup, LeftLinearSet R) ++ Description: ++ An extension of left-module with an explicit linear dependence test. LinearlyExplicitRingOver(R:Ring): Category == LeftModule R with - reducedSystem: Vector % -> Matrix R - ++ \spad{reducedSystem [v1,...,vn]} returns a matrix \spad{M} + leftReducedSystem: Vector % -> Matrix R + ++ \spad{leftReducedSystem [v1,...,vn]} returns a matrix \spad{M} ++ with coefficients in \spad{R} such that the system of equations ++ \spad{c1*v1 + ... + cn*vn = 0$%} has the same solution as ++ \spad{c * M = 0} where \spad{c} is the row vector \spad{[c1,...cn]}. - reducedSystem: (Vector %,%) -> Record(mat: Matrix R,vec: Vector R) + leftReducedSystem: (Vector %,%) -> Record(mat: Matrix R,vec: Vector R) ++ \spad{reducedSystem([v1,...,vn],u)} returns a matrix \spad{M} ++ with coefficients in \spad{R} and a vector \spad{w} such ++ that the system of equations \spad{c1*v1 + ... + cn*vn = u} diff --git a/src/algebra/strap/INT.lsp b/src/algebra/strap/INT.lsp index 0c4f5705..2bd30e1b 100644 --- a/src/algebra/strap/INT.lsp +++ b/src/algebra/strap/INT.lsp @@ -587,22 +587,22 @@ |submod| 205 |squareFreePart| 212 |squareFree| 217 |sizeLess?| 222 |sign| 228 |shift| 233 |sample| 239 |retractIfCan| 243 |retract| 248 |rem| 253 |reducedSystem| - 259 |recip| 281 |rationalIfCan| 286 |rational?| 291 - |rational| 296 |random| 301 |quo| 310 |principalIdeal| 316 - |prime?| 321 |powmod| 326 |positiveRemainder| 333 - |positive?| 339 |permutation| 344 |patternMatch| 350 - |one?| 357 |odd?| 362 |nextItem| 367 |negative?| 372 - |multiEuclidean| 377 |mulmod| 383 |min| 390 |max| 396 - |mask| 402 |length| 407 |lcm| 412 |latex| 423 |invmod| 428 - |init| 434 |inc| 438 |hash| 443 |gcdPolynomial| 448 |gcd| - 454 |factorial| 465 |factor| 470 |extendedEuclidean| 475 - |exquo| 488 |expressIdealMember| 494 |even?| 500 - |euclideanSize| 505 |divide| 510 |differentiate| 516 |dec| - 527 |copy| 532 |convert| 537 |coerce| 567 |characteristic| - 587 |bit?| 591 |binomial| 597 |before?| 603 |base| 609 - |associates?| 613 |addmod| 619 |abs| 626 |Zero| 631 |One| - 635 |OMwrite| 639 D 663 >= 674 > 680 = 686 <= 692 < 698 - - 704 + 715 ** 721 * 733) + 259 |recip| 270 |rationalIfCan| 275 |rational?| 280 + |rational| 285 |random| 290 |quo| 299 |principalIdeal| 305 + |prime?| 310 |powmod| 315 |positiveRemainder| 322 + |positive?| 328 |permutation| 333 |patternMatch| 339 + |one?| 346 |odd?| 351 |nextItem| 356 |negative?| 361 + |multiEuclidean| 366 |mulmod| 372 |min| 379 |max| 385 + |mask| 391 |length| 396 |leftReducedSystem| 401 |lcm| 412 + |latex| 423 |invmod| 428 |init| 434 |inc| 438 |hash| 443 + |gcdPolynomial| 448 |gcd| 454 |factorial| 465 |factor| 470 + |extendedEuclidean| 475 |exquo| 488 |expressIdealMember| + 494 |even?| 500 |euclideanSize| 505 |divide| 510 + |differentiate| 516 |dec| 527 |copy| 532 |convert| 537 + |coerce| 567 |characteristic| 587 |bit?| 591 |binomial| + 597 |before?| 603 |base| 609 |associates?| 613 |addmod| + 619 |abs| 626 |Zero| 631 |One| 635 |OMwrite| 639 D 663 >= + 674 > 680 = 686 <= 692 < 698 - 704 + 715 ** 721 * 733) '((|infinite| . 0) (|noetherian| . 0) (|canonicalsClosed| . 0) (|canonical| . 0) (|canonicalUnitNormal| . 0) (|multiplicativeValuation| . 0) @@ -684,18 +684,18 @@ 9 0 1 2 0 0 0 0 1 2 0 92 0 0 1 3 0 0 0 0 0 52 1 0 0 0 1 1 0 113 0 1 2 0 9 0 0 1 1 0 17 0 1 2 0 0 0 0 91 0 0 0 1 - 1 0 133 0 1 1 0 17 0 1 2 0 0 0 0 53 2 - 0 74 75 0 1 1 0 70 75 1 1 0 70 71 72 - 2 0 74 71 75 76 1 0 92 0 93 1 0 130 0 - 1 1 0 9 0 1 1 0 129 0 1 0 0 0 78 1 0 - 0 0 79 2 0 0 0 0 90 1 0 135 134 1 1 0 - 9 0 1 3 0 0 0 0 0 1 2 0 0 0 0 69 1 0 - 9 0 1 2 0 0 0 0 1 3 0 132 0 131 132 1 - 1 0 9 0 34 1 0 9 0 85 1 0 92 0 1 1 0 - 9 0 43 2 0 136 134 0 1 3 0 0 0 0 0 54 - 2 0 0 0 0 87 2 0 0 0 0 86 1 0 0 0 1 1 - 0 0 0 49 2 0 0 0 0 1 1 0 0 134 1 1 0 - 14 0 68 2 0 0 0 0 1 0 0 0 1 1 0 0 0 + 1 0 133 0 1 1 0 17 0 1 2 0 0 0 0 53 1 + 0 70 71 72 2 0 74 71 75 76 1 0 92 0 + 93 1 0 130 0 1 1 0 9 0 1 1 0 129 0 1 + 0 0 0 78 1 0 0 0 79 2 0 0 0 0 90 1 0 + 135 134 1 1 0 9 0 1 3 0 0 0 0 0 1 2 0 + 0 0 0 69 1 0 9 0 1 2 0 0 0 0 1 3 0 + 132 0 131 132 1 1 0 9 0 34 1 0 9 0 85 + 1 0 92 0 1 1 0 9 0 43 2 0 136 134 0 1 + 3 0 0 0 0 0 54 2 0 0 0 0 87 2 0 0 0 0 + 86 1 0 0 0 1 1 0 0 0 49 2 0 74 75 0 1 + 1 0 70 75 1 2 0 0 0 0 1 1 0 0 134 1 1 + 0 14 0 68 2 0 0 0 0 1 0 0 0 1 1 0 0 0 38 1 0 41 0 42 2 0 127 127 127 128 2 0 0 0 0 94 1 0 0 134 1 1 0 0 0 1 1 0 113 0 114 2 0 137 0 0 1 3 0 139 0 0 0 diff --git a/src/algebra/strap/POLYCAT-.lsp b/src/algebra/strap/POLYCAT-.lsp index 46d17c73..9426e0ee 100644 --- a/src/algebra/strap/POLYCAT-.lsp +++ b/src/algebra/strap/POLYCAT-.lsp @@ -1458,19 +1458,20 @@ 218 0 236 1 9 225 0 237 1 7 225 0 238 3 241 225 239 240 6 242 1 0 225 0 243 1 9 244 0 245 1 7 244 0 246 3 249 244 - 247 248 6 250 1 0 244 0 251 1 0 45 0 - 88 2 0 45 0 19 93 1 0 0 0 203 1 0 148 + 247 248 6 250 1 0 244 0 251 2 0 45 0 + 19 93 1 0 45 0 88 1 0 0 0 203 1 0 148 0 195 2 0 140 139 58 141 1 0 15 0 74 1 0 9 0 73 3 0 0 0 0 9 95 2 0 129 120 130 131 1 0 110 120 121 2 0 0 0 9 213 - 1 0 0 0 210 1 0 20 0 77 3 0 221 0 218 - 221 222 3 0 228 0 225 228 229 1 0 20 + 1 0 0 0 210 1 0 20 0 77 3 0 228 0 225 + 228 229 3 0 221 0 218 221 222 1 0 20 0 34 3 0 0 0 19 63 71 3 0 190 0 0 9 192 1 0 38 0 52 1 0 38 0 39 1 0 56 0 57 2 0 58 58 58 134 1 0 144 58 147 1 0 144 58 145 1 0 148 0 165 2 0 0 0 23 - 24 2 0 0 0 9 97 1 0 244 0 251 1 0 225 - 0 243 1 0 218 0 236 2 0 0 0 9 205 1 0 - 179 120 184 3 0 0 0 19 63 69 3 0 0 0 - 9 45 62 1 0 172 0 186 2 0 10 0 0 216))))) + 24 2 0 0 0 9 97 1 0 218 0 236 1 0 244 + 0 251 1 0 225 0 243 2 0 0 0 9 205 1 0 + 179 120 184 3 0 0 0 9 45 62 3 0 0 0 + 19 63 69 1 0 172 0 186 2 0 10 0 0 + 216))))) '|lookupComplete|)) diff --git a/src/algebra/strap/QFCAT-.lsp b/src/algebra/strap/QFCAT-.lsp index b52baeae..15cc7091 100644 --- a/src/algebra/strap/QFCAT-.lsp +++ b/src/algebra/strap/QFCAT-.lsp @@ -473,12 +473,12 @@ 23 67 0 107 2 67 0 0 0 108 1 23 67 0 109 5 23 0 0 67 67 67 67 110 2 23 111 0 67 112 1 0 94 0 96 1 0 64 0 66 1 0 - 67 0 93 1 0 56 0 61 2 0 113 27 114 - 115 1 0 23 27 28 0 0 0 99 3 0 75 0 68 - 75 76 3 0 84 0 77 84 85 1 0 0 0 10 1 + 67 0 93 1 0 56 0 61 1 0 23 27 28 2 0 + 113 27 114 115 0 0 0 99 3 0 84 0 77 + 84 85 3 0 75 0 68 75 76 1 0 0 0 10 1 0 17 0 20 2 0 0 21 0 22 0 0 0 16 1 0 0 0 55 2 0 0 0 21 36 1 0 0 0 12 1 0 - 45 0 48 1 0 41 0 44 1 0 37 0 40 1 0 + 41 0 44 1 0 45 0 48 1 0 37 0 40 1 0 77 0 80 1 0 68 0 71 1 0 0 56 58 1 0 0 86 91 0 0 29 31 2 0 49 0 0 51))))) '|lookupComplete|)) diff --git a/src/algebra/strap/SINT.lsp b/src/algebra/strap/SINT.lsp index 82ab1e35..32a69f40 100644 --- a/src/algebra/strap/SINT.lsp +++ b/src/algebra/strap/SINT.lsp @@ -600,24 +600,24 @@ |subtractIfCan| 121 |submod| 127 |squareFreePart| 134 |squareFree| 139 |sizeLess?| 144 |size| 150 |sign| 154 |shift| 159 |sample| 165 |retractIfCan| 169 |retract| 174 - |rem| 179 |reducedSystem| 185 |recip| 207 |rationalIfCan| - 212 |rational?| 217 |rational| 222 |random| 227 |quo| 236 - |principalIdeal| 242 |prime?| 247 |powmod| 252 - |positiveRemainder| 259 |positive?| 265 |permutation| 270 - |patternMatch| 276 |or| 283 |one?| 289 |odd?| 294 |not| - 299 |nextItem| 304 |negative?| 309 |multiEuclidean| 314 - |mulmod| 320 |min| 327 |max| 337 |mask| 347 |lookup| 352 - |length| 357 |lcm| 362 |latex| 373 |invmod| 378 |init| 384 - |index| 388 |inc| 393 |hash| 398 |gcdPolynomial| 403 |gcd| - 409 |factorial| 420 |factor| 425 |extendedEuclidean| 430 - |exquo| 443 |expressIdealMember| 449 |even?| 455 - |euclideanSize| 460 |divide| 465 |differentiate| 471 |dec| - 482 |copy| 487 |convert| 492 |coerce| 517 |characteristic| - 537 |bit?| 541 |binomial| 547 |before?| 553 |base| 559 - |associates?| 563 |and| 569 |addmod| 575 |abs| 582 |\\/| - 587 |Zero| 593 |Or| 597 |One| 603 |OMwrite| 607 |Not| 631 - D 636 |And| 647 >= 653 > 659 = 665 <= 671 < 677 |/\\| 683 - - 689 + 700 ** 706 * 718) + |rem| 179 |reducedSystem| 185 |recip| 196 |rationalIfCan| + 201 |rational?| 206 |rational| 211 |random| 216 |quo| 225 + |principalIdeal| 231 |prime?| 236 |powmod| 241 + |positiveRemainder| 248 |positive?| 254 |permutation| 259 + |patternMatch| 265 |or| 272 |one?| 278 |odd?| 283 |not| + 288 |nextItem| 293 |negative?| 298 |multiEuclidean| 303 + |mulmod| 309 |min| 316 |max| 326 |mask| 336 |lookup| 341 + |length| 346 |leftReducedSystem| 351 |lcm| 362 |latex| 373 + |invmod| 378 |init| 384 |index| 388 |inc| 393 |hash| 398 + |gcdPolynomial| 403 |gcd| 409 |factorial| 420 |factor| 425 + |extendedEuclidean| 430 |exquo| 443 |expressIdealMember| + 449 |even?| 455 |euclideanSize| 460 |divide| 465 + |differentiate| 471 |dec| 482 |copy| 487 |convert| 492 + |coerce| 517 |characteristic| 537 |bit?| 541 |binomial| + 547 |before?| 553 |base| 559 |associates?| 563 |and| 569 + |addmod| 575 |abs| 582 |\\/| 587 |Zero| 593 |Or| 597 |One| + 603 |OMwrite| 607 |Not| 631 D 636 |And| 647 >= 653 > 659 = + 665 <= 671 < 677 |/\\| 683 - 689 + 700 ** 706 * 718) '((|noetherian| . 0) (|canonicalsClosed| . 0) (|canonical| . 0) (|canonicalUnitNormal| . 0) (|multiplicativeValuation| . 0) (|noZeroDivisors| . 0) @@ -691,18 +691,18 @@ 0 0 0 0 0 81 1 0 0 0 1 1 0 114 0 1 2 0 9 0 0 1 0 0 61 83 1 0 5 0 1 2 0 0 0 0 78 0 0 0 1 1 0 107 0 1 1 0 5 0 1 2 - 0 0 0 0 64 1 0 30 91 1 1 0 30 31 32 2 - 0 90 91 0 1 2 0 90 31 91 92 1 0 101 0 - 1 1 0 100 0 1 1 0 9 0 1 1 0 99 0 1 0 - 0 0 95 1 0 0 0 96 2 0 0 0 0 63 1 0 - 110 108 1 1 0 9 0 1 3 0 0 0 0 0 1 2 0 - 0 0 0 93 1 0 9 0 1 2 0 0 0 0 1 3 0 - 104 0 105 104 1 2 0 0 0 0 52 1 0 9 0 - 72 1 0 9 0 69 1 0 0 0 45 1 0 101 0 1 - 1 0 9 0 82 2 0 109 108 0 1 3 0 0 0 0 - 0 79 0 0 0 42 2 0 0 0 0 74 0 0 0 41 2 - 0 0 0 0 73 1 0 0 0 1 1 0 84 0 88 1 0 - 0 0 77 1 0 0 108 1 2 0 0 0 0 1 1 0 14 + 0 0 0 0 64 1 0 30 31 32 2 0 90 31 91 + 92 1 0 101 0 1 1 0 100 0 1 1 0 9 0 1 + 1 0 99 0 1 0 0 0 95 1 0 0 0 96 2 0 0 + 0 0 63 1 0 110 108 1 1 0 9 0 1 3 0 0 + 0 0 0 1 2 0 0 0 0 93 1 0 9 0 1 2 0 0 + 0 0 1 3 0 104 0 105 104 1 2 0 0 0 0 + 52 1 0 9 0 72 1 0 9 0 69 1 0 0 0 45 1 + 0 101 0 1 1 0 9 0 82 2 0 109 108 0 1 + 3 0 0 0 0 0 79 0 0 0 42 2 0 0 0 0 74 + 0 0 0 41 2 0 0 0 0 73 1 0 0 0 1 1 0 + 84 0 88 1 0 0 0 77 1 0 30 91 1 2 0 90 + 91 0 1 1 0 0 108 1 2 0 0 0 0 1 1 0 14 0 1 2 0 0 0 0 1 0 0 0 1 1 0 0 84 87 1 0 0 0 57 1 0 75 0 76 2 0 115 115 115 1 1 0 0 108 1 2 0 0 0 0 67 1 0 0 0 1 diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 1e7e8360..bb6faffd 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2292752 . 3486554162) +(2292778 . 3486628450) (-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 NIL (-19 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."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4458 . T) (-4456 . T) (-4455 . T) ((-4463 "*") . T) (-4454 . T) (-4459 . T) (-4453 . T)) +((-4459 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4455 . T) (-4460 . T) (-4454 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ 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 -2060) +(-32 R -1967) ((|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 -1057) (QUOTE (-576))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4461))) +((|HasAttribute| |#1| (QUOTE -4462))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4461 . T) (-4462 . T)) +((-4462 . T) (-4463 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) NIL (-39 UP) ((|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 -2060 UP UPUP -1520) +(-40 -1967 UP UPUP -2583) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4454 |has| (-419 |#2|) (-374)) (-4459 |has| (-419 |#2|) (-374)) (-4453 |has| (-419 |#2|) (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2835 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2835 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2835 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2835 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2835 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2835 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-41 R -2060) +((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2781 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2781 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2781 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2781 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2781 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2781 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +(-41 R -1967) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-317)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4458 |has| |#1| (-568)) (-4456 . T) (-4455 . T)) +((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-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."))) -((-4461 . T) (-4462 . T)) -((-2835 (-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4352) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4352) (|devaluate| |#2|))))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4352) (|devaluate| |#2|))))))) +((-4462 . T) (-4463 . T)) +((-2781 (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|))))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\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| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\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| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4458 . T)) +((-4459 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -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 -2060) +(-54 |Base| R -1967) ((|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 @@ -158,7 +158,7 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. 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.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4461 . T) (-4462 . T)) +((-4462 . T) (-4463 . T)) NIL (-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) @@ -166,65 +166,65 @@ NIL 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}"))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|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}."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -2705) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2648) ((|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 -2705) +(-62 -2648) ((|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 -2705) +(-63 -2648) ((|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 -2705) +(-64 -2648) ((|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 -2705) +(-65 -2648) ((|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 -2705) +(-66 -2648) ((|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 -2705) +(-67 -2648) ((|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 -2705) +(-68 -2648) ((|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 -2705) +(-69 -2648) ((|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 -2705) +(-70 -2648) ((|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 -2705) +(-71 -2648) ((|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 -2705) +(-72 -2648) ((|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 -2705) +(-73 -2648) ((|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 -2705) +(-74 -2648) ((|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 -2705) +(-77 -2648) ((|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 -2705) +(-78 -2648) ((|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 -2705) +(-79 -2648) ((|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 -2705) +(-80 -2648) ((|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 -2705) +(-81 -2648) ((|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 -2705) +(-82 -2648) ((|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 -2705) +(-83 -2648) ((|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 -2705) +(-84 -2648) ((|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 -2705) +(-85 -2648) ((|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 -2705) +(-86 -2648) ((|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 -2705) +(-87 -2648) ((|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 -2705) +(-88 -2648) ((|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 -2705) +(-89 -2648) ((|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 @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-374)))) (-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}."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4461 . T)) +((-4462 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4461 . T) ((-4463 "*") . T) (-4462 . T) (-4458 . T) (-4456 . T) (-4455 . T) (-4454 . T) (-4459 . T) (-4453 . T) (-4452 . T) (-4451 . T) (-4450 . T) (-4449 . T) (-4457 . T) (-4460 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4448 . T)) +((-4462 . T) ((-4464 "*") . T) (-4463 . T) (-4459 . T) (-4457 . T) (-4456 . T) (-4455 . T) (-4460 . T) (-4454 . T) (-4453 . T) (-4452 . T) (-4451 . T) (-4450 . T) (-4458 . T) (-4461 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4449 . T)) NIL (-99 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4458 . T)) +((-4459 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL 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}."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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 -((|HasAttribute| |#1| (QUOTE (-4463 "*")))) +((|HasAttribute| |#1| (QUOTE (-4464 "*")))) (-105) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4461 . T)) +((-4462 . T)) NIL (-106 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,23 +358,23 @@ NIL NIL (-107 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4462 . T)) +((-4463 . T)) 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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2835 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2781 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-112) (QUOTE (-102)))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -392,22 +392,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -2060 UP) +(-116 -1967 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 (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) 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}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-926))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1041))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (-2835 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1171))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-117 |#1|) (QUOTE (-926))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1041))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (-2781 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-862)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1171))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (|HasCategory| (-117 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-926)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4462))) +((|HasAttribute| |#1| (QUOTE -4463))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -418,15 +418,15 @@ NIL 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"))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -434,20 +434,20 @@ NIL NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4461 . T) (-4462 . T)) +((-4462 . T) (-4463 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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."))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2835 (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (-2835 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2781 (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (-2781 (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119)))) (|HasCategory| (-130) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1119))) (|HasCategory| (-130) (LIST (QUOTE -319) (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 @@ -470,13 +470,13 @@ NIL NIL (-135) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4463 "*") . T)) +(((-4464 "*") . T)) NIL -(-136 |minix| -2721 S T$) +(-136 |minix| -2695 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2721 R) +(-137 |minix| -2695 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -498,8 +498,8 @@ NIL 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}."))) -((-4461 . T) (-4451 . T) (-4462 . T)) -((-2835 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4462 . T) (-4452 . T) (-4463 . T)) +((-2781 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (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 @@ -514,7 +514,7 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4458 . T)) +((-4459 . T)) NIL (-147 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -522,9 +522,9 @@ NIL NIL (-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4458 . T)) +((-4459 . T)) NIL -(-149 -2060 UP UPUP) +(-149 -1967 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 @@ -535,14 +535,14 @@ NIL (-151 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasAttribute| |#1| (QUOTE -4461))) +((|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasAttribute| |#1| (QUOTE -4462))) (-152 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-153 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1} \\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 @@ -1198,7 +1198,7 @@ NIL NIL (-317) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-318 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1208,7 +1208,7 @@ 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 -(-320 -2060) +(-320 -1967) ((|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 @@ -1222,8 +1222,8 @@ NIL NIL (-323 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))}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-1041))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (-2835 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-862)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-1171))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-862))) (-12 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| $ (QUOTE (-146)))) (-2835 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| $ (QUOTE (-146)))))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-1041))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (-2781 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-862)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-1171))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1272) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-862))) (-12 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| $ (QUOTE (-146)))) (-2781 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1272 |#1| |#2| |#3| |#4|) (QUOTE (-926))) (|HasCategory| $ (QUOTE (-146)))))) (-324 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 @@ -1234,9 +1234,9 @@ NIL NIL (-326 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."))) -((-4458 -2835 (-12 (|has| |#1| (-568)) (-2835 (|has| |#1| (-1068)) (|has| |#1| (-485)))) (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) ((-4463 "*") |has| |#1| (-568)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-568)) (-4453 |has| |#1| (-568))) -((-2835 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) 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(|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 @@ -1246,8 +1246,8 @@ NIL NIL (-329 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."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3009) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1935) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-330 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 @@ -1258,7 +1258,7 @@ NIL NIL (-332 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-804)))) (-333 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1274,19 +1274,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) (-336 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-337 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."))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-338 S -2060) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-338 S -1967) ((|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 (-379)))) -(-339 -2060) +(-339 -1967) ((|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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-340) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |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")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1308,15 +1308,15 @@ 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 -(-345 S -2060 UP UPUP R) +(-345 S -1967 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 -(-346 -2060 UP UPUP R) +(-346 -1967 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 -(-347 -2060 UP UPUP R) +(-347 -1967 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 @@ -1330,32 +1330,32 @@ NIL NIL (-350 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1057) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) (-351 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|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 -(-352 S -2060 UP UPUP) +(-352 S -1967 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 (-379))) (|HasCategory| |#2| (QUOTE (-374)))) -(-353 -2060 UP UPUP) +(-353 -1967 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."))) -((-4454 |has| (-419 |#2|) (-374)) (-4459 |has| (-419 |#2|) (-374)) (-4453 |has| (-419 |#2|) (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-354 |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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) (-355 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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-356 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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-357 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 @@ -1370,33 +1370,33 @@ NIL NIL (-360) ((|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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-361 R UP -2060) +(-361 R UP -1967) ((|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 (-362 |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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) (-363 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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-364 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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 |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}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| (-927 |#1|) (QUOTE (-146))) (|HasCategory| (-927 |#1|) (QUOTE (-379)))) (|HasCategory| (-927 |#1|) (QUOTE (-148))) (|HasCategory| (-927 |#1|) (QUOTE (-379))) (|HasCategory| (-927 |#1|) (QUOTE (-146)))) (-366 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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) -(-367 -2060 GF) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +(-367 -1967 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 @@ -1404,21 +1404,21 @@ 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 -(-369 -2060 FP FPP) +(-369 -1967 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 (-370 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}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-371 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 NIL (-372 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4458 . T)) +((-4459 . T)) NIL (-373 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1426,7 +1426,7 @@ NIL NIL (-374) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-375 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1442,7 +1442,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-568)))) (-378 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4458 |has| |#1| (-568)) (-4456 . T) (-4455 . T)) +((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) NIL (-379) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1454,7 +1454,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-374)))) (-381 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) NIL (-382 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1463,14 +1463,14 @@ NIL (-383 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) +((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119)))) (-384 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4461 . T)) +((-4462 . T)) NIL (-385 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4456 . T) (-4455 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) NIL (-386 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1490,7 +1490,7 @@ NIL NIL (-390) ((|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}."))) -((-4444 . T) (-4452 . T) (-4125 . T) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4445 . T) (-4453 . T) (-4161 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-391 |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}."))) @@ -1498,11 +1498,11 @@ NIL NIL (-392 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-393 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) NIL (-394) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) @@ -1514,7 +1514,7 @@ NIL NIL (-396 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-397 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1526,7 +1526,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-862)))) (-399) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-400) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1538,13 +1538,13 @@ NIL NIL (-402 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) NIL (-403) ((|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 -(-404 -2060 UP UPUP R) +(-404 -1967 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 @@ -1568,11 +1568,11 @@ 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 -(-410 -2705 |returnType| -1912 |symbols|) +(-410 -2648 |returnType| -1867 |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 -(-411 -2060 UP) +(-411 -1967 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 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.}")) (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1586,15 +1586,15 @@ NIL NIL (-414) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-415 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4444)) (|HasAttribute| |#1| (QUOTE -4452))) +((|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#1| (QUOTE -4453))) (-416) ((|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\"."))) -((-4125 . T) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4161 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-417 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."))) @@ -1606,15 +1606,15 @@ NIL NIL (-419 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."))) -((-4448 -12 (|has| |#1| (-6 -4459)) (|has| |#1| (-464)) (|has| |#1| (-6 -4448))) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-832))) (-2835 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4459)) (|HasAttribute| |#1| (QUOTE -4448)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4449 -12 (|has| |#1| (-6 -4460)) (|has| |#1| (-464)) (|has| |#1| (-6 -4449))) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-832))) (-2781 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-862)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-420 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 NIL (-421 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|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{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) NIL (-422 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1628,11 +1628,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-425 R -2060 UP A) +(-425 R -1967 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4458 . T)) +((-4459 . T)) NIL -(-426 R -2060 UP A |ibasis|) +(-426 R -1967 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1057) (|devaluate| |#2|)))) @@ -1646,12 +1646,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-429 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\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."))) -((-4458 |has| |#1| (-568)) (-4456 . T) (-4455 . T)) +((-4459 |has| |#1| (-568)) (-4457 . T) (-4456 . T)) NIL (-430 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."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1240))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1240)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1240))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1240)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) (-431 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 @@ -1678,17 +1678,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) (-437 S) ((|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4461 . T) (-4451 . T) (-4462 . T)) +((-4462 . T) (-4452 . T) (-4463 . T)) NIL -(-438 R -2060) +(-438 R -1967) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-439 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4448 -12 (|has| |#1| (-6 -4448)) (|has| |#2| (-6 -4448))) (-4455 . T) (-4456 . T) (-4458 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#2| (QUOTE -4448)))) -(-440 R -2060) +((-4449 -12 (|has| |#1| (-6 -4449)) (|has| |#2| (-6 -4449))) (-4456 . T) (-4457 . T) (-4459 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4449)) (|HasAttribute| |#2| (QUOTE -4449)))) +(-440 R -1967) ((|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 @@ -1698,17 +1698,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-442 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}."))) -((-4458 -2835 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) ((-4463 "*") |has| |#1| (-568)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-568)) (-4453 |has| |#1| (-568))) +((-4459 -2781 (|has| |#1| (-1068)) (|has| |#1| (-485))) (-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) ((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-568)) (-4454 |has| |#1| (-568))) NIL -(-443 R -2060) +(-443 R -1967) ((|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 -(-444 R -2060) +(-444 R -1967) ((|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)))) -(-445 R -2060) +(-445 R -1967) ((|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 @@ -1716,7 +1716,7 @@ 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 -(-447 R -2060 UP) +(-447 R -1967 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 -1057) (QUOTE (-48))))) @@ -1748,7 +1748,7 @@ 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 -(-455 R UP -2060) +(-455 R UP -1967) ((|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 @@ -1786,16 +1786,16 @@ NIL NIL (-464) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-465 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4458 |has| (-419 (-969 |#1|)) (-568)) (-4456 . T) (-4455 . T)) +((-4459 |has| (-419 (-969 |#1|)) (-568)) (-4457 . T) (-4456 . T)) ((|HasCategory| (-419 (-969 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-969 |#1|)) (QUOTE (-568)))) (-466 |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"))) -(((-4463 "*") |has| |#2| (-174)) (-4454 |has| |#2| (-568)) (-4459 |has| |#2| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (-2835 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2835 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4459)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#2| (QUOTE (-926))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-467 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 @@ -1822,7 +1822,7 @@ NIL NIL (-473 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) NIL (-474 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1830,7 +1830,7 @@ NIL NIL (-475 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) (-476 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1860,7 +1860,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -2060 R) +(-483 |lv| -1967 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1870,23 +1870,23 @@ NIL NIL (-485) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4458 . T)) +((-4459 . T)) NIL (-486 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|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."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119)))) (-488 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)}"))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) (-489) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-490) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1894,29 +1894,29 @@ NIL NIL (-491 |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."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4352) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102)))) (-492) ((|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 NIL (-493 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4463 "*") |has| |#2| (-174)) (-4454 |has| |#2| (-568)) (-4459 |has| |#2| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . 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T) (-4456 . T) (-4459 . 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(|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))))) (|HasCategory| (-576) (QUOTE (-862))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1068)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195))))) (-2781 (|HasCategory| |#2| (QUOTE (-1068))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-1119)))) (|HasAttribute| |#2| (QUOTE -4459)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1068)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195))))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))))) (-495) ((|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 NIL (-496 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}."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-497 -2060 UP UPUP R) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-497 -1967 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 @@ -1926,12 +1926,12 @@ NIL NIL (-499) ((|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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2835 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2781 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) (-500 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 -((|HasAttribute| |#1| (QUOTE -4461)) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) +((|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-501 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|) |#1| $) "\\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| |#1|) $) "\\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| |#1|) $) "\\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|) |#1| $) "\\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|) |#1|) $) "\\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|) |#1|) $) "\\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|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,33 +1952,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -2060 UP |AlExt| |AlPol|) +(-506 -1967 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-507) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| $ (QUOTE (-1068))) (|HasCategory| $ (LIST (QUOTE -1057) (QUOTE (-576))))) (-508 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-509 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."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-510 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 -(-511 R UP -2060) +(-511 R UP -1967) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-512 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-112) (QUOTE (-1119))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-112) (QUOTE (-102)))) (-513 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) @@ -1992,7 +1992,7 @@ 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 -(-516 -2060 |Expon| |VarSet| |DPoly|) +(-516 -1967 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1195))))) @@ -2042,36 +2042,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-804)))) (-528 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-529) ((|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 NIL (-530 |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}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((-2835 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((-2781 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) (-531 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}."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-532 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."))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-533 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 -((|HasAttribute| |#3| (QUOTE -4462))) +((|HasAttribute| |#3| (QUOTE -4463))) (-534 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "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. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4462))) +((|HasAttribute| |#7| (QUOTE -4463))) (-535 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."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4463 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-536) ((|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 @@ -2104,7 +2104,7 @@ 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 -(-544 K -2060 |Par|) +(-544 K -1967 |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 @@ -2128,7 +2128,7 @@ 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 -(-550 K -2060 |Par|) +(-550 K -1967 |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 @@ -2158,7 +2158,7 @@ NIL NIL (-557) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b

1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b

1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b

1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b

1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4459 . T) (-4460 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-558) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2178,13 +2178,13 @@ NIL NIL (-562 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4352) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102)))) -(-563 R -2060) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102)))) +(-563 R -1967) ((|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 -(-564 R0 -2060 UP UPUP R) +(-564 R0 -1967 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 @@ -2194,7 +2194,7 @@ NIL NIL (-566 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."))) -((-4125 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4161 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-567 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."))) @@ -2202,9 +2202,9 @@ NIL NIL (-568) ((|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."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-569 R -2060) +(-569 R -1967) ((|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 @@ -2216,7 +2216,7 @@ 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 -(-572 R -2060 L) +(-572 R -1967 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 -668) (|devaluate| |#2|)))) @@ -2224,31 +2224,31 @@ 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 -(-574 -2060 UP UPUP R) +(-574 -1967 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 -(-575 -2060 UP) +(-575 -1967 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 (-576) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4443 . T) (-4449 . T) (-4453 . T) (-4448 . T) (-4459 . T) (-4460 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4444 . T) (-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-577) ((|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 -(-578 R -2060 L) +(-578 R -1967 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 -668) (|devaluate| |#2|)))) -(-579 R -2060) +(-579 R -1967) ((|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 -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1158)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) -(-580 -2060 UP) +(-580 -1967 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 @@ -2256,27 +2256,27 @@ 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 -(-582 -2060) +(-582 -1967) ((|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 (-583 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."))) -((-4125 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4161 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-584) ((|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 -(-585 R -2060) +(-585 R -1967) ((|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 -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) -(-586 -2060 UP) +(-586 -1967 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 -(-587 R -2060) +(-587 R -1967) ((|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 @@ -2298,21 +2298,21 @@ NIL NIL (-592 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-593 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) (-594) ((|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 -(-595 R -2060) +(-595 R -1967) ((|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 -(-596 E -2060) +(-596 E -1967) ((|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 @@ -2320,9 +2320,9 @@ 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 -(-598 -2060) +(-598 -1967) ((|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}."))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) ((|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-599 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) @@ -2350,19 +2350,19 @@ NIL NIL (-605 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2835 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (-2835 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2781 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (-2781 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-606 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 NIL (-607 |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}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) (-608 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4463 "*") |has| |#1| (-568)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-568)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-568)))) (-609) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2376,7 +2376,7 @@ 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 -(-612 R -2060 FG) +(-612 R -1967 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 @@ -2386,12 +2386,12 @@ NIL NIL (-614 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-615 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 -((|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-862))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#3| (QUOTE (-1119)))) +((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-862))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#3| (QUOTE (-1119)))) (-616 |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|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\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| ((|#1| $) "\\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| ((|#1| $) "\\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|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2406,19 +2406,19 @@ NIL NIL (-619 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4458 -2835 (-2758 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4456 . T) (-4455 . T)) -((-2835 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4459 -2781 (-2696 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) +((-2781 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-620 |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."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4352) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-102)))) (-621 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 NIL (-622 |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| |#2| "failed") |#1| $) "\\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| |#2| "failed") |#1| $) "\\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| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4462 . T)) +((-4463 . T)) NIL (-623 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2436,7 +2436,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-627 -2060 UP) +(-627 -1967 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2458,19 +2458,19 @@ NIL NIL (-632 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4458 . T)) +((-4459 . T)) NIL (-633 A R S) ((|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}."))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-860)))) -(-634 R -2060) +(-634 R -1967) ((|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 (-635 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-4456 . T) (-4455 . T) ((-4463 "*") . T) (-4454 . T) (-4458 . T)) +((-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4455 . T) (-4459 . T)) ((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (-636 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\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 \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) @@ -2486,7 +2486,7 @@ NIL NIL (-639 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4458 . T)) +((-4459 . T)) NIL (-640 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2496,30 +2496,30 @@ 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 -(-642 R -2060) +(-642 R -1967) ((|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 -(-643 |lv| -2060) +(-643 |lv| -1967) ((|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 (-644) ((|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."))) -((-4462 . T)) -((-12 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4352) (QUOTE (-52))))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1177) (QUOTE (-862))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (QUOTE (-1119)))) +((-4463 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4391) (QUOTE (-52))))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1177) (QUOTE (-862))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (QUOTE (-1119)))) (-645 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-646 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4456 . T) (-4455 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) NIL (-647 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4458 -2835 (-2758 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4456 . T) (-4455 . T)) -((-2835 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4459 -2781 (-2696 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4457 . T) (-4456 . T)) +((-2781 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-648 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 @@ -2531,9 +2531,9 @@ NIL (-650 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 -((-2746 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) +((-2684 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) (-651 R) -((|constructor| (NIL "An extension of left-module 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}.") (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{reducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) +((|constructor| (NIL "An extension of left-module 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}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL NIL (-652 S) @@ -2554,8 +2554,8 @@ NIL NIL (-656 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."))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-657 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2566,8 +2566,8 @@ NIL NIL (-659 S) ((|substitute| (($ |#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."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-660 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 @@ -2579,22 +2579,22 @@ NIL (-662 A S) ((|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| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\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}..) )}.") (($ |#2| $ (|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| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\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|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4462))) +((|HasAttribute| |#1| (QUOTE -4463))) (-663 S) ((|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 -(-664 R -2060 L) +(-664 R -1967 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 (-665 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-666 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-667 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2602,15 +2602,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-668 A) ((|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}."))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-669 -2060 UP) +(-669 -1967 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)))) -(-670 A -2190) +(-670 A -4020) ((|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}}"))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-671 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} 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}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} 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}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} 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}. \\spad{D} is the derivation to use."))) @@ -2626,7 +2626,7 @@ NIL NIL (-674 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|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{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-803)))) (-675 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([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 exists."))) @@ -2634,7 +2634,7 @@ NIL NIL (-676 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4456 . T) (-4455 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4457 . T) (-4456 . T)) ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-174)))) (-677 A S) ((|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| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) @@ -2642,13 +2642,13 @@ NIL NIL (-678 S) ((|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}."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL -(-679 -2060) +(-679 -1967) ((|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 -(-680 -2060 |Row| |Col| M) +(-680 -1967 |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 @@ -2658,8 +2658,8 @@ NIL NIL (-682 |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."))) -((-4458 . T) (-4461 . T) (-4455 . T) (-4456 . T)) -((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4463 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2835 (|HasAttribute| |#2| (QUOTE (-4463 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4459 . T) (-4462 . T) (-4456 . T) (-4457 . T)) +((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2781 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-683) ((|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 @@ -2679,7 +2679,7 @@ NIL (-687 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 -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-688) ((|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 @@ -2723,10 +2723,10 @@ NIL (-698 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. 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.")) (|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.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i]} and \\spad{colList = [j<1>,j<2>,...,j]},{} then \\spad{x(i,j)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i]} and \\spad{colList = [j<1>,j<2>,...,j]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i,j)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4463 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) +((|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) (-699 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. 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.")) (|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.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i]} and \\spad{colList = [j<1>,j<2>,...,j]},{} then \\spad{x(i,j)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i]} and \\spad{colList = [j<1>,j<2>,...,j]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i,j)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4461 . T) (-4462 . T)) +((-4462 . T) (-4463 . T)) NIL (-700 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|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")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|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}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|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."))) @@ -2734,8 +2734,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568)))) (-701 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."))) -((-4461 . T) (-4462 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4463 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4463 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4464 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-702 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 @@ -2744,7 +2744,7 @@ 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 -(-704 S -2060 FLAF FLAS) +(-704 S -1967 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}.")) 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T) (-4460 |has| (-711) (-6 -4460)) (-4457 |has| (-711) (-6 -4457)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . 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T)) +((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-2781 (|HasCategory| (-711) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-2781 (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195))))) (-2781 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (-2781 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1041))) (|HasCategory| (-711) (QUOTE (-1221))) (-12 (|HasCategory| (-711) (QUOTE (-1021))) (|HasCategory| (-711) (QUOTE (-1221)))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-926)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-926))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-1221)))) (|HasCategory| (-711) (QUOTE (-1079))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-374)))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-2781 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4461)) (|HasAttribute| (-711) (QUOTE -4458)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1195)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-146)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-926)))) (|HasCategory| (-711) (QUOTE (-360))))) (-707 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}."))) -((-4462 . T)) +((-4463 . T)) NIL (-708 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2768,13 +2768,13 @@ NIL ((|constructor| (NIL "\\indented{1}{} 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 -(-710 OV E -2060 PG) +(-710 OV E -1967 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 (-711) ((|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}"))) -((-4125 . T) (-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4161 . T) (-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-712 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."))) @@ -2782,7 +2782,7 @@ NIL NIL (-713) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4460 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4461 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-714 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2800,7 +2800,7 @@ 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 -(-718 S -2052 I) +(-718 S -1992 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 @@ -2810,7 +2810,7 @@ NIL NIL (-720 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) NIL (-721 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2820,25 +2820,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding 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 -(-723 R |Mod| -2730 -1678 |exactQuo|) +(-723 R |Mod| -2679 -4168 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-724 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4457 |has| |#1| (-374)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4459)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-725 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-726 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . T)) +((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-727 R |Mod| -2730 -1678 |exactQuo|) +(-727 R |Mod| -2679 -4168 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4458 . T)) +((-4459 . T)) NIL (-728 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2846,11 +2846,11 @@ NIL NIL (-729 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) NIL -(-730 -2060) +(-730 -1967) ((|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]]}."))) -((-4458 . T)) +((-4459 . T)) NIL (-731 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2874,7 +2874,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-360))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-379)))) (-736 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4454 |has| |#1| (-374)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 |has| |#1| (-374)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-737 S) ((|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."))) @@ -2884,7 +2884,7 @@ 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 -(-739 -2060 UP) +(-739 -1967 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 @@ -2902,8 +2902,8 @@ NIL NIL (-743 |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."))) -(((-4463 "*") |has| |#2| (-174)) (-4454 |has| |#2| (-568)) (-4459 |has| |#2| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (-2835 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2835 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4459)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4464 "*") |has| |#2| (-174)) (-4455 |has| |#2| (-568)) (-4460 |has| |#2| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#2| (QUOTE (-926))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-876 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-744 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2918,15 +2918,15 @@ NIL NIL (-747 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . T)) +((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-862)))) (-748 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4451 . T) (-4462 . T)) +((-4452 . T) (-4463 . T)) NIL (-749 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4461 . T) (-4451 . T) (-4462 . T)) +((-4462 . T) (-4452 . T) (-4463 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-750) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) @@ -2938,7 +2938,7 @@ NIL NIL (-752 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|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}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4456 . T) (-4455 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL (-753 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2954,7 +2954,7 @@ NIL NIL (-756 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) NIL (-757) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -3036,11 +3036,11 @@ 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 -(-777 -2060) +(-777 -1967) ((|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 -(-778 P -2060) +(-778 P -1967) ((|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 @@ -3048,7 +3048,7 @@ NIL NIL NIL NIL -(-780 UP -2060) +(-780 UP -1967) ((|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 @@ -3062,9 +3062,9 @@ NIL NIL (-783) ((|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."))) -(((-4463 "*") . T)) +(((-4464 "*") . T)) NIL -(-784 R -2060) +(-784 R -1967) ((|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 @@ -3084,7 +3084,7 @@ 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 -(-789 -2060 |ExtF| |SUEx| |ExtP| |n|) +(-789 -1967 |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 @@ -3098,23 +3098,23 @@ NIL NIL (-792 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."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . 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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 NIL (-794 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.")) 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T)) +((|HasCategory| |#1| (QUOTE (-926))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-795 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|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 ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-796 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular 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} \\indented{1}{[2] \\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)} \\indented{1}{[3] \\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}{[4] \\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.}"))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-797 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) @@ -3166,25 +3166,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-379)))) (-809 R) ((|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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) NIL -(-810 -2835 R OS S) +(-810 -2781 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-811 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2835 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) +((-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2781 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1018 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (-812) ((|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 -(-813 R -2060 L) +(-813 R -1967 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 -(-814 R -2060) +(-814 R -1967) ((|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 @@ -3192,7 +3192,7 @@ 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 -(-816 R -2060) +(-816 R -1967) ((|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 @@ -3200,11 +3200,11 @@ 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 -(-818 -2060 UP UPUP R) +(-818 -1967 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 -(-819 -2060 UP L LQ) +(-819 -1967 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 @@ -3212,41 +3212,41 @@ 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 -(-821 -2060 UP L LQ) +(-821 -1967 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 -(-822 -2060 UP) +(-822 -1967 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 -(-823 -2060 L UP A LO) +(-823 -1967 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 -(-824 -2060 UP) +(-824 -1967 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)))) -(-825 -2060 LO) +(-825 -1967 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}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-826 -2060 LODO) +(-826 -1967 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL -(-827 -2721 S |f|) +(-827 -2695 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4455 |has| |#2| (-1068)) (-4456 |has| |#2| (-1068)) (-4458 |has| |#2| (-6 -4458)) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST 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T) (-4456 . T) (-4455 . T)) +(((-4464 "*") |has| |#2| (-374)) (-4455 |has| |#2| (-374)) (-4460 |has| |#2| (-374)) (-4454 |has| |#2| (-374)) (-4459 . T) (-4457 . T) (-4456 . T)) ((|HasCategory| |#2| (QUOTE (-374)))) (-830 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -3258,7 +3258,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-862)))) (-832) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-833) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -3286,7 +3286,7 @@ NIL NIL (-839 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-238)))) (-840) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3298,7 +3298,7 @@ NIL NIL (-842 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4461 . T) (-4451 . T) (-4462 . T)) +((-4462 . T) (-4452 . T) (-4463 . T)) NIL (-843) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3310,8 +3310,8 @@ NIL NIL (-845 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."))) -((-4458 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2835 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2835 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4459 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2781 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-846 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 @@ -3322,7 +3322,7 @@ NIL NIL (-848 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . T)) +((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) (-849) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3350,13 +3350,13 @@ NIL NIL (-855 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4458 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2835 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2835 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4459 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2781 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-856) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-857 -2721 S) +(-857 -2695 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3370,7 +3370,7 @@ NIL NIL (-860) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4458 . T)) +((-4459 . T)) NIL (-861 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a a= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3386,19 +3386,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) (-864 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(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 right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes 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}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(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.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\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| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} 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{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(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}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) NIL (-865 R C) ((|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 (-374))) (|HasCategory| |#1| (QUOTE (-568)))) -(-866 R |sigma| -2843) +(-866 R |sigma| -3574) ((|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."))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) -(-867 |x| R |sigma| -2843) +(-867 |x| R |sigma| -3574) ((|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}."))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) (-868 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) @@ -3442,7 +3442,7 @@ NIL NIL (-878 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . T)) +((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (-879 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3454,24 +3454,24 @@ NIL NIL (-881 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-882 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-883 |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)."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-882 |#1|) (QUOTE (-926))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-148))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-882 |#1|) (QUOTE (-1041))) (|HasCategory| (-882 |#1|) (QUOTE (-832))) (-2835 (|HasCategory| (-882 |#1|) (QUOTE (-832))) (|HasCategory| (-882 |#1|) (QUOTE (-862)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-1171))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-237))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-238))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -882) (|devaluate| |#1|)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (QUOTE (-317))) (|HasCategory| (-882 |#1|) (QUOTE (-557))) (|HasCategory| (-882 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-882 |#1|) (QUOTE (-926))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-148))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-882 |#1|) (QUOTE (-1041))) (|HasCategory| (-882 |#1|) (QUOTE (-832))) (-2781 (|HasCategory| (-882 |#1|) (QUOTE (-832))) (|HasCategory| (-882 |#1|) (QUOTE (-862)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-1171))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-882 |#1|) (QUOTE (-237))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (QUOTE (-238))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -526) (QUOTE (-1195)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -882) (|devaluate| |#1|)) (LIST (QUOTE -882) (|devaluate| |#1|)))) (|HasCategory| (-882 |#1|) (QUOTE (-317))) (|HasCategory| (-882 |#1|) (QUOTE (-557))) (|HasCategory| (-882 |#1|) (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-882 |#1|) (QUOTE (-926)))) (|HasCategory| (-882 |#1|) (QUOTE (-146))))) (-884 |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)}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (-2835 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (-2781 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-862))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-885 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 (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))))) (-886) ((|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 @@ -3531,7 +3531,7 @@ NIL (-900 |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 (-2746 (|HasCategory| |#2| (QUOTE (-1068)))) (-2746 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (-2746 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) +((-12 (-2684 (|HasCategory| |#2| (QUOTE (-1068)))) (-2684 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (-2684 (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195))))) (-901 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 @@ -3540,7 +3540,7 @@ 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 -(-903 R -2052) +(-903 R -1992) ((|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 @@ -3572,7 +3572,7 @@ 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 -(-911 UP -2060) +(-911 UP -1967) ((|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 @@ -3586,11 +3586,11 @@ NIL NIL (-914 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) NIL (-915 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4458 . T)) +((-4459 . T)) NIL (-916 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) @@ -3603,14 +3603,14 @@ NIL (-918 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 (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-919 |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 NIL (-920 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not 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.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(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."))) -((-4458 . T)) +((-4459 . T)) NIL (-921 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3618,8 +3618,8 @@ NIL NIL (-922 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4458 . T)) -((-2835 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) +((-4459 . T)) +((-2781 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-862)))) (-923 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 @@ -3634,13 +3634,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-146)))) (-926) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\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.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-927 |p|) ((|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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) -(-928 R0 -2060 UP UPUP R) +(-928 R0 -1967 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 @@ -3654,7 +3654,7 @@ NIL NIL (-931 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-932 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) @@ -3668,7 +3668,7 @@ 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 -(-935 -2060) +(-935 -1967) ((|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 @@ -3678,17 +3678,17 @@ NIL NIL (-937) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-938) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4463 "*") . T)) +(((-4464 "*") . T)) NIL -(-939 -2060 P) +(-939 -1967 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-940 |xx| -2060) +(-940 |xx| -1967) ((|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 @@ -3712,7 +3712,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-946 R -2060) +(-946 R -1967) ((|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 @@ -3724,7 +3724,7 @@ 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 -(-949 S R -2060) +(-949 S R -1967) ((|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 @@ -3744,11 +3744,11 @@ 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 -899) (|devaluate| |#1|)))) -(-954 R -2060 -2052) +(-954 R -1967 -1992) ((|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 -(-955 -2052) +(-955 -1992) ((|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 @@ -3770,8 +3770,8 @@ NIL NIL (-960 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-961 |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 @@ -3791,12 +3791,12 @@ NIL (-965 S R E |VarSet|) ((|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| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\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.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\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| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\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| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\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| |#4|) (|:| |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| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|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| $)) $ $ |#4|) "\\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| |#4|)) "\\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|) $ |#4|) "\\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| |#4| "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| |#2|) $) "\\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| $) $ |#4|) "\\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| |#4|) (|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)}.") (($ $ |#4| (|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| |#4|)) "\\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|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-926))) (|HasAttribute| |#2| (QUOTE -4459)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) +((|HasCategory| |#2| (QUOTE (-926))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-966 R E |VarSet|) ((|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}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL -(-967 E V R P -2060) +(-967 E V R P -1967) ((|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 @@ -3806,9 +3806,9 @@ NIL NIL (-969 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}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4459)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-970 E V R P -2060) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1195) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-970 E V R P -1967) ((|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 (-464)))) @@ -3830,13 +3830,13 @@ NIL NIL (-975 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"))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-976) ((|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 -(-977 -2060) +(-977 -1967) ((|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 @@ -3850,12 +3850,12 @@ NIL NIL (-980 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}"))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4459))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4460))) (-981 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"))) -((-4458 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2835 (-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 (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-2835 (-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 (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) +((-4459 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2781 (-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 (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-2781 (-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 (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-862))))) (-982) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3878,7 +3878,7 @@ NIL NIL (-987 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4461 . T) (-4462 . T)) +((-4462 . T) (-4463 . T)) NIL (-988 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3898,7 +3898,7 @@ NIL NIL (-992 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-993) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3910,7 +3910,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-568)))) (-995 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4461 . T)) +((-4462 . T)) NIL (-996 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3926,7 +3926,7 @@ NIL NIL (-999 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-1000 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3944,7 +3944,7 @@ 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 -(-1004 K R UP -2060) +(-1004 K R UP -1967) ((|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 @@ -3974,7 +3974,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1171)))) (-1011 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1012 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3986,7 +3986,7 @@ NIL NIL (-1014 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4461 . T) (-4462 . T)) +((-4462 . T) (-4463 . T)) NIL (-1015 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) @@ -3994,7 +3994,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-862))) (|HasCategory| |#2| (QUOTE (-300)))) (-1016 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4454 |has| |#1| (-300)) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 |has| |#1| (-300)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1017 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -4002,12 +4002,12 @@ NIL NIL (-1018 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.}"))) -((-4454 |has| |#1| (-300)) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2835 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4455 |has| |#1| (-300)) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1195)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-557)))) (-1019 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}."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1020 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4016,14 +4016,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1022 -2060 UP UPUP |radicnd| |n|) +(-1022 -1967 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4454 |has| (-419 |#2|) (-374)) (-4459 |has| (-419 |#2|) (-374)) (-4453 |has| (-419 |#2|) (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2835 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2835 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2835 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2835 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2835 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2835 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +((-4455 |has| (-419 |#2|) (-374)) (-4460 |has| (-419 |#2|) (-374)) (-4454 |has| (-419 |#2|) (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2781 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2781 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2781 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2781 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2781 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2781 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (-1023 |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."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2835 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-576) (QUOTE (-926))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1041))) (|HasCategory| (-576) (QUOTE (-832))) (-2781 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-862)))) (|HasCategory| (-576) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1171))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1195)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-926)))) (|HasCategory| (-576) (QUOTE (-146))))) (-1024) ((|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 @@ -4043,7 +4043,7 @@ NIL (-1028 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-1119)))) +((|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-1119)))) (-1029 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -4054,21 +4054,21 @@ NIL NIL (-1031) ((|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}}"))) -((-4454 . T) (-4459 . T) (-4453 . T) (-4456 . T) (-4455 . T) ((-4463 "*") . T) (-4458 . T)) +((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) NIL -(-1032 R -2060) +(-1032 R -1967) ((|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 -(-1033 R -2060) +(-1033 R -1967) ((|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 -(-1034 -2060 UP) +(-1034 -1967 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 -(-1035 -2060 UP) +(-1035 -1967 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 @@ -4102,9 +4102,9 @@ NIL NIL (-1043 |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"))) -((-4454 . T) (-4459 . T) (-4453 . T) (-4456 . T) (-4455 . T) ((-4463 "*") . T) (-4458 . T)) -((-2835 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576))))) -(-1044 -2060 L) +((-4455 . T) (-4460 . T) (-4454 . T) (-4457 . T) (-4456 . T) ((-4464 "*") . T) (-4459 . T)) +((-2781 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1057) (QUOTE (-576))))) +(-1044 -1967 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 @@ -4114,12 +4114,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1119)))) (-1046 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1047 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4463 "*")))) +((|HasAttribute| |#1| (QUOTE (-4464 "*")))) (-1048 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -4140,14 +4140,14 @@ 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 -(-1053 -2060 |Expon| |VarSet| |FPol| |LFPol|) +(-1053 -1967 |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"))) -(((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1054) ((|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.}"))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4352) (QUOTE (-52))))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4391) (QUOTE (-52))))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102)))) (-1055) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4190,7 +4190,7 @@ NIL NIL (-1065 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) ((-12 (|HasCategory| (-792 |#1| (-876 |#2|)) (QUOTE (-1119))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -792) (|devaluate| |#1|) (LIST (QUOTE -876) (|devaluate| |#2|)))))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-792 |#1| (-876 |#2|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-876 |#2|) (QUOTE (-379))) (|HasCategory| (-792 |#1| (-876 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-792 |#1| (-876 |#2|)) (QUOTE (-102)))) (-1066) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) @@ -4202,9 +4202,9 @@ NIL NIL (-1068) ((|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."))) -((-4458 . T)) +((-4459 . T)) NIL -(-1069 |xx| -2060) +(-1069 |xx| -1967) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4218,12 +4218,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (QUOTE (-568))) (|HasCategory| |#4| (QUOTE (-174)))) (-1072 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4461 . T) (-4456 . T) (-4455 . T)) +((-4462 . T) (-4457 . T) (-4456 . T)) NIL (-1073 |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}."))) -((-4461 . T) (-4456 . T) (-4455 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2835 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874))))) +((-4462 . T) (-4457 . T) (-4456 . T)) +((|HasCategory| |#3| (QUOTE (-174))) (-2781 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1119))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-874))))) (-1074 |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 @@ -4246,7 +4246,7 @@ NIL NIL (-1079) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1080 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4254,19 +4254,19 @@ NIL NIL (-1081) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4449 . T) (-4453 . T) (-4448 . T) (-4459 . T) (-4460 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1082) ((|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}"))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4352) (QUOTE (-52))))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1195))) (LIST (QUOTE |:|) (QUOTE -4391) (QUOTE (-52))))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1119))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-1119))) (|HasCategory| (-1195) (QUOTE (-862))) (|HasCategory| (-52) (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (QUOTE (-102)))) (-1083 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1195))))) (-1084 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|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| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| $)) $ $ |#3|) "\\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| $)) $ $ |#3|) "\\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| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\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}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\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.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\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}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\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|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\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| (($ $ |#3|) "\\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| ((|#3| $) "\\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}}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL (-1085) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -4290,7 +4290,7 @@ NIL NIL (-1090 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\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)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-1091 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\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}{[2] \\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.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -4308,11 +4308,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1095 |Base| R -2060) +(-1095 |Base| R -1967) ((|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 -(-1096 |Base| R -2060) +(-1096 |Base| R -1967) ((|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 @@ -4326,8 +4326,8 @@ NIL NIL (-1099 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."))) -((-4454 |has| |#1| (-374)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2835 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1195))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))))) +((-4455 |has| |#1| (-374)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . 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(|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4354,8 +4354,8 @@ NIL NIL (-1106 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"))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . 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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 @@ -4398,7 +4398,7 @@ NIL NIL (-1117 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4451 . T)) +((-4452 . T)) NIL (-1118 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4414,8 +4414,8 @@ NIL NIL (-1121 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)}}"))) -((-4461 . T) (-4451 . T) (-4462 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4462 . T) (-4452 . T) (-4463 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-1122 |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 ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL @@ -4442,7 +4442,7 @@ NIL NIL (-1128 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\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}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-1129) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4458,8 +4458,8 @@ NIL NIL (-1132 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4455 |has| |#3| (-1068)) (-4456 |has| |#3| (-1068)) (-4458 |has| |#3| (-6 -4458)) (-4461 . 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(((|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 @@ -4468,7 +4468,7 @@ 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 -(-1135 R -2060) +(-1135 R -1967) ((|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 @@ -4486,19 +4486,19 @@ NIL NIL (-1139) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4449 . T) (-4453 . T) (-4448 . T) (-4459 . T) (-4460 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4450 . T) (-4454 . T) (-4449 . T) (-4460 . T) (-4461 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1140 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4461 . T) (-4462 . T)) +((-4462 . T) (-4463 . T)) NIL (-1141 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4463 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4464 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) (-1142 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-4461 . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4462 . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1143 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4506,17 +4506,17 @@ NIL NIL (-1144 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."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-926))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4459)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2835 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-926))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-926)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1145 |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}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1146 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}"))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL -(-1147 UP -2060) +(-1147 UP -1967) ((|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 @@ -4570,19 +4570,19 @@ NIL NIL (-1160 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."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))) (-2835 (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (-2835 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))))) (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))) (-2781 (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119)))) (-2781 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1159) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-1119))))) (|HasCategory| (-1159 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-1159 |#1| |#2|) (QUOTE (-102)))) (-1161 |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}."))) -((-4458 . T) (-4450 |has| |#2| (-6 (-4463 "*"))) (-4461 . T) (-4455 . T) (-4456 . T)) -((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4463 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2835 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (-2835 (|HasAttribute| |#2| (QUOTE (-4463 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4459 . T) (-4451 |has| |#2| (-6 (-4464 "*"))) (-4462 . T) (-4456 . T) (-4457 . T)) +((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-374))) (-2781 (|HasAttribute| |#2| (QUOTE (-4464 "*"))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1162 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1163) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-1164 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4590,12 +4590,12 @@ NIL NIL (-1165 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1166 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}."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1167 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 @@ -4606,8 +4606,8 @@ NIL NIL (-1169 |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."))) -((-4462 . T)) -((-12 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4352) (|devaluate| |#2|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2835 (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (QUOTE (-1119)))) +((-4463 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#2|)))))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-862))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2781 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (QUOTE (-1119)))) (-1170) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4634,16 +4634,16 @@ NIL NIL (-1176 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) -((-4462 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4463 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1177) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2835 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (-2835 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2781 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (-2781 (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119)))) (|HasCategory| (-145) (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1119))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-1178 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4461 . T) (-4462 . T)) -((-12 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4282) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4352) (|devaluate| |#1|)))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (-2835 (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|)) (QUOTE (-102)))) +((-4462 . T) (-4463 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4391) (|devaluate| |#1|)))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-1119))) (|HasCategory| (-1177) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (-2781 (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|)) (QUOTE (-102)))) (-1179 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|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*(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 = sum(i+j=k,a)}.")) (|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 @@ -4674,9 +4674,9 @@ NIL NIL (-1186 |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. 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We may integrate a series when we can divide coefficients by integers.")) (|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}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2835 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4295) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1992) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3009) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1935) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-1194) ((|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} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4818,8 +4818,8 @@ NIL NIL (-1222 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4462 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4463 . T) (-4462 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1119))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1223 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4828,7 +4828,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1225 R -2060) +(-1225 R -1967) ((|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 @@ -4836,7 +4836,7 @@ 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 -(-1227 R -2060) +(-1227 R -1967) ((|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 -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -899) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -899) (|devaluate| |#1|))))) @@ -4846,12 +4846,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-379)))) (-1229 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\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)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-1230 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) (-1231 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4864,7 +4864,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) -(-1234 -2060) +(-1234 -1967) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4890,7 +4890,7 @@ NIL NIL (-1240) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1241) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4914,7 +4914,7 @@ NIL NIL (-1246 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|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."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1247 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) @@ -4922,16 +4922,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-1248 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1249 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . 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T)) +((|HasCategory| |#2| (QUOTE (-926))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-390))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -899) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -899) (QUOTE (-576))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-390)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -905) (QUOTE (-576)))))) (-12 (|HasCategory| (-1101) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (QUOTE (-576)))) (-2781 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (-2781 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1195)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (-2781 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-926)))) (|HasCategory| |#2| (QUOTE (-146))))) (-1260 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 @@ -4978,15 +4978,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1171)))) (-1262 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4457 |has| |#1| (-374)) (-4459 |has| |#1| (-6 -4459)) (-4456 . T) (-4455 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4458 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL (-1263 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 -915) (QUOTE (-1195)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3563) (LIST (|devaluate| |#2|) (QUOTE (-1195)))))) +((|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3581) (LIST (|devaluate| |#2|) (QUOTE (-1195)))))) (-1264 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1265 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4998,7 +4998,7 @@ NIL NIL (-1267 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and 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 and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1268 S |Coef| ULS) ((|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)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) @@ -5006,24 +5006,24 @@ NIL NIL (-1269 |Coef| ULS) ((|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)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1270 |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)}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2835 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4295) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1992) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3009) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1935) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-1271 |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."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4453 |has| |#1| (-374)) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2835 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2835 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4295) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1992) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4454 |has| |#1| (-374)) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2781 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3009) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1935) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-1272 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))}."))) -(((-4463 "*") |has| (-1271 |#2| |#3| |#4|) (-174)) (-4454 |has| (-1271 |#2| |#3| |#4|) (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-174))) (-2835 (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-568)))) +(((-4464 "*") |has| (-1271 |#2| |#3| |#4|) (-174)) (-4455 |has| (-1271 |#2| |#3| |#4|) (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-174))) (-2781 (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1271 |#2| |#3| |#4|) (LIST (QUOTE -1057) (QUOTE (-576)))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1271 |#2| |#3| |#4|) (QUOTE (-568)))) (-1273 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4462))) +((|HasAttribute| |#1| (QUOTE -4463))) (-1274 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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!| ((|#1| $ |#1|) "\\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| ((|#1| $ "last" |#1|) "\\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})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\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| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|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.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|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| ((|#1| $ "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}}.") ((|#1| $ "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}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5035,20 +5035,20 @@ NIL (-1276 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasSignature| |#2| (LIST (QUOTE -1992) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4295) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1195))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1221))) (|HasSignature| |#2| (LIST (QUOTE -1935) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3009) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1195))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) (-1277 |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."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1278 |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))}.}")) (|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}."))) -(((-4463 "*") |has| |#1| (-174)) (-4454 |has| |#1| (-568)) (-4455 . T) (-4456 . T) (-4458 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2835 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2835 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4295) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1992) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) +(((-4464 "*") |has| |#1| (-174)) (-4455 |has| |#1| (-568)) (-4456 . T) (-4457 . T) (-4459 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2781 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1195)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1131))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3581) (LIST (|devaluate| |#1|) (QUOTE (-1195)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2781 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1221))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3009) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1195))))) (|HasSignature| |#1| (LIST (QUOTE -1935) (LIST (LIST (QUOTE -656) (QUOTE (-1195))) (|devaluate| |#1|))))))) (-1279 |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=f(y,y',..,y)} such that \\spad{y(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 -(-1280 -2060 UP L UTS) +(-1280 -1967 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 (-568)))) @@ -5066,7 +5066,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1284 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) NIL (-1285 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -5074,8 +5074,8 @@ NIL NIL (-1286 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4462 . T) (-4461 . T)) -((-2835 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2835 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2835 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2835 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4463 . T) (-4462 . T)) +((-2781 (-12 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2781 (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2781 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (-2781 (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119)))) (|HasCategory| |#1| (QUOTE (-862))) (|HasCategory| (-576) (QUOTE (-862))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-1287) ((|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|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5102,13 +5102,13 @@ NIL NIL (-1293 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4456 . T) (-4455 . T)) +((-4457 . T) (-4456 . T)) NIL (-1294 R) ((|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 -(-1295 K R UP -2060) +(-1295 K R UP -1967) ((|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 @@ -5122,56 +5122,56 @@ NIL NIL (-1298 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4456 |has| |#1| (-174)) (-4455 |has| |#1| (-174)) (-4458 . T)) +((-4457 |has| |#1| (-174)) (-4456 |has| |#1| (-174)) (-4459 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) (-1299 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. 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. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4462 . T) (-4461 . T)) +((-4463 . T) (-4462 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1119))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-874)))) (|HasCategory| |#4| (QUOTE (-102)))) (-1300 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})"))) -((-4455 . T) (-4456 . T) (-4458 . T)) +((-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1301 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4458 . T) (-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4454))) +((-4459 . T) (-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4455))) (-1302 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL (-1303 |vl| R) ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) +((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL -(-1304 S -2060) +(-1304 S -1967) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1305 -2060) +(-1305 -1967) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4453 . T) (-4459 . T) (-4454 . T) ((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +((-4454 . T) (-4460 . T) (-4455 . T) ((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL (-1306 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4454))) +((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4455))) (-1307 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) +((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) NIL (-1308 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4454 |has| |#1| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4454))) +((-4455 |has| |#1| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4455))) (-1309 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4458 . T) (-4459 |has| |#1| (-6 -4459)) (-4454 |has| |#1| (-6 -4454)) (-4456 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4459)) (|HasAttribute| |#1| (QUOTE -4454))) +((-4459 . T) (-4460 |has| |#1| (-6 -4460)) (-4455 |has| |#1| (-6 -4455)) (-4457 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4459)) (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4455))) (-1310 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4454 |has| |#2| (-6 -4454)) (-4456 . T) (-4455 . T) (-4458 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4454))) +((-4455 |has| |#2| (-6 -4455)) (-4457 . T) (-4456 . T) (-4459 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4455))) (-1311) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL @@ -5190,7 +5190,7 @@ NIL NIL (-1315 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4463 "*") . T) (-4455 . T) (-4456 . T) (-4458 . T)) +(((-4464 "*") . T) (-4456 . T) (-4457 . T) (-4459 . T)) NIL NIL NIL @@ -5208,4 +5208,4 @@ NIL NIL NIL NIL -((-3 NIL 2292732 2292737 2292742 2292747) (-2 NIL 2292712 2292717 2292722 2292727) (-1 NIL 2292692 2292697 2292702 2292707) (0 NIL 2292672 2292677 2292682 2292687) (-1315 "ZMOD.spad" 2292481 2292494 2292610 2292667) (-1314 "ZLINDEP.spad" 2291547 2291558 2292471 2292476) (-1313 "ZDSOLVE.spad" 2281492 2281514 2291537 2291542) (-1312 "YSTREAM.spad" 2280987 2280998 2281482 2281487) (-1311 "YDIAGRAM.spad" 2280621 2280630 2280977 2280982) (-1310 "XRPOLY.spad" 2279841 2279861 2280477 2280546) (-1309 "XPR.spad" 2277636 2277649 2279559 2279658) (-1308 "XPOLY.spad" 2277191 2277202 2277492 2277561) (-1307 "XPOLYC.spad" 2276510 2276526 2277117 2277186) (-1306 "XPBWPOLY.spad" 2274947 2274967 2276290 2276359) (-1305 "XF.spad" 2273410 2273425 2274849 2274942) (-1304 "XF.spad" 2271853 2271870 2273294 2273299) (-1303 "XFALG.spad" 2268901 2268917 2271779 2271848) (-1302 "XEXPPKG.spad" 2268152 2268178 2268891 2268896) (-1301 "XDPOLY.spad" 2267766 2267782 2268008 2268077) (-1300 "XALG.spad" 2267426 2267437 2267722 2267761) (-1299 "WUTSET.spad" 2263229 2263246 2267036 2267063) (-1298 "WP.spad" 2262428 2262472 2263087 2263154) (-1297 "WHILEAST.spad" 2262226 2262235 2262418 2262423) (-1296 "WHEREAST.spad" 2261897 2261906 2262216 2262221) (-1295 "WFFINTBS.spad" 2259560 2259582 2261887 2261892) (-1294 "WEIER.spad" 2257782 2257793 2259550 2259555) (-1293 "VSPACE.spad" 2257455 2257466 2257750 2257777) (-1292 "VSPACE.spad" 2257148 2257161 2257445 2257450) (-1291 "VOID.spad" 2256825 2256834 2257138 2257143) (-1290 "VIEW.spad" 2254505 2254514 2256815 2256820) (-1289 "VIEWDEF.spad" 2249706 2249715 2254495 2254500) (-1288 "VIEW3D.spad" 2233667 2233676 2249696 2249701) (-1287 "VIEW2D.spad" 2221558 2221567 2233657 2233662) (-1286 "VECTOR.spad" 2220079 2220090 2220330 2220357) (-1285 "VECTOR2.spad" 2218718 2218731 2220069 2220074) (-1284 "VECTCAT.spad" 2216622 2216633 2218686 2218713) (-1283 "VECTCAT.spad" 2214333 2214346 2216399 2216404) (-1282 "VARIABLE.spad" 2214113 2214128 2214323 2214328) (-1281 "UTYPE.spad" 2213757 2213766 2214103 2214108) (-1280 "UTSODETL.spad" 2213052 2213076 2213713 2213718) (-1279 "UTSODE.spad" 2211268 2211288 2213042 2213047) (-1278 "UTS.spad" 2206215 2206243 2209735 2209832) (-1277 "UTSCAT.spad" 2203694 2203710 2206113 2206210) (-1276 "UTSCAT.spad" 2200817 2200835 2203238 2203243) (-1275 "UTS2.spad" 2200412 2200447 2200807 2200812) (-1274 "URAGG.spad" 2195085 2195096 2200402 2200407) (-1273 "URAGG.spad" 2189722 2189735 2195041 2195046) (-1272 "UPXSSING.spad" 2187367 2187393 2188803 2188936) (-1271 "UPXS.spad" 2184663 2184691 2185499 2185648) (-1270 "UPXSCONS.spad" 2182422 2182442 2182795 2182944) (-1269 "UPXSCCA.spad" 2180993 2181013 2182268 2182417) (-1268 "UPXSCCA.spad" 2179706 2179728 2180983 2180988) (-1267 "UPXSCAT.spad" 2178295 2178311 2179552 2179701) (-1266 "UPXS2.spad" 2177838 2177891 2178285 2178290) (-1265 "UPSQFREE.spad" 2176252 2176266 2177828 2177833) (-1264 "UPSCAT.spad" 2174039 2174063 2176150 2176247) (-1263 "UPSCAT.spad" 2171532 2171558 2173645 2173650) (-1262 "UPOLYC.spad" 2166572 2166583 2171374 2171527) (-1261 "UPOLYC.spad" 2161504 2161517 2166308 2166313) (-1260 "UPOLYC2.spad" 2160975 2160994 2161494 2161499) (-1259 "UP.spad" 2158081 2158096 2158468 2158621) (-1258 "UPMP.spad" 2156981 2156994 2158071 2158076) (-1257 "UPDIVP.spad" 2156546 2156560 2156971 2156976) (-1256 "UPDECOMP.spad" 2154791 2154805 2156536 2156541) (-1255 "UPCDEN.spad" 2154000 2154016 2154781 2154786) (-1254 "UP2.spad" 2153364 2153385 2153990 2153995) (-1253 "UNISEG.spad" 2152717 2152728 2153283 2153288) (-1252 "UNISEG2.spad" 2152214 2152227 2152673 2152678) (-1251 "UNIFACT.spad" 2151317 2151329 2152204 2152209) (-1250 "ULS.spad" 2141101 2141129 2142046 2142475) (-1249 "ULSCONS.spad" 2132235 2132255 2132605 2132754) (-1248 "ULSCCAT.spad" 2129972 2129992 2132081 2132230) (-1247 "ULSCCAT.spad" 2127817 2127839 2129928 2129933) (-1246 "ULSCAT.spad" 2126049 2126065 2127663 2127812) (-1245 "ULS2.spad" 2125563 2125616 2126039 2126044) (-1244 "UINT8.spad" 2125440 2125449 2125553 2125558) (-1243 "UINT64.spad" 2125316 2125325 2125430 2125435) (-1242 "UINT32.spad" 2125192 2125201 2125306 2125311) (-1241 "UINT16.spad" 2125068 2125077 2125182 2125187) (-1240 "UFD.spad" 2124133 2124142 2124994 2125063) (-1239 "UFD.spad" 2123260 2123271 2124123 2124128) (-1238 "UDVO.spad" 2122141 2122150 2123250 2123255) (-1237 "UDPO.spad" 2119634 2119645 2122097 2122102) (-1236 "TYPE.spad" 2119566 2119575 2119624 2119629) (-1235 "TYPEAST.spad" 2119485 2119494 2119556 2119561) (-1234 "TWOFACT.spad" 2118137 2118152 2119475 2119480) (-1233 "TUPLE.spad" 2117623 2117634 2118036 2118041) (-1232 "TUBETOOL.spad" 2114490 2114499 2117613 2117618) (-1231 "TUBE.spad" 2113137 2113154 2114480 2114485) (-1230 "TS.spad" 2111736 2111752 2112702 2112799) (-1229 "TSETCAT.spad" 2098863 2098880 2111704 2111731) (-1228 "TSETCAT.spad" 2085976 2085995 2098819 2098824) (-1227 "TRMANIP.spad" 2080342 2080359 2085682 2085687) (-1226 "TRIMAT.spad" 2079305 2079330 2080332 2080337) (-1225 "TRIGMNIP.spad" 2077832 2077849 2079295 2079300) (-1224 "TRIGCAT.spad" 2077344 2077353 2077822 2077827) (-1223 "TRIGCAT.spad" 2076854 2076865 2077334 2077339) (-1222 "TREE.spad" 2075312 2075323 2076344 2076371) (-1221 "TRANFUN.spad" 2075151 2075160 2075302 2075307) (-1220 "TRANFUN.spad" 2074988 2074999 2075141 2075146) (-1219 "TOPSP.spad" 2074662 2074671 2074978 2074983) (-1218 "TOOLSIGN.spad" 2074325 2074336 2074652 2074657) (-1217 "TEXTFILE.spad" 2072886 2072895 2074315 2074320) (-1216 "TEX.spad" 2070032 2070041 2072876 2072881) (-1215 "TEX1.spad" 2069588 2069599 2070022 2070027) (-1214 "TEMUTL.spad" 2069143 2069152 2069578 2069583) (-1213 "TBCMPPK.spad" 2067236 2067259 2069133 2069138) (-1212 "TBAGG.spad" 2066286 2066309 2067216 2067231) (-1211 "TBAGG.spad" 2065344 2065369 2066276 2066281) (-1210 "TANEXP.spad" 2064752 2064763 2065334 2065339) (-1209 "TALGOP.spad" 2064476 2064487 2064742 2064747) (-1208 "TABLE.spad" 2062445 2062468 2062715 2062742) (-1207 "TABLEAU.spad" 2061926 2061937 2062435 2062440) (-1206 "TABLBUMP.spad" 2058729 2058740 2061916 2061921) (-1205 "SYSTEM.spad" 2057957 2057966 2058719 2058724) (-1204 "SYSSOLP.spad" 2055440 2055451 2057947 2057952) (-1203 "SYSPTR.spad" 2055339 2055348 2055430 2055435) (-1202 "SYSNNI.spad" 2054521 2054532 2055329 2055334) (-1201 "SYSINT.spad" 2053925 2053936 2054511 2054516) (-1200 "SYNTAX.spad" 2050131 2050140 2053915 2053920) (-1199 "SYMTAB.spad" 2048199 2048208 2050121 2050126) (-1198 "SYMS.spad" 2044222 2044231 2048189 2048194) (-1197 "SYMPOLY.spad" 2043229 2043240 2043311 2043438) (-1196 "SYMFUNC.spad" 2042730 2042741 2043219 2043224) (-1195 "SYMBOL.spad" 2040233 2040242 2042720 2042725) (-1194 "SWITCH.spad" 2037004 2037013 2040223 2040228) (-1193 "SUTS.spad" 2034052 2034080 2035471 2035568) (-1192 "SUPXS.spad" 2031335 2031363 2032184 2032333) (-1191 "SUP.spad" 2028055 2028066 2028828 2028981) (-1190 "SUPFRACF.spad" 2027160 2027178 2028045 2028050) (-1189 "SUP2.spad" 2026552 2026565 2027150 2027155) (-1188 "SUMRF.spad" 2025526 2025537 2026542 2026547) (-1187 "SUMFS.spad" 2025163 2025180 2025516 2025521) (-1186 "SULS.spad" 2014934 2014962 2015892 2016321) (-1185 "SUCHTAST.spad" 2014703 2014712 2014924 2014929) (-1184 "SUCH.spad" 2014385 2014400 2014693 2014698) (-1183 "SUBSPACE.spad" 2006500 2006515 2014375 2014380) (-1182 "SUBRESP.spad" 2005670 2005684 2006456 2006461) (-1181 "STTF.spad" 2001769 2001785 2005660 2005665) (-1180 "STTFNC.spad" 1998237 1998253 2001759 2001764) (-1179 "STTAYLOR.spad" 1990872 1990883 1998118 1998123) (-1178 "STRTBL.spad" 1988923 1988940 1989072 1989099) (-1177 "STRING.spad" 1987710 1987719 1987931 1987958) (-1176 "STREAM.spad" 1984511 1984522 1987118 1987133) (-1175 "STREAM3.spad" 1984084 1984099 1984501 1984506) (-1174 "STREAM2.spad" 1983212 1983225 1984074 1984079) (-1173 "STREAM1.spad" 1982918 1982929 1983202 1983207) (-1172 "STINPROD.spad" 1981854 1981870 1982908 1982913) (-1171 "STEP.spad" 1981055 1981064 1981844 1981849) (-1170 "STEPAST.spad" 1980289 1980298 1981045 1981050) (-1169 "STBL.spad" 1978373 1978401 1978540 1978555) (-1168 "STAGG.spad" 1977448 1977459 1978363 1978368) (-1167 "STAGG.spad" 1976521 1976534 1977438 1977443) (-1166 "STACK.spad" 1975761 1975772 1976011 1976038) (-1165 "SREGSET.spad" 1973429 1973446 1975371 1975398) (-1164 "SRDCMPK.spad" 1971990 1972010 1973419 1973424) (-1163 "SRAGG.spad" 1967133 1967142 1971958 1971985) (-1162 "SRAGG.spad" 1962296 1962307 1967123 1967128) (-1161 "SQMATRIX.spad" 1959839 1959857 1960755 1960842) (-1160 "SPLTREE.spad" 1954235 1954248 1959119 1959146) (-1159 "SPLNODE.spad" 1950823 1950836 1954225 1954230) (-1158 "SPFCAT.spad" 1949632 1949641 1950813 1950818) (-1157 "SPECOUT.spad" 1948184 1948193 1949622 1949627) (-1156 "SPADXPT.spad" 1939779 1939788 1948174 1948179) (-1155 "spad-parser.spad" 1939244 1939253 1939769 1939774) (-1154 "SPADAST.spad" 1938945 1938954 1939234 1939239) (-1153 "SPACEC.spad" 1923144 1923155 1938935 1938940) (-1152 "SPACE3.spad" 1922920 1922931 1923134 1923139) (-1151 "SORTPAK.spad" 1922469 1922482 1922876 1922881) (-1150 "SOLVETRA.spad" 1920232 1920243 1922459 1922464) (-1149 "SOLVESER.spad" 1918760 1918771 1920222 1920227) (-1148 "SOLVERAD.spad" 1914786 1914797 1918750 1918755) (-1147 "SOLVEFOR.spad" 1913248 1913266 1914776 1914781) (-1146 "SNTSCAT.spad" 1912848 1912865 1913216 1913243) (-1145 "SMTS.spad" 1911120 1911146 1912413 1912510) (-1144 "SMP.spad" 1908595 1908615 1908985 1909112) (-1143 "SMITH.spad" 1907440 1907465 1908585 1908590) (-1142 "SMATCAT.spad" 1905550 1905580 1907384 1907435) (-1141 "SMATCAT.spad" 1903592 1903624 1905428 1905433) (-1140 "SKAGG.spad" 1902555 1902566 1903560 1903587) (-1139 "SINT.spad" 1901495 1901504 1902421 1902550) (-1138 "SIMPAN.spad" 1901223 1901232 1901485 1901490) (-1137 "SIG.spad" 1900553 1900562 1901213 1901218) (-1136 "SIGNRF.spad" 1899671 1899682 1900543 1900548) (-1135 "SIGNEF.spad" 1898950 1898967 1899661 1899666) (-1134 "SIGAST.spad" 1898335 1898344 1898940 1898945) (-1133 "SHP.spad" 1896263 1896278 1898291 1898296) (-1132 "SHDP.spad" 1883941 1883968 1884450 1884549) (-1131 "SGROUP.spad" 1883549 1883558 1883931 1883936) (-1130 "SGROUP.spad" 1883155 1883166 1883539 1883544) (-1129 "SGCF.spad" 1876294 1876303 1883145 1883150) (-1128 "SFRTCAT.spad" 1875224 1875241 1876262 1876289) (-1127 "SFRGCD.spad" 1874287 1874307 1875214 1875219) (-1126 "SFQCMPK.spad" 1868924 1868944 1874277 1874282) (-1125 "SFORT.spad" 1868363 1868377 1868914 1868919) (-1124 "SEXOF.spad" 1868206 1868246 1868353 1868358) (-1123 "SEX.spad" 1868098 1868107 1868196 1868201) (-1122 "SEXCAT.spad" 1865870 1865910 1868088 1868093) (-1121 "SET.spad" 1864158 1864169 1865255 1865294) (-1120 "SETMN.spad" 1862608 1862625 1864148 1864153) (-1119 "SETCAT.spad" 1861930 1861939 1862598 1862603) (-1118 "SETCAT.spad" 1861250 1861261 1861920 1861925) (-1117 "SETAGG.spad" 1857799 1857810 1861230 1861245) (-1116 "SETAGG.spad" 1854356 1854369 1857789 1857794) (-1115 "SEQAST.spad" 1854059 1854068 1854346 1854351) (-1114 "SEGXCAT.spad" 1853215 1853228 1854049 1854054) (-1113 "SEG.spad" 1853028 1853039 1853134 1853139) (-1112 "SEGCAT.spad" 1851953 1851964 1853018 1853023) (-1111 "SEGBIND.spad" 1851711 1851722 1851900 1851905) (-1110 "SEGBIND2.spad" 1851409 1851422 1851701 1851706) (-1109 "SEGAST.spad" 1851123 1851132 1851399 1851404) (-1108 "SEG2.spad" 1850558 1850571 1851079 1851084) (-1107 "SDVAR.spad" 1849834 1849845 1850548 1850553) (-1106 "SDPOL.spad" 1847167 1847178 1847458 1847585) (-1105 "SCPKG.spad" 1845256 1845267 1847157 1847162) (-1104 "SCOPE.spad" 1844409 1844418 1845246 1845251) (-1103 "SCACHE.spad" 1843105 1843116 1844399 1844404) (-1102 "SASTCAT.spad" 1843014 1843023 1843095 1843100) (-1101 "SAOS.spad" 1842886 1842895 1843004 1843009) (-1100 "SAERFFC.spad" 1842599 1842619 1842876 1842881) (-1099 "SAE.spad" 1840069 1840085 1840680 1840815) (-1098 "SAEFACT.spad" 1839770 1839790 1840059 1840064) (-1097 "RURPK.spad" 1837429 1837445 1839760 1839765) (-1096 "RULESET.spad" 1836882 1836906 1837419 1837424) (-1095 "RULE.spad" 1835122 1835146 1836872 1836877) (-1094 "RULECOLD.spad" 1834974 1834987 1835112 1835117) (-1093 "RTVALUE.spad" 1834709 1834718 1834964 1834969) (-1092 "RSTRCAST.spad" 1834426 1834435 1834699 1834704) (-1091 "RSETGCD.spad" 1830804 1830824 1834416 1834421) (-1090 "RSETCAT.spad" 1820740 1820757 1830772 1830799) (-1089 "RSETCAT.spad" 1810696 1810715 1820730 1820735) (-1088 "RSDCMPK.spad" 1809148 1809168 1810686 1810691) (-1087 "RRCC.spad" 1807532 1807562 1809138 1809143) (-1086 "RRCC.spad" 1805914 1805946 1807522 1807527) (-1085 "RPTAST.spad" 1805616 1805625 1805904 1805909) (-1084 "RPOLCAT.spad" 1784976 1784991 1805484 1805611) (-1083 "RPOLCAT.spad" 1764049 1764066 1784559 1784564) (-1082 "ROUTINE.spad" 1759470 1759479 1762234 1762261) (-1081 "ROMAN.spad" 1758798 1758807 1759336 1759465) (-1080 "ROIRC.spad" 1757878 1757910 1758788 1758793) (-1079 "RNS.spad" 1756781 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155606 155614 155705 155710) (-139 "CATAST.spad" 155224 155232 155596 155601) (-138 "CASEAST.spad" 154938 154946 155214 155219) (-137 "CARTEN.spad" 150305 150329 154928 154933) (-136 "CARTEN2.spad" 149695 149722 150295 150300) (-135 "CARD.spad" 146990 146998 149669 149690) (-134 "CAPSLAST.spad" 146764 146772 146980 146985) (-133 "CACHSET.spad" 146388 146396 146754 146759) (-132 "CABMON.spad" 145943 145951 146378 146383) (-131 "BYTEORD.spad" 145618 145626 145933 145938) (-130 "BYTE.spad" 145045 145053 145608 145613) (-129 "BYTEBUF.spad" 142743 142751 144053 144080) (-128 "BTREE.spad" 141699 141709 142233 142260) (-127 "BTOURN.spad" 140587 140597 141189 141216) (-126 "BTCAT.spad" 139979 139989 140555 140582) (-125 "BTCAT.spad" 139391 139403 139969 139974) (-124 "BTAGG.spad" 138857 138865 139359 139386) (-123 "BTAGG.spad" 138343 138353 138847 138852) (-122 "BSTREE.spad" 136967 136977 137833 137860) (-121 "BRILL.spad" 135164 135175 136957 136962) (-120 "BRAGG.spad" 134104 134114 135154 135159) (-119 "BRAGG.spad" 133008 133020 134060 134065) (-118 "BPADICRT.spad" 130882 130894 131137 131230) (-117 "BPADIC.spad" 130546 130558 130808 130877) (-116 "BOUNDZRO.spad" 130202 130219 130536 130541) (-115 "BOP.spad" 125384 125392 130192 130197) (-114 "BOP1.spad" 122850 122860 125374 125379) (-113 "BOOLE.spad" 122500 122508 122840 122845) (-112 "BOOLEAN.spad" 121938 121946 122490 122495) (-111 "BMODULE.spad" 121650 121662 121906 121933) (-110 "BITS.spad" 121033 121041 121248 121275) (-109 "BINDING.spad" 120446 120454 121023 121028) (-108 "BINARY.spad" 118460 118468 118816 118909) (-107 "BGAGG.spad" 117665 117675 118440 118455) (-106 "BGAGG.spad" 116878 116890 117655 117660) (-105 "BFUNCT.spad" 116442 116450 116858 116873) (-104 "BEZOUT.spad" 115582 115609 116392 116397) (-103 "BBTREE.spad" 112310 112320 115072 115099) (-102 "BASTYPE.spad" 111982 111990 112300 112305) (-101 "BASTYPE.spad" 111652 111662 111972 111977) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) \ No newline at end of file +((-3 NIL 2292758 2292763 2292768 2292773) (-2 NIL 2292738 2292743 2292748 2292753) (-1 NIL 2292718 2292723 2292728 2292733) (0 NIL 2292698 2292703 2292708 2292713) (-1315 "ZMOD.spad" 2292507 2292520 2292636 2292693) (-1314 "ZLINDEP.spad" 2291573 2291584 2292497 2292502) (-1313 "ZDSOLVE.spad" 2281518 2281540 2291563 2291568) (-1312 "YSTREAM.spad" 2281013 2281024 2281508 2281513) (-1311 "YDIAGRAM.spad" 2280647 2280656 2281003 2281008) (-1310 "XRPOLY.spad" 2279867 2279887 2280503 2280572) (-1309 "XPR.spad" 2277662 2277675 2279585 2279684) (-1308 "XPOLY.spad" 2277217 2277228 2277518 2277587) (-1307 "XPOLYC.spad" 2276536 2276552 2277143 2277212) (-1306 "XPBWPOLY.spad" 2274973 2274993 2276316 2276385) (-1305 "XF.spad" 2273436 2273451 2274875 2274968) (-1304 "XF.spad" 2271879 2271896 2273320 2273325) (-1303 "XFALG.spad" 2268927 2268943 2271805 2271874) (-1302 "XEXPPKG.spad" 2268178 2268204 2268917 2268922) (-1301 "XDPOLY.spad" 2267792 2267808 2268034 2268103) (-1300 "XALG.spad" 2267452 2267463 2267748 2267787) (-1299 "WUTSET.spad" 2263255 2263272 2267062 2267089) (-1298 "WP.spad" 2262454 2262498 2263113 2263180) (-1297 "WHILEAST.spad" 2262252 2262261 2262444 2262449) (-1296 "WHEREAST.spad" 2261923 2261932 2262242 2262247) (-1295 "WFFINTBS.spad" 2259586 2259608 2261913 2261918) (-1294 "WEIER.spad" 2257808 2257819 2259576 2259581) (-1293 "VSPACE.spad" 2257481 2257492 2257776 2257803) (-1292 "VSPACE.spad" 2257174 2257187 2257471 2257476) (-1291 "VOID.spad" 2256851 2256860 2257164 2257169) (-1290 "VIEW.spad" 2254531 2254540 2256841 2256846) (-1289 "VIEWDEF.spad" 2249732 2249741 2254521 2254526) (-1288 "VIEW3D.spad" 2233693 2233702 2249722 2249727) (-1287 "VIEW2D.spad" 2221584 2221593 2233683 2233688) (-1286 "VECTOR.spad" 2220105 2220116 2220356 2220383) (-1285 "VECTOR2.spad" 2218744 2218757 2220095 2220100) (-1284 "VECTCAT.spad" 2216648 2216659 2218712 2218739) (-1283 "VECTCAT.spad" 2214359 2214372 2216425 2216430) (-1282 "VARIABLE.spad" 2214139 2214154 2214349 2214354) (-1281 "UTYPE.spad" 2213783 2213792 2214129 2214134) (-1280 "UTSODETL.spad" 2213078 2213102 2213739 2213744) (-1279 "UTSODE.spad" 2211294 2211314 2213068 2213073) (-1278 "UTS.spad" 2206241 2206269 2209761 2209858) (-1277 "UTSCAT.spad" 2203720 2203736 2206139 2206236) (-1276 "UTSCAT.spad" 2200843 2200861 2203264 2203269) (-1275 "UTS2.spad" 2200438 2200473 2200833 2200838) (-1274 "URAGG.spad" 2195111 2195122 2200428 2200433) (-1273 "URAGG.spad" 2189748 2189761 2195067 2195072) (-1272 "UPXSSING.spad" 2187393 2187419 2188829 2188962) (-1271 "UPXS.spad" 2184689 2184717 2185525 2185674) (-1270 "UPXSCONS.spad" 2182448 2182468 2182821 2182970) (-1269 "UPXSCCA.spad" 2181019 2181039 2182294 2182443) (-1268 "UPXSCCA.spad" 2179732 2179754 2181009 2181014) (-1267 "UPXSCAT.spad" 2178321 2178337 2179578 2179727) (-1266 "UPXS2.spad" 2177864 2177917 2178311 2178316) (-1265 "UPSQFREE.spad" 2176278 2176292 2177854 2177859) (-1264 "UPSCAT.spad" 2174065 2174089 2176176 2176273) (-1263 "UPSCAT.spad" 2171558 2171584 2173671 2173676) (-1262 "UPOLYC.spad" 2166598 2166609 2171400 2171553) (-1261 "UPOLYC.spad" 2161530 2161543 2166334 2166339) (-1260 "UPOLYC2.spad" 2161001 2161020 2161520 2161525) (-1259 "UP.spad" 2158107 2158122 2158494 2158647) (-1258 "UPMP.spad" 2157007 2157020 2158097 2158102) (-1257 "UPDIVP.spad" 2156572 2156586 2156997 2157002) (-1256 "UPDECOMP.spad" 2154817 2154831 2156562 2156567) (-1255 "UPCDEN.spad" 2154026 2154042 2154807 2154812) (-1254 "UP2.spad" 2153390 2153411 2154016 2154021) (-1253 "UNISEG.spad" 2152743 2152754 2153309 2153314) (-1252 "UNISEG2.spad" 2152240 2152253 2152699 2152704) (-1251 "UNIFACT.spad" 2151343 2151355 2152230 2152235) (-1250 "ULS.spad" 2141127 2141155 2142072 2142501) (-1249 "ULSCONS.spad" 2132261 2132281 2132631 2132780) (-1248 "ULSCCAT.spad" 2129998 2130018 2132107 2132256) (-1247 "ULSCCAT.spad" 2127843 2127865 2129954 2129959) (-1246 "ULSCAT.spad" 2126075 2126091 2127689 2127838) (-1245 "ULS2.spad" 2125589 2125642 2126065 2126070) (-1244 "UINT8.spad" 2125466 2125475 2125579 2125584) (-1243 "UINT64.spad" 2125342 2125351 2125456 2125461) (-1242 "UINT32.spad" 2125218 2125227 2125332 2125337) (-1241 "UINT16.spad" 2125094 2125103 2125208 2125213) (-1240 "UFD.spad" 2124159 2124168 2125020 2125089) (-1239 "UFD.spad" 2123286 2123297 2124149 2124154) (-1238 "UDVO.spad" 2122167 2122176 2123276 2123281) (-1237 "UDPO.spad" 2119660 2119671 2122123 2122128) (-1236 "TYPE.spad" 2119592 2119601 2119650 2119655) (-1235 "TYPEAST.spad" 2119511 2119520 2119582 2119587) (-1234 "TWOFACT.spad" 2118163 2118178 2119501 2119506) (-1233 "TUPLE.spad" 2117649 2117660 2118062 2118067) (-1232 "TUBETOOL.spad" 2114516 2114525 2117639 2117644) (-1231 "TUBE.spad" 2113163 2113180 2114506 2114511) (-1230 "TS.spad" 2111762 2111778 2112728 2112825) (-1229 "TSETCAT.spad" 2098889 2098906 2111730 2111757) (-1228 "TSETCAT.spad" 2086002 2086021 2098845 2098850) (-1227 "TRMANIP.spad" 2080368 2080385 2085708 2085713) (-1226 "TRIMAT.spad" 2079331 2079356 2080358 2080363) (-1225 "TRIGMNIP.spad" 2077858 2077875 2079321 2079326) (-1224 "TRIGCAT.spad" 2077370 2077379 2077848 2077853) (-1223 "TRIGCAT.spad" 2076880 2076891 2077360 2077365) (-1222 "TREE.spad" 2075338 2075349 2076370 2076397) (-1221 "TRANFUN.spad" 2075177 2075186 2075328 2075333) (-1220 "TRANFUN.spad" 2075014 2075025 2075167 2075172) (-1219 "TOPSP.spad" 2074688 2074697 2075004 2075009) (-1218 "TOOLSIGN.spad" 2074351 2074362 2074678 2074683) (-1217 "TEXTFILE.spad" 2072912 2072921 2074341 2074346) (-1216 "TEX.spad" 2070058 2070067 2072902 2072907) (-1215 "TEX1.spad" 2069614 2069625 2070048 2070053) (-1214 "TEMUTL.spad" 2069169 2069178 2069604 2069609) (-1213 "TBCMPPK.spad" 2067262 2067285 2069159 2069164) (-1212 "TBAGG.spad" 2066312 2066335 2067242 2067257) (-1211 "TBAGG.spad" 2065370 2065395 2066302 2066307) (-1210 "TANEXP.spad" 2064778 2064789 2065360 2065365) (-1209 "TALGOP.spad" 2064502 2064513 2064768 2064773) (-1208 "TABLE.spad" 2062471 2062494 2062741 2062768) (-1207 "TABLEAU.spad" 2061952 2061963 2062461 2062466) (-1206 "TABLBUMP.spad" 2058755 2058766 2061942 2061947) (-1205 "SYSTEM.spad" 2057983 2057992 2058745 2058750) (-1204 "SYSSOLP.spad" 2055466 2055477 2057973 2057978) (-1203 "SYSPTR.spad" 2055365 2055374 2055456 2055461) (-1202 "SYSNNI.spad" 2054547 2054558 2055355 2055360) (-1201 "SYSINT.spad" 2053951 2053962 2054537 2054542) (-1200 "SYNTAX.spad" 2050157 2050166 2053941 2053946) (-1199 "SYMTAB.spad" 2048225 2048234 2050147 2050152) (-1198 "SYMS.spad" 2044248 2044257 2048215 2048220) (-1197 "SYMPOLY.spad" 2043255 2043266 2043337 2043464) (-1196 "SYMFUNC.spad" 2042756 2042767 2043245 2043250) (-1195 "SYMBOL.spad" 2040259 2040268 2042746 2042751) (-1194 "SWITCH.spad" 2037030 2037039 2040249 2040254) (-1193 "SUTS.spad" 2034078 2034106 2035497 2035594) (-1192 "SUPXS.spad" 2031361 2031389 2032210 2032359) (-1191 "SUP.spad" 2028081 2028092 2028854 2029007) (-1190 "SUPFRACF.spad" 2027186 2027204 2028071 2028076) (-1189 "SUP2.spad" 2026578 2026591 2027176 2027181) (-1188 "SUMRF.spad" 2025552 2025563 2026568 2026573) (-1187 "SUMFS.spad" 2025189 2025206 2025542 2025547) (-1186 "SULS.spad" 2014960 2014988 2015918 2016347) (-1185 "SUCHTAST.spad" 2014729 2014738 2014950 2014955) (-1184 "SUCH.spad" 2014411 2014426 2014719 2014724) (-1183 "SUBSPACE.spad" 2006526 2006541 2014401 2014406) (-1182 "SUBRESP.spad" 2005696 2005710 2006482 2006487) (-1181 "STTF.spad" 2001795 2001811 2005686 2005691) (-1180 "STTFNC.spad" 1998263 1998279 2001785 2001790) (-1179 "STTAYLOR.spad" 1990898 1990909 1998144 1998149) (-1178 "STRTBL.spad" 1988949 1988966 1989098 1989125) (-1177 "STRING.spad" 1987736 1987745 1987957 1987984) (-1176 "STREAM.spad" 1984537 1984548 1987144 1987159) (-1175 "STREAM3.spad" 1984110 1984125 1984527 1984532) (-1174 "STREAM2.spad" 1983238 1983251 1984100 1984105) (-1173 "STREAM1.spad" 1982944 1982955 1983228 1983233) (-1172 "STINPROD.spad" 1981880 1981896 1982934 1982939) (-1171 "STEP.spad" 1981081 1981090 1981870 1981875) (-1170 "STEPAST.spad" 1980315 1980324 1981071 1981076) (-1169 "STBL.spad" 1978399 1978427 1978566 1978581) (-1168 "STAGG.spad" 1977474 1977485 1978389 1978394) (-1167 "STAGG.spad" 1976547 1976560 1977464 1977469) (-1166 "STACK.spad" 1975787 1975798 1976037 1976064) (-1165 "SREGSET.spad" 1973455 1973472 1975397 1975424) (-1164 "SRDCMPK.spad" 1972016 1972036 1973445 1973450) (-1163 "SRAGG.spad" 1967159 1967168 1971984 1972011) (-1162 "SRAGG.spad" 1962322 1962333 1967149 1967154) (-1161 "SQMATRIX.spad" 1959865 1959883 1960781 1960868) (-1160 "SPLTREE.spad" 1954261 1954274 1959145 1959172) (-1159 "SPLNODE.spad" 1950849 1950862 1954251 1954256) (-1158 "SPFCAT.spad" 1949658 1949667 1950839 1950844) (-1157 "SPECOUT.spad" 1948210 1948219 1949648 1949653) (-1156 "SPADXPT.spad" 1939805 1939814 1948200 1948205) (-1155 "spad-parser.spad" 1939270 1939279 1939795 1939800) (-1154 "SPADAST.spad" 1938971 1938980 1939260 1939265) (-1153 "SPACEC.spad" 1923170 1923181 1938961 1938966) (-1152 "SPACE3.spad" 1922946 1922957 1923160 1923165) (-1151 "SORTPAK.spad" 1922495 1922508 1922902 1922907) (-1150 "SOLVETRA.spad" 1920258 1920269 1922485 1922490) (-1149 "SOLVESER.spad" 1918786 1918797 1920248 1920253) (-1148 "SOLVERAD.spad" 1914812 1914823 1918776 1918781) (-1147 "SOLVEFOR.spad" 1913274 1913292 1914802 1914807) (-1146 "SNTSCAT.spad" 1912874 1912891 1913242 1913269) (-1145 "SMTS.spad" 1911146 1911172 1912439 1912536) (-1144 "SMP.spad" 1908621 1908641 1909011 1909138) (-1143 "SMITH.spad" 1907466 1907491 1908611 1908616) (-1142 "SMATCAT.spad" 1905576 1905606 1907410 1907461) (-1141 "SMATCAT.spad" 1903618 1903650 1905454 1905459) (-1140 "SKAGG.spad" 1902581 1902592 1903586 1903613) (-1139 "SINT.spad" 1901521 1901530 1902447 1902576) (-1138 "SIMPAN.spad" 1901249 1901258 1901511 1901516) (-1137 "SIG.spad" 1900579 1900588 1901239 1901244) (-1136 "SIGNRF.spad" 1899697 1899708 1900569 1900574) (-1135 "SIGNEF.spad" 1898976 1898993 1899687 1899692) (-1134 "SIGAST.spad" 1898361 1898370 1898966 1898971) (-1133 "SHP.spad" 1896289 1896304 1898317 1898322) (-1132 "SHDP.spad" 1883967 1883994 1884476 1884575) (-1131 "SGROUP.spad" 1883575 1883584 1883957 1883962) (-1130 "SGROUP.spad" 1883181 1883192 1883565 1883570) (-1129 "SGCF.spad" 1876320 1876329 1883171 1883176) (-1128 "SFRTCAT.spad" 1875250 1875267 1876288 1876315) (-1127 "SFRGCD.spad" 1874313 1874333 1875240 1875245) (-1126 "SFQCMPK.spad" 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(-1107 "SDVAR.spad" 1849860 1849871 1850574 1850579) (-1106 "SDPOL.spad" 1847193 1847204 1847484 1847611) (-1105 "SCPKG.spad" 1845282 1845293 1847183 1847188) (-1104 "SCOPE.spad" 1844435 1844444 1845272 1845277) (-1103 "SCACHE.spad" 1843131 1843142 1844425 1844430) (-1102 "SASTCAT.spad" 1843040 1843049 1843121 1843126) (-1101 "SAOS.spad" 1842912 1842921 1843030 1843035) (-1100 "SAERFFC.spad" 1842625 1842645 1842902 1842907) (-1099 "SAE.spad" 1840095 1840111 1840706 1840841) (-1098 "SAEFACT.spad" 1839796 1839816 1840085 1840090) (-1097 "RURPK.spad" 1837455 1837471 1839786 1839791) (-1096 "RULESET.spad" 1836908 1836932 1837445 1837450) (-1095 "RULE.spad" 1835148 1835172 1836898 1836903) (-1094 "RULECOLD.spad" 1835000 1835013 1835138 1835143) (-1093 "RTVALUE.spad" 1834735 1834744 1834990 1834995) (-1092 "RSTRCAST.spad" 1834452 1834461 1834725 1834730) (-1091 "RSETGCD.spad" 1830830 1830850 1834442 1834447) (-1090 "RSETCAT.spad" 1820766 1820783 1830798 1830825) (-1089 "RSETCAT.spad" 1810722 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"RLINSET.spad" 1743416 1743427 1743702 1743707) (-1069 "RINTERP.spad" 1743304 1743324 1743406 1743411) (-1068 "RING.spad" 1742774 1742783 1743284 1743299) (-1067 "RING.spad" 1742252 1742263 1742764 1742769) (-1066 "RIDIST.spad" 1741644 1741653 1742242 1742247) (-1065 "RGCHAIN.spad" 1740172 1740188 1741074 1741101) (-1064 "RGBCSPC.spad" 1739953 1739965 1740162 1740167) (-1063 "RGBCMDL.spad" 1739483 1739495 1739943 1739948) (-1062 "RF.spad" 1737125 1737136 1739473 1739478) (-1061 "RFFACTOR.spad" 1736587 1736598 1737115 1737120) (-1060 "RFFACT.spad" 1736322 1736334 1736577 1736582) (-1059 "RFDIST.spad" 1735318 1735327 1736312 1736317) (-1058 "RETSOL.spad" 1734737 1734750 1735308 1735313) (-1057 "RETRACT.spad" 1734165 1734176 1734727 1734732) (-1056 "RETRACT.spad" 1733591 1733604 1734155 1734160) (-1055 "RETAST.spad" 1733403 1733412 1733581 1733586) (-1054 "RESULT.spad" 1731001 1731010 1731588 1731615) (-1053 "RESRING.spad" 1730348 1730395 1730939 1730996) (-1052 "RESLATC.spad" 1729672 1729683 1730338 1730343) (-1051 "REPSQ.spad" 1729403 1729414 1729662 1729667) (-1050 "REP.spad" 1726957 1726966 1729393 1729398) (-1049 "REPDB.spad" 1726664 1726675 1726947 1726952) (-1048 "REP2.spad" 1716322 1716333 1726506 1726511) (-1047 "REP1.spad" 1710518 1710529 1716272 1716277) (-1046 "REGSET.spad" 1708279 1708296 1710128 1710155) (-1045 "REF.spad" 1707614 1707625 1708234 1708239) (-1044 "REDORDER.spad" 1706820 1706837 1707604 1707609) (-1043 "RECLOS.spad" 1705603 1705623 1706307 1706400) (-1042 "REALSOLV.spad" 1704743 1704752 1705593 1705598) (-1041 "REAL.spad" 1704615 1704624 1704733 1704738) (-1040 "REAL0Q.spad" 1701913 1701928 1704605 1704610) (-1039 "REAL0.spad" 1698757 1698772 1701903 1701908) (-1038 "RDUCEAST.spad" 1698478 1698487 1698747 1698752) (-1037 "RDIV.spad" 1698133 1698158 1698468 1698473) (-1036 "RDIST.spad" 1697700 1697711 1698123 1698128) (-1035 "RDETRS.spad" 1696564 1696582 1697690 1697695) (-1034 "RDETR.spad" 1694703 1694721 1696554 1696559) (-1033 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(-996 "PSETPK.spad" 1624308 1624324 1638753 1638758) (-995 "PSETCAT.spad" 1618228 1618251 1624288 1624303) (-994 "PSETCAT.spad" 1612122 1612147 1618184 1618189) (-993 "PSCURVE.spad" 1611105 1611113 1612112 1612117) (-992 "PSCAT.spad" 1609888 1609917 1611003 1611100) (-991 "PSCAT.spad" 1608761 1608792 1609878 1609883) (-990 "PRTITION.spad" 1607459 1607467 1608751 1608756) (-989 "PRTDAST.spad" 1607178 1607186 1607449 1607454) (-988 "PRS.spad" 1596740 1596757 1607134 1607139) (-987 "PRQAGG.spad" 1596175 1596185 1596708 1596735) (-986 "PROPLOG.spad" 1595747 1595755 1596165 1596170) (-985 "PROPFUN2.spad" 1595370 1595383 1595737 1595742) (-984 "PROPFUN1.spad" 1594768 1594779 1595360 1595365) (-983 "PROPFRML.spad" 1593336 1593347 1594758 1594763) (-982 "PROPERTY.spad" 1592824 1592832 1593326 1593331) (-981 "PRODUCT.spad" 1590506 1590518 1590790 1590845) (-980 "PR.spad" 1588898 1588910 1589597 1589724) (-979 "PRINT.spad" 1588650 1588658 1588888 1588893) (-978 "PRIMES.spad" 1586903 1586913 1588640 1588645) (-977 "PRIMELT.spad" 1584984 1584998 1586893 1586898) (-976 "PRIMCAT.spad" 1584611 1584619 1584974 1584979) (-975 "PRIMARR.spad" 1583463 1583473 1583641 1583668) (-974 "PRIMARR2.spad" 1582230 1582242 1583453 1583458) (-973 "PREASSOC.spad" 1581612 1581624 1582220 1582225) (-972 "PPCURVE.spad" 1580749 1580757 1581602 1581607) (-971 "PORTNUM.spad" 1580524 1580532 1580739 1580744) (-970 "POLYROOT.spad" 1579373 1579395 1580480 1580485) (-969 "POLY.spad" 1576708 1576718 1577223 1577350) (-968 "POLYLIFT.spad" 1575973 1575996 1576698 1576703) (-967 "POLYCATQ.spad" 1574091 1574113 1575963 1575968) (-966 "POLYCAT.spad" 1567561 1567582 1573959 1574086) (-965 "POLYCAT.spad" 1560369 1560392 1566769 1566774) (-964 "POLY2UP.spad" 1559821 1559835 1560359 1560364) (-963 "POLY2.spad" 1559418 1559430 1559811 1559816) (-962 "POLUTIL.spad" 1558359 1558388 1559374 1559379) (-961 "POLTOPOL.spad" 1557107 1557122 1558349 1558354) (-960 "POINT.spad" 1555792 1555802 1555879 1555906) (-959 "PNTHEORY.spad" 1552494 1552502 1555782 1555787) (-958 "PMTOOLS.spad" 1551269 1551283 1552484 1552489) (-957 "PMSYM.spad" 1550818 1550828 1551259 1551264) (-956 "PMQFCAT.spad" 1550409 1550423 1550808 1550813) (-955 "PMPRED.spad" 1549888 1549902 1550399 1550404) (-954 "PMPREDFS.spad" 1549342 1549364 1549878 1549883) (-953 "PMPLCAT.spad" 1548422 1548440 1549274 1549279) (-952 "PMLSAGG.spad" 1548007 1548021 1548412 1548417) (-951 "PMKERNEL.spad" 1547586 1547598 1547997 1548002) (-950 "PMINS.spad" 1547166 1547176 1547576 1547581) (-949 "PMFS.spad" 1546743 1546761 1547156 1547161) (-948 "PMDOWN.spad" 1546033 1546047 1546733 1546738) (-947 "PMASS.spad" 1545043 1545051 1546023 1546028) (-946 "PMASSFS.spad" 1544010 1544026 1545033 1545038) (-945 "PLOTTOOL.spad" 1543790 1543798 1544000 1544005) (-944 "PLOT.spad" 1538713 1538721 1543780 1543785) (-943 "PLOT3D.spad" 1535177 1535185 1538703 1538708) (-942 "PLOT1.spad" 1534334 1534344 1535167 1535172) (-941 "PLEQN.spad" 1521624 1521651 1534324 1534329) (-940 "PINTERP.spad" 1521246 1521265 1521614 1521619) (-939 "PINTERPA.spad" 1521030 1521046 1521236 1521241) (-938 "PI.spad" 1520639 1520647 1521004 1521025) (-937 "PID.spad" 1519609 1519617 1520565 1520634) (-936 "PICOERCE.spad" 1519266 1519276 1519599 1519604) (-935 "PGROEB.spad" 1517867 1517881 1519256 1519261) (-934 "PGE.spad" 1509484 1509492 1517857 1517862) (-933 "PGCD.spad" 1508374 1508391 1509474 1509479) (-932 "PFRPAC.spad" 1507523 1507533 1508364 1508369) (-931 "PFR.spad" 1504186 1504196 1507425 1507518) (-930 "PFOTOOLS.spad" 1503444 1503460 1504176 1504181) (-929 "PFOQ.spad" 1502814 1502832 1503434 1503439) (-928 "PFO.spad" 1502233 1502260 1502804 1502809) (-927 "PF.spad" 1501807 1501819 1502038 1502131) (-926 "PFECAT.spad" 1499489 1499497 1501733 1501802) (-925 "PFECAT.spad" 1497199 1497209 1499445 1499450) (-924 "PFBRU.spad" 1495087 1495099 1497189 1497194) (-923 "PFBR.spad" 1492647 1492670 1495077 1495082) (-922 "PERM.spad" 1488454 1488464 1492477 1492492) (-921 "PERMGRP.spad" 1483224 1483234 1488444 1488449) (-920 "PERMCAT.spad" 1481885 1481895 1483204 1483219) (-919 "PERMAN.spad" 1480417 1480431 1481875 1481880) (-918 "PENDTREE.spad" 1479641 1479651 1479929 1479934) (-917 "PDSPC.spad" 1478454 1478464 1479631 1479636) (-916 "PDSPC.spad" 1477265 1477277 1478444 1478449) (-915 "PDRING.spad" 1477107 1477117 1477245 1477260) (-914 "PDMOD.spad" 1476923 1476935 1477075 1477102) (-913 "PDEPROB.spad" 1475938 1475946 1476913 1476918) (-912 "PDEPACK.spad" 1469978 1469986 1475928 1475933) (-911 "PDECOMP.spad" 1469448 1469465 1469968 1469973) (-910 "PDECAT.spad" 1467804 1467812 1469438 1469443) (-909 "PDDOM.spad" 1467242 1467255 1467794 1467799) (-908 "PDDOM.spad" 1466678 1466693 1467232 1467237) (-907 "PCOMP.spad" 1466531 1466544 1466668 1466673) (-906 "PBWLB.spad" 1465119 1465136 1466521 1466526) (-905 "PATTERN.spad" 1459658 1459668 1465109 1465114) (-904 "PATTERN2.spad" 1459396 1459408 1459648 1459653) (-903 "PATTERN1.spad" 1457732 1457748 1459386 1459391) (-902 "PATRES.spad" 1455307 1455319 1457722 1457727) (-901 "PATRES2.spad" 1454979 1454993 1455297 1455302) (-900 "PATMATCH.spad" 1453176 1453207 1454687 1454692) (-899 "PATMAB.spad" 1452605 1452615 1453166 1453171) (-898 "PATLRES.spad" 1451691 1451705 1452595 1452600) (-897 "PATAB.spad" 1451455 1451465 1451681 1451686) (-896 "PARTPERM.spad" 1449463 1449471 1451445 1451450) (-895 "PARSURF.spad" 1448897 1448925 1449453 1449458) (-894 "PARSU2.spad" 1448694 1448710 1448887 1448892) (-893 "script-parser.spad" 1448214 1448222 1448684 1448689) (-892 "PARSCURV.spad" 1447648 1447676 1448204 1448209) (-891 "PARSC2.spad" 1447439 1447455 1447638 1447643) (-890 "PARPCURV.spad" 1446901 1446929 1447429 1447434) (-889 "PARPC2.spad" 1446692 1446708 1446891 1446896) (-888 "PARAMAST.spad" 1445820 1445828 1446682 1446687) (-887 "PAN2EXPR.spad" 1445232 1445240 1445810 1445815) (-886 "PALETTE.spad" 1444202 1444210 1445222 1445227) (-885 "PAIR.spad" 1443189 1443202 1443790 1443795) (-884 "PADICRC.spad" 1440430 1440448 1441601 1441694) (-883 "PADICRAT.spad" 1438338 1438350 1438559 1438652) (-882 "PADIC.spad" 1438033 1438045 1438264 1438333) (-881 "PADICCT.spad" 1436582 1436594 1437959 1438028) (-880 "PADEPAC.spad" 1435271 1435290 1436572 1436577) (-879 "PADE.spad" 1434023 1434039 1435261 1435266) (-878 "OWP.spad" 1433263 1433293 1433881 1433948) (-877 "OVERSET.spad" 1432836 1432844 1433253 1433258) (-876 "OVAR.spad" 1432617 1432640 1432826 1432831) (-875 "OUT.spad" 1431703 1431711 1432607 1432612) (-874 "OUTFORM.spad" 1421095 1421103 1431693 1431698) (-873 "OUTBFILE.spad" 1420513 1420521 1421085 1421090) (-872 "OUTBCON.spad" 1419519 1419527 1420503 1420508) (-871 "OUTBCON.spad" 1418523 1418533 1419509 1419514) (-870 "OSI.spad" 1417998 1418006 1418513 1418518) (-869 "OSGROUP.spad" 1417916 1417924 1417988 1417993) (-868 "ORTHPOL.spad" 1416401 1416411 1417833 1417838) (-867 "OREUP.spad" 1415854 1415882 1416081 1416120) (-866 "ORESUP.spad" 1415155 1415179 1415534 1415573) (-865 "OREPCTO.spad" 1413012 1413024 1415075 1415080) (-864 "OREPCAT.spad" 1407159 1407169 1412968 1413007) (-863 "OREPCAT.spad" 1401196 1401208 1407007 1407012) (-862 "ORDSET.spad" 1400368 1400376 1401186 1401191) (-861 "ORDSET.spad" 1399538 1399548 1400358 1400363) (-860 "ORDRING.spad" 1398928 1398936 1399518 1399533) (-859 "ORDRING.spad" 1398326 1398336 1398918 1398923) (-858 "ORDMON.spad" 1398181 1398189 1398316 1398321) (-857 "ORDFUNS.spad" 1397313 1397329 1398171 1398176) (-856 "ORDFIN.spad" 1397133 1397141 1397303 1397308) (-855 "ORDCOMP.spad" 1395598 1395608 1396680 1396709) (-854 "ORDCOMP2.spad" 1394891 1394903 1395588 1395593) (-853 "OPTPROB.spad" 1393529 1393537 1394881 1394886) (-852 "OPTPACK.spad" 1385938 1385946 1393519 1393524) (-851 "OPTCAT.spad" 1383617 1383625 1385928 1385933) (-850 "OPSIG.spad" 1383271 1383279 1383607 1383612) (-849 "OPQUERY.spad" 1382820 1382828 1383261 1383266) (-848 "OP.spad" 1382562 1382572 1382642 1382709) (-847 "OPERCAT.spad" 1382028 1382038 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T)) @@ -826,8 +826,8 @@ (|has| |#3| (-1068)) (|has| |#3| (-805)) (|has| |#3| (-805)) -((((-419 (-576))) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2835 (|has| |#1| (-374)) (|has| |#1| (-568))) ((|#2|) |has| |#1| (-374)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-419 (-576))) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2835 (|has| |#1| (-374)) (|has| |#1| (-568)))) +((((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2781 (|has| |#1| (-374)) (|has| |#1| (-568))) ((|#2|) |has| |#1| (-374)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) -2781 (|has| |#1| (-374)) (|has| |#1| (-568)))) (((|#2|) . T)) ((((-874)) . T)) ((((-874)) . T)) @@ -841,37 +841,37 @@ ((((-419 (-576))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) ((($) . T) (((-419 (-576))) . 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T)) (|has| (-419 |#2|) (-148)) (|has| (-419 |#2|) (-146)) @@ -884,15 +884,15 @@ (|has| |#1| (-568)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((((-874)) . T)) -((((-2 (|:| -4282 (-1177)) (|:| -4352 |#1|))) . T)) +((((-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) (|has| |#1| (-38 (-419 (-576)))) -((((-400) (-2 (|:| -4282 (-1177)) (|:| -4352 |#1|))) . T)) +((((-400) (-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#2| (-1171)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) ((((-874)) . T) (((-1200)) . T)) ((((-874)) . T) (((-1200)) . T)) ((((-1200)) . T)) @@ -910,7 +910,7 @@ ((((-400) (-1177)) . T)) (|has| |#1| (-568)) ((((-1253 (-576)) $) . T) (((-576) |#1|) . T)) -(-2835 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2781 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) . T)) @@ -928,7 +928,7 @@ ((((-656 |#1|)) . T)) ((((-874)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -(-2835 (|has| |#1| (-862)) (|has| |#1| (-1119))) +(-2781 (|has| |#1| (-862)) (|has| |#1| (-1119))) (((|#2|) |has| |#2| (-319 |#2|))) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -939,14 +939,14 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) . T)) (|has| |#2| (-379)) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) -(-2835 (|has| |#1| (-102)) (|has| |#1| (-862)) (|has| |#1| (-1119))) +(-2781 (|has| |#1| (-102)) (|has| |#1| (-862)) (|has| |#1| (-1119))) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . 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T)) (|has| |#1| (-568)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-568)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) @@ -1112,7 +1112,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#1| (-148)) -(((|#2| (-245 (-3485 |#1|) (-783)) (-876 |#1|)) . T)) +(((|#2| (-245 (-3500 |#1|) (-783)) (-876 |#1|)) . T)) (((|#1| (-543 |#3|) |#3|) . T)) (|has| |#1| (-146)) (((#0=(-419 (-576)) #0#) |has| |#2| (-374)) (($ $) . T)) @@ -1126,12 +1126,12 @@ (|has| |#1| (-146)) ((((-419 (-576))) |has| |#2| (-374)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) -(-2835 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) -(-2835 (|has| |#1| (-360)) (|has| |#1| (-379))) +(-2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +(-2781 (|has| |#1| (-360)) (|has| |#1| (-379))) ((((-1161 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) -(((|#2|) . T) (((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (|has| |#3| (-805)) (|has| |#3| (-805)) ((((-874)) . T)) @@ -1159,18 +1159,18 @@ ((((-874)) . T)) ((((-874)) . T)) (((|#1| |#2|) . T)) -((((-1195)) -2835 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195)))) (((-1101)) . T)) +((((-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195)))) (((-1101)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-624 $)) . T)) (((|#1| (-419 (-576))) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . 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T)) -((((-1195)) -2835 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) +((((-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-876 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-840)) @@ -1194,10 +1194,10 @@ ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T)) ((((-576)) . T) (($) . T) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (|has| (-1113 |#1|) (-1119)) -(((|#2| |#2|) -2835 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068)))) -(((|#2|) -2835 (|has| |#2| (-174)) (|has| |#2| (-374)))) -((((-576) (-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2835 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068)))) +(((|#2| |#2|) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068)))) +(((|#2|) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)))) +((((-576) (-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T) ((|#1| |#2|) . 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T)) (((|#1|) |has| |#1| (-319 |#1|))) @@ -1307,21 +1307,21 @@ (|has| |#1| (-379)) ((((-1195) $) |has| |#1| (-526 (-1195) $)) (($ $) |has| |#1| (-319 $)) ((|#1| |#1|) |has| |#1| (-319 |#1|)) (((-1195) |#1|) |has| |#1| (-526 (-1195) |#1|))) ((((-1195)) |has| |#1| (-915 (-1195)))) -(-2835 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2781 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-400) |#1|) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2835 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) (((|#2|) . T) (((-874)) . T)) ((((-874)) . T)) (((|#2|) . T)) ((((-927 |#1|)) . T)) ((((-874)) . T) (((-1200)) . T)) ((((-1200)) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2835 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) -((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) -2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) +((((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) |has| |#1| (-174)) (($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) @@ -1330,7 +1330,7 @@ (((|#1|) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) (((|#1| |#1|) . T)) (((#0=(-882 |#1|)) |has| #0# (-319 #0#))) -((((-576)) . T) (($) -2835 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2835 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T)) +((((-576)) . T) (($) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) (((-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-1057 (-419 (-576))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-805)) (|has| |#2| (-805)) @@ -1339,7 +1339,7 @@ (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (|has| |#2| (-1068)) ((($) . T) (((-576)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1221)) (((#0=(-576) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) @@ -1353,14 +1353,14 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-419 (-576)) #0#) . T)) (|has| |#1| (-374)) ((((-576)) . T) (((-419 (-576))) . T) (($) . T)) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) ((((-874)) . T)) ((((-874)) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) . T)) -((($ $) . T) ((#0=(-419 (-576)) #0#) -2835 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1| |#1|) . T)) +((($ $) . T) ((#0=(-419 (-576)) #0#) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1| |#1|) . T)) ((((-874)) . T)) (((|#1|) . T)) ((((-548)) |has| |#3| (-626 (-548)))) @@ -1368,32 +1368,32 @@ (((|#1| |#2|) . T)) (|has| |#1| (-860)) (|has| |#1| (-860)) -((($) . T) (((-419 (-576))) -2835 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) +((($) . T) (((-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . T)) ((((-576) |#3|) . T)) (((|#2|) . 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T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) +((($) -2781 (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576))))) ((((-576)) |has| #0=(-419 |#2|) (-651 (-576))) ((#0#) . T)) ((($) . T) (((-576)) . T)) ((((-576) (-145)) . T)) -((((-576) (-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T) ((|#1| |#2|) . T)) +((((-576) (-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T) ((|#1| |#2|) . T)) ((((-419 (-576))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((((-874)) . T)) ((((-927 |#1|)) . T)) (|has| |#1| (-374)) @@ -1401,11 +1401,11 @@ (|has| |#1| (-374)) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-860)) -((($) -2835 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (((-419 (-576))) -2835 (|has| |#1| (-374)) (|has| |#1| (-360))) ((|#1|) . 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T)) -(-2835 (|has| |#1| (-148)) (-12 (|has| |#1| (-374)) (|has| |#2| (-148)))) +(-2781 (|has| |#1| (-148)) (-12 (|has| |#1| (-374)) (|has| |#2| (-148)))) (((|#4|) . T)) -(-2835 (|has| |#1| (-146)) (-12 (|has| |#1| (-374)) (|has| |#2| (-146)))) +(-2781 (|has| |#1| (-146)) (-12 (|has| |#1| (-374)) (|has| |#2| (-146)))) ((((-1177) |#1|) . T)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -1697,24 +1697,24 @@ (((|#3|) . T)) ((((-1278 |#1| |#2| |#3|)) |has| |#1| (-374))) ((($) . T) (((-576)) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T)) -((((-419 (-576))) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1193 |#1| |#2| |#3|)) |has| |#1| (-374)) (((-576)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-419 (-576))) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-576)) . T) (($) . T)) +((((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (((-1193 |#1| |#2| |#3|)) |has| |#1| (-374)) (((-576)) . T) (($) . T) ((|#1|) . 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T)) (|has| |#2| (-148)) (|has| |#1| (-485)) -(-2835 (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068))) +(-2781 (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068))) (|has| |#1| (-374)) ((((-874)) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -1747,8 +1747,8 @@ (|has| |#1| (-860)) ((((-874)) . T)) (((|#2|) . 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T)) ((((-874)) . T)) -(-2835 (|has| |#1| (-102)) (|has| |#1| (-1119))) -(((|#2| (-494 (-3485 |#1|) (-783)) (-876 |#1|)) . T)) +(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(((|#2| (-494 (-3500 |#1|) (-783)) (-876 |#1|)) . T)) ((((-419 (-576))) . #0=(|has| |#2| (-374))) (($) . #0#)) (((|#1| (-543 (-1195)) (-1195)) . T)) (((|#1|) . T)) @@ -1778,19 +1778,19 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -4282 (-1177)) (|:| -4352 |#1|))) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -4282 (-1195)) (|:| -4352 (-52)))) . T)) +((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((((-1195) (-52)) . 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T) (((-576)) |has| |#1| (-1057 (-576))) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576))))) (|has| |#1| (-862)) (|has| |#1| (-862)) @@ -1810,15 +1810,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) (((|#1|) |has| |#1| (-174))) (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) -(((|#3|) -2835 (|has| |#3| (-174)) (|has| |#3| (-374)))) -((($) -2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) -(-2835 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-926))) -((($) -2835 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . 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T)) @@ -1827,7 +1827,7 @@ (|has| |#1| (-832)) (|has| |#1| (-832)) (((|#1|) . T)) -(-2835 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-860)) (|has| |#1| (-860)) (|has| |#1| (-860)) @@ -1836,14 +1836,14 @@ ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((((-1195)) |has| |#1| (-915 (-1195))) (((-1101)) . T)) (((|#1|) . T)) (|has| |#1| (-860)) -(((#0=(-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) #0#) |has| (-2 (|:| -4282 (-1177)) (|:| -4352 (-52))) (-319 (-2 (|:| -4282 (-1177)) (|:| -4352 (-52)))))) +(((#0=(-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) #0#) |has| (-2 (|:| -4300 (-1177)) (|:| -4391 (-52))) (-319 (-2 (|:| -4300 (-1177)) (|:| -4391 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (|has| |#1| (-1119)) ((((-874)) . T) (((-1200)) . T)) @@ -1867,14 +1867,14 @@ (((|#1| (-783) (-1101)) . T)) (((|#3|) . T)) ((((-145)) . T)) -((((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) (((-576)) -2835 (|has| |#1| (-860)) (|has| |#1| (-1057 (-576)))) ((|#1|) . T)) +((((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) (((-576)) -2781 (|has| |#1| (-860)) (|has| |#1| (-1057 (-576)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-145)) . 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T)) +((($) -2781 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (-12 (|has| |#1| (-374)) (|has| |#2| (-237))))) ((($) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|)))) ((((-990)) . T)) ((((-990)) . T) (((-874)) . T)) @@ -2034,7 +2034,7 @@ ((($) . T)) (((|#1|) . T)) ((((-112)) . T)) -(-2835 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((((-576)) . T)) (((|#1| (-576)) . T)) ((($) . T)) @@ -2058,7 +2058,7 @@ (((|#1| (-783)) . T)) ((((-874)) . T)) (|has| |#1| (-1119)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (((|#1|) . T)) ((((-1177) |#1|) . T)) ((($) . T)) @@ -2078,20 +2078,20 @@ ((((-576)) . T)) ((((-576)) . T)) ((((-874)) . T)) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-360))) ((((-874)) . T)) (|has| |#1| (-148)) (((|#3|) . T)) ((((-874)) . 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T)) (((|#3|) |has| |#3| (-1068))) @@ -2334,15 +2334,15 @@ ((($) . T)) ((((-1195)) |has| |#2| (-915 (-1195)))) ((((-874)) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-485)) (|has| |#1| (-379)) (|has| |#1| (-379)) (|has| |#1| (-379)) (|has| |#1| (-374)) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1068)) (|has| |#1| (-1131))) -((($) -2835 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-360)))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-485)) (|has| |#1| (-568)) (|has| |#1| (-1068)) (|has| |#1| (-1131))) +((($) -2781 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-360)))) ((((-117 |#1|)) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-360)) @@ -2353,7 +2353,7 @@ (|has| |#1| (-38 (-419 (-576)))) (((|#2|) . T) (((-874)) . T)) (((|#2|) . T) (((-874)) . T)) -((($ (-1195)) -2835 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) +((($ (-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) @@ -2364,18 +2364,18 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-862)) -((((-2 (|:| -4282 (-1177)) (|:| -4352 |#1|))) . T)) +((((-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) |has| (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)) (-319 (-2 (|:| -4282 |#1|) (|:| -4352 |#2|)))) ((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119)))) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) |has| (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)) (-319 (-2 (|:| -4300 |#1|) (|:| -4391 |#2|)))) ((|#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-576) |#1|))) (((|#3|) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-379)) -(-2835 (-12 (|has| (-1278 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1278 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) +(-2781 (-12 (|has| (-1278 |#1| |#2| |#3|) (-238)) (|has| |#1| (-374))) (-12 (|has| (-1278 |#1| |#2| |#3|) (-237)) (|has| |#1| (-374))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-862)) (|has| |#1| (-15 * (|#1| (-783) |#1|))) @@ -2394,17 +2394,17 @@ (((|#1|) |has| |#1| (-374))) (((|#1|) |has| |#1| (-374))) ((((-874)) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((($ $) . T) (((-624 $) $) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) ((($) . T) (((-1272 |#1| |#2| |#3| |#4|)) . T) (((-419 (-576))) . 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T)) -((((-1195)) -2835 (-12 (|has| |#3| (-915 (-1195))) (|has| |#3| (-1068))) (-12 (|has| |#3| (-917 (-1195))) (|has| |#3| (-1068))))) +((((-1195)) -2781 (-12 (|has| |#3| (-915 (-1195))) (|has| |#3| (-1068))) (-12 (|has| |#3| (-917 (-1195))) (|has| |#3| (-1068))))) ((((-656 (-792 |#1| (-876 |#2|)))) . T) (((-874)) . T)) ((((-548)) |has| (-792 |#1| (-876 |#2|)) (-626 (-548)))) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) @@ -2413,17 +2413,17 @@ (((|#3|) -12 (|has| |#3| (-319 |#3|)) (|has| |#3| (-1119)))) (((|#1|) |has| |#1| (-174))) ((((-874)) . T)) -(-2835 (|has| |#2| (-464)) (|has| |#2| (-926))) +(-2781 (|has| |#2| (-464)) (|has| |#2| (-926))) (((|#1|) . T)) ((($) . T)) ((($) |has| |#1| (-568)) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) -((($) -2835 (|has| |#1| (-174)) (|has| |#1| (-568))) ((|#1|) . 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T)) ((((-576)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2431,14 +2431,14 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((((-576)) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) (((#0=(-1271 |#2| |#3| |#4|)) . T) (((-419 (-576))) |has| #0# (-38 (-419 (-576)))) (($) . T)) ((((-576)) . T)) ((($) . T)) (|has| |#1| (-374)) -(-2835 (-12 (|has| (-1278 |#1| |#2| |#3|) (-148)) (|has| |#1| (-374))) (|has| |#1| (-148))) -(-2835 (-12 (|has| (-1278 |#1| |#2| |#3|) (-146)) (|has| |#1| (-374))) (|has| |#1| (-146))) +(-2781 (-12 (|has| (-1278 |#1| |#2| |#3|) (-148)) (|has| |#1| (-374))) (|has| |#1| (-148))) +(-2781 (-12 (|has| (-1278 |#1| |#2| |#3|) (-146)) (|has| |#1| (-374))) (|has| |#1| (-146))) (|has| |#1| (-374)) (|has| |#1| (-146)) (|has| |#1| (-148)) @@ -2456,29 +2456,29 @@ (((|#2|) . 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T) (($ $) -2835 (|has| |#1| (-300)) (|has| |#1| (-374))) ((#0=(-419 (-576)) #0#) |has| |#1| (-374))) +(((|#1| |#1|) . T) (($ $) -2781 (|has| |#1| (-300)) (|has| |#1| (-374))) ((#0=(-419 (-576)) #0#) |has| |#1| (-374))) ((((-969 |#1|)) . T)) -((((-2 (|:| -4282 (-1195)) (|:| -4352 (-52)))) . T)) +((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) ((($) . T)) ((((-576) |#1|) . T)) ((((-1195)) |has| (-419 |#2|) (-915 (-1195)))) -(((|#1|) . T) (($) -2835 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) +(((|#1|) . T) (($) -2781 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) ((((-548)) |has| |#2| (-626 (-548)))) ((((-701 |#2|)) . T) (((-874)) . T)) (((|#1|) . T)) @@ -2486,24 +2486,24 @@ (((|#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) ((((-882 |#1|)) . 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T)) @@ -2609,11 +2609,11 @@ (|has| |#2| (-146)) (|has| |#2| (-148)) ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) -(-2835 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) ((((-576)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-576)) . T)) (((|#2|) . T)) -((((-1195)) -2835 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((((-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-374))) ((((-419 |#2|)) . T)) @@ -2622,10 +2622,10 @@ ((((-874)) . T)) ((((-874)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((((-576)) . T) (($) . T) (((-419 (-576))) . T)) ((((-1195) |#1|) |has| |#1| (-526 (-1195) |#1|)) ((|#1| |#1|) |has| |#1| (-319 |#1|))) -(((|#1|) -2835 (|has| |#1| (-174)) (|has| |#1| (-374)))) +(((|#1|) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)))) (((|#1|) . 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T)) -(-2835 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-374)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1271 |#2| |#3| |#4|)) . T) (((-419 (-576))) |has| #0# (-38 (-419 (-576))))) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) -(-2835 (-12 (|has| |#1| (-317)) (|has| |#1| (-926))) (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2835 (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068))) +(-2781 (-12 (|has| |#1| (-317)) (|has| |#1| (-926))) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068))) ((((-576)) |has| |#1| (-651 (-576))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-874)) . T)) @@ -2794,7 +2794,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . 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T) (((-576)) . T)) -((((-2 (|:| -4282 (-1177)) (|:| -4352 (-52)))) . T)) +((((-2 (|:| -4300 (-1177)) (|:| -4391 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((((-874)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-576)) . T)) (((|#1| (-419 (-576))) . T)) (((|#1|) . T)) -(-2835 (|has| |#1| (-300)) (|has| |#1| (-374))) +(-2781 (|has| |#1| (-300)) (|has| |#1| (-374))) ((((-145)) . T)) ((((-576)) |has| #0=(-419 |#2|) (-651 (-576))) ((#0#) . T) (((-419 (-576))) . T) (($) . T)) (|has| |#1| (-860)) @@ -2842,7 +2842,7 @@ ((((-874)) . T)) ((((-874)) . T)) ((((-189)) . T) (((-874)) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-874)) . T)) ((((-874)) . T)) @@ -2857,10 +2857,10 @@ ((((-1177)) . 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T) (((-576)) . T) (((-419 (-576))) . T) (($) . T)) (((|#2|) . T)) -((($ (-1195)) -2835 (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))))) +((($ (-1195)) -2781 (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))))) (((#0=(-419 (-576)) #0#) . T) (($ $) . T)) ((((-576)) . T)) (((|#1|) . T)) @@ -2899,12 +2899,12 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (|has| |#1| (-832)) (((#0=(-927 |#1|) #0#) . T) (($ $) . T) ((#1=(-419 (-576)) #1#) . T)) ((((-419 |#2|)) . T)) (|has| |#1| (-860)) -((((-1222 |#1|)) . T) (((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-1222 |#1|)) . T) (((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) (((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) . T) ((#1=(-576) #1#) . T) (($ $) . T)) ((((-927 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#2|) |has| |#2| (-1068)) (((-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068)))) @@ -2921,35 +2921,35 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) -((((-2 (|:| -4282 (-1195)) (|:| -4352 (-52)))) . T)) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) +((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) ((((-576) |#3|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -4282 (-1195)) (|:| -4352 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -4300 (-1195)) (|:| -4391 #0#))) . T)) (|has| |#1| (-360)) ((((-576)) . T)) ((((-874)) . 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T)) -((($) -2835 (|has| |#1| (-238)) (|has| |#1| (-237)))) +((($) -2781 (|has| |#1| (-238)) (|has| |#1| (-237)))) ((((-576)) . T)) (((|#2|) . T) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((|#1|) . T) (($) . T) (((-576)) . T)) -(-2835 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3014,7 +3014,7 @@ (|has| |#2| (-1041)) ((($) . T)) (|has| |#1| (-926)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3024,32 +3024,32 @@ (|has| |#1| (-374)) ((((-927 |#1|)) . T)) ((($) . T) (((-576)) . T) ((|#1|) . T) (((-419 (-576))) . 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T)) -(((#0=(-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) #0#) |has| (-2 (|:| -4282 (-1195)) (|:| -4352 (-52))) (-319 (-2 (|:| -4282 (-1195)) (|:| -4352 (-52)))))) +(((#0=(-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) #0#) |has| (-2 (|:| -4300 (-1195)) (|:| -4391 (-52))) (-319 (-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))))) ((((-1177)) . T)) (|has| |#1| (-926)) (|has| |#2| (-374)) (((|#1|) . T) (($) . T) (((-576)) . T)) -(-2835 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2781 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-874)) . T)) (((|#1|) . T)) @@ -3066,11 +3066,11 @@ (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -(-2835 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) (|has| |#1| (-38 (-419 (-576)))) (-12 (|has| |#1| (-557)) (|has| |#1| (-840))) ((((-874)) . T)) -((((-1195)) -2835 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))))) +((((-1195)) -2781 (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))))) (|has| |#1| (-374)) ((((-1195)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195))))) (|has| |#1| (-374)) @@ -3083,11 +3083,11 @@ ((((-576) |#1|) . T)) ((((-1195)) |has| |#1| (-915 (-1195)))) (((|#1|) . T)) -(-2835 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) +(-2781 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360))) (((|#2|) |has| |#1| (-374))) (((|#2|) |has| |#1| (-374))) ((((-576)) . T) (($) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) @@ -3119,34 +3119,34 @@ (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#2|) |has| |#1| (-374))) ((((-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-390)))) (((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-576))))) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) (((|#1|) . T)) ((($) . T) (((-576)) . T) ((|#2|) . T)) (|has| |#1| (-374)) (((|#3|) . T)) ((((-1177)) . T) (((-518)) . T) (((-227)) . T) (((-576)) . T)) (((|#1|) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-568)) (((|#4| |#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) -(-2835 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2781 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1068)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) -((((-2 (|:| -4282 (-1177)) (|:| -4352 |#1|))) . T)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4300 (-1177)) (|:| -4391 |#1|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (|has| |#1| (-38 (-419 (-576)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-419 (-576)))) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) ((($) . T)) (|has| |#1| (-148)) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-379))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-379))) (|has| |#1| (-148)) ((($) . T)) ((((-593 |#1|)) . T)) @@ -3162,7 +3162,7 @@ ((((-419 (-576))) |has| |#2| (-1057 (-576))) (((-576)) |has| |#2| (-1057 (-576))) (((-1195)) |has| |#2| (-1057 (-1195))) ((|#2|) . T)) (((#0=(-419 |#2|) #0#) . T) ((#1=(-419 (-576)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2835 (|has| |#1| (-146)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-360))) (|has| |#1| (-148)) ((((-874)) . T)) ((($) . T)) @@ -3182,15 +3182,15 @@ ((((-419 |#2|)) . T)) ((((-874)) . T)) (((|#1|) . T)) -((((-1195)) -2835 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) -(-2835 (|has| |#1| (-102)) (|has| |#1| (-1119))) +((((-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195))))) +(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) (|has| |#1| (-803)) (|has| |#1| (-803)) ((((-874)) . T)) ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-874)) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3199,7 +3199,7 @@ ((((-1272 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-419 (-576))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-568)) (((-419 (-576))) |has| |#1| (-568))) ((((-874)) . T)) -(-2835 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068)))) +(-2781 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068)))) ((((-874)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3212,10 +3212,10 @@ ((((-874)) . T)) (((|#2|) . T)) ((((-576)) . T)) -((((-1195)) -2835 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) +((((-1195)) -2781 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) ((((-874)) . T)) ((((-576)) . T)) -(-2835 (|has| |#2| (-805)) (|has| |#2| (-862))) +(-2781 (|has| |#2| (-805)) (|has| |#2| (-862))) ((((-171 (-390))) . T) (((-227)) . T) (((-390)) . T)) ((((-874)) . T)) ((((-874)) . T)) @@ -3227,10 +3227,10 @@ (((|#1|) . T) (($) . T) (((-419 (-576))) . T)) (|has| |#1| (-374)) (|has| |#1| (-374)) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) ((((-576) $) . T) (((-656 (-576)) $) . T)) -(-2835 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)) (|has| |#1| (-1131)) (|has| |#1| (-1119))) +(-2781 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-485)) (|has| |#1| (-738)) (|has| |#1| (-915 (-1195))) (|has| |#1| (-1068)) (|has| |#1| (-1131)) (|has| |#1| (-1119))) (|has| |#1| (-1171)) ((((-927 |#1|)) . T) (((-419 (-576))) . T) (($) . T)) ((($) . T)) @@ -3240,20 +3240,20 @@ (((#0=(-117 |#1|) $) |has| #0# (-296 #0# #0#))) (((|#1|) |has| |#1| (-174))) ((((-326 |#1|)) . T) (((-576)) . T)) -(-2835 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2781 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) ((((-874)) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-874)) . T)) -((((-1195)) -2835 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((((-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) (((|#1|) |has| |#1| (-319 |#1|))) ((((-576) |#1|) . T) (((-1253 (-576)) $) . T)) (((|#1| |#2|) . T)) ((((-1195) |#1|) . T)) -(((|#1|) -2835 (|has| |#1| (-174)) (|has| |#1| (-374)))) +(((|#1|) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)))) (((|#1|) . T)) ((($ (-1195)) . T)) -(((|#1|) -2835 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-1068)))) +(((|#1|) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-1068)))) ((((-576)) . T) (((-419 (-576))) . T)) (((|#1|) . T)) (|has| |#1| (-568)) @@ -3262,15 +3262,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-419 |#2|)) . T) (((-419 (-576))) . T) (($) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) (|has| |#1| (-374)) (|has| |#1| (-568)) ((($) . T)) (|has| |#1| (-1119)) ((((-792 |#1| (-876 |#2|))) |has| (-792 |#1| (-876 |#2|)) (-319 (-792 |#1| (-876 |#2|))))) -(-2835 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +(-2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3279,17 +3279,17 @@ (((|#1| (-783)) . T)) (|has| |#1| (-238)) (((|#1| (-543 (-1107 (-1195)))) . T)) -((($) -2835 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))))) +((($) -2781 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))))) ((((-593 |#1|)) . T) (((-419 (-576))) . T) (($) . T) (((-576)) . T)) ((((-576)) . T) (((-419 (-576))) . T) (($) . T)) -((((-2 (|:| -4282 (-1177)) (|:| -4352 (-52)))) . T)) +((((-2 (|:| -4300 (-1177)) (|:| -4391 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-576)) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (|has| |#2| (-374)) ((((-874)) . T)) ((((-874)) . T)) -(-2835 (|has| |#3| (-805)) (|has| |#3| (-862))) +(-2781 (|has| |#3| (-805)) (|has| |#3| (-862))) ((((-874)) . T)) ((((-1139)) . T) (((-874)) . T)) ((((-548)) . T) (((-874)) . T)) @@ -3300,14 +3300,14 @@ ((((-576)) . T)) (((|#3|) . T)) ((((-874)) . T)) -(-2835 (|has| |#1| (-317)) (|has| |#1| (-374)) (|has| |#1| (-360))) -((((-576)) . 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T) (($) -2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((-876 |#1|)) . T)) +((((-1144 |#1| |#2|)) . T) ((|#2|) . T) (($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576))))) (((-576)) . T)) +((((-1191 |#1|)) . T) (((-576)) . T) (($) -2781 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) (((-1101)) . T) ((|#1|) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576)))))) +(-2781 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-568)) (|has| |#1| (-1068))) (((#0=(-593 |#1|) #0#) . T) (($ $) . T) ((#1=(-419 (-576)) #1#) . T)) ((($ $) . T) ((#0=(-419 (-576)) #0#) . T)) -((((-1144 |#1| (-1195))) . T) (((-576)) . T) (((-1107 (-1195))) . T) (($) -2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576))))) (((-1195)) . T)) +((((-1144 |#1| (-1195))) . T) (((-576)) . T) (((-1107 (-1195))) . T) (($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576))))) (((-1195)) . T)) (((|#1|) |has| |#1| (-174))) (((|#1| (-1286 |#1|) (-1286 |#1|)) . T)) ((((-593 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) @@ -3317,13 +3317,13 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-419 (-576))) . T)) -(((|#2|) |has| |#2| (-6 (-4463 "*")))) +(((|#2|) |has| |#2| (-6 (-4464 "*")))) (((|#1|) . T)) ((((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((|#1|) . T) (((-576)) . T)) (((|#1|) . T)) ((((-874)) . T)) ((((-304 |#3|)) . T)) -(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . T) (($ $) -2835 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) +(((#0=(-419 (-576)) #0#) |has| |#2| (-38 (-419 (-576)))) ((|#2| |#2|) . T) (($ $) -2781 (|has| |#2| (-174)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) @@ -3331,29 +3331,29 @@ (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) (((|#1|) . T) (((-419 (-576))) . T) (($) . T)) -((($ $) -2835 (|has| |#1| (-174)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1| |#1|) . T) ((#0=(-419 (-576)) #0#) |has| |#1| (-38 (-419 (-576))))) -((($ $) -2835 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1| |#1|) . 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T)) (((|#1|) |has| |#1| (-174))) -(-2835 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) +(-2781 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-1068))) (((|#1|) . T)) (((|#1|) . T)) -(-2835 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2781 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) (((|#1|) . T)) ((((-419 (-576))) . T) (((-576)) . T) (($) . T)) ((((-548)) . T)) ((((-874)) . T)) -((($) -2835 (-12 (|has| |#3| (-238)) (|has| |#3| (-1068))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1068))))) +((($) -2781 (-12 (|has| |#3| (-238)) (|has| |#3| (-1068))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1068))))) ((((-576)) . 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T)) @@ -3421,11 +3421,11 @@ ((($) |has| |#1| (-379))) (|has| |#2| (-832)) (|has| |#2| (-832)) -((((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) (((-419 (-576))) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2|) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) +((((-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2|) |has| |#1| (-374)) (($) . T) ((|#1|) . T)) ((($ (-1195)) |has| |#1| (-915 (-1195)))) (((|#1|) . T) (((-576)) |has| |#1| (-1057 (-576))) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576))))) -((($) -2835 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360)))) -(((|#1|) . T) (((-419 (-576))) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) . T)) +((($) -2781 (-12 (|has| |#1| (-238)) (|has| |#1| (-374))) (-12 (|has| |#1| (-237)) (|has| |#1| (-374))) (|has| |#1| (-360)))) +(((|#1|) . T) (((-419 (-576))) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) ((((-576)) |has| |#1| (-899 (-576))) (((-390)) |has| |#1| (-899 (-390)))) (((|#1|) . T)) @@ -3440,7 +3440,7 @@ (|has| |#1| (-374)) (|has| |#1| (-374)) (((|#4|) -12 (|has| |#4| (-319 |#4|)) (|has| |#4| (-1119)))) -(((|#2|) -2835 (|has| |#2| (-6 (-4463 "*"))) (|has| |#2| (-174)))) +(((|#2|) -2781 (|has| |#2| (-6 (-4464 "*"))) (|has| |#2| (-174)))) (((|#2|) . T)) (|has| |#1| (-374)) (((|#2|) . T)) @@ -3454,12 +3454,12 @@ (((|#2| (-783)) . T)) ((((-1195)) . T)) ((((-882 |#1|)) . T)) -(-2835 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) -(-2835 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-805)) (|has| |#3| (-1068))) +(-2781 (|has| |#3| (-21)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) +(-2781 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-132)) (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-805)) (|has| |#3| (-1068))) ((((-874)) . T)) (((|#1|) . T)) -(-2835 (|has| |#2| (-805)) (|has| |#2| (-862))) -(-2835 (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (-12 (|has| |#1| (-862)) (|has| |#2| (-862)))) +(-2781 (|has| |#2| (-805)) (|has| |#2| (-862))) +(-2781 (-12 (|has| |#1| (-805)) (|has| |#2| (-805))) (-12 (|has| |#1| (-862)) (|has| |#2| (-862)))) ((((-882 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-379)) @@ -3477,7 +3477,7 @@ (((|#1|) . T)) ((((-874)) . T)) ((($) . T) ((|#2|) . T) (((-419 (-576))) . T) (((-576)) |has| |#2| (-651 (-576)))) -(-2835 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| |#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) @@ -3486,7 +3486,7 @@ (((|#1|) . T)) ((((-874)) . T)) (|has| |#2| (-926)) -((((-2 (|:| -4282 (-1195)) (|:| -4352 (-52)))) . T)) +((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) ((((-548)) |has| |#2| (-626 (-548))) (((-905 (-390))) |has| |#2| (-626 (-905 (-390)))) (((-905 (-576))) |has| |#2| (-626 (-905 (-576))))) ((((-874)) . T)) ((((-874)) . T)) @@ -3496,7 +3496,7 @@ ((((-1191 |#1|)) . T) (((-874)) . T)) ((((-874)) . T)) ((((-419 (-576))) |has| |#2| (-1057 (-419 (-576)))) (((-576)) |has| |#2| (-1057 (-576))) ((|#2|) . T) (((-876 |#1|)) . T)) -((((-1195)) -2835 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195)))) (((-1101)) . T)) +((((-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195)))) (((-1101)) . T)) ((((-117 |#1|)) . T) (($) . T) (((-419 (-576))) . T)) ((((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) (((-576)) |has| |#1| (-1057 (-576))) ((|#1|) . T) (((-1195)) . T)) ((((-874)) . T)) @@ -3515,10 +3515,10 @@ ((((-656 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|)))) ((($) . T) (((-576)) . T) (((-1272 |#1| |#2| |#3| |#4|)) . T) (((-419 (-576))) . 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T)) @@ -3532,16 +3532,16 @@ ((((-419 |#2|) |#3|) . T)) ((((-874)) . T)) (((|#1|) . T)) -(-2835 (|has| |#1| (-102)) (|has| |#1| (-1119))) -(((|#2| (-494 (-3485 |#1|) (-783))) . T)) +(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(((|#2| (-494 (-3500 |#1|) (-783))) . T)) ((((-576) |#1|) . T)) ((((-1177)) . T) (((-874)) . T)) (((|#2| |#2|) . T)) (((|#1| (-543 (-1195))) . T)) -(-2835 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2781 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) ((((-576)) . T)) (((|#2|) . T)) -((($) -2835 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))))) +((($) -2781 (-12 (|has| |#2| (-238)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))))) (((|#2|) . T)) ((((-1195)) |has| |#1| (-915 (-1195))) (((-1101)) . T)) (((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) @@ -3550,9 +3550,9 @@ ((($) . T) (((-419 (-576))) . T)) ((($) . T)) ((($) . T)) -(-2835 (|has| |#1| (-862)) (|has| |#1| (-1119))) +(-2781 (|has| |#1| (-862)) (|has| |#1| (-1119))) (((|#1|) . T)) -((($) -2835 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2781 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-874)) . T)) ((((-145)) . T)) (((|#1|) . T) (((-419 (-576))) . T)) @@ -3561,7 +3561,7 @@ ((((-874)) . T)) (((|#1|) . T)) (|has| |#1| (-1171)) -((($ (-1195)) -2835 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) +((($ (-1195)) -2781 (|has| (-419 |#2|) (-915 (-1195))) (|has| (-419 |#2|) (-917 (-1195))))) (((|#1|) . T)) (((|#1| (-543 (-876 |#2|)) (-876 |#2|) (-792 |#1| (-876 |#2|))) . T)) ((((-419 $) (-419 $)) |has| |#1| (-568)) (($ $) . T) ((|#1| |#1|) . T)) @@ -3586,44 +3586,44 @@ (|has| |#1| (-1119)) (|has| |#1| (-1119)) (|has| |#2| (-374)) -(((|#1|) . T) (($) -2835 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) +(((|#1|) . T) (($) -2781 (|has| |#1| (-300)) (|has| |#1| (-374))) (((-419 (-576))) |has| |#1| (-374))) (|has| |#1| (-374)) (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576)))) -((($) -2835 (|has| |#2| (-238)) (|has| |#2| (-237)))) +((($) -2781 (|has| |#2| (-238)) (|has| |#2| (-237)))) ((((-576)) . T)) (|has| |#1| (-1119)) -((($ (-1195)) -2835 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((($ (-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) ((((-1195)) -12 (|has| |#4| (-915 (-1195))) (|has| |#4| (-1068)))) ((((-1195)) -12 (|has| |#3| (-915 (-1195))) (|has| |#3| (-1068)))) (((|#1|) . T)) (|has| |#1| (-238)) -(((|#2| (-245 (-3485 |#1|) (-783))) . T)) +(((|#2| (-245 (-3500 |#1|) (-783))) . 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T) (((-576)) |has| |#1| (-1057 (-576))) (((-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) (((-1195)) . T)) ((($) . T)) @@ -3749,12 +3749,12 @@ (((#0=(-1272 |#1| |#2| |#3| |#4|)) |has| #0# (-319 #0#))) ((($) . T)) (((|#1|) . T)) -((($ $) -2835 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((#0=(-419 (-576)) #0#) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2| |#2|) |has| |#1| (-374)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -2835 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((#0=(-419 (-576)) #0#) -2835 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374)))) +((($ $) -2781 (|has| |#1| (-174)) (|has| |#1| (-374)) (|has| |#1| (-568))) ((#0=(-419 (-576)) #0#) -2781 (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-374))) ((|#2| |#2|) |has| |#1| (-374)) ((|#1| |#1|) . T)) +(((|#1| |#1|) . 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T)) -(-2835 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) -(-2835 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-805)) (|has| |#2| (-805)))) +(-2781 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-374)) (|has| |#2| (-805)) (|has| |#2| (-1068))) +(-2781 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-132)) (|has| |#2| (-132))) (-12 (|has| |#1| (-805)) (|has| |#2| (-805)))) ((((-1278 |#1| |#2| |#3|)) |has| |#1| (-374))) ((($) . T) (((-882 |#1|)) . T) (((-419 (-576))) . T)) ((((-1278 |#1| |#2| |#3|)) |has| |#1| (-374))) @@ -3797,15 +3797,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-419 |#2|)) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-360))) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-548)) |has| |#1| (-626 (-548)))) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-548)) |has| |#1| (-626 (-548)))) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-548)) |has| |#1| (-626 (-548)))) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-419 (-576)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-419 (-576))) . T) (($) . T)) @@ -3825,7 +3825,7 @@ ((((-874)) . T)) ((((-874)) . T)) ((((-874)) . T)) -(-2835 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-2781 (|has| |#1| (-238)) (|has| |#1| (-237))) (((|#1|) . T) (((-874)) . T) (((-1200)) . T)) ((((-1200)) . T)) ((((-874)) . T)) @@ -3834,21 +3834,21 @@ ((($) . T) (((-576)) . T) (((-117 |#1|)) . T) (((-419 (-576))) . T)) (((|#1|) -12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (((|#1| (-543 (-876 |#2|)) (-876 |#2|) (-792 |#1| (-876 |#2|))) . T)) -((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2835 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) +((((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) |has| |#2| (-174)) (($) -2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-419 (-576))) |has| |#2| (-38 (-419 (-576)))) ((|#2|) . T) (((-576)) |has| |#2| (-651 (-576)))) ((($) . T) (((-576)) . T)) -((($) -2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((((-1123)) . T)) ((((-874)) . T)) ((((-1200)) . T) (((-874)) . T)) ((((-1200)) . T) (((-874)) . T)) ((((-1200)) . T)) ((((-1200)) . T)) -((($) -2835 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2781 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) ((($) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) ((($) . T) (((-576)) . T)) -((($) -2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) +((($) -2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#1| |#2| (-245 |#1| |#2|) (-245 |#1| |#2|)) . T)) (|has| |#2| (-926)) ((((-874)) . T)) @@ -3864,7 +3864,7 @@ (((|#1| |#1|) |has| |#1| (-174))) ((((-711)) . T)) ((((-711)) . T)) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) ((((-1200)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1200)) . T)) @@ -3875,20 +3875,20 @@ (((|#1|) |has| |#1| (-174)) (((-419 (-576))) |has| |#1| (-568)) (($) |has| |#1| (-568))) ((((-419 (-576))) . T) (($) . T)) (((|#1| (-576)) . T)) -((($ (-1195)) -2835 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195)))) (($ (-1101)) . T)) +((($ (-1195)) -2781 (|has| |#1| (-915 (-1195))) (|has| |#1| (-917 (-1195)))) (($ (-1101)) . T)) ((((-419 (-576))) . T) (((-576)) . T) (($) . T)) (((|#1|) |has| |#1| (-174))) ((((-1200)) . T)) ((((-1200)) . T)) ((((-1200)) . T)) ((((-1200)) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-360))) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-1200)) . T)) ((((-1200)) . T)) (|has| |#1| (-374)) (|has| |#1| (-374)) -(-2835 (|has| |#1| (-174)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-174)) (|has| |#1| (-568))) (((|#1| (-576)) . T)) (((|#1| (-419 (-576))) . T)) (((|#1| (-783)) . T)) @@ -3896,24 +3896,24 @@ (((|#1| (-543 |#2|) |#2|) . T)) ((((-576) |#1|) . T)) ((((-576) |#1|) . T)) -(-2835 (|has| |#1| (-102)) (|has| |#1| (-1119))) -(-2835 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237))) +(-2781 (|has| |#1| (-102)) (|has| |#1| (-1119))) +(-2781 (|has| (-419 |#2|) (-238)) (|has| (-419 |#2|) (-237))) ((((-576) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-905 (-390))) . T) (((-905 (-576))) . T) (((-1195)) . T) (((-548)) . 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T)) (|has| |#2| (-1068)) ((((-1195)) -12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) -(-2835 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-738)) (|has| |#2| (-738)))) +(-2781 (-12 (|has| |#1| (-485)) (|has| |#2| (-485))) (-12 (|has| |#1| (-738)) (|has| |#2| (-738)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-374)) @@ -3946,7 +3946,7 @@ (((|#1| |#2|) . T)) ((((-576)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-576)) . T)) -(-2835 (|has| |#1| (-360)) (|has| |#1| (-379))) +(-2781 (|has| |#1| (-360)) (|has| |#1| (-379))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-419 (-576))) . T) (($) . T) (((-576)) . T)) @@ -3955,11 +3955,11 @@ ((($) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((|#1|) . T) (((-576)) |has| |#1| (-651 (-576)))) ((($) . T) (((-576)) |has| |#1| (-651 (-576))) ((|#1|) . T) (((-419 (-576))) |has| |#1| (-38 (-419 (-576))))) (((|#2|) |has| |#2| (-1119)) (((-576)) -12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) (((-419 (-576))) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119)))) -(-2835 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-2781 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) (((|#1|) . T)) ((((-548)) |has| |#1| (-626 (-548)))) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-862)) (|has| |#1| (-1119)))) ((((-576) $) . T) (((-656 (-576)) $) . T)) ((($) . T) (((-419 (-576))) . T)) (|has| |#1| (-926)) @@ -3971,14 +3971,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-576)) . T)) ((((-1200)) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-568))) -(-2835 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-568))) +(-2781 (|has| |#1| (-21)) (|has| |#1| (-860))) (((|#2|) . T)) -(-2835 (|has| |#1| (-21)) (|has| |#1| (-860))) +(-2781 (|has| |#1| (-21)) (|has| |#1| (-860))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-874)) -2835 (-12 (|has| |#1| (-625 (-874))) (|has| |#2| (-625 (-874)))) (-12 (|has| |#1| (-1119)) (|has| |#2| (-1119))))) +((((-874)) -2781 (-12 (|has| |#1| (-625 (-874))) (|has| |#2| (-625 (-874)))) (-12 (|has| |#1| (-1119)) (|has| |#2| (-1119))))) ((((-419 |#2|) |#3|) . T)) ((((-419 (-576))) . T) (($) . T)) (|has| |#1| (-38 (-419 (-576)))) @@ -4002,7 +4002,7 @@ ((((-1200)) . T)) ((((-576)) . T)) (((|#2|) . T)) -((((-1195)) -2835 (-12 (|has| (-1193 |#1| |#2| |#3|) (-915 (-1195))) (|has| |#1| (-374))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))))) +((((-1195)) -2781 (-12 (|has| (-1193 |#1| |#2| |#3|) (-915 (-1195))) (|has| |#1| (-374))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195)))))) ((((-1195)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195))))) ((((-1195)) -12 (|has| |#1| (-15 * (|#1| (-783) |#1|))) (|has| |#1| (-915 (-1195))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4017,11 +4017,11 @@ ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) ((((-1159 |#1| |#2|)) . T)) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) -(((|#2|) . T) (((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) -((((-2 (|:| -4282 (-1195)) (|:| -4352 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) +((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1041)) -(((|#2|) . T) (((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) ((($) . T)) ((((-874)) . T)) ((((-548)) |has| |#2| (-626 (-548))) (((-905 (-576))) |has| |#2| (-626 (-905 (-576)))) (((-905 (-390))) |has| |#2| (-626 (-905 (-390)))) (((-390)) . #0=(|has| |#2| (-1041))) (((-227)) . #0#)) @@ -4030,7 +4030,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576)))) -((((-1195)) -2835 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) +((((-1195)) -2781 (|has| |#2| (-915 (-1195))) (|has| |#2| (-917 (-1195))))) ((((-874)) . T)) (((|#2|) . T)) ((((-874)) . T)) @@ -4040,15 +4040,15 @@ ((((-1193 |#1| |#2| |#3|)) . T)) ((((-1193 |#1| |#2| |#3|)) . T) (((-1186 |#1| |#2| |#3|)) . T)) ((((-874)) . T)) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) ((((-576) |#1|) . T)) ((((-1193 |#1| |#2| |#3|)) |has| |#1| (-374))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-374)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2835 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068))) (($) |has| |#4| (-1068)) (((-576)) -12 (|has| |#4| (-651 (-576))) (|has| |#4| (-1068)))) -(((|#2|) . T) ((|#3|) -2835 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) (($) |has| |#3| (-1068)) (((-576)) -12 (|has| |#3| (-651 (-576))) (|has| |#3| (-1068)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2781 (|has| |#4| (-174)) (|has| |#4| (-374)) (|has| |#4| (-1068))) (($) |has| |#4| (-1068)) (((-576)) -12 (|has| |#4| (-651 (-576))) (|has| |#4| (-1068)))) +(((|#2|) . T) ((|#3|) -2781 (|has| |#3| (-174)) (|has| |#3| (-374)) (|has| |#3| (-1068))) (($) |has| |#3| (-1068)) (((-576)) -12 (|has| |#3| (-651 (-576))) (|has| |#3| (-1068)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -4062,7 +4062,7 @@ ((((-189)) . T) (((-874)) . T)) ((((-874)) . T)) (((|#1|) . T)) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) ((((-130)) . T) (((-874)) . T)) ((((-576) |#1|) . T) (((-1253 (-576)) $) . T)) ((((-130)) . T)) @@ -4071,14 +4071,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) (($ $) . T) (((-576) |#1|) . T)) ((($ $) . T) (((-419 (-576)) |#1|) . T)) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-926))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-464)) (|has| |#1| (-926))) ((($ (-1195)) |has| |#1| (-1068))) -(-2835 (|has| |#1| (-862)) (|has| |#1| (-1119))) +(-2781 (|has| |#1| (-862)) (|has| |#1| (-1119))) ((((-874)) . T)) ((((-874)) . T)) ((((-874)) . T)) (((|#1| (-543 |#2|)) . T)) -((((-2 (|:| -4282 (-1195)) (|:| -4352 (-52)))) . T)) +((((-2 (|:| -4300 (-1195)) (|:| -4391 (-52)))) . T)) ((((-576) (-130)) . T)) (((|#1| (-576)) . T)) (((|#1| (-419 (-576))) . T)) @@ -4093,8 +4093,8 @@ ((((-1200)) . T)) ((((-874)) . T) (((-1200)) . T)) ((((-874)) . T) (((-1200)) . T)) -(-2835 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) -(-2835 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) +(-2781 (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) +(-2781 (|has| |#1| (-464)) (|has| |#1| (-568)) (|has| |#1| (-926))) ((($) . T)) (((|#2| (-543 (-876 |#1|))) . T)) ((((-1200)) . T)) @@ -4109,7 +4109,7 @@ ((((-1200)) . T)) ((((-874)) . T) (((-1200)) . T)) ((((-1200)) . T)) -((((-874)) -2835 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) +((((-874)) -2781 (|has| |#1| (-625 (-874))) (|has| |#1| (-1119)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1177) |#1|) . T)) @@ -4117,7 +4117,7 @@ ((((-419 |#2|)) . T)) (|has| |#1| (-568)) (|has| |#1| (-568)) -((((-2 (|:| -4282 |#1|) (|:| -4352 |#2|))) . T)) +((((-2 (|:| -4300 |#1|) (|:| -4391 |#2|))) . T)) (((|#2| (-783)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-419 (-576))) . T)) @@ -4127,14 +4127,14 @@ ((((-576)) . T) (($) . T)) (((|#2| $) |has| |#2| (-296 |#2| |#2|))) (((|#1| (-656 |#1|)) |has| |#1| (-860))) -(-2835 (|has| |#1| (-238)) (|has| |#1| (-360))) -(-2835 (|has| |#1| (-374)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-238)) (|has| |#1| (-360))) +(-2781 (|has| |#1| (-374)) (|has| |#1| (-360))) ((((-1282 |#1|)) . T) (((-576)) . T) ((|#2|) . T) (((-419 (-576))) |has| |#2| (-1057 (-419 (-576))))) (|has| |#1| (-1119)) (((|#1|) . T)) ((((-419 (-576))) . T) (($) . T)) -((((-1282 |#1|)) . T) (((-576)) . T) (($) -2835 (|has| |#2| (-374)) (|has| |#2| (-464)) (|has| |#2| (-568)) (|has| |#2| (-926))) (((-1101)) . T) ((|#2|) . T) (((-419 (-576))) -2835 (|has| |#2| (-38 (-419 (-576)))) (|has| |#2| (-1057 (-419 (-576)))))) -((((-1018 |#1|)) . T) ((|#1|) . T) (((-576)) -2835 (|has| (-1018 |#1|) (-1057 (-576))) (|has| |#1| (-1057 (-576)))) (((-419 (-576))) -2835 (|has| (-1018 |#1|) (-1057 (-419 (-576)))) (|has| |#1| (-1057 (-419 (-576)))))) +((((-1282 |#1|)) . T) (((-576)) . 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197595) ((-1186 . -388) 197547) ((-1106 . -1077) T) ((-449 . -102) T) ((-185 . -1119) T) ((-258 . -34) T) ((-257 . -34) T) ((-794 . -1077) T) ((-792 . -1077) T) ((-743 . -915) 197524) ((-466 . -1077) T) ((-59 . -501) 197508) ((-1053 . -1075) 197482) ((-531 . -501) 197466) ((-528 . -501) 197450) ((-509 . -501) 197434) ((-508 . -501) 197418) ((-250 . -526) 197351) ((-1053 . -111) 197318) ((-1193 . -915) 197231) ((-1192 . -915) 197137) ((-682 . -1131) T) ((-1186 . -915) 196970) ((-657 . -93) T) ((-1145 . -915) 196954) ((-365 . -1171) T) ((-332 . -1075) 196936) ((-31 . -502) 196917) ((-258 . -806) 196896) ((-258 . -805) 196875) ((-257 . -806) 196854) ((-257 . -805) 196833) ((-31 . -625) 196799) ((-50 . -1077) T) ((-258 . -738) 196777) ((-257 . -738) 196755) ((-1230 . -1119) T) ((-682 . -23) T) ((-593 . -1077) T) ((-530 . -1077) T) ((-390 . -1075) 196720) ((-332 . -111) 196695) ((-73 . -394) T) ((-73 . -407) T) ((-1043 . -38) 196632) ((-706 . -412) 196614) ((-99 . -102) T) ((-723 . -1119) 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T) ((-839 . -1068) T) ((-724 . -966) 193871) ((-713 . -862) T) ((-486 . -625) 193853) ((-1272 . -1070) 193758) ((-592 . -658) 193730) ((-576 . -658) 193702) ((-507 . -658) 193652) ((-839 . -238) 193631) ((-135 . -862) T) ((-1272 . -652) 193523) ((-670 . -1119) T) ((-1208 . -616) 193502) ((-562 . -1212) 193481) ((-347 . -1119) T) ((-329 . -374) 193460) ((-419 . -148) 193439) ((-419 . -146) 193418) ((-981 . -1131) 193317) ((-245 . -915) 193249) ((-827 . -1131) 193227) ((-666 . -864) 193211) ((-491 . -616) 193190) ((-536 . -1236) T) ((-562 . -107) 193140) ((-1023 . -388) 193122) ((-1023 . -349) 193104) ((-1195 . -625) 193086) ((-97 . -1119) T) ((-981 . -23) 192897) ((-489 . -21) T) ((-489 . -25) T) ((-827 . -23) 192749) ((-1195 . -626) 192671) ((-59 . -19) 192655) ((-1191 . -738) T) ((-1144 . -738) T) ((-1106 . -1119) T) ((-528 . -19) 192639) ((-508 . -19) 192623) ((-59 . -616) 192600) ((-1022 . -237) 192537) ((-918 . -102) 192487) ((-866 . -738) T) ((-794 . -1119) T) ((-528 . -616) 192464) ((-508 . -616) 192441) ((-792 . -1119) T) ((-792 . -1084) 192408) ((-473 . -1119) T) ((-466 . -1119) T) ((-598 . -729) 192383) ((-661 . -1119) T) ((-1278 . -47) 192360) ((-1272 . -102) T) ((-1271 . -47) 192330) ((-1250 . -47) 192307) ((-1230 . -174) 192258) ((-1192 . -317) 192237) ((-1186 . -317) 192216) ((-1115 . -628) 192197) ((-1109 . -628) 192178) ((-1099 . -568) 192129) ((-1099 . -1240) 192080) ((-1023 . -915) NIL) ((-1092 . -628) 192061) ((-682 . -132) T) ((-639 . -1131) T) ((-1085 . -628) 192042) ((-1055 . -628) 192023) ((-1038 . -628) 192004) ((-726 . -1075) 191974) ((-711 . -658) 191924) ((-284 . -1119) T) ((-85 . -453) T) ((-85 . -407) T) ((-724 . -909) 191827) ((-723 . -174) T) ((-50 . -1119) T) ((-607 . -47) 191804) ((-227 . -660) 191769) ((-593 . -1119) T) ((-530 . -1119) T) ((-499 . -832) T) ((-499 . -937) T) ((-370 . -1240) T) ((-364 . -1240) T) ((-356 . -1240) T) ((-329 . -1131) T) ((-326 . -1070) 191679) ((-323 . -1070) 191608) ((-108 . -1240) T) ((-638 . -628) 191589) ((-370 . -568) T) ((-219 . -937) T) ((-219 . -832) T) ((-326 . -652) 191499) ((-323 . -652) 191428) ((-364 . -568) T) ((-356 . -568) T) ((-495 . -628) 191409) ((-108 . -568) T) ((-670 . -729) 191379) ((-1186 . -1041) NIL) ((-220 . -628) 191360) ((-329 . -23) T) ((-67 . -1236) T) ((-1019 . -625) 191292) ((-706 . -272) 191274) ((-706 . -232) 191256) ((-1315 . -1171) T) ((-726 . -111) 191221) ((-1310 . -21) T) ((-656 . -34) T) ((-250 . -501) 191205) ((-1310 . -25) T) ((-1308 . -132) T) ((-1306 . -132) T) ((-1299 . -102) T) ((-1121 . -1117) 191189) ((-173 . -1119) T) ((-1282 . -625) 191155) ((-1278 . -1236) T) ((-1271 . -1236) T) ((-1271 . -1057) 191090) ((-1250 . -1236) T) ((-969 . -926) 191069) ((-1250 . -899) NIL) ((-1250 . -897) 191021) ((-1250 . -1057) 190987) ((-527 . -628) 190971) ((-1230 . -526) 190938) ((-1208 . -626) NIL) ((-1208 . -625) 190920) ((-493 . -926) 190899) ((-1161 . -1142) 190844) ((-1106 . -729) 190693) ((-1081 . -660) 190665) ((-969 . -660) 190554) ((-794 . -729) 190383) ((-609 . -502) 190364) ((-597 . -502) 190345) ((-609 . -625) 190311) ((-597 . -625) 190277) ((-548 . -625) 190259) ((-591 . -1236) T) ((-548 . -626) 190240) ((-792 . -729) 190089) ((-1096 . -102) T) ((-635 . -658) 190061) ((-392 . -25) T) ((-392 . -21) T) ((-493 . -660) 189950) ((-473 . -729) 189921) ((-466 . -729) 189770) ((-1006 . -102) T) ((-1065 . -1229) 189699) ((-918 . -319) 189637) ((-888 . -93) T) ((-749 . -102) T) ((-118 . -658) 189567) ((-617 . -628) 189549) ((-726 . -628) 189503) ((-693 . -93) T) ((-543 . -25) T) ((-688 . -93) T) ((-676 . -625) 189485) ((-657 . -502) 189466) ((-657 . -625) 189419) ((-142 . -102) T) ((-44 . -132) T) ((-608 . -1236) T) ((-607 . -1236) T) ((-354 . -1077) T) ((-299 . -1131) T) ((-490 . -93) T) ((-419 . -237) 189370) ((-366 . -625) 189352) ((-363 . -625) 189334) ((-355 . -625) 189316) ((-273 . -626) 189064) ((-273 . -625) 189046) ((-253 . -625) 189028) ((-253 . -626) 188889) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1160 . -625) 188871) ((-1139 . -652) 188858) ((-1139 . -1070) 188845) ((-831 . -738) T) ((-831 . -869) T) ((-614 . -298) 188822) ((-593 . -729) 188787) ((-491 . -626) NIL) ((-491 . -625) 188769) ((-530 . -729) 188714) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-927 . -625) 188696) ((-927 . -626) 188678) ((-398 . -738) T) ((-884 . -1075) 188630) ((-884 . -111) 188568) ((-726 . -1068) T) ((-724 . -1262) 188552) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 188484) ((-390 . -807) T) ((-169 . -1236) T) ((-225 . -1119) T) ((-390 . -804) T) ((-59 . -626) 188445) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -625) 188357) ((-227 . -738) T) ((-528 . -626) 188318) ((-528 . -625) 188230) ((-509 . -625) 188162) ((-508 . -626) 188123) ((-508 . -625) 188035) ((-1099 . -374) 187986) ((-40 . -423) 187963) ((-77 . -1236) T) ((-883 . -926) NIL) ((-370 . -339) 187947) ((-370 . -374) T) ((-364 . -339) 187931) ((-364 . -374) T) ((-356 . -339) 187915) ((-356 . -374) T) ((-326 . -294) 187894) ((-108 . -374) T) ((-70 . -1236) T) ((-1250 . -349) 187846) ((-883 . -660) 187791) ((-1250 . -388) 187743) ((-981 . -132) 187598) ((-827 . -132) 187469) ((-975 . -663) 187453) ((-1106 . -174) 187364) ((-975 . -384) 187348) ((-1081 . -806) T) ((-1081 . -803) T) ((-884 . -628) 187246) ((-794 . -174) 187137) ((-792 . -174) 187048) ((-828 . -47) 187010) ((-1081 . -738) T) ((-337 . -501) 186994) ((-969 . -738) T) ((-1299 . -319) 186932) ((-1278 . -915) 186845) ((-466 . -174) 186756) ((-250 . -296) 186708) ((-1271 . -915) 186614) ((-1270 . -1075) 186449) ((-1250 . -915) 186282) ((-493 . -738) T) ((-1249 . -1075) 186090) ((-1230 . -300) 186069) ((-1205 . -1236) T) ((-1202 . -379) T) ((-1201 . -379) T) ((-1165 . -152) 186053) ((-1139 . -102) T) ((-1137 . -1119) T) ((-1099 . -23) T) ((-1099 . -1131) T) ((-1094 . -102) T) ((-1076 . -625) 186020) ((-1022 . -421) 185992) ((-944 . -972) T) ((-749 . -319) 185930) ((-75 . -1236) T) ((-676 . -393) 185902) ((-171 . -926) 185855) ((-30 . -972) T) ((-112 . -856) T) ((-1 . -625) 185837) ((-1018 . -909) 185758) ((-129 . -663) 185740) ((-50 . -632) 185724) ((-706 . -658) 185659) ((-607 . -915) 185572) ((-450 . -102) T) ((-129 . -384) 185554) ((-142 . -319) NIL) ((-884 . -1068) T) ((-845 . -862) 185533) ((-81 . -1236) T) ((-723 . -300) T) ((-40 . -1077) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 185515) ((-171 . -660) 185389) ((-519 . -625) 185371) ((-362 . -148) 185353) ((-362 . -146) T) ((-370 . -1131) T) ((-364 . -1131) T) ((-356 . -1131) T) ((-1023 . -317) T) ((-931 . -317) T) ((-884 . -248) T) ((-108 . -1131) T) ((-884 . -238) 185332) ((-1270 . -111) 185153) ((-1249 . -111) 184942) ((-250 . -1274) 184926) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 184913) ((-323 . -319) 184854) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1023 . -1041) T) ((-31 . -628) 184835) ((-108 . -23) T) ((-666 . -1070) 184819) ((-250 . -616) 184796) ((-343 . -1119) T) ((-666 . -652) 184766) ((-1272 . -38) 184658) ((-1259 . -926) 184637) ((-112 . -1119) T) ((-828 . -1236) T) ((-425 . -1236) T) ((-1054 . -102) T) ((-1259 . -660) 184526) ((-883 . -806) NIL) ((-867 . -660) 184500) ((-883 . -803) NIL) ((-828 . -899) NIL) ((-883 . -738) T) ((-1106 . -526) 184373) ((-794 . -526) 184320) ((-792 . -526) 184272) ((-583 . -660) 184259) ((-828 . -1057) 184087) ((-466 . -526) 184030) ((-400 . -401) T) ((-1270 . -628) 183843) ((-1249 . -628) 183591) ((-60 . -1236) T) ((-633 . -862) 183570) ((-512 . -673) T) ((-1165 . -995) 183539) ((-1043 . -658) 183476) ((-1022 . -464) T) ((-711 . -860) T) ((-522 . -804) T) ((-486 . -1075) 183311) ((-512 . -113) T) ((-354 . -1119) T) ((-323 . -1171) NIL) ((-299 . -132) T) ((-406 . -1119) T) ((-882 . -1077) T) ((-706 . -381) 183278) ((-365 . -658) 183208) ((-225 . -632) 183185) ((-337 . -296) 183137) ((-486 . -111) 182958) ((-1270 . -1068) T) ((-1249 . -1068) T) ((-828 . -388) 182942) ((-836 . -1236) T) ((-171 . -738) T) ((-1301 . -1236) T) ((-666 . -102) T) ((-1270 . -248) 182921) ((-1270 . -238) 182873) ((-1249 . -238) 182778) ((-1249 . -248) 182757) ((-1022 . -414) NIL) ((-682 . -651) 182705) ((-326 . -38) 182615) ((-323 . -38) 182544) ((-69 . -625) 182526) ((-329 . -505) 182492) ((-48 . -658) 182442) ((-1208 . -298) 182421) ((-1244 . -862) T) ((-1132 . -1131) 182399) ((-83 . -1236) T) ((-61 . -625) 182381) ((-491 . -298) 182360) ((-1301 . -1057) 182337) ((-1183 . -1119) T) ((-1132 . -23) 182189) ((-828 . -915) 182125) ((-1259 . -738) T) ((-1121 . -1236) T) ((-486 . -628) 181951) ((-362 . -237) T) ((-1106 . -300) 181882) ((-983 . -1119) T) ((-906 . -102) T) ((-794 . -300) 181793) ((-337 . -19) 181777) ((-59 . -298) 181754) ((-792 . -300) 181685) ((-867 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 181662) ((-337 . -616) 181639) ((-508 . -298) 181616) ((-466 . -300) 181547) ((-1054 . -319) 181398) ((-888 . -502) 181379) ((-888 . -625) 181345) ((-693 . -502) 181326) ((-583 . -738) T) ((-688 . -502) 181307) ((-693 . -625) 181257) ((-688 . -625) 181223) ((-674 . -625) 181205) ((-490 . -502) 181186) ((-490 . -625) 181152) ((-250 . -626) 181113) ((-250 . -502) 181090) ((-139 . -502) 181071) ((-138 . -502) 181052) ((-134 . -502) 181033) ((-250 . -625) 180925) ((-215 . -102) T) ((-139 . -625) 180891) ((-138 . -625) 180857) ((-134 . -625) 180823) ((-1166 . -34) T) ((-960 . -1236) T) ((-354 . -729) 180768) ((-682 . -25) T) ((-682 . -21) T) ((-1195 . -628) 180749) ((-341 . -1236) T) ((-486 . -1068) T) ((-647 . -429) 180714) ((-619 . -429) 180679) ((-1139 . -1171) T) ((-1271 . -317) 180658) ((-724 . -1070) 180481) ((-593 . -300) T) ((-530 . -300) T) ((-1250 . -317) 180460) ((-486 . -238) 180412) ((-486 . -248) 180391) ((-451 . -1236) T) ((-724 . -652) 180220) ((-1250 . -1041) NIL) ((-1099 . -132) T) ((-884 . -807) 180199) ((-145 . -102) T) ((-40 . -1119) T) ((-884 . -804) 180178) ((-656 . -1029) 180162) ((-592 . -1077) T) ((-576 . -1077) T) ((-507 . -1077) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 180146) ((-323 . -412) 180107) ((-364 . -132) T) ((-356 . -132) T) ((-1200 . -1119) T) ((-1139 . -38) 180094) ((-1113 . -625) 180061) ((-108 . -132) T) ((-971 . -1119) T) ((-938 . -1119) T) ((-783 . -1119) T) ((-684 . -1119) T) ((-713 . -148) T) ((-117 . -148) T) ((-1308 . -21) T) ((-1308 . -25) T) ((-1306 . -21) T) ((-1306 . -25) T) ((-676 . -1075) 180045) ((-543 . -862) T) ((-512 . -862) T) ((-376 . -1236) T) ((-366 . -1075) 179997) ((-363 . -1075) 179949) ((-355 . -1075) 179901) ((-258 . -1236) T) ((-257 . -1236) T) ((-273 . -1075) 179744) ((-253 . -1075) 179587) ((-676 . -111) 179566) ((-829 . -1240) 179545) ((-559 . -856) T) ((-326 . -917) 179511) ((-366 . -111) 179449) ((-363 . -111) 179387) ((-355 . -111) 179325) ((-273 . -111) 179154) ((-253 . -111) 178983) ((-323 . -917) NIL) ((-635 . -423) 178967) ((-44 . -21) T) ((-44 . -25) T) ((-827 . -651) 178873) ((-829 . -568) 178852) ((-258 . -1057) 178679) ((-257 . -1057) 178506) ((-127 . -120) 178490) ((-927 . -1075) 178455) ((-724 . -102) T) ((-711 . -1077) T) ((-609 . -628) 178436) ((-597 . -628) 178417) ((-548 . -630) 178320) ((-354 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -625) 178302) ((-927 . -111) 178258) ((-40 . -729) 178203) ((-882 . -1119) T) ((-676 . -628) 178180) ((-657 . -628) 178161) ((-366 . -628) 178098) ((-363 . -628) 178035) ((-355 . -628) 177972) ((-559 . -1119) T) ((-337 . -626) 177933) ((-337 . -625) 177845) ((-273 . -628) 177598) ((-253 . -628) 177383) ((-188 . -1236) T) ((-1249 . -804) 177336) ((-1249 . -807) 177289) ((-258 . -388) 177258) ((-257 . -388) 177227) ((-666 . -38) 177197) ((-620 . -34) T) ((-494 . -1131) 177175) ((-487 . -34) T) ((-1132 . -132) 177046) ((-981 . -25) 176857) ((-927 . -628) 176807) ((-886 . -625) 176789) ((-981 . -21) 176744) ((-827 . -25) 176577) ((-827 . -21) 176488) ((-1242 . -379) T) ((-635 . -1077) T) ((-1197 . -568) 176467) ((-1191 . -47) 176444) ((-366 . -1068) T) ((-363 . -1068) T) ((-494 . -23) 176296) ((-355 . -1068) T) ((-273 . -1068) T) ((-253 . -1068) T) ((-1144 . -47) 176268) ((-118 . -1077) T) ((-1053 . -660) 176242) ((-975 . -34) T) ((-366 . -238) 176221) ((-366 . -248) T) ((-363 . -238) 176200) ((-363 . -248) T) ((-355 . -238) 176179) ((-355 . -248) T) ((-273 . -336) 176151) ((-253 . -336) 176108) ((-273 . -238) 176087) ((-1176 . -152) 176071) ((-258 . -915) 176003) ((-257 . -915) 175935) ((-1161 . -909) 175856) ((-1101 . -862) T) ((-1253 . -1236) 175834) ((-426 . -1131) T) ((-1073 . -23) T) ((-1043 . -860) T) ((-927 . -1068) T) ((-332 . -660) 175816) ((-713 . -237) T) ((-682 . -234) 175761) ((-1230 . -1021) 175727) ((-1192 . -937) 175706) ((-1186 . -937) 175685) ((-1186 . -832) NIL) ((-1018 . -1070) 175581) ((-984 . -1236) T) ((-927 . -248) T) ((-829 . -374) 175560) ((-396 . -23) T) ((-128 . -1119) 175538) ((-122 . -1119) 175516) ((-927 . -238) T) ((-129 . -34) T) ((-390 . -660) 175481) ((-1018 . -652) 175429) ((-882 . -729) 175416) ((-1315 . -658) 175388) ((-1065 . -152) 175353) ((-1012 . -1236) T) ((-874 . -1236) T) ((-40 . -174) T) ((-706 . -423) 175335) ((-724 . -319) 175322) ((-848 . -660) 175282) ((-839 . -660) 175256) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 175235) ((-592 . -1119) T) ((-576 . -1119) T) ((-507 . -1119) T) ((-1191 . -1236) T) ((-250 . -298) 175212) ((-1144 . -1236) T) ((-866 . -1236) T) ((-323 . -272) 175173) ((-323 . -232) 175134) ((-1191 . -899) NIL) ((-55 . -1119) T) ((-1144 . -899) 174993) ((-130 . -862) T) ((-1191 . -1057) 174873) ((-1144 . -1057) 174756) ((-185 . -625) 174738) ((-866 . -1057) 174634) ((-794 . -296) 174561) ((-829 . -1131) T) ((-1053 . -738) T) ((-1065 . -995) 174490) ((-614 . -663) 174474) ((-1022 . -909) 174381) ((-1018 . -102) T) ((-829 . -23) T) ((-724 . -1171) 174359) ((-706 . -1077) T) ((-614 . -384) 174343) ((-362 . -464) T) ((-354 . -300) T) ((-1287 . -1119) T) ((-254 . -1119) T) ((-411 . -102) T) ((-299 . -21) T) ((-299 . -25) T) ((-372 . -738) T) ((-722 . -1119) T) ((-711 . -1119) T) ((-372 . -485) T) ((-1230 . -625) 174325) ((-1191 . -388) 174309) ((-1144 . -388) 174293) ((-1043 . -423) 174255) ((-142 . -231) 174237) ((-390 . -806) T) ((-390 . -803) T) ((-882 . -174) T) ((-390 . -738) T) ((-723 . -625) 174219) ((-724 . -38) 174048) ((-1286 . -1284) 174032) ((-362 . -414) T) ((-1286 . -1119) 173982) ((-1209 . -1119) T) ((-592 . -729) 173969) ((-576 . -729) 173956) ((-507 . -729) 173921) ((-1272 . -658) 173811) ((-326 . -641) 173790) ((-848 . -738) T) ((-839 . -738) T) ((-1134 . -1236) T) ((-656 . -1236) T) ((-1099 . -651) 173738) ((-1191 . -915) 173681) ((-1144 . -915) 173665) ((-827 . -234) 173556) ((-674 . -1075) 173540) ((-108 . -651) 173522) ((-494 . -132) 173393) ((-1197 . -1131) T) ((-831 . -1236) T) ((-969 . -47) 173362) ((-635 . -1119) T) ((-674 . -111) 173341) ((-503 . -625) 173307) ((-337 . -298) 173284) ((-398 . -1236) T) ((-334 . -1236) T) ((-493 . -47) 173241) ((-1197 . -23) T) ((-118 . -1119) T) ((-103 . -102) 173191) ((-1298 . -1131) T) ((-560 . -862) T) ((-227 . -1236) T) ((-1073 . -132) T) ((-1043 . -1077) T) ((-1298 . -23) T) ((-831 . -1057) 173175) ((-1216 . -625) 173157) ((-1022 . -736) 173129) ((-1139 . -840) T) ((-711 . -729) 173094) ((-598 . -625) 173076) ((-398 . -1057) 173060) ((-365 . -1077) T) ((-396 . -132) T) ((-334 . -1057) 173044) ((-1124 . -1119) T) ((-1099 . -21) T) ((-1099 . -25) T) ((-227 . -899) 173026) ((-1023 . -937) T) ((-91 . -34) T) ((-1023 . -832) T) ((-931 . -937) T) ((-1018 . -319) 172991) ((-888 . -628) 172972) ((-499 . -1240) T) ((-726 . -660) 172932) ((-693 . -628) 172913) ((-688 . -628) 172894) ((-219 . -1240) T) ((-419 . -909) 172815) ((-227 . -1057) 172775) ((-40 . -300) T) ((-499 . -568) T) ((-490 . -628) 172756) ((-370 . -25) T) ((-326 . -658) 172411) ((-323 . -658) 172325) ((-370 . -21) T) ((-364 . -25) T) ((-364 . -21) T) ((-219 . -568) T) ((-356 . -25) T) ((-356 . -21) T) ((-329 . -234) 172271) ((-250 . -628) 172248) ((-139 . -628) 172229) ((-138 . -628) 172210) ((-134 . -628) 172191) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1077) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1081 . -1236) T) ((-969 . -1236) T) ((-725 . -1236) T) ((-670 . -625) 172173) ((-493 . -1236) T) ((-749 . -748) 172157) ((-347 . -625) 172139) ((-68 . -394) T) ((-68 . -407) T) ((-1121 . -107) 172123) ((-1081 . -899) 172105) ((-969 . -899) 172030) ((-665 . -1131) T) ((-635 . -729) 172017) ((-493 . -899) NIL) ((-1165 . -102) T) ((-1113 . -630) 172001) ((-1081 . -1057) 171983) ((-97 . -625) 171965) ((-489 . -148) T) ((-969 . -1057) 171845) ((-118 . -729) 171790) ((-724 . -917) 171697) ((-665 . -23) T) ((-493 . -1057) 171573) ((-1106 . -626) NIL) ((-1106 . -625) 171555) ((-794 . -626) NIL) ((-794 . -625) 171516) ((-792 . -626) 171150) ((-792 . -625) 171064) ((-1132 . -651) 170970) ((-473 . -625) 170952) ((-466 . -625) 170934) ((-466 . -626) 170795) ((-1054 . -231) 170741) ((-884 . -926) 170720) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 170702) ((-590 . -102) T) ((-366 . -1305) 170686) ((-363 . -1305) 170670) ((-355 . -1305) 170654) ((-128 . -526) 170587) ((-122 . -526) 170520) ((-523 . -804) T) ((-523 . -807) T) ((-522 . -806) T) ((-103 . -319) 170458) ((-224 . -102) 170408) ((-711 . -174) T) ((-706 . -1119) T) ((-884 . -660) 170324) ((-65 . -395) T) ((-284 . -625) 170306) ((-65 . -407) T) ((-969 . -388) 170290) ((-882 . -300) T) ((-50 . -625) 170272) ((-1018 . -38) 170220) ((-1139 . -658) 170192) ((-593 . -625) 170174) ((-493 . -388) 170158) ((-593 . -626) 170140) ((-530 . -625) 170122) ((-927 . -1305) 170109) ((-883 . -1236) T) ((-713 . -464) T) ((-507 . -526) 170075) ((-1297 . -1236) T) ((-1296 . -1236) T) ((-499 . -374) T) ((-366 . -379) 170054) ((-363 . -379) 170033) ((-355 . -379) 170012) ((-726 . -738) T) ((-219 . -374) T) ((-117 . -464) T) ((-1309 . -1300) 169996) ((-883 . -897) 169973) ((-883 . -899) NIL) ((-981 . -862) 169872) ((-827 . -862) 169823) ((-1243 . -102) T) ((-666 . -668) 169807) ((-1222 . -34) T) ((-173 . -625) 169789) ((-1132 . -25) 169622) ((-1132 . -21) 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168628) ((-1099 . -234) 168501) ((-499 . -1131) T) ((-365 . -1119) T) ((-219 . -1131) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1057) 168397) ((-304 . -909) 168354) ((-329 . -862) T) ((-1249 . -660) 168162) ((-884 . -806) 168141) ((-884 . -803) 168120) ((-884 . -738) T) ((-499 . -23) T) ((-370 . -234) 168093) ((-364 . -234) 168066) ((-356 . -234) 168039) ((-176 . -464) T) ((-86 . -453) T) ((-224 . -319) 167977) ((-86 . -407) T) ((-225 . -625) 167959) ((-108 . -234) 167946) ((-219 . -23) T) ((-1310 . -1303) 167925) ((-689 . -1057) 167909) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-1259 . -1236) T) ((-137 . -482) 167864) ((-867 . -1236) T) ((-666 . -658) 167823) ((-48 . -1119) T) ((-724 . -272) 167807) ((-724 . -232) 167791) ((-883 . -915) NIL) ((-583 . -1236) T) ((-1259 . -899) NIL) ((-902 . -102) T) ((-898 . -102) T) ((-400 . -1119) T) ((-171 . -388) 167775) ((-171 . -349) 167759) ((-1259 . -1057) 167639) ((-867 . -1057) 167535) ((-1161 . -102) T) ((-1018 . -917) 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. -1119) T) ((-250 . -678) 165043) ((-250 . -663) 165027) ((-670 . -111) 165006) ((-598 . -628) 164990) ((-326 . -423) 164974) ((-250 . -384) 164958) ((-1178 . -240) 164905) ((-1018 . -272) 164889) ((-1018 . -232) 164873) ((-74 . -1236) T) ((-48 . -174) T) ((-713 . -399) T) ((-713 . -144) T) ((-1309 . -102) T) ((-1217 . -1236) T) ((-1216 . -628) 164855) ((-1107 . -1236) T) ((-1106 . -1075) 164698) ((-1095 . -1236) T) ((-273 . -926) 164677) ((-253 . -926) 164656) ((-794 . -1075) 164479) ((-792 . -1075) 164322) ((-620 . -1236) T) ((-1183 . -625) 164304) ((-1106 . -111) 164133) ((-1065 . -102) T) ((-487 . -1236) T) ((-473 . -1075) 164104) ((-466 . -1075) 163947) ((-676 . -660) 163931) ((-883 . -317) T) ((-794 . -111) 163740) ((-792 . -111) 163569) ((-366 . -660) 163521) ((-363 . -660) 163473) ((-355 . -660) 163425) ((-273 . -660) 163314) ((-253 . -660) 163203) ((-1177 . -862) T) ((-1107 . -1057) 163187) ((-473 . -111) 163148) ((-466 . -111) 162977) ((-1095 . -1057) 162954) ((-1019 . -34) 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. -317) 161262) ((-430 . -23) T) ((-40 . -625) 161244) ((-40 . -626) 161228) ((-108 . -1011) 161210) ((-117 . -881) 161194) ((-661 . -628) 161178) ((-48 . -526) 161144) ((-1222 . -1029) 161128) ((-1200 . -625) 161095) ((-1208 . -34) T) ((-971 . -625) 161061) ((-938 . -625) 161043) ((-1132 . -862) 160994) ((-783 . -625) 160976) ((-684 . -625) 160958) ((-529 . -1236) T) ((-1259 . -317) 160937) ((-1176 . -319) 160875) ((-1160 . -34) T) ((-491 . -34) T) ((-1111 . -1236) T) ((-489 . -464) T) ((-1053 . -1236) T) ((-1106 . -1068) T) ((-50 . -628) 160844) ((-794 . -1068) T) ((-792 . -1068) T) ((-659 . -240) 160828) ((-644 . -240) 160774) ((-1197 . -21) T) ((-593 . -628) 160724) ((-530 . -628) 160654) ((-494 . -234) 160545) ((-1197 . -25) T) ((-1106 . -336) 160506) ((-466 . -1068) T) ((-1106 . -238) 160485) ((-794 . -336) 160462) ((-794 . -238) T) ((-792 . -336) 160434) ((-743 . -1240) 160413) ((-531 . -34) T) ((-337 . -663) 160397) ((-528 . -34) T) ((-59 . -34) T) ((-509 . -34) T) ((-508 . 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159644) ((-1139 . -1077) T) ((-103 . -126) 159628) ((-304 . -652) 159570) ((-811 . -23) T) ((-1308 . -1303) 159546) ((-1306 . -1303) 159525) ((-1286 . -296) 159477) ((-419 . -319) 159442) ((-1272 . -1119) T) ((-1161 . -917) 159365) ((-882 . -625) 159347) ((-848 . -1057) 159316) ((-205 . -799) T) ((-204 . -799) T) ((-203 . -799) T) ((-202 . -799) T) ((-201 . -799) T) ((-200 . -799) T) ((-199 . -799) T) ((-198 . -799) T) ((-197 . -799) T) ((-196 . -799) T) ((-559 . -625) 159298) ((-507 . -1021) T) ((-283 . -851) T) ((-282 . -851) T) ((-281 . -851) T) ((-280 . -851) T) ((-48 . -300) T) ((-279 . -851) T) ((-278 . -851) T) ((-277 . -851) T) ((-195 . -799) T) ((-624 . -862) T) ((-666 . -423) 159282) ((-682 . -237) 159233) ((-225 . -628) 159195) ((-110 . -862) T) ((-665 . -21) T) ((-665 . -25) T) ((-1309 . -38) 159165) ((-118 . -296) 159116) ((-1286 . -19) 159100) ((-1286 . -616) 159077) ((-1299 . -1119) T) ((-362 . -1070) 159022) ((-1096 . -1119) T) ((-1006 . -1119) T) ((-980 . -132) T) 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T) ((-494 . -862) 158035) ((-499 . -651) 158017) ((-982 . -625) 157999) ((-1022 . -917) 157908) ((-219 . -651) 157890) ((-227 . -416) T) ((-674 . -660) 157874) ((-55 . -625) 157856) ((-1191 . -937) 157835) ((-743 . -1131) T) ((-527 . -1236) T) ((-522 . -1236) T) ((-520 . -1236) T) ((-362 . -102) T) ((-1235 . -1102) T) ((-1139 . -856) T) ((-830 . -862) T) ((-743 . -23) T) ((-354 . -1075) 157780) ((-1166 . -107) 157764) ((-1287 . -625) 157746) ((-1193 . -23) T) ((-1193 . -1131) T) ((-1192 . -1131) T) ((-1192 . -23) T) ((-527 . -1057) 157730) ((-1186 . -1131) T) ((-1145 . -1131) T) ((-354 . -111) 157659) ((-1023 . -1240) T) ((-127 . -1236) T) ((-931 . -1240) T) ((-1186 . -23) T) ((-1161 . -272) 157643) ((-706 . -296) NIL) ((-726 . -1236) T) ((-1161 . -232) 157627) ((-1145 . -23) T) ((-1094 . -1119) T) ((-1023 . -568) T) ((-931 . -568) T) ((-255 . -1236) T) ((-189 . -1236) T) ((-163 . -1236) T) ((-158 . -1236) T) ((-254 . -625) 157609) ((-827 . -237) 157506) ((-811 . -132) T) ((-722 . 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154339) ((-1023 . -1131) T) ((-535 . -319) 154277) ((-1022 . -360) NIL) ((-142 . -526) NIL) ((-878 . -658) 154222) ((-990 . -23) T) ((-931 . -1131) T) ((-931 . -23) T) ((-362 . -38) 154187) ((-884 . -915) 154146) ((-882 . -1075) 154133) ((-82 . -625) 154115) ((-40 . -1068) T) ((-882 . -111) 154100) ((-730 . -1236) T) ((-713 . -102) T) ((-706 . -625) 154082) ((-614 . -1236) T) ((-608 . -568) 154061) ((-439 . -1131) T) ((-350 . -1070) 154045) ((-215 . -1119) T) ((-176 . -1070) 153977) ((-486 . -47) 153947) ((-40 . -238) 153919) ((-40 . -248) T) ((-135 . -102) T) ((-117 . -102) T) ((-607 . -568) 153898) ((-350 . -652) 153882) ((-706 . -626) 153790) ((-326 . -526) 153756) ((-176 . -652) 153688) ((-323 . -526) 153580) ((-499 . -234) 153567) ((-1270 . -1057) 153551) ((-1249 . -1057) 153337) ((-1018 . -423) 153321) ((-219 . -234) 153308) ((-439 . -23) T) ((-1139 . -174) T) ((-1272 . -300) T) ((-666 . -729) 153278) ((-145 . -1119) T) ((-48 . -1021) T) ((-419 . -272) 153262) ((-419 . -232) 153246) ((-305 . -240) 153196) ((-883 . -937) T) ((-883 . -832) NIL) ((-882 . -628) 153168) ((-876 . -862) T) ((-1249 . -349) 153138) ((-1249 . -388) 153108) ((-1099 . -237) 152987) ((-224 . -1140) 152971) ((-304 . -917) 152930) ((-1286 . -298) 152907) ((-370 . -237) 152886) ((-364 . -237) 152865) ((-486 . -1236) T) ((-356 . -237) 152844) ((-108 . -237) T) ((-1230 . -660) 152769) ((-1022 . -658) 152699) ((-980 . -21) T) ((-980 . -25) T) ((-747 . -21) T) ((-747 . -25) T) ((-727 . -21) T) ((-727 . -25) T) ((-723 . -660) 152664) ((-465 . -21) T) ((-465 . -25) T) ((-350 . -102) T) ((-176 . -102) T) ((-1018 . -1077) T) ((-882 . -1068) T) ((-786 . -102) T) ((-1271 . -374) 152643) ((-1270 . -915) 152549) ((-1250 . -374) 152528) ((-1249 . -915) 152379) ((-1195 . -1236) T) ((-1043 . -625) 152361) ((-419 . -840) 152314) ((-1193 . -505) 152280) ((-171 . -937) 152211) ((-1192 . -505) 152177) ((-1186 . -505) 152143) ((-724 . -1119) T) ((-1145 . -505) 152109) ((-592 . -1075) 152096) ((-576 . -1075) 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. -1240) 141341) ((-493 . -1240) 141320) ((-1081 . -568) T) ((-969 . -568) 141251) ((-1191 . -23) T) ((-1170 . -1102) T) ((-1144 . -23) T) ((-866 . -23) T) ((-493 . -568) 141182) ((-1161 . -729) 141114) ((-682 . -1070) 141098) ((-1165 . -526) 141031) ((-682 . -652) 141015) ((-1054 . -626) NIL) ((-1054 . -625) 140997) ((-96 . -1102) T) ((-1315 . -1075) 140984) ((-878 . -729) 140954) ((-1315 . -111) 140939) ((-1230 . -47) 140908) ((-1186 . -862) NIL) ((-258 . -132) T) ((-257 . -132) T) ((-1123 . -1119) T) ((-1022 . -1119) T) ((-62 . -625) 140890) ((-1099 . -909) 140759) ((-1043 . -804) T) ((-1043 . -807) T) ((-1278 . -25) T) ((-1278 . -21) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-882 . -660) 140746) ((-1250 . -21) T) ((-1250 . -25) T) ((-1046 . -152) 140730) ((-1023 . -234) 140717) ((-884 . -832) 140696) ((-884 . -937) T) ((-724 . -296) 140623) ((-608 . -21) T) ((-350 . -658) 140582) ((-108 . -909) NIL) ((-608 . -25) T) ((-607 . -21) T) ((-176 . -658) 140499) ((-40 . -738) T) ((-224 . 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135288) ((-284 . -1236) T) ((-326 . -628) 134852) ((-323 . -628) 134735) ((-50 . -1236) T) ((-402 . -658) 134704) ((-661 . -1057) 134688) ((-639 . -102) T) ((-593 . -1236) T) ((-530 . -1236) T) ((-224 . -501) 134672) ((-1286 . -34) T) ((-633 . -658) 134631) ((-299 . -1070) 134618) ((-137 . -628) 134602) ((-299 . -652) 134589) ((-647 . -729) 134573) ((-619 . -729) 134557) ((-682 . -38) 134517) ((-329 . -102) T) ((-1139 . -1075) 134504) ((-85 . -625) 134486) ((-50 . -1057) 134470) ((-1106 . -388) 134454) ((-794 . -388) 134438) ((-711 . -738) T) ((-711 . -806) T) ((-711 . -803) T) ((-60 . -57) 134400) ((-593 . -1057) 134387) ((-530 . -1057) 134364) ((-173 . -1236) T) ((-334 . -132) T) ((-326 . -1068) 134254) ((-323 . -1068) T) ((-171 . -1131) T) ((-792 . -388) 134238) ((-45 . -152) 134188) ((-1023 . -1011) 134170) ((-466 . -388) 134154) ((-419 . -174) T) ((-326 . -248) 134133) ((-323 . -248) T) ((-323 . -238) NIL) ((-304 . -1119) 133915) ((-227 . -132) T) ((-1139 . -111) 133900) ((-171 . -23) T) ((-811 . -148) 133879) ((-811 . -146) 133858) ((-258 . -651) 133764) ((-257 . -651) 133670) ((-329 . -294) 133636) ((-1176 . -526) 133569) ((-489 . -658) 133519) ((-494 . -909) 133386) ((-1152 . -1119) T) ((-227 . -1079) T) ((-827 . -319) 133324) ((-1106 . -915) 133259) ((-794 . -915) 133202) ((-792 . -915) 133186) ((-1308 . -38) 133156) ((-1306 . -38) 133126) ((-1259 . -1131) T) ((-867 . -1131) T) ((-466 . -915) 133103) ((-870 . -1119) T) ((-1259 . -23) T) ((-1139 . -628) 133075) ((-1081 . -132) T) ((-583 . -1131) T) ((-867 . -23) T) ((-635 . -738) T) ((-366 . -937) T) ((-363 . -937) T) ((-299 . -102) T) ((-355 . -937) T) ((-989 . -1102) T) ((-969 . -132) T) ((-828 . -234) 133020) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1065 . -526) 132921) ((-706 . -926) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 132872) ((-687 . -319) 132810) ((-225 . -1236) T) ((-647 . -773) T) ((-619 . -773) T) ((-1250 . -862) NIL) ((-1099 . -1070) 132720) ((-1022 . -300) T) ((-706 . -660) 132670) ((-258 . -25) T) ((-362 . -1119) T) ((-258 . -21) T) ((-257 . -25) T) ((-257 . -21) T) ((-153 . -38) 132654) ((-2 . -102) T) ((-927 . -937) T) ((-1099 . -652) 132522) ((-494 . -1293) 132492) ((-1139 . -1068) T) ((-723 . -317) T) ((-370 . -1070) 132444) ((-364 . -1070) 132396) ((-356 . -1070) 132348) ((-370 . -652) 132300) ((-225 . -1057) 132277) ((-364 . -652) 132229) ((-108 . -1070) 132179) ((-356 . -652) 132131) ((-304 . -729) 132073) ((-713 . -1077) T) ((-499 . -464) T) ((-419 . -526) 131985) ((-108 . -652) 131935) ((-219 . -464) T) ((-1139 . -238) T) ((-305 . -152) 131885) ((-1018 . -626) 131846) ((-1018 . -625) 131828) ((-1008 . -625) 131810) ((-117 . -1077) T) ((-666 . -1075) 131794) ((-227 . -505) T) ((-411 . -625) 131776) ((-411 . -626) 131753) ((-1073 . -1293) 131723) ((-666 . -111) 131702) ((-682 . -917) 131625) ((-1161 . -501) 131609) ((-1310 . -658) 131568) ((-392 . -658) 131537) ((-63 . -453) T) ((-63 . -407) T) ((-1178 . -102) T) ((-883 . -132) T) ((-496 . -102) 131487) ((-1137 . -1236) T) ((-1315 . -379) T) ((-1099 . -102) T) ((-1080 . -102) T) ((-362 . -729) 131432) ((-743 . -148) 131411) ((-743 . -146) 131390) ((-666 . -628) 131308) ((-1043 . -660) 131245) ((-535 . -1119) 131223) ((-370 . -102) T) ((-364 . -102) T) ((-356 . -102) T) ((-108 . -102) T) ((-516 . -1119) T) ((-365 . -660) 131168) ((-1191 . -651) 131116) ((-1144 . -651) 131064) ((-396 . -521) 131043) ((-845 . -860) 131022) ((-706 . -738) T) ((-390 . -1240) T) ((-343 . -1236) T) ((-1250 . -1011) 130974) ((-350 . -1077) T) ((-112 . -1236) T) ((-176 . -1077) T) ((-103 . -625) 130906) ((-1193 . -146) 130885) ((-1193 . -148) 130864) ((-390 . -568) T) ((-1192 . -148) 130843) ((-1192 . -146) 130822) ((-1186 . -146) 130729) ((-419 . -300) T) ((-1186 . -148) 130636) ((-1145 . -148) 130615) ((-1145 . -146) 130594) ((-329 . -38) 130435) ((-171 . -132) T) ((-323 . -807) NIL) ((-323 . -804) NIL) ((-666 . -1068) T) ((-48 . -660) 130385) ((-1132 . -1070) 130286) ((-906 . -628) 130263) ((-1132 . -652) 130185) ((-1185 . -102) T) ((-1013 . -102) T) ((-1012 . -21) T) ((-128 . -1029) 130169) ((-122 . -1029) 130153) ((-1012 . -25) T) ((-918 . -120) 130137) ((-1177 . -102) T) ((-1259 . -132) T) ((-1191 . -25) T) ((-1191 . -21) T) ((-354 . -1236) T) ((-1144 . -25) T) ((-867 . -132) T) ((-406 . -1236) T) ((-1144 . -21) T) ((-866 . -25) T) ((-866 . -21) T) ((-794 . -317) 130116) ((-1178 . -319) 129911) ((-1176 . -501) 129895) ((-1169 . -152) 129845) ((-659 . -102) 129795) ((-644 . -102) T) ((-1165 . -625) 129757) ((-583 . -132) T) ((-633 . -860) 129736) ((-1165 . -626) 129697) ((-1043 . -803) T) ((-1043 . -806) T) ((-1043 . -738) T) ((-827 . -917) 129566) ((-724 . -1075) 129389) ((-496 . -319) 129327) ((-465 . -429) 129297) ((-362 . -174) T) ((-299 . -38) 129284) ((-258 . -234) 129175) ((-257 . -234) 129066) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-278 . -102) T) ((-354 . -1057) 129043) ((-277 . -102) T) ((-214 . 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126511) ((-1023 . -148) T) ((-1023 . -146) NIL) ((-390 . -1131) T) ((-334 . -25) T) ((-332 . -23) T) ((-960 . -862) 126490) ((-724 . -336) 126467) ((-493 . -651) 126415) ((-40 . -1057) 126303) ((-724 . -238) T) ((-713 . -729) 126290) ((-350 . -1119) T) ((-176 . -1119) T) ((-341 . -862) T) ((-430 . -464) 126240) ((-390 . -23) T) ((-370 . -38) 126205) ((-364 . -38) 126170) ((-356 . -38) 126135) ((-80 . -453) T) ((-80 . -407) T) ((-227 . -25) T) ((-227 . -21) T) ((-848 . -1131) T) ((-108 . -38) 126085) ((-839 . -1131) T) ((-786 . -1119) T) ((-117 . -729) 126072) ((-684 . -1057) 126056) ((-624 . -102) T) ((-848 . -23) T) ((-839 . -23) T) ((-1176 . -296) 126008) ((-1132 . -319) 125946) ((-494 . -1070) 125847) ((-1121 . -240) 125831) ((-64 . -408) T) ((-64 . -407) T) ((-1170 . -102) T) ((-110 . -102) T) ((-494 . -652) 125753) ((-40 . -388) 125730) ((-96 . -102) T) ((-665 . -864) 125714) ((-1191 . -234) 125701) ((-1154 . -1102) T) ((-1081 . -21) T) ((-1081 . -25) T) ((-1073 . -1070) 125685) 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123147) ((-1018 . -248) 123126) ((-1018 . -238) 123105) ((-1278 . -148) 123084) ((-1271 . -148) 123063) ((-845 . -1119) T) ((-1271 . -146) 123042) ((-1270 . -1240) 123021) ((-1250 . -146) 122928) ((-1250 . -148) 122835) ((-1249 . -1240) 122814) ((-390 . -132) T) ((-227 . -234) 122801) ((-176 . -174) T) ((-576 . -899) 122783) ((0 . -1119) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1236) T) ((-49 . -1119) T) ((-1272 . -660) 122688) ((-1270 . -568) 122639) ((-726 . -1131) T) ((-1249 . -568) 122590) ((-576 . -1057) 122572) ((-607 . -148) 122551) ((-607 . -146) 122530) ((-507 . -1057) 122473) ((-1154 . -1156) T) ((-87 . -395) T) ((-87 . -407) T) ((-884 . -374) T) ((-848 . -132) T) ((-839 . -132) T) ((-981 . -658) 122417) ((-726 . -23) T) ((-518 . -625) 122383) ((-514 . -625) 122365) ((-827 . -658) 122144) ((-1310 . -1077) T) ((-390 . -1079) T) ((-1045 . -1119) 122122) ((-55 . -1057) 122104) ((-918 . -34) T) ((-494 . -319) 122042) ((-604 . -102) T) ((-1176 . -626) 122003) ((-1176 . -625) 121935) ((-1197 . -1070) 121818) ((-45 . -102) T) ((-829 . -102) T) ((-1197 . -652) 121715) ((-1287 . -1236) T) ((-1259 . -25) T) ((-1259 . -21) T) ((-1081 . -234) 121702) ((-867 . -25) T) ((-254 . -1236) T) ((-44 . -378) 121686) ((-867 . -21) T) ((-743 . -464) 121637) ((-1309 . -625) 121619) ((-722 . -1236) T) ((-711 . -1236) T) ((-1298 . -1070) 121589) ((-1073 . -319) 121527) ((-683 . -1102) T) ((-618 . -1102) T) ((-402 . -1119) T) ((-583 . -25) T) ((-583 . -21) T) ((-182 . -1102) T) ((-162 . -1102) T) ((-157 . -1102) T) ((-155 . -1102) T) ((-1298 . -652) 121497) ((-633 . -1119) T) ((-711 . -899) 121479) ((-1286 . -1236) T) ((-229 . -319) 121417) ((-145 . -379) T) ((-1209 . -1236) T) ((-1065 . -626) 121359) ((-1065 . -625) 121302) ((-323 . -926) NIL) ((-1244 . -856) T) ((-1132 . -917) 121171) ((-711 . -1057) 121116) ((-723 . -937) T) ((-486 . -1240) 121095) ((-1192 . -464) 121074) ((-1186 . -464) 121053) ((-340 . -102) T) ((-884 . -1131) T) ((-329 . -658) 120935) ((-326 . -660) 120664) ((-323 . -660) 120593) ((-486 . -568) 120544) ((-350 . -526) 120510) ((-562 . -152) 120460) ((-40 . -317) T) ((-855 . -625) 120442) ((-713 . -300) T) ((-884 . -23) T) ((-390 . -505) T) ((-1099 . -272) 120412) ((-1099 . -232) 120382) ((-524 . -102) T) ((-419 . -626) 120189) ((-419 . -625) 120171) ((-270 . -625) 120153) ((-117 . -300) T) ((-1272 . -738) T) ((-635 . -1236) T) ((-1311 . -1119) T) ((-1270 . -374) 120132) ((-1249 . -374) 120111) ((-1299 . -34) T) ((-1244 . -1119) T) ((-118 . -1236) T) ((-108 . -272) 120093) ((-108 . -232) 120075) ((-1197 . -102) T) ((-489 . -1119) T) ((-535 . -501) 120059) ((-749 . -34) T) ((-665 . -1070) 120043) ((-665 . -652) 120013) ((-883 . -234) NIL) ((-142 . -34) T) ((-118 . -897) 119990) ((-118 . -899) NIL) ((-635 . -1057) 119873) ((-1298 . -102) T) ((-1278 . -237) 119832) ((-656 . -862) 119811) ((-1271 . -237) 119763) ((-1250 . -237) 119586) ((-305 . -102) T) ((-724 . -379) 119565) ((-118 . -1057) 119542) ((-402 . -729) 119526) ((-607 . -237) 119485) ((-633 . -729) 119469) ((-1124 . -1236) T) ((-45 . -319) 119273) ((-828 . -146) 119252) ((-828 . -148) 119231) ((-299 . -658) 119203) ((-1309 . -393) 119182) ((-831 . -862) T) ((-1288 . -1119) T) ((-1178 . -231) 119129) ((-398 . -862) 119108) ((-1278 . -35) 119074) ((-1278 . -1224) 119040) ((-1278 . -1221) 119006) ((-1271 . -1221) 118972) ((-527 . -132) T) ((-1271 . -1224) 118938) ((-1250 . -1221) 118904) ((-1250 . -1224) 118870) ((-1278 . -95) 118836) ((-1271 . -95) 118802) ((-430 . -909) 118723) ((-647 . -625) 118692) ((-619 . -625) 118661) ((-227 . -862) T) ((-1271 . -35) 118627) ((-1270 . -1131) T) ((-1250 . -95) 118593) ((-1139 . -660) 118565) ((-1250 . -35) 118531) ((-1249 . -1131) T) ((-605 . -152) 118513) ((-1099 . -360) 118492) ((-176 . -300) T) ((-118 . -388) 118469) ((-118 . -349) 118446) ((-171 . -234) 118371) ((-882 . -317) T) ((-323 . -806) NIL) ((-323 . -803) NIL) ((-326 . -738) 118220) ((-323 . -738) T) ((-486 . -374) 118199) ((-370 . -360) 118178) ((-364 . -360) 118157) ((-356 . -360) 118136) ((-326 . -485) 118115) ((-1270 . -23) T) ((-1249 . -23) T) ((-730 . -1131) T) ((-726 . -132) T) ((-665 . -102) T) ((-489 . -729) 118080) ((-45 . -292) 118030) ((-105 . -1119) T) ((-68 . -625) 118012) ((-989 . -102) T) ((-876 . -102) T) ((-635 . -915) 117971) ((-1310 . -1119) T) ((-392 . -1119) T) ((-1259 . -234) 117958) ((-1235 . -1119) T) ((-82 . -1236) T) ((-1132 . -272) 117927) ((-1081 . -862) T) ((-118 . -915) NIL) ((-794 . -937) 117906) ((-725 . -862) T) ((-543 . -1119) T) ((-512 . -1119) T) ((-366 . -1240) T) ((-363 . -1240) T) ((-355 . -1240) T) ((-273 . -1240) 117885) ((-253 . -1240) 117864) ((-545 . -872) T) ((-1132 . -232) 117833) ((-1177 . -840) T) ((-1161 . -1075) 117817) ((-402 . -773) T) ((-706 . -1236) T) ((-703 . -1057) 117801) ((-366 . -568) T) ((-363 . -568) T) ((-355 . -568) T) ((-273 . -568) 117732) ((-253 . -568) 117663) ((-537 . -1102) T) ((-1161 . -111) 117642) ((-465 . -756) 117612) ((-878 . -1075) 117582) ((-829 . -38) 117524) ((-706 . -897) 117506) ((-706 . -899) 117488) ((-305 . -319) 117292) ((-1176 . -298) 117269) ((-927 . -1240) T) ((-1099 . -658) 117164) ((-1023 . -464) T) ((-682 . -423) 117148) ((-878 . -111) 117113) ((-931 . -464) T) ((-706 . -1057) 117058) ((-927 . -568) T) ((-545 . -625) 117040) ((-593 . -937) T) ((-499 . -1070) 116990) ((-486 . -1131) T) ((-530 . -937) T) ((-494 . -917) 116859) ((-65 . -625) 116841) ((-219 . -1070) 116791) ((-499 . -652) 116741) ((-370 . -658) 116678) ((-364 . -658) 116615) ((-356 . -658) 116552) ((-644 . -231) 116498) ((-219 . -652) 116448) ((-108 . -658) 116398) ((-486 . -23) T) ((-1139 . -806) T) ((-884 . -132) T) ((-1139 . -803) T) ((-1301 . -1303) 116377) ((-1139 . -738) T) ((-666 . -660) 116351) ((-304 . -625) 116092) ((-1161 . -628) 116010) ((-1054 . -34) T) ((-828 . -237) 115961) ((-592 . -317) T) ((-576 . -317) T) ((-507 . -317) T) ((-1310 . -729) 115931) ((-706 . -388) 115913) ((-706 . -349) 115895) ((-489 . -174) T) ((-392 . -729) 115865) ((-878 . -628) 115800) ((-883 . -862) NIL) ((-576 . -1041) T) ((-507 . -1041) T) ((-1152 . -625) 115782) ((-1132 . -243) 115761) ((-216 . -102) T) ((-1169 . -102) T) ((-71 . -625) 115743) ((-1043 . -1236) T) ((-1161 . -1068) T) ((-1197 . -38) 115640) ((-870 . -625) 115622) ((-576 . -557) T) ((-682 . -1077) T) ((-743 . -966) 115575) ((-365 . -1236) T) ((-1161 . -238) 115554) ((-1101 . -1119) T) ((-1053 . -25) T) ((-1053 . -21) T) ((-1022 . -1075) 115499) ((-922 . -102) T) ((-878 . -1068) T) ((-706 . -915) NIL) ((-366 . -339) 115483) ((-366 . -374) T) ((-363 . -339) 115467) ((-363 . -374) T) ((-355 . -339) 115451) ((-355 . -374) T) ((-499 . -102) T) ((-1298 . -38) 115421) ((-558 . -862) T) ((-535 . -699) 115371) ((-219 . -102) T) ((-1043 . -1057) 115251) ((-1022 . -111) 115180) ((-1193 . -992) 115149) ((-1192 . -992) 115111) ((-532 . -152) 115095) ((-1099 . -381) 115074) ((-362 . -625) 115056) ((-332 . -21) T) ((-365 . -1057) 115033) ((-332 . -25) T) ((-1186 . -992) 115002) ((-48 . -1236) T) 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. -628) 112547) ((-512 . -526) NIL) ((-494 . -243) 112526) ((-419 . -628) 112424) ((-980 . -1070) 112307) ((-747 . -1070) 112277) ((-980 . -652) 112174) ((-1191 . -146) 112153) ((-747 . -652) 112123) ((-465 . -1070) 112093) ((-1191 . -148) 112072) ((-1144 . -148) 112051) ((-1144 . -146) 112030) ((-647 . -1075) 112014) ((-619 . -1075) 111998) ((-465 . -652) 111968) ((-1193 . -1277) 111952) ((-1193 . -1264) 111929) ((-1192 . -1269) 111890) ((-682 . -1119) T) ((-682 . -1072) 111830) ((-1192 . -1264) 111800) ((-560 . -1119) T) ((-499 . -1171) T) ((-1192 . -1267) 111784) ((-1186 . -1248) 111745) ((-830 . -275) 111729) ((-219 . -1171) T) ((-354 . -937) T) ((-99 . -1236) T) ((-647 . -111) 111708) ((-619 . -111) 111687) ((-1186 . -1264) 111664) ((-855 . -1068) 111643) ((-1186 . -1246) 111627) ((-527 . -25) T) ((-507 . -312) T) ((-523 . -23) T) ((-522 . -25) T) ((-520 . -25) T) ((-519 . -23) T) ((-430 . -1070) 111601) ((-419 . -1068) T) ((-329 . -1077) T) ((-706 . -317) T) ((-430 . -652) 111575) ((-108 . -860) T) ((-724 . -738) T) ((-419 . -248) T) ((-419 . -238) 111554) ((-390 . -234) 111541) ((-499 . -38) 111491) ((-219 . -38) 111441) ((-486 . -505) 111407) ((-1243 . -379) T) ((-1177 . -1163) T) ((-1120 . -102) T) ((-839 . -234) 111380) ((-713 . -625) 111362) ((-713 . -626) 111277) ((-726 . -21) T) ((-726 . -25) T) ((-1154 . -102) T) ((-494 . -658) 111056) ((-245 . -909) 110923) ((-135 . -625) 110905) ((-117 . -625) 110887) ((-158 . -25) T) ((-1308 . -1119) T) ((-884 . -651) 110835) ((-1306 . -1119) T) ((-877 . -1236) T) ((-980 . -102) T) ((-747 . -102) T) ((-727 . -102) T) ((-465 . -102) T) ((-828 . -464) 110786) ((-44 . -1119) T) ((-1107 . -862) T) ((-1082 . -319) 110637) ((-676 . -132) T) ((-1073 . -658) 110606) ((-682 . -729) 110590) ((-299 . -1077) T) ((-366 . -132) T) ((-363 . -132) T) ((-355 . -132) T) ((-273 . -132) T) ((-253 . -132) T) ((-396 . -658) 110559) ((-1315 . -1236) T) ((-430 . -102) T) ((-153 . -1119) T) ((-45 . -231) 110509) ((-1023 . -909) NIL) 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106274) ((-1193 . -652) 106171) ((-1192 . -652) 106012) ((-723 . -1240) T) ((-1186 . -652) 105808) ((-1176 . -663) 105792) ((-1145 . -652) 105689) ((-831 . -397) 105673) ((-723 . -568) T) ((-607 . -909) 105584) ((-326 . -897) 105568) ((-326 . -899) 105493) ((-323 . -897) 105454) ((-140 . -1236) T) ((-137 . -1236) T) ((-115 . -1236) T) ((-323 . -899) NIL) ((-811 . -319) 105419) ((-329 . -729) 105260) ((-398 . -397) 105244) ((-334 . -333) 105221) ((-497 . -102) T) ((-486 . -25) T) ((-486 . -21) T) ((-430 . -38) 105195) ((-326 . -1057) 104858) ((-227 . -1221) T) ((-227 . -1224) T) ((-3 . -625) 104840) ((-323 . -1057) 104770) ((-884 . -234) 104715) ((-2 . -1119) T) ((-2 . |RecordCategory|) T) ((-1132 . -1077) 104693) ((-845 . -625) 104675) ((-1081 . -237) T) ((-592 . -937) T) ((-576 . -832) T) ((-576 . -937) T) ((-507 . -937) T) ((-137 . -1057) 104659) ((-227 . -95) T) ((-171 . -148) 104638) ((-75 . -453) T) ((0 . -625) 104620) ((-75 . -407) T) ((-171 . -146) 104571) ((-227 . -35) T) ((-49 . -625) 104553) ((-489 . -1077) T) ((-499 . -272) 104535) ((-499 . -232) 104517) ((-496 . -987) 104501) ((-219 . -272) 104483) ((-219 . -232) 104465) ((-81 . -453) T) ((-81 . -407) T) ((-1165 . -34) T) ((-743 . -102) T) ((-665 . -658) 104424) ((-1045 . -625) 104391) ((-512 . -296) 104341) ((-326 . -388) 104310) ((-323 . -388) 104271) ((-323 . -349) 104232) ((-1104 . -625) 104214) ((-828 . -966) 104161) ((-674 . -132) T) ((-1259 . -146) 104140) ((-1259 . -148) 104119) ((-1193 . -102) T) ((-1192 . -102) T) ((-1186 . -102) T) ((-1178 . -1119) T) ((-1145 . -102) T) ((-1094 . -1236) T) ((-224 . -34) T) ((-299 . -729) 104106) ((-1178 . -622) 104082) ((-605 . -319) NIL) ((-1278 . -1277) 104066) ((-1169 . -231) 104016) ((-496 . -1119) 103994) ((-450 . -1236) T) ((-402 . -625) 103976) ((-522 . -862) T) ((-1139 . -1236) T) ((-1278 . -1264) 103953) ((-1271 . -1269) 103914) ((-1271 . -1264) 103884) ((-1271 . -1267) 103868) ((-1250 . -1248) 103829) ((-1250 . -1264) 103806) ((-1250 . -1246) 103790) 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-1119) T) ((-280 . -1119) T) ((-279 . -1119) T) ((-278 . -1119) T) ((-277 . -1119) T) ((-214 . -1119) T) ((-213 . -1119) T) ((-171 . -1224) 100186) ((-171 . -1221) 100164) ((-211 . -1119) T) ((-210 . -1119) T) ((-117 . -1068) T) ((-209 . -1119) T) ((-208 . -1119) T) ((-205 . -1119) T) ((-204 . -1119) T) ((-203 . -1119) T) ((-202 . -1119) T) ((-201 . -1119) T) ((-200 . -1119) T) ((-199 . -1119) T) ((-198 . -1119) T) ((-197 . -1119) T) ((-196 . -1119) T) ((-195 . -1119) T) ((-245 . -102) 99896) ((-171 . -35) 99874) ((-171 . -95) 99852) ((-666 . -1057) 99748) ((-494 . -1077) 99726) ((-1132 . -1119) 99478) ((-1161 . -34) T) ((-682 . -501) 99462) ((-73 . -1236) T) ((-105 . -625) 99444) ((-906 . -1236) T) ((-1310 . -625) 99426) ((-392 . -625) 99408) ((-350 . -628) 99360) ((-176 . -628) 99277) ((-1235 . -502) 99258) ((-743 . -38) 99107) ((-583 . -1224) T) ((-583 . -1221) T) ((-543 . -625) 99089) ((-532 . -319) 99027) ((-512 . -625) 99009) ((-512 . -626) 98991) ((-1235 . -625) 98957) ((-1186 . 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95998) ((-299 . -300) T) ((-1250 . -1070) 95788) ((-1101 . -625) 95770) ((-1101 . -626) 95751) ((-419 . -926) 95730) ((-1230 . -132) T) ((-50 . -1131) T) ((-1186 . -412) 95682) ((-1043 . -937) T) ((-1022 . -738) T) ((-855 . -660) 95655) ((-724 . -899) NIL) ((-608 . -1070) 95615) ((-593 . -1131) T) ((-530 . -1131) T) ((-607 . -1070) 95498) ((-1176 . -34) T) ((-1023 . -319) NIL) ((-827 . -501) 95482) ((-608 . -652) 95455) ((-365 . -937) T) ((-607 . -652) 95352) ((-927 . -234) 95339) ((-419 . -660) 95255) ((-50 . -23) T) ((-723 . -132) T) ((-724 . -1057) 95135) ((-593 . -23) T) ((-108 . -526) NIL) ((-530 . -23) T) ((-171 . -421) 95106) ((-1159 . -1119) T) ((-1301 . -1300) 95090) ((-743 . -917) 95067) ((-713 . -807) T) ((-713 . -804) T) ((-1139 . -317) T) ((-390 . -148) T) ((-290 . -625) 95049) ((-289 . -625) 95031) ((-1249 . -1011) 95001) ((-48 . -937) T) ((-687 . -501) 94985) ((-258 . -1293) 94955) ((-257 . -1293) 94925) ((-1107 . -237) T) ((-1195 . -862) T) ((-1139 . -1041) T) ((-1065 . -34) T) ((-848 . -148) 94904) ((-848 . -146) 94883) ((-749 . -107) 94867) ((-624 . -133) T) ((-1197 . -1077) T) ((-494 . -1119) 94619) ((-1193 . -917) 94532) ((-1192 . -917) 94438) ((-1186 . -917) 94199) ((-883 . -464) T) ((-85 . -1236) T) ((-142 . -107) 94181) ((-1145 . -917) 94165) ((-724 . -388) 94149) ((-845 . -628) 94017) ((-1309 . -738) T) ((-1298 . -1077) T) ((-1278 . -102) T) ((-1139 . -557) T) ((-591 . -102) T) ((-130 . -502) 93999) ((-1271 . -102) T) ((-402 . -1075) 93983) ((-1191 . -966) 93952) ((-44 . -296) 93929) ((-130 . -625) 93896) ((-52 . -625) 93878) ((-1144 . -966) 93845) ((-665 . -423) 93829) ((-1250 . -102) T) ((-1177 . -526) NIL) ((-674 . -25) T) ((-633 . -1075) 93813) ((-674 . -21) T) ((-980 . -658) 93723) ((-747 . -658) 93668) ((-727 . -658) 93640) ((-402 . -111) 93619) ((-224 . -261) 93603) ((-1073 . -1072) 93543) ((-1073 . -1119) T) ((-1023 . -1171) T) ((-830 . -1119) T) ((-465 . -658) 93458) ((-647 . -660) 93442) ((-633 . -111) 93421) ((-619 . -660) 93405) 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. -296) 92189) ((-489 . -111) 92145) ((-665 . -1077) T) ((-1191 . -909) 92048) ((-1144 . -909) 92030) ((-828 . -1070) 91873) ((-1297 . -1102) T) ((-1259 . -464) 91804) ((-828 . -652) 91653) ((-1296 . -1102) T) ((-1106 . -132) T) ((-1073 . -729) 91595) ((-1046 . -526) 91528) ((-794 . -132) T) ((-792 . -132) T) ((-583 . -464) T) ((-633 . -1068) T) ((-604 . -1119) T) ((-545 . -175) T) ((-473 . -132) T) ((-466 . -132) T) ((-390 . -237) T) ((-1018 . -1236) T) ((-45 . -1119) T) ((-396 . -729) 91498) ((-829 . -1119) T) ((-488 . -526) 91431) ((-475 . -526) 91364) ((-1311 . -628) 91346) ((-465 . -378) 91316) ((-45 . -622) 91295) ((-411 . -1236) T) ((-326 . -312) T) ((-839 . -237) 91274) ((-489 . -628) 91224) ((-1250 . -319) 91109) ((-682 . -625) 91071) ((-59 . -862) 91050) ((-1023 . -412) 91032) ((-560 . -625) 91014) ((-811 . -658) 90973) ((-827 . -616) 90950) ((-528 . -862) 90929) ((-508 . -862) 90908) ((-1018 . -1057) 90804) ((-40 . -1240) T) ((-245 . -917) 90673) ((-50 . -132) T) ((-593 . -132) T) ((-530 . -132) T) ((-304 . -660) 90533) ((-354 . -339) 90510) ((-354 . -374) T) ((-332 . -333) 90487) ((-329 . -296) 90445) ((-40 . -568) T) ((-390 . -1221) T) ((-390 . -1224) T) ((-1054 . -1212) 90420) ((-1208 . -240) 90370) ((-1186 . -232) 90322) ((-1186 . -272) 90274) ((-340 . -1119) T) ((-390 . -95) T) ((-390 . -35) T) ((-1054 . -107) 90220) ((-489 . -1068) T) ((-1310 . -1075) 90204) ((-491 . -240) 90154) ((-1178 . -501) 90088) ((-1301 . -1070) 90072) ((-392 . -1075) 90056) ((-1301 . -652) 90026) ((-489 . -248) T) ((-828 . -102) T) ((-726 . -148) 90005) ((-726 . -146) 89984) ((-496 . -501) 89968) ((-497 . -346) 89937) ((-524 . -1119) T) ((-1310 . -111) 89916) ((-1018 . -388) 89900) ((-425 . -102) T) ((-392 . -111) 89879) ((-1018 . -349) 89863) ((-288 . -1002) 89847) ((-287 . -1002) 89831) ((-1023 . -917) NIL) ((-1308 . -625) 89813) ((-1306 . -625) 89795) ((-110 . -526) NIL) ((-1191 . -1262) 89779) ((-866 . -864) 89763) ((-1197 . -1119) T) ((-103 . -1236) T) ((-969 . -966) 89724) ((-829 . -729) 89666) ((-1250 . -1171) NIL) ((-493 . -966) 89611) ((-1081 . -144) T) ((-60 . -102) 89561) ((-44 . -625) 89543) ((-78 . -625) 89525) ((-362 . -660) 89470) ((-1298 . -1119) T) ((-523 . -862) T) ((-299 . -296) 89449) ((-354 . -1131) T) ((-305 . -1119) T) ((-1018 . -915) 89408) ((-305 . -622) 89387) ((-1310 . -628) 89336) ((-1278 . -38) 89233) ((-1271 . -38) 89074) ((-1250 . -38) 88870) ((-499 . -1077) T) ((-392 . -628) 88854) ((-219 . -1077) T) ((-354 . -23) T) ((-153 . -625) 88836) ((-845 . -807) 88815) ((-845 . -804) 88794) ((-1235 . -628) 88775) ((-608 . -38) 88748) ((-607 . -38) 88645) ((-882 . -568) T) ((-225 . -132) T) ((-329 . -1021) 88611) ((-79 . -625) 88593) ((-724 . -317) 88572) ((-304 . -738) 88474) ((-836 . -102) T) ((-876 . -856) T) ((-304 . -485) 88453) ((-1301 . -102) T) ((-40 . -374) T) ((-884 . -148) 88432) ((-497 . -658) 88414) ((-884 . -146) 88393) ((-1177 . -501) 88375) ((-1310 . -1068) T) ((-494 . -526) 88308) ((-1165 . -1236) T) ((-981 . -625) 88290) ((-659 . -501) 88274) ((-644 . -501) 88205) ((-827 . -625) 87898) ((-48 . -27) T) ((-1197 . -729) 87795) ((-969 . -909) 87774) ((-665 . -1119) T) ((-873 . -872) T) ((-448 . -375) 87748) ((-743 . -658) 87658) ((-493 . -909) 87633) ((-1121 . -102) T) ((-989 . -1119) T) ((-876 . -1119) T) ((-828 . -319) 87620) ((-545 . -539) T) ((-545 . -588) T) ((-1306 . -393) 87592) ((-1073 . -526) 87525) ((-1178 . -296) 87501) ((-245 . -272) 87470) ((-245 . -232) 87439) ((-258 . -1070) 87340) ((-257 . -1070) 87241) ((-1298 . -729) 87211) ((-1185 . -93) T) ((-1013 . -93) T) ((-829 . -174) 87190) ((-258 . -652) 87112) ((-257 . -652) 87034) ((-1233 . -502) 87011) ((-590 . -1236) T) ((-229 . -526) 86944) ((-633 . -807) 86923) ((-633 . -804) 86902) ((-1233 . -625) 86814) ((-224 . -1236) T) ((-687 . -625) 86746) ((-1193 . -658) 86656) ((-1176 . -1029) 86640) ((-960 . -102) 86570) ((-362 . -738) T) ((-873 . -625) 86552) ((-1192 . -658) 86434) ((-1186 . -658) 86271) ((-1145 . -658) 86181) ((-1250 . -412) 86133) ((-1132 . -501) 86117) ((-60 . -319) 86055) ((-341 . -102) T) ((-1230 . -21) T) ((-1230 . -25) T) ((-40 . -1131) T) ((-723 . -21) T) ((-639 . -625) 86037) ((-527 . -333) 86016) ((-723 . -25) T) ((-451 . -102) T) ((-108 . -296) NIL) ((-938 . -1131) T) ((-40 . -23) T) ((-783 . -1131) T) ((-576 . -1240) T) ((-507 . -1240) T) ((-1023 . -272) 85998) ((-329 . -625) 85980) ((-1023 . -232) 85962) ((-171 . -167) 85946) ((-592 . -568) T) ((-576 . -568) T) ((-507 . -568) T) ((-783 . -23) T) ((-1270 . -148) 85925) ((-1270 . -146) 85904) ((-1178 . -616) 85880) ((-1249 . -146) 85805) ((-1046 . -501) 85789) ((-1243 . -1236) T) ((-1249 . -148) 85714) ((-1301 . -1307) 85693) ((-883 . -909) NIL) ((-488 . -501) 85677) ((-475 . -501) 85661) ((-535 . -34) T) ((-665 . -729) 85631) ((-1278 . -917) 85544) ((-1271 . -917) 85450) ((-1250 . -917) 85211) ((-112 . -986) T) ((-1197 . -174) 85162) ((-674 . -862) 85141) ((-376 . -102) T) ((-607 . -917) 85054) ((-245 . -243) 85033) ((-258 . -102) T) 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-616) 83758) ((-670 . -21) T) ((-670 . -25) T) ((-605 . -1163) T) ((-1132 . -296) 83735) ((-347 . -25) T) ((-347 . -21) T) ((-902 . -1236) T) ((-898 . -1236) T) ((-1308 . -1075) 83719) ((-245 . -658) 83498) ((-507 . -374) T) ((-1306 . -1075) 83482) ((-1301 . -38) 83452) ((-1270 . -1221) 83418) ((-1270 . -1224) 83384) ((-1259 . -909) 83287) ((-1191 . -1070) 83110) ((-1161 . -1236) T) ((-1144 . -1070) 82953) ((-866 . -1070) 82937) ((-644 . -616) 82912) ((-1270 . -95) 82878) ((-1270 . -237) 82830) ((-1253 . -102) 82808) ((-1191 . -652) 82637) ((-1144 . -652) 82486) ((-866 . -652) 82456) ((-1250 . -232) 82408) ((-1106 . -25) T) ((-561 . -1119) T) ((-1106 . -21) T) ((-980 . -1077) T) ((-543 . -804) T) ((-543 . -807) T) ((-118 . -1240) T) ((-878 . -1236) T) ((-635 . -568) T) ((-794 . -25) T) ((-794 . -21) T) ((-792 . -21) T) ((-792 . -25) T) ((-747 . -1077) T) ((-727 . -1077) T) ((-682 . -1075) 82392) ((-529 . -1102) T) ((-473 . -25) T) ((-118 . -568) T) ((-473 . -21) T) ((-466 . -25) T) ((-466 . -21) T) ((-1250 . -272) 82344) ((-1170 . -93) T) ((-1161 . -1057) 82240) ((-829 . -300) 82219) ((-1249 . -1221) 82185) ((-835 . -1119) T) ((-983 . -986) T) ((-682 . -111) 82164) ((-629 . -1236) T) ((-305 . -526) 81956) ((-1249 . -1224) 81922) ((-1249 . -237) 81781) ((-1244 . -379) T) ((-258 . -319) 81719) ((-257 . -319) 81657) ((-1241 . -856) T) ((-1178 . -626) NIL) ((-1178 . -625) 81639) ((-1161 . -388) 81623) ((-1139 . -832) T) ((-1139 . -937) T) ((-96 . -93) T) ((-1132 . -616) 81600) ((-1099 . -626) 81584) ((-1099 . -625) 81566) ((-1023 . -658) 81516) ((-931 . -658) 81453) ((-827 . -298) 81430) ((-496 . -625) 81362) ((-620 . -152) 81309) ((-499 . -729) 81259) ((-430 . -1077) T) ((-494 . -501) 81243) ((-439 . -658) 81202) ((-337 . -862) 81181) ((-350 . -660) 81155) ((-50 . -21) T) ((-50 . -25) T) ((-219 . -729) 81105) ((-171 . -736) 81076) ((-176 . -660) 81008) ((-593 . -21) T) ((-593 . -25) T) ((-530 . -25) T) ((-530 . -21) T) ((-487 . -152) 80958) ((-1080 . -625) 80940) ((-1012 . -102) T) ((-874 . -102) T) ((-828 . -917) 80840) ((-811 . -423) 80803) ((-40 . -132) T) ((-711 . -374) T) ((-713 . -738) T) ((-713 . -806) T) ((-713 . -803) T) ((-214 . -910) T) ((-592 . -1131) T) ((-576 . -1131) T) ((-507 . -1131) T) ((-370 . -625) 80785) ((-364 . -625) 80767) ((-356 . -625) 80749) ((-66 . -408) T) ((-66 . -407) T) ((-108 . -626) 80679) ((-108 . -625) 80621) ((-213 . -910) T) ((-975 . -152) 80605) ((-783 . -132) T) ((-682 . -628) 80523) ((-135 . -738) T) ((-117 . -738) T) ((-1270 . -35) 80489) ((-1073 . -501) 80473) ((-592 . -23) T) ((-576 . -23) T) ((-507 . -23) T) ((-1249 . -95) 80439) ((-1249 . -35) 80405) ((-1191 . -102) T) ((-1144 . -102) T) ((-866 . -102) T) ((-229 . -501) 80389) ((-1308 . -111) 80368) ((-1306 . -111) 80347) ((-44 . -1075) 80331) ((-1309 . -1236) T) ((-1308 . -628) 80277) ((-1308 . -1068) T) ((-1306 . -628) 80206) ((-1306 . -1068) T) ((-1259 . -1262) 80190) ((-867 . -864) 80174) ((-1197 . -300) 80153) ((-1123 . -1236) T) ((-110 . -296) 80103) ((-1022 . -1236) T) ((-129 . -152) 80085) ((-1161 . -915) 80044) ((-44 . -111) 80023) ((-1241 . -1119) T) ((-1200 . -1281) T) ((-1186 . -860) NIL) ((-1185 . -502) 80004) ((-682 . -1068) T) ((-1185 . -625) 79970) ((-1177 . -625) 79952) ((-486 . -237) 79904) ((-1082 . -622) 79879) ((-1013 . -502) 79860) ((-74 . -453) T) ((-74 . -407) T) ((-1082 . -1119) T) ((-153 . -1075) 79844) ((-1013 . -625) 79810) ((-682 . -238) 79789) ((-583 . -566) 79773) ((-366 . -148) 79752) ((-366 . -146) 79703) ((-363 . -148) 79682) ((-363 . -146) 79633) ((-355 . -148) 79612) ((-355 . -146) 79563) ((-273 . -146) 79542) ((-273 . -148) 79521) ((-253 . -148) 79500) ((-118 . -374) T) ((-253 . -146) 79479) ((-1177 . -626) NIL) ((-153 . -111) 79458) ((-1022 . -1057) 79346) ((-1176 . -1236) T) ((-706 . -1240) T) ((-811 . -1077) T) ((-711 . -1131) T) ((-1022 . -388) 79323) ((-518 . -1236) T) ((-514 . -1236) T) ((-927 . -146) T) ((-927 . -148) 79305) ((-882 . -132) T) ((-827 . -1075) 79226) ((-711 . -23) T) 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. -526) 36944) ((-1081 . -729) 36931) ((-794 . -909) 36834) ((-743 . -1075) 36677) ((-792 . -909) 36659) ((-969 . -729) 36508) ((-1144 . -526) 36460) ((-1297 . -1119) T) ((-1296 . -1119) T) ((-466 . -909) 36435) ((-493 . -729) 36284) ((-67 . -625) 36266) ((-639 . -1236) T) ((-743 . -111) 36095) ((-960 . -501) 36079) ((-1298 . -660) 36039) ((-1193 . -1075) 35922) ((-829 . -738) T) ((-1192 . -1075) 35757) ((-1186 . -1075) 35547) ((-329 . -1236) T) ((-1145 . -1075) 35430) ((-1022 . -1240) T) ((-1113 . -102) 35408) ((-827 . -388) 35377) ((-591 . -625) 35359) ((-558 . -1119) T) ((-1022 . -568) T) ((-1193 . -111) 35228) ((-1192 . -111) 35049) ((-1186 . -111) 34818) ((-1145 . -111) 34687) ((-1124 . -1122) 34651) ((-390 . -860) T) ((-1278 . -625) 34633) ((-1271 . -625) 34615) ((-884 . -658) 34552) ((-1250 . -625) 34534) ((-1250 . -626) NIL) ((-245 . -298) 34511) ((-40 . -464) T) ((-227 . -174) T) ((-171 . -1119) T) ((-743 . -628) 34296) ((-706 . -148) T) ((-706 . -146) NIL) ((-608 . -625) 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. -174) T) ((-867 . -729) 31087) ((-496 . -1236) T) ((-969 . -526) 31034) ((-665 . -738) T) ((-583 . -729) 31021) ((-1053 . -1077) T) ((-706 . -237) NIL) ((-493 . -526) 30964) ((-960 . -19) 30948) ((-960 . -616) 30925) ((-1099 . -1236) T) ((-1080 . -1236) T) ((-828 . -626) NIL) ((-828 . -625) 30907) ((-1230 . -652) 30804) ((-1230 . -1070) 30687) ((-1023 . -1075) 30637) ((-425 . -625) 30619) ((-258 . -296) 30596) ((-370 . -1236) T) ((-364 . -1236) T) ((-356 . -1236) T) ((-257 . -296) 30573) ((-499 . -926) NIL) ((-326 . -29) 30543) ((-108 . -1236) T) ((-1022 . -1131) T) ((-219 . -926) NIL) ((-1099 . -1057) 30439) ((-931 . -1075) 30391) ((-1023 . -111) 30325) ((-1022 . -23) T) ((-723 . -1070) 30290) ((-931 . -111) 30228) ((-749 . -707) 30212) ((-723 . -652) 30177) ((-273 . -272) 30161) ((-273 . -232) 30145) ((-439 . -1075) 30129) ((-390 . -1077) T) ((-245 . -628) 29927) ((-706 . -1224) NIL) ((-499 . -660) 29877) ((-486 . -658) 29759) ((-108 . -897) 29741) ((-108 . -899) 29723) ((-706 . 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. -1075) 24877) ((-1250 . -1075) 24667) ((-1271 . -111) 24488) ((-1250 . -111) 24257) ((-1230 . -319) 24244) ((-1022 . -132) T) ((-927 . -658) 24194) ((-376 . -625) 24176) ((-362 . -568) T) ((-299 . -317) T) ((-608 . -1075) 24136) ((-607 . -1075) 24019) ((-593 . -1070) 23984) ((-530 . -1070) 23929) ((-372 . -1119) T) ((-332 . -1119) T) ((-258 . -625) 23890) ((-257 . -625) 23851) ((-593 . -652) 23816) ((-530 . -652) 23761) ((-706 . -421) 23728) ((-647 . -23) T) ((-619 . -23) T) ((-40 . -909) 23635) ((-670 . -102) T) ((-608 . -111) 23588) ((-607 . -111) 23457) ((-390 . -1119) T) ((-347 . -102) T) ((-171 . -300) 23368) ((-1249 . -860) 23321) ((-726 . -1077) T) ((-624 . -1236) T) ((-1166 . -526) 23254) ((-1209 . -847) 23238) ((-1132 . -915) 23170) ((-848 . -1119) T) ((-839 . -1119) T) ((-837 . -1119) T) ((-97 . -102) T) ((-145 . -862) T) ((-624 . -897) 23154) ((-1170 . -1236) T) ((-110 . -1236) T) ((-1106 . -102) T) ((-1082 . -34) T) ((-794 . -102) T) ((-792 . -102) T) ((-1278 . -628) 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. -399) T) ((-430 . -738) T) ((-713 . -1240) T) ((-1161 . -651) 18771) ((-592 . -881) 18755) ((-1301 . -1075) 18739) ((-1178 . -1212) 18715) ((-713 . -568) T) ((-127 . -1119) 18693) ((-726 . -1119) T) ((-670 . -38) 18663) ((-494 . -915) 18595) ((-255 . -1119) T) ((-189 . -1119) T) ((-365 . -414) T) ((-326 . -148) 18574) ((-326 . -146) 18553) ((-117 . -568) T) ((-129 . -526) NIL) ((-323 . -148) 18509) ((-323 . -146) 18465) ((-48 . -464) T) ((-163 . -1119) T) ((-158 . -1119) T) ((-1178 . -107) 18412) ((-794 . -1171) 18390) ((-1301 . -111) 18369) ((-701 . -34) T) ((-604 . -1236) T) ((-562 . -34) T) ((-496 . -107) 18353) ((-258 . -298) 18330) ((-257 . -298) 18307) ((-1242 . -856) T) ((-883 . -296) 18258) ((-45 . -1236) T) ((-1230 . -917) 18239) ((-829 . -1236) T) ((-828 . -1068) T) ((-674 . -658) 18208) ((-1197 . -47) 18185) ((-828 . -336) 18147) ((-1106 . -38) 17996) ((-828 . -238) 17975) ((-794 . -38) 17804) ((-792 . -38) 17653) ((-1134 . -502) 17634) ((-466 . -38) 17483) ((-1134 . -625) 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((-171 . -628) 238) ((-1208 . -526) 30) ((-888 . -1119) T) ((-693 . -1119) T) ((-688 . -1119) T) ((-674 . -1119) T)) \ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index b297b513..8b64c5b5 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3486554160) -(4464 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3486628447) +(4465 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -488,665 +488,665 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |tracePowMod| |returnTypeOf| |presuper| |oddlambert| - |quadratic?| |inverseIntegralMatrixAtInfinity| |nothing| - |showTheSymbolTable| |string| |showRegion| |iicot| |branchPoint?| - |idealiser| |scanOneDimSubspaces| |sign| |getRef| |algebraicVariables| - |nthExponent| |internalSubPolSet?| |createPrimitiveElement| - |lazyVariations| |predicate| |pushucoef| |polygon?| |digit| - |shiftLeft| |critBonD| |top| |showClipRegion| |minimize| |entry?| - |OMcloseConn| |closed?| |ParCondList| |primitivePart| |f02akf| - |cot2tan| |title| |continue| |genericRightTraceForm| |nullary| - |zeroDim?| |stoseInvertibleSetreg| |read!| |fortranCompilerName| - |finiteBound| |setScreenResolution| |domainTemplate| - |wordInStrongGenerators| |updatF| |splitConstant| |redPol| |cotIfCan| - |readByte!| |s17aef| |cothIfCan| |truncate| |alphanumeric| |s21bbf| - |perfectNthPower?| |ode1| |list?| |OMgetEndBVar| |doubleFloatFormat| - |removeSquaresIfCan| |closedCurve?| |tanAn| |e| |rightRankPolynomial| - |FormatRoman| |copies| |d02gbf| |factorList| |newTypeLists| - |normalDenom| |c02agf| |overlabel| |autoReduced?| |constant| - |yCoordinates| |readInt16!| |f2df| |commutative?| |aQuadratic| - |resetAttributeButtons| |factorGroebnerBasis| |resetNew| |nthr| - |setStatus!| |randomR| |numberOfComponents| |iiacosh| |head| - |reduceBasisAtInfinity| |varselect| |Vectorise| |lexGroebner| - |cosIfCan| |reorder| |charthRoot| |OMgetError| |augment| |f07aef| - |outputAsScript| |f02xef| |call| - |solveLinearPolynomialEquationByRecursion| |f02awf| |rational| - |basisOfMiddleNucleus| |calcRanges| |mantissa| |tanIfCan| - |linearlyDependentOverZ?| |mainContent| |antiAssociative?| - |parameters| |resultantEuclidean| |setrest!| |addPoint| |unitVector| - |skewSFunction| |transpose| |distance| - |createLowComplexityNormalBasis| |hash| |readBytes!| |myDegree| - |sumOfDivisors| |airyAi| |zeroMatrix| |tableau| - |branchPointAtInfinity?| |useSingleFactorBound?| |reduced?| ** |count| - |moebiusMu| |s17dcf| |extractPoint| |factorAndSplit| |finiteBasis| - |iisin| |degreeSubResultantEuclidean| |jacobian| |degreeSubResultant| - |increase| |bipolarCylindrical| |startPolynomial| |dark| |substring?| - |iiasin| |removeSinhSq| |iiperm| |reducedQPowers| |identityMatrix| - |traverse| |antiCommutator| |romberg| |se2rfi| |cAsinh| |lifting| - |edf2df| |RemainderList| |figureUnits| |SturmHabicht| |trigs2explogs| - |pointData| |scan| |d01gaf| |bivariatePolynomials| |s19abf| |suffix?| - |trailingCoefficient| |norm| |checkForZero| |ReduceOrder| - |GospersMethod| |f01brf| |addmod| |leftPower| |getExplanations| - |divisorCascade| |symmetricSquare| |bipolar| |contract| - |linearAssociatedOrder| |smith| |basisOfNucleus| |numberOfMonomials| - |node?| |cup| |readInt32!| |jacobi| |prefix?| |approxNthRoot| |atoms| - |s17akf| |showTheRoutinesTable| |factorsOfDegree| |modulus| |interval| - |simpleBounds?| |connectTo| |rationalPoints| |gcdPrimitive| - |OMgetObject| |chebyshevT| |linearMatrix| |numberOfPrimitivePoly| - |cyclotomicDecomposition| |janko2| |qfactor| |c05adf| |cartesian| - |inverse| |numer| |retractIfCan| |init| |setMaxPoints| |cyclic?| - |primintfldpoly| |equiv| |selectPolynomials| |cycleSplit!| |asimpson| - |degree| |acscIfCan| |controlPanel| |denom| |leadingExponent| - |quotient| |cTan| |remove!| |triangSolve| |OMsupportsSymbol?| - |curveColor| |empty?| |associatedSystem| |minrank| |cSin| |less?| - |lowerCase| |compose| |hspace| |typeList| |elaboration| - |genericLeftDiscriminant| |OMputBind| |fractRagits| |pi| |localReal?| - |epilogue| |makeYoungTableau| |hostByteOrder| |viewThetaDefault| - |formula| |outputForm| |infix?| |dmpToP| |empty| |swapRows!| - |screenResolution3D| |infinity| |jordanAlgebra?| |readLineIfCan!| - |edf2ef| |nextSubsetGray| |irForm| |leftNorm| |maxdeg| |mask| |e02baf| - |coefficient| |graphs| |ptree| |complexNumericIfCan| |univariateSolve| - |primeFrobenius| |selectIntegrationRoutines| |cTanh| |primeFactor| - |HermiteIntegrate| |constantCoefficientRicDE| |doubleRank| |factorset| - |extension| |fortranInteger| |irreducibleFactors| |oddInfiniteProduct| - |iilog| |hasoln| |max| |negative?| |triangular?| |viewWriteDefault| - |kernel| |e02akf| |s21bcf| |OMgetVariable| |userOrdered?| - |commutativeEquality| |nrows| |mapExpon| |elementary| |swapColumns!| - |d02bhf| |listLoops| |list| |lfintegrate| |map| |tanhIfCan| |minordet| - |totolex| |clearCache| |hermiteH| |ncols| |lhs| |aCubic| |isAnd| - |bivariate?| |SFunction| |e01saf| |draw| |generic| |computeBasis| - |e02daf| |torsionIfCan| |leftZero| |rhs| |step| |loopPoints| - |innerEigenvectors| |totalDegree| |singRicDE| |bracket| |OMconnectTCP| - |outputAsTex| |basisOfCommutingElements| |exprHasWeightCosWXorSinWX| - |brillhartTrials| |concat| |safeCeiling| |legendre| |hessian| |f07fef| - |OMReadError?| |mpsode| |bindings| |string?| |isTimes| |cyclicEqual?| - |lepol| |currentEnv| |generalizedEigenvector| |chiSquare| - |extendedSubResultantGcd| |semiSubResultantGcdEuclidean1| |merge| - |leastMonomial| |roman| |float?| |triangularSystems| |getOrder| - |univariatePolynomial| |f01maf| |spherical| |useSingleFactorBound| - |voidMode| |times!| |lyndonIfCan| |graphState| |makeObject| |mat| - |stopTableGcd!| |HenselLift| |e01bff| |setAdaptive| |qelt| |isobaric?| - |freeOf?| |c06gbf| |listexp| |getGoodPrime| |setMaxPoints3D| |linear| - |coef| |rightPower| |indicialEquations| |iiabs| |possiblyInfinite?| - |qsetelt| |physicalLength| |exprHasAlgebraicWeight| - |resultantEuclideannaif| |sumOfSquares| |laurentIfCan| |duplicates| - |hdmpToDmp| |critT| |merge!| |tryFunctionalDecomposition?| - |writeByte!| |multiset| |xRange| |highCommonTerms| |testModulus| - |d01fcf| |acosIfCan| |Gamma| |seed| |polynomial| - |stoseLastSubResultant| |elem?| |principalIdeal| - |differentialVariables| |positiveSolve| |yRange| |imagJ| - |rightExactQuotient| |iiasec| |bernoulli| |completeHensel| |pdct| - |tableForDiscreteLogarithm| |constantKernel| |f01ref| |maxColIndex| - |integerIfCan| |recur| |zRange| |monicDivide| |e04mbf| - |complexEigenvalues| |OMgetEndObject| |imagI| |ceiling| - |leftFactorIfCan| |sort| |dualSignature| |trigs| |tab| |separate| - |map!| |anticoord| |elaborate| |sin2csc| |readUInt8!| |multiple?| - |primPartElseUnitCanonical| |internal?| |dec| |c05pbf| |extractIfCan| - |doublyTransitive?| |composite| |qsetelt!| |OMgetType| |s17adf| - |mapCoef| |toseInvertible?| |nand| |rombergo| |LyndonWordsList1| - |replace| |limitedint| |characteristicSerie| |eulerPhi| |rischDEsys| - |exQuo| |viewDefaults| |backOldPos| |OMreceive| |getIdentifier| - |sumOfKthPowerDivisors| |exp1| |difference| |complexEigenvectors| - |changeVar| |elaborateFile| |createNormalPoly| |low| |symFunc| - |random| |insertRoot!| |clearTheSymbolTable| |makeVariable| - |nextSublist| |sincos| |postfix| |LyndonBasis| |newSubProgram| - |sorted?| |currentCategoryFrame| |fortranDouble| |bivariateSLPEBR| - |graeffe| F2FG |algebraic?| |kind| |heapSort| |fillPascalTriangle| - |stFuncN| |subtractIfCan| |df2fi| |testDim| |mathieu11| - |polynomialZeros| |patternMatchTimes| |ldf2lst| |acsch| |op| - |cosSinInfo| |tubeRadius| |inR?| |ocf2ocdf| |raisePolynomial| - |unravel| |hclf| |d01anf| |indices| |factor| - |rewriteIdealWithRemainder| |logIfCan| |elRow2!| |pointSizeDefault| - |gcdcofact| |orbits| |comp| |shanksDiscLogAlgorithm| SEGMENT |entries| - |integralLastSubResultant| |tryFunctionalDecomposition| |sqrt| - |iCompose| |before?| |checkRur| |f04mbf| |OMencodingSGML| |addPoint2| - |s13aaf| |LowTriBddDenomInv| |real| |insertMatch| |coth2tanh| - |getGraph| |rules| |internalSubQuasiComponent?| |rootNormalize| - |d03faf| |factorSquareFree| |stFunc1| |balancedFactorisation| - |disjunction| |dominantTerm| |lieAdmissible?| |imag| |pureLex| |mesh?| - |singleFactorBound| |direction| |fracPart| |fullPartialFraction| - |directProduct| |f02aff| |LiePolyIfCan| |linearPart| |An| |toroidal| - |scripted?| |intPatternMatch| |one?| |inputOutputBinaryFile| - |mainPrimitivePart| |rewriteIdealWithHeadRemainder| |yCoord| - |evaluate| |antisymmetric?| |normInvertible?| |union| |pushNewContour| - GF2FG |quartic| |polyPart| |key?| |rootOfIrreduciblePoly| |predicates| - |brace| |removeIrreducibleRedundantFactors| |purelyAlgebraic?| - |OMgetEndApp| |arguments| |numeric| |torsion?| |compactFraction| - |lazyPrem| |complete| |prefixRagits| |maxIndex| |e02ahf| |wholeRagits| - |e04fdf| |destruct| |byteBuffer| |iiacsc| |radical| |rquo| - |wordsForStrongGenerators| |cosh2sech| |e02bcf| - |nativeModuleExtension| |normFactors| |lastSubResultantElseSplit| - |component| |round| |slex| |interpretString| |members| |rotatez| - |sechIfCan| |genericRightNorm| |OMputEndError| |firstNumer| |ref| - |nsqfree| |blue| |imagK| |quotedOperators| |zero?| |coerceS| |check| - |rk4a| |shiftRight| |copy| |OMParseError?| |roughEqualIdeals?| - |nextPrimitivePoly| |restorePrecision| |normal01| |hermite| - |radicalOfLeftTraceForm| |rotatex| |atanIfCan| |nextIrreduciblePoly| - |removeRoughlyRedundantFactorsInPol| |upperCase?| |shellSort| - |squareFreeLexTriangular| |monomial| |randnum| |heap| |errorInfo| - |deepestInitial| |toScale| |null?| |module| |cyclicEntries| |palgLODE| - |bandedJacobian| |multivariate| |algebraicCoefficients?| - |outlineRender| |binaryFunction| |repeating?| |localAbs| |vspace| - |sub| |rootOf| |reducedContinuedFraction| |normalize| - |showScalarValues| |variables| |prime?| |listOfLists| - |setVariableOrder| |rowEchLocal| |lyndon| |wholePart| |OMputError| - |addPointLast| |leftRank| |prinb| |parametric?| - |purelyTranscendental?| |viewport2D| |condition| |infRittWu?| |match?| - |measure2Result| |setColumn!| |fill!| |setRow!| |extractTop!| - |autoCoerce| |iomode| |d01aqf| |noValueMode| |baseRDE| |OMopenString| - |rspace| |f07adf| |zeroOf| |OMUnknownCD?| |shuffle| |setlast!| - |recolor| |genus| |mathieu22| |interpret| |changeBase| |paraboloidal| - |ramifiedAtInfinity?| |c06fqf| |yellow| |lazyIrreducibleFactors| - |drawComplex| |makeRecord| |binaryTree| |dictionary| |debug| |cCsc| - |complexLimit| |bezoutResultant| |notelem| |f04faf| - |irreducibleFactor| |secIfCan| |sizeLess?| |antisymmetricTensors| - |attributeData| |po| D |taylor| |gcdPolynomial| |close| |OMgetSymbol| - |fullDisplay| |lexTriangular| |c06gsf| F |numberOfVariables| |cCos| - |inspect| |laurent| |clearTable!| |mapDown!| |addMatchRestricted| - |roughSubIdeal?| |eisensteinIrreducible?| |safetyMargin| |shufflein| - |equality| |e02ajf| |puiseux| |csc2sin| |display| - |coercePreimagesImages| |rightNorm| |readUInt16!| - |unrankImproperPartitions1| |palgextint0| |const| |makeTerm| |clip| - |stronglyReduce| |stopMusserTrials| |taylorIfCan| |resetVariableOrder| - |associative?| |subHeight| |setDifference| |e02bef| |generic?| - |elliptic?| |palgRDE| |inv| |sparsityIF| |makeViewport2D| - |regularRepresentation| |c06eaf| |resultant| |iicosh| |s18def| - |makeSketch| |ground?| |nextPrime| |revert| - |rightRegularRepresentation| |paren| |coerceImages| - |encodingDirectory| |euler| |clearDenominator| |drawToScale| - |subresultantSequence| |ground| |flagFactor| - |unrankImproperPartitions0| |quotientByP| |rootSimp| |coHeight| - |gradient| |fortran| |power| |rightMinimalPolynomial| |minGbasis| - |f04axf| |input| |leadingMonomial| |infix| |bounds| |chiSquare1| - |lookupFunction| |iiGamma| |zeroSquareMatrix| |e04jaf| |plus!| - |numberOfFractionalTerms| |npcoef| |nthRootIfCan| |reflect| - |leadingCoefficient| |library| |adaptive?| |axes| |groebner?| - |getMatch| |size| EQ |leftTrace| |updatD| |pmComplexintegrate| - |primitiveMonomials| |print| |OMputApp| |odd?| |debug3D| - |rangeIsFinite| |showTheIFTable| |binaryTournament| |rightDivide| - |expintegrate| |dihedral| |arity| |resolve| |reductum| |iidsum| - |makeprod| |positive?| |messagePrint| |meatAxe| |binding| |ran| - |splitLinear| |groebner| |evenlambert| |iicos| |qualifier| |setleft!| - |solid| |compound?| |mkcomm| |linearlyDependent?| |ef2edf| |decrease| - |numberOfDivisors| |set| |iiacos| |c06gcf| |diff| |alphabetic?| - |ignore?| 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|setLegalFortranSourceExtensions| |radicalRoots| - |complexForm| |binary| |mapUnivariate| |pile| |character?| - |limitedIntegrate| |inverseLaplace| |cCosh| |e01bef| |hcrf| - |karatsuba| |roughUnitIdeal?| |erf| |powmod| |lfextlimint| - |OMputObject| |imagE| |front| |d01apf| |vectorise| |log| |insert!| - |systemSizeIF| |solve| |constantLeft| |rowEchelonLocal| |s17dlf| - |OMputString| |weakBiRank| |stoseInvertibleSet| |evenInfiniteProduct| - |symmetric?| |s17def| |bumptab| |li| |pop!| |space| |integral?| - |subset?| |coleman| |wreath| |setelt| |reverse| |partitions| |iicsch| - |floor| |e01baf| |dilog| |sturmSequence| |lambert| |algSplitSimple| - |categoryMode| |countRealRootsMultiple| |setOrder| |sncndn| - |explimitedint| |subResultantChain| |sin| |lazyPseudoRemainder| - |blankSeparate| |acschIfCan| |selectPDERoutines| |explicitlyEmpty?| - |getlo| |leftUnits| |minimalPolynomial| |numFunEvals| |cos| - |OMgetAttr| |resultantReduitEuclidean| |structuralConstants| - |setfirst!| 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|rationalPower| |unary?| |atan| - |absolutelyIrreducible?| |wrregime| |constantOpIfCan| |lagrange| - |dioSolve| |leftDiscriminant| |bandedHessian| |thetaCoord| - |showFortranOutputStack| |acot| |operation| |e04ycf| |perspective| - |credPol| |OMunhandledSymbol| |normalElement| |sturmVariationsOf| - |primextintfrac| |subSet| |f07fdf| |asec| - |halfExtendedSubResultantGcd2| |readLine!| |semicolonSeparate| - |linearPolynomials| |fortranCarriageReturn| |complexExpand| - |perfectNthRoot| |aromberg| |indicialEquation| |cn| |acsc| - |binomThmExpt| |s18dcf| |mdeg| |crest| |fTable| |makeUnit| |prefix| - |iterationVar| |sinh| |clipPointsDefault| |maxRowIndex| |fixPredicate| - |queue| |ratDenom| |seriesToOutputForm| |changeName| |completeSmith| - |unitNormalize| |cosh| |normalForm| |nullity| - |noncommutativeJordanAlgebra?| |saturate| |tower| |integral| - |monomRDEsys| |normalDeriv| |Lazard2| |mainKernel| |tanh| |lazyPquo| - |eq| |sts2stst| |leader| |simpson| |var1StepsDefault| - |strongGenerators| |normalizedDivide| |remove| |has?| |frst| |coth| - |iter| |findBinding| |initializeGroupForWordProblem| |delay| |more?| - |nlde| |insertTop!| |vertConcat| |obj| |semiResultantEuclideannaif| - |sech| |derivative| |cyclotomic| |laplacian| |uniform| |infLex?| - |last| |aQuartic| |fortranReal| |completeEchelonBasis| |bit?| |cache| - |csch| |cschIfCan| |internalInfRittWu?| |invmod| |f04adf| - |cyclicGroup| |assoc| |closeComponent| |randomLC| |cardinality| - |polyred| |asinh| |squareFreeFactors| |nextItem| |categoryFrame| - |complexNumeric| |setright!| |clearTheFTable| |deref| - |cyclicSubmodule| |acosh| |OMgetEndBind| |enterPointData| |copyInto!| - |lazyGintegrate| |omError| |slash| |mkAnswer| |symbol?| |sech2cosh| - |atanh| |factorByRecursion| |inGroundField?| |setsubMatrix!| - |resultantReduit| |kernels| |perfectSqrt| |leftMult| |expPot| - |supersub| |exprHasLogarithmicWeights| |acoth| |critMonD1| - |selectfirst| |cAsech| |cyclicParents| |operator| |sh| |permutation| - |tablePow| |f04jgf| |matrixGcd| |e01bgf| |asech| |level| - |transcendent?| |exp| |physicalLength!| |unparse| |mvar| |rootKerSimp| - |someBasis| |conjugates| |bitCoef| |schema| |separant| |simpsono| - |presub| |diagonalMatrix| |deepCopy| - |removeRoughlyRedundantFactorsInPols| |univariate| |isPower| |e04gcf| - |halfExtendedResultant1| |overbar| |lazyPremWithDefault| |multiple| - |powerAssociative?| |extractProperty| |c06gqf| |isImplies| |row| - |virtualDegree| |prologue| |collectQuasiMonic| |isList| - |characteristic| |applyQuote| |compile| |iExquo| |OMencodingXML| - |child?| |setEpilogue!| |table| |factorSFBRlcUnit| |dn| |ffactor| - |infinite?| |concat!| |convergents| |index?| |setleaves!| |redpps| - |subCase?| |new| |OMreadFile| |OMputEndBVar| |monomials| |cycles| - |pToHdmp| |push| |iisec| |fprindINFO| |just| |moduloP| |nodeOf?| - |radicalEigenvalues| |refine| |bfEntry| - |stoseInternalLastSubResultant| |ruleset| |fortranCharacter| - |genericRightDiscriminant| |cCsch| |clearTheIFTable| |dihedralGroup| - |retract| |rename!| |semiResultantEuclidean1| |nil?| |basisOfCenter| - |matrixConcat3D| |curveColorPalette| |enumerate| |sizePascalTriangle| - |lastSubResultant| |sort!| |mainValue| |complexZeros| |dimension| - |topPredicate| |symmetricGroup| |normalizeIfCan| |mapGen| |OMopenFile| - |high| |s18adf| |convert| |complexRoots| |s18aef| |prime| |iiatan| - |fortranDoubleComplex| |dflist| |nodes| |sequence| |setAdaptive3D| - |numberOfFactors| |quadratic| |nthFlag| |pole?| |s19aaf| - |localIntegralBasis| |typeForm| |nil| |rur| |fmecg| |normal?| - |radicalEigenvector| |btwFact| |selectsecond| - |indiceSubResultantEuclidean| |internalAugment| |box| - |doubleResultant| |headReduce| |Ei| |rightLcm| |principalAncestors| - |packageCall| |enterInCache| |lazyPseudoDivide| |listBranches| - |quasiMonic?| |d02cjf| |printStats!| |reduceLODE| |exactQuotient| - |intcompBasis| |semiDegreeSubResultantEuclidean| |mainExpression| - |simplify| |accuracyIF| |totalLex| |increment| |s17dgf| |approximate| - |curryRight| |remainder| |solveid| |wholeRadix| |divide| - |zeroSetSplitIntoTriangularSystems| |represents| |quatern| |lfunc| - |certainlySubVariety?| |complex| |stop| |reducedDiscriminant| - |getVariableOrder| |minIndex| |triangulate| |scale| |left| |cAsin| - |mapBivariate| |SturmHabichtSequence| |knownInfBasis| |s19adf| - |irCtor| |SturmHabichtMultiple| |pomopo!| |numberOfCycles| |exponent| - |right| |expIfCan| |mulmod| |OMconnOutDevice| |realEigenvalues| - |rischDE| |repSq| |linear?| |eigenvectors| |mightHaveRoots| - |karatsubaOnce| |newReduc| |back| |cycleRagits| |ratpart| - |buildSyntax| |failed| |initial| |totalGroebner| |setchildren!| - |irVar| |roughBase?| |defineProperty| |Frobenius| |LiePoly| - |readIfCan!| |extendedIntegrate| |normalise| |digit?| |iitanh| - |select!| |subResultantGcdEuclidean| |c06fuf| |powers| |option?| - |solveLinearPolynomialEquation| |kovacic| |imagk| |f02bjf| |middle| - |polarCoordinates| |is?| |constantRight| |consnewpol| - |leftRankPolynomial| |rubiksGroup| |Si| |directSum| |totalfract| - |superHeight| |binarySearchTree| |monomialIntPoly| |minimumDegree| - |shallowExpand| |acoshIfCan| |sample| |assign| |enqueue!| - |setPredicates| |htrigs| |dual| |purelyAlgebraicLeadingMonomial?| - |graphImage| |clearFortranOutputStack| |typeLists| |mindegTerm| - |factorPolynomial| |complexElementary| |solveLinear| |atrapezoidal| - |leviCivitaSymbol| |ptFunc| |exponential1| |shallowCopy| |bits| - |s20adf| |infieldIntegrate| |ListOfTerms| - |unprotectedRemoveRedundantFactors| |cycleLength| |identification| - |expressIdealMember| |rightCharacteristicPolynomial| |order| - |useEisensteinCriterion?| |stoseInvertible?sqfreg| |submod| |member?| - |integralRepresents| |minPoints3D| |mathieu24| |laguerre| |setPoly| - |polar| |removeConstantTerm| |setIntersection| - |cyclotomicFactorization| |Is| |overset?| |whitePoint| - |PollardSmallFactor| |OMputAttr| |linkToFortran| |symbol| |factor1| - |wronskianMatrix| |length| |hue| |cAcot| |s17agf| |dfRange| |quote| - |Aleph| |linearDependenceOverZ| |zCoord| |expression| |f02adf| - |prepareDecompose| |scripts| |generalLambert| - |conditionsForIdempotents| |lexico| |edf2efi| |moreAlgebraic?| - |pointLists| |setClosed| |drawComplexVectorField| |integer| |key| - |unitNormal| |socf2socdf| |extendedResultant| |OMencodingBinary| - |signatureAst| |real?| |changeWeightLevel| |palgRDE0| |redmat| - |parent| |leftMinimalPolynomial| |generalPosition| |integrate| - |kroneckerDelta| |besselY| |problemPoints| |upDateBranches| - |makeGraphImage| |algebraicOf| |unit| |filename| |super| |basicSet| - |bytes| |mathieu12| |s18acf| |airyBi| |f01qef| |multiplyCoefficients| - |chvar| |goto| |generalizedInverse| |multMonom| |minPol| |youngGroup| - |imaginary| |squareFreePolynomial| |divergence| |rarrow| |whileLoop| - |algint| |lyndon?| |parse| |irreducible?| |corrPoly| |currentScope| - |depth| |palgLODE0| |viewpoint| |setClipValue| |nthFractionalTerm| - |printStatement| |d02gaf| |hitherPlane| |getConstant| |rightQuotient| - |pseudoQuotient| |d01asf| |doubleDisc| |signAround| |sinhcosh| - |uniform01| |inverseColeman| |setvalue!| |closed| |iiasinh| |harmonic| - |outputBinaryFile| |setScreenResolution3D| |entry| |extendIfCan| - |Hausdorff| |trivialIdeal?| |subresultantVector| |say| - |expandTrigProducts| |e04dgf| |monicCompleteDecompose| UTS2UP - |patternMatch| |lighting| |arg1| |iidprod| |distribute| |radPoly| - |rootDirectory| |bezoutMatrix| |minRowIndex| |ScanRoman| - |semiIndiceSubResultantEuclidean| |iisqrt2| |BumInSepFFE| |arg2| - |e04ucf| |dimensionsOf| |optional?| |cos2sec| |reset| |hdmpToP| - |s19acf| |alphanumeric?| |fortranLogical| |internalIntegrate| - |nextLatticePermutation| |sum| |operators| |pade| - |numericalOptimization| |generators| |branchIfCan| |inc| |support| - |e02aef| |setref| |cAtan| |addiag| |numberOfOperations| |conditions| - RF2UTS |cfirst| |magnitude| |write| |quadraticForm| |linears| - |OMsupportsCD?| |green| |pointColor| |tanintegrate| |bigEndian| - |removeDuplicates| |match| |completeEval| |save| |choosemon| |options| - |iibinom| |lp| |d01ajf| |goodPoint| |leftDivide| |relationsIdeal| - |completeHermite| |dom| |fortranLiteralLine| |OMlistCDs| |cSinh| - |create| |outputSpacing| |rootProduct| |numberOfIrreduciblePoly| - |hasSolution?| |OMputEndObject| |countRealRoots| |firstDenom| - |removeZero| |kmax| |endSubProgram| |partialDenominators| |groebgen| - |nil| |infinite| |arbitraryExponent| |approximate| |complex| - |shallowMutable| |canonical| |noetherian| |central| + |Record| |Union| |setvalue!| |llprop| |symmetricProduct| |denomRicDE| + |stirling2| |match| |save| |internalSubPolSet?| + |rationalApproximation| |string| |rightUnits| |lp| |currentScope| + |float?| |setImagSteps| |root| |getVariableOrder| |groebSolve| + |degreeSubResultantEuclidean| |infix| |numberOfPrimitivePoly| + |innerSolve1| |factorByRecursion| |lastSubResultantElseSplit| + |tubePlot| |OMUnknownCD?| |mesh?| |semicolonSeparate| |hconcat| + |badNum| |transcendenceDegree| |extensionDegree| |title| + |associative?| |identification| |nothing| |f02ajf| + |lastSubResultantEuclidean| |bfEntry| |lllp| |rightDiscriminant| + |removeIrreducibleRedundantFactors| |acschIfCan| |clikeUniv| + |fortranDouble| |predicate| |printCode| |tanIfCan| |besselI| + |newTypeLists| |coercePreimagesImages| |top| |optional?| |less?| + |leftRegularRepresentation| |rightTraceMatrix| |index?| |relerror| + |signatureAst| |e| |e02agf| |continue| |isPlus| + |resultantEuclideannaif| |LyndonCoordinates| |gcdcofact| |prime?| + |s20acf| |triangular?| |alternatingGroup| |optAttributes| + |eyeDistance| |readIfCan!| |getButtonValue| |s17agf| + |numberOfIrreduciblePoly| |linearAssociatedLog| |axesColorDefault| + |getExplanations| |brillhartIrreducible?| |string?| |startPolynomial| + |mappingMode| |anticoord| |bit?| |s18aef| |OMwrite| |power!| + |tubePointsDefault| |multiEuclideanTree| |hMonic| |constant| + |palgint0| |singleFactorBound| |jacobian| |bounds| |d02bbf| + |OMputEndApp| |unparse| |fortranCompilerName| |setCondition!| + |reciprocalPolynomial| |f02bbf| |hash| |zeroDim?| |characteristic| + |schwerpunkt| |monicRightDivide| |curryRight| |setRow!| |dequeue!| + |multiset| |linearPolynomials| ** |count| |rotatex| |repSq| + |tracePowMod| |hex| |rightNorm| |lfextendedint| |polyRicDE| |mantissa| + |bivariateSLPEBR| |parameters| |safeFloor| |OMgetError| |component| + |inGroundField?| |selectNonFiniteRoutines| |measure| + |internalSubQuasiComponent?| |splitSquarefree| + |setLegalFortranSourceExtensions| |color| |closedCurve| + |symmetricPower| |lambert| |multiplyExponents| |recoverAfterFail| + |algebraicCoefficients?| |OMUnknownSymbol?| |colorDef| |divideIfCan| + |radPoly| |laurentRep| |extendedIntegrate| |imagE| |youngGroup| + |substring?| |evaluate| |wholeRagits| |hasSolution?| + |leviCivitaSymbol| |c06gbf| |divisorCascade| |associatorDependence| + |innerEigenvectors| |mix| |cAsec| |coordinate| |elaborate| |quotient| + |OMgetFloat| |bombieriNorm| |iiasech| |testModulus| |isTimes| + |suffix?| |exprToUPS| |splitNodeOf!| |lazyResidueClass| |ef2edf| + |tan2trig| |cyclic| |expenseOfEvaluation| |innerSolve| |bernoulliB| + |isOp| |cfirst| |unitsColorDefault| |complexZeros| |argumentListOf| + |UpTriBddDenomInv| |iExquo| |OMputBVar| |prefix?| |doubleRank| |Is| + |remainder| |extractTop!| |vertConcat| |back| |linear?| + |showArrayValues| |variationOfParameters| |list?| |readUInt16!| + |branchPointAtInfinity?| |interpolate| |d01gaf| |coerceL| + |stoseInvertibleSetreg| |swapRows!| |determinant| |partition| |numer| + |retractIfCan| |viewDeltaYDefault| |rootNormalize| |algSplitSimple| + |f2st| |atanIfCan| |augment| |hexDigit| |cotIfCan| |rubiksGroup| + |denom| |qPot| |limit| |tanh2coth| |flagFactor| |cdr| |radicalRoots| + |OMputInteger| |indiceSubResultantEuclidean| |simpleBounds?| + |findCycle| |cAcoth| |bsolve| |elColumn2!| |returnType!| + |outlineRender| |maxint| |c02aff| |debug3D| |pi| |OMputEndObject| + |createGenericMatrix| |rootDirectory| |perspective| |formula| + |numberOfHues| |imaginary| |infix?| |e04fdf| |OMgetEndBind| + |initiallyReduce| |infinity| |sin2csc| |ptFunc| |listexp| + |insertRoot!| |mask| |totalDegree| |front| |f02fjf| |antisymmetric?| + |ptree| |completeSmith| |basisOfRightNucleus| |basisOfLeftNucloid| + |setScreenResolution| |sizeMultiplication| |tubePoints| |cyclicEqual?| + |lowerBound| |untab| |fintegrate| |critpOrder| |cTan| + |leftScalarTimes!| |e02dff| |step| |nilFactor| |dmp2rfi| + |functionIsFracPolynomial?| |magnitude| |hclf| |kernel| |solveid| + |decrease| |goodnessOfFit| |cycleRagits| |nrows| |concat| |host| + |OMencodingXML| |reverseLex| |factorset| |sinhIfCan| |list| + |constantOperator| |semiResultantEuclideannaif| |dimension| + |clearCache| |bivariatePolynomials| |ncols| |lhs| |eigenvectors| + |stoseSquareFreePart| |rootBound| |overset?| |draw| |fractionPart| + |unrankImproperPartitions1| |useSingleFactorBound?| |clipSurface| + |unrankImproperPartitions0| |rhs| |nextIrreduciblePoly| |read!| + |genericRightMinimalPolynomial| |satisfy?| |Si| |weighted| |iomode| + |curryLeft| |curve| |readByte!| |f07aef| |conditionP| + |screenResolution3D| |positive?| |connectTo| |monicRightFactorIfCan| + |zeroDimPrime?| |d03faf| |credPol| |currentEnv| |byteBuffer| + |generalizedContinuumHypothesisAssumed| |gethi| |mainKernel| + |frobenius| |rangeIsFinite| |countRealRoots| |df2mf| |categoryMode| + |invertIfCan| |binaryFunction| |complexForm| |s14aaf| |bumptab1| + |makeObject| |squareMatrix| |readUInt8!| |gcdprim| |listYoungTableaus| + |qelt| |clearTheSymbolTable| |representationType| |meshFun2Var| + |squareFreePolynomial| |linear| |enterPointData| |unitNormalize| + |coef| |transform| |bezoutMatrix| |exponential1| |qsetelt| + |continuedFraction| |d01apf| |singRicDE| |rightScalarTimes!| + |atanhIfCan| |deriv| |squareFree| |domainTemplate| |remove!| |xRange| + |internalZeroSetSplit| |assign| |extractBottom!| |lepol| + |normInvertible?| |quadraticForm| |polynomial| |d01anf| |wholeRadix| + |numberOfDivisors| |getGoodPrime| |ratpart| |yRange| |lazyPquo| + |groebnerFactorize| |linearDependence| |extension| |unmakeSUP| + |alternating| |createMultiplicationTable| |iflist2Result| + |pointColorDefault| |s19abf| |zRange| |child?| |normalized?| |gensym| + |part?| |decompose| |sort| |palgextint0| |derivative| |makeSeries| + |complex?| |map!| |outputAsScript| |getOperator| |squareFreePrim| + |whitePoint| |directSum| |dAndcExp| |dec| |e02ddf| |topPredicate| + |qsetelt!| |quotientByP| |normalizeAtInfinity| + |removeRoughlyRedundantFactorsInPol| |jordanAlgebra?| |OMputEndAtp| + |rationalPoints| |setTopPredicate| |deepestTail| |reduced?| + |OMunhandledSymbol| |kind| |repeating?| |bumprow| |length| + |oneDimensionalArray| |sh| |showTheIFTable| |firstDenom| |d01aqf| + |factorSquareFree| |deleteRoutine!| |binary| |op| |setelt!| |scripts| + |ratPoly| |prevPrime| |extractIndex| |random| |zeroDimPrimary?| + |multiple?| |univariate| |resetBadValues| |makeVariable| |e01bhf| + |vectorise| |rootRadius| |iiacsc| |constantIfCan| SEGMENT + |basisOfRightAnnihilator| |exportedOperators| |gramschmidt| + |environment| |iisec| |divergence| |integerBound| |copyInto!| + |normalForm| |unaryFunction| |countRealRootsMultiple| |shallowCopy| + |rdregime| |acsch| |generalizedEigenvector| |bracket| |swap!| + |LyndonWordsList| |generalizedEigenvectors| |iiacos| |divide| |factor| + |minRowIndex| |buildSyntax| |multinomial| |useNagFunctions| |linears| + |pushNewContour| |indices| |comp| |jacobiIdentity?| |const| |elements| + |sqrt| |triangSolve| |trailingCoefficient| |dmpToHdmp| |depth| + |twoFactor| |fortranInteger| |hasTopPredicate?| |palgint| |squareTop| + |semiResultantEuclidean2| |real| |setMaxPoints3D| + |stoseInvertible?reg| |rootSimp| |union| |iisqrt3| |f02xef| |f01bsf| + |cyclicCopy| |totalfract| |eigenvector| |trueEqual| |imag| |nthRoot| + |identity| |halfExtendedResultant2| |getProperty| |setEpilogue!| + |PollardSmallFactor| |even?| |gcdPrimitive| |directProduct| + |factorOfDegree| |symmetricGroup| |cyclotomic| |normalElement| + |rename| |upperCase?| |localAbs| |permutation| |readLineIfCan!| + |removeZero| |moebiusMu| |makingStats?| |expintegrate| + |primitivePart!| |applyRules| |mindeg| |in?| |nextPartition| + |exponents| |primPartElseUnitCanonical| |brace| |stFunc1| |e02bdf| + |nextSublist| |arguments| |createIrreduciblePoly| |mapUnivariate| + |insert!| |fglmIfCan| |numeric| |copy| |uncouplingMatrices| + |validExponential| |noValueMode| |destruct| |saturate| |distFact| + |radical| |inf| |chiSquare| |UnVectorise| |rquo| |rectangularMatrix| + |identitySquareMatrix| |surface| |expint| |toseLastSubResultant| + |OMserve| |rarrow| |createPrimitivePoly| |lazyGintegrate| + |zeroSetSplitIntoTriangularSystems| |bits| |setOrder| |elRow2!| + |totalGroebner| |OMconnectTCP| |mathieu23| GF2FG |primitiveElement| + |makeTerm| |iiacoth| |ScanRoman| |rk4| |norm| |fprindINFO| |prem| + |coefChoose| |OMsupportsCD?| |rightPower| |rk4qc| |definingPolynomial| + |monomial| |OMsupportsSymbol?| |stripCommentsAndBlanks| |match?| + |call| |curve?| |makeResult| |irreducibleFactors| |autoCoerce| + |setProperty| |rightGcd| |c06gcf| |multivariate| |monomialIntPoly| + |coHeight| |vspace| |factorSFBRlcUnit| |extendedEuclidean| + |roughBasicSet| |laplacian| |variables| |solveInField| |dihedral| + |sturmVariationsOf| |d01fcf| |prepareSubResAlgo| |points| + |inHallBasis?| |OMputAttr| |any?| |operation| |normalizeIfCan| + |selectAndPolynomials| |condition| |baseRDEsys| |csch2sinh| |range| + |systemSizeIF| |shellSort| |iitan| |edf2ef| |mapUnivariateIfCan| + |balancedFactorisation| |critM| |s17dcf| |sincos| |close| |cLog| + |tanQ| |ldf2vmf| |lazy?| |tablePow| F |bubbleSort!| |anfactor| + |digits| |baseRDE| |interpret| |integral| |htrigs| |putProperties| + |minus!| |fortranLiteralLine| |makeRecord| |singular?| |debug| + |fractRadix| |split!| |display| |pseudoDivide| |binaryTree| |legendre| + |roughEqualIdeals?| |omError| |wordsForStrongGenerators| |ceiling| + |sncndn| D |taylor| |upperCase!| |setchildren!| |pointSizeDefault| + |createNormalElement| |setProperties| |leaf?| |genericPosition| + |lazyIntegrate| |var2StepsDefault| |fibonacci| |s20adf| |laurent| + |checkForZero| |listRepresentation| |B1solve| |OMreadStr| |besselJ| + |leadingIdeal| |coord| |solveLinearlyOverQ| |puiseux| |gradient| + |minimumDegree| |var1StepsDefault| |exponent| |rational?| |quartic| + |oddInfiniteProduct| |mainExpression| |jordanAdmissible?| + |monicCompleteDecompose| |genericLeftTrace| |intChoose| |acosIfCan| + |ParCondList| |multiplyCoefficients| |s01eaf| |leftExtendedGcd| + |reindex| |irreducibleRepresentation| |stopTableGcd!| |primextintfrac| + |inv| |input| |arity| |removeSquaresIfCan| |generic| |varselect| + |binomial| |ode| |safetyMargin| |leftQuotient| |doubleDisc| |ground?| + |library| |monomRDEsys| |symmetricTensors| |dual| |toScale| + |replaceKthElement| EQ |mapSolve| |firstUncouplingMatrix| + |cycleSplit!| |ground| |postfix| |radicalEigenvectors| |dictionary| + |stFunc2| |diagonals| |makeYoungTableau| |univariateSolve| |vark| + |curveColorPalette| |conjunction| |leadingMonomial| |log2| + |pascalTriangle| |aspFilename| |solve1| |OMread| |wordInGenerators| + |setStatus!| |OMlistCDs| |readBytes!| |qualifier| |leadingCoefficient| + |c06ecf| |nextsousResultant2| |getProperties| |row| |rationalPower| + |mergeFactors| |setOfMinN| |size| |leftFactorIfCan| |OMgetEndAttr| + |oddintegers| |primitiveMonomials| |print| |set| |strongGenerators| + |leftOne| |hessian| |preprocess| |localIntegralBasis| |prinpolINFO| + |resolve| |findBinding| |viewport2D| |difference| |reductum| |Gamma| + |rationalPoint?| |build| |compactFraction| |startTable!| |car| + |universe| |irDef| |e01sbf| |fortran| |fixedPoint| |nextPrimitivePoly| + |property| |nextItem| |fixedPointExquo| |simplify| |s13aaf| + |partitions| |splitDenominator| |diophantineSystem| |expIfCan| + |midpoints| |makeEq| |divisors| |makeSin| |leadingSupport| UTS2UP + |setClosed| |closedCurve?| |chvar| |primitivePart| |one?| |pair?| + |ldf2lst| |generator| |HenselLift| |shufflein| |categories| |laplace| + |RemainderList| |purelyAlgebraicLeadingMonomial?| |virtualDegree| + |Vectorise| |lintgcd| |e02aef| |setprevious!| |getStream| + |integralAtInfinity?| |signAround| |leftFactor| |chineseRemainder| + |computeBasis| |asecIfCan| |true| |primeFrobenius| |trapezoidal| + |category| |tube| |s18aff| |asimpson| |sylvesterSequence| + |coerceImages| |cCsc| |modularGcdPrimitive| |null?| |setPoly| |rur| + |domain| |middle| |cSinh| |setleft!| |enumerate| |dioSolve| + |firstSubsetGray| |unary?| |collectUpper| |e01sff| |midpoint| + |package| |atoms| |node| |dualSignature| |myDegree| |removeSinSq| + |OMputEndBind| |insert| |normalizedDivide| |lazyEvaluate| |pushdown| + |lazyPrem| |hostByteOrder| |getMatch| |minimumExponent| + |initializeGroupForWordProblem| |argscript| |search| + |complexEigenvectors| |flatten| |show| |seed| |f07fef| + |fortranLinkerArgs| |repeating| |cycleEntry| |particularSolution| + |startStats!| |collect| |infRittWu?| |parabolic| |aLinear| |mulmod| + |restorePrecision| |categoryFrame| |printHeader| |OMencodingUnknown| + |accuracyIF| |iicsch| |fractionFreeGauss!| |squareFreePart| + |isQuotient| |trace| |endOfFile?| |appendPoint| |f02akf| |exists?| + |setref| |maxRowIndex| |FormatRoman| |rightExtendedGcd| + |LowTriBddDenomInv| |drawComplexVectorField| |graphImage| + |lexGroebner| |trim| |inputOutputBinaryFile| + |selectIntegrationRoutines| |cosSinInfo| |incr| |extract!| + |indicialEquationAtInfinity| |patternMatch| |figureUnits| |script| + |complexLimit| |goto| |module| |integralMatrixAtInfinity| + |removeRedundantFactorsInPols| |sinIfCan| |hi| |equality| |e01bff| + |isOr| |encodingDirectory| |imagj| |subMatrix| |e02daf| + |expextendedint| |weierstrass| |directory| |rdHack1| |headRemainder| + |getBadValues| |degree| |genericLeftMinimalPolynomial| |has?| + |comparison| |integralBasisAtInfinity| |asinIfCan| |fmecg| + |polarCoordinates| |bag| |subscript| |leftDiscriminant| |region| |tex| + |height| |realSolve| |absolutelyIrreducible?| |bitTruth| |polar| + |complete| |logGamma| |create| |solid| |sizePascalTriangle| + |boundOfCauchy| |stoseLastSubResultant| |listConjugateBases| + |OMReadError?| |nextsubResultant2| |viewThetaDefault| |s17akf| |trigs| + |sumOfDivisors| |mkPrim| |changeVar| |units| |outerProduct| |write!| + |iiacot| |prologue| |functionIsContinuousAtEndPoints| |gcdcofactprim| + |rightOne| |extractClosed| |measure2Result| |delay| |truncate| + |isExpt| |cap| |explogs2trigs| |isConnected?| |modifyPointData| + |leftTrace| |equation| |setTex!| |point| |functionIsOscillatory| + |perfectSquare?| |derivationCoordinates| |clearFortranOutputStack| + |OMconnOutDevice| |normal01| |setright!| |cAtan| |fixPredicate| + |totalLex| |zag| |insertMatch| |pToDmp| |comment| |bezoutResultant| + |laguerreL| |cot2tan| |associates?| |cTanh| |tubeRadius| |center| + |copies| |acothIfCan| |floor| |SturmHabicht| |log10| |hasPredicate?| + |isAtom| |cosIfCan| |moduleSum| |mainPrimitivePart| |showAll?| + |deepExpand| |series| |lighting| |viewPhiDefault| |localUnquote| + |code| |elem?| |bitand| |generalizedInverse| |discriminantEuclidean| + |writeInt8!| |hasHi| |mirror| |declare| |e02ajf| |setAdaptive| + |complexElementary| |euler| |bitior| |univariatePolynomialsGcds| + |torsionIfCan| |cyclicEntries| |normal?| |meshPar1Var| |is?| + |numericIfCan| |permutations| |acscIfCan| |central?| |setFormula!| + |makeSUP| |traceMatrix| |isNot| |prefixRagits| |rule| + |showTheRoutinesTable| |generate| |coerceP| |FormatArabic| + |modifyPoint| |nonQsign| |bandedHessian| |typeLists| |jokerMode| + |wrregime| |removeConstantTerm| |tubeRadiusDefault| |updatD| + |normalDeriv| |outputSpacing| |min| |lastSubResultant| |compound?| + |alphanumeric| |setPosition| |compiledFunction| |mpsode| |eof?| + |outputForm| |companionBlocks| |incrementBy| |diagonal| |tab| |airyAi| + |matrix| |elaborateFile| |notelem| |UP2ifCan| |collectQuasiMonic| + |powerSum| |definingEquations| |nthCoef| |expand| |element?| + |setColumn!| |more?| |unknownEndian| |number?| |getCode| |twist| + |lowerCase!| |addiag| |queue| |filterWhile| |froot| |zeroVector| + |maxrank| |dot| |idealiserMatrix| |genericRightTraceForm| |hermite| + |primeFactor| |doubleComplex?| |inR?| |filterUntil| |increment| + |e01baf| |coth2tanh| |mightHaveRoots| |principalIdeal| + |realEigenvalues| |pushup| |conical| |clearTheFTable| |iisech| + |select| |setValue!| |s15adf| |sup| |trigs2explogs| |iroot| |reorder| + |minColIndex| |palgextint| |OMsetEncoding| |initiallyReduced?| + |properties| |iidprod| |csc2sin| |medialSet| |lift| |clearDenominator| + |removeCoshSq| |multMonom| |parseString| + |rewriteIdealWithHeadRemainder| |radicalEigenvector| |constantRight| + |isobaric?| |scaleRoots| |solveLinear| |translate| |reduce| |quoByVar| + |leftZero| |mindegTerm| |palgLODE| |result| |maxIndex| + |divideExponents| |factorsOfDegree| |flexibleArray| |e02adf| + |controlPanel| |rroot| |f04faf| |constantOpIfCan| |callForm?| + |addBadValue| |extend| |pmComplexintegrate| Y |rootProduct| |mkcomm| + |content| |thetaCoord| |lllip| |setUnion| |pseudoRemainder| + |numberOfOperations| |setIntersection| |bothWays| |separate| |sort!| + |monomialIntegrate| |createNormalPoly| |ord| |alternative?| |bindings| + |HermiteIntegrate| |label| |dmpToP| |droot| |charClass| |zeroMatrix| + |nlde| |removeRedundantFactors| |isList| |usingTable?| + |sylvesterMatrix| |complementaryBasis| |ratDenom| |eigenMatrix| + |fill!| |bat| |viewSizeDefault| |inrootof| |quasiComponent| |ideal| + |light| |ocf2ocdf| |s17dgf| |eulerE| |maxrow| |karatsubaOnce| + |radicalOfLeftTraceForm| |nullary| |btwFact| |deref| |df2ef| + |hexDigit?| |subscriptedVariables| |getGraph| |pointData| + |specialTrigs| |rischDE| |imports| |orthonormalBasis| |copy!| |df2st| + |sturmSequence| |drawToScale| |diag| |charthRoot| |s21bbf| + |associator| |consnewpol| |cCos| |outputAsFortran| |distribute| + |errorKind| |cot2trig| |parents| |minPol| |bandedJacobian| |e02ahf| + |yCoord| |modulus| |euclideanNormalForm| |freeOf?| |atrapezoidal| + |constructor| |showFortranOutputStack| |column| |loopPoints| + |logical?| |children| |makeMulti| |quasiRegular| |byte| + |leadingExponent| |s17ajf| |tanh2trigh| |option| |f04atf| + |generalTwoFactor| |OMputApp| |iibinom| |showSummary| |shrinkable| + |quasiAlgebraicSet| |trace2PowMod| |external?| |ip4Address| + |cyclotomicFactorization| RF2UTS |bitLength| |recur| + |linearlyDependent?| |mainValue| |interactiveEnv| |replace| + |stronglyReduced?| |constantCoefficientRicDE| |ode1| + |seriesToOutputForm| |flexible?| |insertTop!| |showAttributes| + |tableau| |low| |size?| |subQuasiComponent?| |denomLODE| |empty| + |raisePolynomial| |f02aaf| |newReduc| |outputList| |knownInfBasis| + |overbar| |unit?| |integer?| |permanent| |d02cjf| |dihedralGroup| + |monomials| |stack| |rightTrim| |scan| |setErrorBound| |critBonD| + |name| |double| |selectsecond| |nullSpace| |invertibleElseSplit?| + |inspect| |iCompose| |addPoint| |linearAssociatedExp| |leftTrim| + |sparsityIF| |coerceS| |body| |perfectNthPower?| |cyclicSubmodule| + |leftRankPolynomial| |simplifyLog| |OMputError| |plot| |int| + |subresultantSequence| |mainCharacterization| |product| |interval| + |null| |rk4f| |autoReduced?| |quasiRegular?| |e04ycf| |paraboloidal| + |var1Steps| |reduction| |status| |submod| |signature| |horizConcat| + |not| |tRange| |pop!| |hitherPlane| BY |cycleTail| + |transcendentalDecompose| |bytes| |dimensions| + |genericLeftDiscriminant| |normalizedAssociate| |dim| |and| |odd?| + |d01ajf| |vector| |setMaxPoints| |tab1| |acoshIfCan| |output| + |symFunc| |aCubic| |printingInfo?| |capacity| |d02kef| |changeName| + |or| |differentiate| |monicDivide| |ran| |Hausdorff| |makeprod| + |rootPower| |zoom| |OMgetAttr| |integralBasis| |shift| + |stiffnessAndStabilityOfODEIF| |xor| |primes| |critB| |voidMode| + |prepareDecompose| |scalarMatrix| |normDeriv2| |s19adf| + |rangePascalTriangle| |nextLatticePermutation| |declare!| |unravel| + |case| |principal?| |generalInfiniteProduct| |cycles| |assert| + |inverseIntegralMatrixAtInfinity| |traverse| |e02bbf| |port| + |showClipRegion| |xn| |closeComponent| |pattern| |moebius| |Zero| + |printStats!| |removeSuperfluousCases| |cubic| |cylindrical| + |leftMinimalPolynomial| |randomR| |lazyPremWithDefault| |linearPart| + |numerator| |One| |f04asf| |edf2fi| |rename!| |iicosh| + |commutativeEquality| |computeCycleLength| |musserTrials| |t| + |setAdaptive3D| |fixedDivisor| |e02zaf| NOT |clearTable!| |c06ekf| + |unitVector| |exprHasLogarithmicWeights| |headAst| |check| + |makeViewport2D| |functorData| |ramifiedAtInfinity?| |s18dcf| OR + |totalDifferential| |s21bdf| |before?| |Ci| |rowEch| |nullary?| + |sayLength| |minPoly| |computePowers| |subtractIfCan| |message| AND + |c06ebf| |internalIntegrate0| |addPointLast| |reducedSystem| + |viewDefaults| |combineFeatureCompatibility| |numberOfNormalPoly| + |charpol| |member?| |escape| |goodPoint| |space| |getConstant| + |stiffnessAndStabilityFactor| |schema| |basisOfCommutingElements| + |OMputBind| |mathieu12| |resultantReduitEuclidean| |permutationGroup| + |segment| |besselK| |elt| |e04mbf| |createZechTable| + |algebraicVariables| |makeCos| |partialFraction| |binaryTournament| + |iiacsch| |leastPower| |isAnd| |operators| |cond| + |primPartElseUnitCanonical!| |powers| |univcase| |splitLinear| + |trivialIdeal?| |sechIfCan| |generalLambert| |ruleset| |meshPar2Var| + |birth| |createThreeSpace| |maxdeg| |numberOfMonomials| |compdegd| + |conjug| |times!| |cyclic?| |fi2df| |antiCommutator| |minimize| + |viewport3D| |nor| |prolateSpheroidal| |zeroDimensional?| |npcoef| + |reduceLODE| |reify| |prinshINFO| |compBound| |cExp| |cons| + |getMultiplicationTable| |randomLC| |irCtor| |symmetricRemainder| + |second| |nullity| |externalList| |mapDown!| |pastel| |geometric| + |generalPosition| |s18def| |suchThat| |powerAssociative?| + |numberOfFactors| |numberOfComponents| |cRationalPower| |An| |third| + |rewriteIdealWithRemainder| |OMgetInteger| |pToHdmp| + |semiResultantEuclidean1| |critMonD1| |showTheSymbolTable| + |rightTrace| |regularRepresentation| |c06fqf| |child| |cycle| |mdeg| + |pquo| |skewSFunction| |checkRur| |cAtanh| |mapExpon| |void| |rk4a| + |showAllElements| |mapExponents| |radix| |df2fi| |rotate!| * + |polygamma| |leftRank| |f02axf| |backOldPos| |e02def| |summation| + |constantToUnaryFunction| |readInt8!| |systemCommand| |OMlistSymbols| + |littleEndian| |superHeight| |leftDivide| |rotatey| |cAcsch| + |conditionsForIdempotents| |f02wef| |divisor| |integralRepresents| + |removeRoughlyRedundantFactorsInContents| |nextPrimitiveNormalPoly| + |structuralConstants| |f02abf| |enqueue!| |separant| + |complexEigenvalues| |integral?| + |solveLinearPolynomialEquationByFractions| |romberg| |leaves| |source| + |iipow| |exprHasWeightCosWXorSinWX| |s18acf| |factorGroebnerBasis| + |pade| |option?| |rightDivide| |f01mcf| = |yCoordinates| |bat1| + |makeSketch| |elseBranch| |contains?| |e02baf| |bivariate?| + |fractRagits| |normal| |noncommutativeJordanAlgebra?| |node?| + |macroExpand| |symbolTableOf| |nthExponent| |subresultantVector| + |clipBoolean| |regime| |plusInfinity| |createLowComplexityTable| + |entry?| |iifact| |divideIfCan!| |hypergeometric0F1| |withPredicates| + |expr| < |exactQuotient| |exteriorDifferential| |rightQuotient| + |genericRightNorm| |selectfirst| |minusInfinity| |nextColeman| + |setPrologue!| |d01amf| |whatInfinity| |nthRootIfCan| |char| + |adaptive| > |reopen!| |lyndonIfCan| + |removeSuperfluousQuasiComponents| |split| |makeCrit| + |SturmHabichtMultiple| |dequeue| |quadratic| + |selectMultiDimensionalRoutines| |OMgetBind| <= |primintfldpoly| + |nil?| |pushdterm| |OMreceive| |target| |iiacosh| |extractProperty| + |yellow| |cardinality| |crest| >= |addMatchRestricted| |groebner| + |subPolSet?| |getZechTable| |integrate| |numerators| |ranges| + |toroidal| |reseed| |testDim| |variable| |OMgetEndBVar| |aQuadratic| + |transpose| |exptMod| |showRegion| |c06eaf| |shiftRight| + |outputGeneral| |critMTonD1| |zeroSetSplit| |iterators| |isEquiv| + |push| |prinb| |elementary| |lexico| |type| |positiveRemainder| + |rightRemainder| |quickSort| |setfirst!| |taylorRep| |relationsIdeal| + + |readUInt32!| |OMsend| |se2rfi| |removeRedundantFactorsInContents| + |leftRecip| |d03edf| |outputFixed| |numericalOptimization| + |solveLinearPolynomialEquation| |OMgetEndObject| - |float| + |intermediateResultsIF| |f04mbf| |nextPrime| |mainCoefficients| + |brillhartTrials| |airyBi| |minPoints3D| |coefficient| |cup| + |logIfCan| |overlap| / |subset?| |extractSplittingLeaf| |mappingAst| + |poisson| |stirling1| |setnext!| |reflect| |sign| |localReal?| + |symbol| |decreasePrecision| |id| |simplifyExp| |exponentialOrder| + |expandTrigProducts| |cAsech| |simpsono| |SFunction| |pomopo!| + |genericRightTrace| |expression| |resetNew| |rightAlternative?| |lo| + |intcompBasis| |expandLog| |graphState| |kroneckerDelta| + |padicallyExpand| |realRoots| |nthFlag| |graphStates| |plenaryPower| + |integer| |fTable| |mapUp!| |doubleFloatFormat| |getIdentifier| + |readInt16!| |OMputEndError| |value| |OMcloseConn| |headReduced?| + |eigenvalues| |mapdiv| |badValues| |patternVariable| |elRow1!| + |pseudoQuotient| |isMult| |toseInvertibleSet| |c06gqf| |head| + |shiftRoots| |semiLastSubResultantEuclidean| |mathieu11| + |roughSubIdeal?| |basisOfCenter| |leftReducedSystem| |Lazard| |lquo| + |iiatanh| |keys| |interReduce| |generators| |polyred| |e04naf| + |setStatus| |equiv| |distance| |edf2efi| |monicDecomposeIfCan| + |symbolTable| |getRef| |pushuconst| |att2Result| |graphs| + |coerceListOfPairs| |abs| GE |algDsolve| |parametric?| |iicot| + |cAsinh| |safeCeiling| |OMParseError?| |inRadical?| |scripted?| + |kovacic| |completeHermite| GT |acotIfCan| |evenlambert| |vedf2vef| + |c02agf| |pushFortranOutputStack| |BasicMethod| |monic?| + |realElementary| |ridHack1| |readInt32!| |imagI| LE |OMencodingSGML| + |coleman| |swapColumns!| |revert| |popFortranOutputStack| |ratDsolve| + |viewDeltaXDefault| |pole?| |radicalSimplify| |polCase| + |computeCycleEntry| LT |exactQuotient!| |complexNormalize| + |complement| |d01alf| |numberOfCycles| |algebraicDecompose| |rootPoly| + |mathieu24| |adaptive?| |lazyPseudoQuotient| |sortConstraints| + |e04dgf| |red| |cyclicParents| |f01qef| |closed?| |OMgetEndApp| + |wordInStrongGenerators| |factorsOfCyclicGroupSize| + |semiDegreeSubResultantEuclidean| |mat| |createNormalPrimitivePoly| + |sumOfKthPowerDivisors| |rewriteSetWithReduction| + |reduceBasisAtInfinity| |e01saf| |bringDown| |nthr| |makeUnit| + |eisensteinIrreducible?| |reducedForm| |d01asf| |iicoth| |presub| + |partialNumerators| |deepestInitial| |semiDiscriminantEuclidean| + |epilogue| |polynomialZeros| |open| |pow| |selectPolynomials| + |branchPoint?| |d01bbf| |pr2dmp| |startTableGcd!| |oblateSpheroidal| + |branchIfCan| |index| |getMeasure| |rightLcm| |tree| |arbitrary| + |matrixConcat3D| |modularGcd| |moreAlgebraic?| |isImplies| + |diagonalProduct| |createPrimitiveNormalPoly| |complexNumericIfCan| + |stoseInvertible?| |gcdPolynomial| |iicos| + |createLowComplexityNormalBasis| |lifting| |firstNumer| |modTree| + |incrementKthElement| |removeZeroes| |sn| |quasiMonicPolynomials| + |imagk| |setMinPoints3D| |frst| |purelyTranscendental?| + |rightRegularRepresentation| |fortranLiteral| |commutator| + |squareFreeFactors| |jacobi| |pair| |pleskenSplit| |operations| + |OMclose| |point?| |OMputFloat| |polyRDE| |inverseIntegralMatrix| + |bright| |lprop| |intPatternMatch| |s19aaf| |prod| + |univariatePolynomials| |precision| |wreath| |iteratedInitials| |exp1| + |overlabel| |e01sef| |conjugate| |torsion?| |mesh| |axes| |pointColor| + |leftCharacteristicPolynomial| |addPoint2| |euclideanSize| |besselY| + |problemPoints| |s17adf| |eval| |d01akf| |chebyshevU| |KrullNumber| + |pdct| |d02bhf| |viewPosDefault| |idealiser| |subTriSet?| + |balancedBinaryTree| |stosePrepareSubResAlgo| |iterationVar| + |extendedint| |weakBiRank| |OMbindTCP| |singularitiesOf| |pointLists| + |listLoops| |coefficients| |dimensionOfIrreducibleRepresentation| + |laguerre| |patternMatchTimes| |selectOrPolynomials| |hcrf| |s21baf| + |edf2df| |writeBytes!| |error| |createPrimitiveElement| |quoted?| + |updatF| |support| |morphism| |width| |principalAncestors| |position!| + |closed| |numberOfComputedEntries| |d03eef| |minIndex| |setEmpty!| + |lazyIrreducibleFactors| |digamma| |f04maf| |palgLODE0| + |triangularSystems| |paren| |diagonalMatrix| |optimize| + |repeatUntilLoop| |ksec| |isAbsolutelyIrreducible?| |rules| |latex| + |f02bjf| |connect| |cyclotomicDecomposition| |OMgetSymbol| |nthExpon| + |function| |factorials| |exprex| |checkPrecision| |subHeight| + |deepCopy| |cAcosh| |shuffle| |getMultiplicationMatrix| + |binarySearchTree| |approxNthRoot| |antiCommutative?| |palgintegrate| + |largest| |terms| |subst| |ref| |lagrange| |removeDuplicates!| |qroot| + |implies| |selectPDERoutines| |sts2stst| |sin?| |primlimintfrac| + |ddFact| |stoseInternalLastSubResultant| |mr| |nsqfree| |trapezoidalo| + |expressIdealMember| |explicitlyFinite?| |groebner?| |tanintegrate| + |setleaves!| |linearlyDependentOverZ?| |iprint| |abelianGroup| + |mapCoef| |argumentList!| |lowerCase| |cos2sec| |clipPointsDefault| + |optional| |tableForDiscreteLogarithm| |e01daf| |OMputEndAttr| + |purelyAlgebraic?| |hostPlatform| |block| |multisect| |sumOfSquares| + |integers| |numberOfChildren| |leftAlternative?| |putColorInfo| + |listOfLists| |rootsOf| |normalDenom| |integralMatrix| + |scanOneDimSubspaces| |findConstructor| |move| |any| |root?| |bottom!| + |orbits| |real?| |initials| |triangulate| |upDateBranches| |close!| + |evaluateInverse| |chiSquare1| |varList| |packageCall| + |stoseInvertibleSet| |getCurve| |dfRange| |viewWriteDefault| |objects| + |rem| |lfintegrate| |lazyVariations| |prime| |cschIfCan| + |factorFraction| |degreePartition| |iiasinh| |karatsuba| |find| |dark| + |base| |quo| |euclideanGroebner| |cPower| |setAttributeButtonStep| + |degreeSubResultant| |sqfrFactor| |fullDisplay| |getOrder| |viewpoint| + |noLinearFactor?| |mainMonomial| |setDifference| |ParCond| + |primaryDecomp| |direction| |fortranCarriageReturn| + |possiblyNewVariety?| |legendreP| |janko2| |finiteBound| + |primextendedint| |div| |rootSplit| |d01gbf| |powern| |setlast!| + |graeffe| |lcm| |tensorProduct| |OMputSymbol| |ode2| |asinhIfCan| + |mvar| |init| |delete| |exquo| |removeRoughlyRedundantFactorsInPols| + |rationalIfCan| |explicitlyEmpty?| |putGraph| |makeFR| |bigEndian| + |fortranCharacter| |components| |leadingTerm| |round| ~= |blue| + |toseInvertible?| |rightCharacteristicPolynomial| |numFunEvals3D| + |symbolIfCan| |constantKernel| |append| |redpps| |mainContent| + |setsubMatrix!| |rotate| |#| |primitive?| |monomial?| + |resetAttributeButtons| |hdmpToP| |ravel| |normalise| |iisinh| |gcd| + |minPoints| |atom?| |cAcsc| |adaptive3D?| ~ |outputFloating| + |standardBasisOfCyclicSubmodule| |compose| |laurentIfCan| + |symmetricSquare| |reshape| |shanksDiscLogAlgorithm| |delete!| |false| + |setVariableOrder| |inconsistent?| |square?| |typeForm| + |explicitEntries?| |pushucoef| |showTheFTable| |retractable?| + |lookupFunction| |enterInCache| |f04mcf| |rightFactorCandidate| + |quote| |returnTypeOf| |makeGraphImage| |scale| |tValues| + |stoseIntegralLastSubResultant| |over| |apply| |lexTriangular| |cSech| + |evenInfiniteProduct| |iiasin| |changeWeightLevel| |/\\| |e02bef| + |tanhIfCan| |iiatan| |exprToXXP| |complexExpand| |first| + |internalDecompose| |harmonic| |roughUnitIdeal?| |e02akf| + |OMgetString| |\\/| |nthFactor| |monomRDE| |increase| + |internalInfRittWu?| |componentUpperBound| |rest| |padicFraction| + |setClipValue| |univariatePolynomial| |ipow| |toseSquareFreePart| + |previous| |recolor| |delta| |linGenPos| |d02raf| |weight| F2FG |plus| + |update| |coerce| |createRandomElement| |separateDegrees| |qfactor| + |useEisensteinCriterion| |rewriteIdealWithQuasiMonicGenerators| + |rightRank| |writeUInt8!| |getlo| |fracPart| |duplicates?| |construct| + |removeDuplicates| |screenResolution| |plotPolar| |rootKerSimp| + |resultantReduit| |nand| |isPower| |expenseOfEvaluationIF| |Beta| + |constDsolve| |datalist| |genericRightDiscriminant| |f01ref| + |limitedint| |subCase?| |cAcos| |setPredicates| |redPo| |s13adf| + |upperCase| |sec2cos| |digit?| |times| |push!| |antiAssociative?| + |entries| |top!| |lifting1| |s14abf| |imagK| |s19acf| |order| + |bipolar| |getOperands| |lookup| |upperBound| |collectUnder| |slex| + |algebraicSort| |cycleElt| |cAsin| |duplicates| |hspace| |iiGamma| + |position| |lazyPseudoDivide| |powmod| |rowEchLocal| |Aleph| + |innerint| |highCommonTerms| |SturmHabichtCoefficients| |polygon?| + |lowerCase?| |style| |limitPlus| |c06gsf| |symmetric?| + |viewWriteAvailable| |definingInequation| |removeSinhSq| |lambda| + |adjoint| |algebraicOf| |OMmakeConn| |subspace| |weights| |monom| + |rank| |crushedSet| |nthFractionalTerm| |RittWuCompare| |denominators| + |palgRDE0| |generic?| |minordet| |fortranDoubleComplex| |invmod| + |perfectNthRoot| |drawComplex| |neglist| |c05adf| |outputBinaryFile| + |pdf2df| |presuper| |contractSolve| |subResultantGcd| |genus| + |leftRemainder| |algebraic?| |expintfldpoly| |recip| |f01maf| + |messagePrint| |perfectSqrt| |s21bcf| |currentSubProgram| + |viewZoomDefault| |rightZero| |unvectorise| |common| |s17aff| + |setLabelValue| |completeEval| |setFieldInfo| |readable?| |intensity| + |clipWithRanges| |coordinates| |e04gcf| |rombergo| + |fullPartialFraction| |leftUnits| |loadNativeModule| |makeViewport3D| + |tryFunctionalDecomposition?| |simpson| |maxColIndex| |s13acf| + |OMgetEndAtp| |ricDsolve| |characteristicSerie| |basisOfRightNucloid| + |invertible?| |reverse!| |writeLine!| |iitanh| |iiexp| |cCsch| + |OMreadFile| |printInfo| |ramified?| |someBasis| |multiEuclidean| + |reduceByQuasiMonic| |alphanumeric?| |rationalFunction| |contract| + |rightUnit| |leftExactQuotient| |resultantEuclidean| |argument| + |numberOfImproperPartitions| |digit| |quotedOperators| + |useEisensteinCriterion?| |hdmpToDmp| |zeroSquareMatrix| |lists| |log| + |listBranches| |leftTraceMatrix| |integralLastSubResultant| + |var2Steps| |linearDependenceOverZ| |scopes| |mapBivariate| + |increasePrecision| |typeList| |rightMult| |outputArgs| |lfextlimint| + |lyndon| |iiperm| |processTemplate| |elliptic?| |mergeDifference| + |factorial| |qinterval| |discreteLog| |sample| |setelt| + |numberOfVariables| |homogeneous?| |generateIrredPoly| |f02aef| + |interpretString| |erf| |unit| |groebnerIdeal| |dflist| UP2UTS + |aromberg| |realZeros| |selectFiniteRoutines| |printStatement| + |s17def| |mainVariable| |startTableInvSet!| |biRank| |totolex| + |f04adf| |mathieu22| |heapSort| |cartesian| |henselFact| |li| + |setScreenResolution3D| |leftMult| |redmat| |eq?| |changeNameToObjf| + |zero| |changeMeasure| |qqq| |insertBottom!| |choosemon| |reverse| + |spherical| |writable?| |showIntensityFunctions| |oddlambert| |dilog| + |nary?| |palglimint| |singularAtInfinity?| |d02gbf| |infiniteProduct| + |integerIfCan| |lflimitedint| |meatAxe| |eulerPhi| |OMgetVariable| + |sin| |topFortranOutputStack| |LyndonWordsList1| + |halfExtendedResultant1| |minimalPolynomial| |And| |select!| + |beauzamyBound| |rst| |OMputEndBVar| |makeFloatFunction| |leftLcm| + |cos| |fortranLogical| |SturmHabichtSequence| |superscript| |f02aff| + |Or| |linearAssociatedOrder| |unknown| |characteristicSet| + |clearTheIFTable| |noKaratsuba| |coshIfCan| |tanNa| |tan| |critT| + |isOpen?| |solveRetract| |curry| |Not| |pol| |quasiMonic?| + |seriesSolve| |setrest!| |cCoth| |zCoord| |cot| |zero?| |shiftLeft| + |characteristicPolynomial| |realEigenvectors| |e04jaf| + |leadingBasisTerm| |tryFunctionalDecomposition| |sumSquares| + |reducedQPowers| |conjugates| |sec| |basisOfLeftAnnihilator| + |matrixDimensions| |mainForm| |stoseInvertible?sqfreg| |primintegrate| + |OMputObject| |wholePart| |quadratic?| |expPot| |csc| |palgRDE| + |mainVariables| |elaboration| |nodes| |indicialEquation| |logpart| + |leadingCoefficientRicDE| |LagrangeInterpolation| |leftGcd| + |rewriteSetByReducingWithParticularGenerators| |asin| |test| |e02dcf| + |basicSet| |generalizedContinuumHypothesisAssumed?| |changeBase| + |fillPascalTriangle| |differentialVariables| |shallowExpand| |d02gaf| + |bumptab| |members| |rischDEsys| |acos| |hermiteH| |tanSum| + |fortranComplex| |contours| |palglimint0| |parts| |pmintegrate| + |iidsum| |inverse| |extendIfCan| |simplifyPower| + |getSyntaxFormsFromFile| |atan| |cyclicGroup| |numFunEvals| |tan2cot| + |phiCoord| |associatedEquations| |useSingleFactorBound| |exprToGenUPS| + |maxPoints3D| |acot| |semiResultantReduitEuclidean| |monicModulo| + |invmultisect| |subResultantGcdEuclidean| |tanAn| |binding| |c06frf| + |f02adf| |parent| |asec| |kmax| |factorList| |internalIntegrate| + |smith| |factorPolynomial| |deleteProperty!| |asechIfCan| + |identityMatrix| |userOrdered?| |cn| |acsc| |every?| |linSolve| + |merge!| |plus!| |irreducibleFactor| |remove| |prindINFO| + |OMputVariable| |prefix| |sinh| |internal?| |leastAffineMultiple| + |LiePolyIfCan| |mainDefiningPolynomial| |OMputAtp| |pile| + |extendedSubResultantGcd| |LazardQuotient| |resultant| |cosh| |f02agf| + |newLine| |stopTable!| |tower| |binomThmExpt| |e02gaf| |last| |imagi| + |updateStatus!| |bitCoef| |supersub| |tanh| |represents| |eq| |leader| + |sequence| |psolve| |hyperelliptic| |assoc| |fixedPoints| |whileLoop| + |sequences| |sqfree| |cscIfCan| |coth| |clip| |iter| |stFuncN| + |positiveSolve| |just| |outputAsTex| |obj| |alphabetic| |exQuo| |sech| + |mapmult| |curveColor| |semiIndiceSubResultantEuclidean| |s15aef| + |halfExtendedSubResultantGcd1| |lSpaceBasis| + |solveLinearPolynomialEquationByRecursion| |rotatez| |s17dhf| |cache| + |csch| |bfKeys| |s14baf| |indicialEquations| + |semiSubResultantGcdEuclidean2| |invertibleSet| |lowerPolynomial| + |composites| |integralDerivationMatrix| |unexpand| |asinh| + |getDatabase| |Nul| |diff| |c06fuf| |complexNumeric| + |rightRankPolynomial| |dn| |sub| |acosh| |endSubProgram| |uniform| + |subNode?| |basisOfNucleus| |f2df| |basis| |insertionSort!| + |linkToFortran| |f04jgf| |atanh| |integralCoordinates| |mapGen| + |stoseInvertibleSetsqfreg| |iicsc| |kernels| |secIfCan| + |squareFreeLexTriangular| |solve| |nextSubsetGray| |OMgetEndError| + |acoth| |c05pbf| |minset| |extractPoint| |numberOfFractionalTerms| + |operator| |initTable!| |iFTable| |semiSubResultantGcdEuclidean1| + |algintegrate| |OMconnInDevice| |s17aef| |asech| |level| |exp| + |Lazard2| |OMopenString| |disjunction| |rightRecip| |character?| + |c05nbf| |probablyZeroDim?| |cosh2sech| |selectODEIVPRoutines| + |writeByte!| |rCoord| |routines| |irVar| |maxPoints| |gbasis| LODO2FUN + |complexSolve| |slash| |multiple| |quatern| |explimitedint| + |youngDiagram| |ScanFloatIgnoreSpacesIfCan| |imagJ| |algint| |moduloP| + |printInfo!| |coth2trigh| |applyQuote| |compile| |infieldIntegrate| + |chainSubResultants| |f04qaf| |ReduceOrder| |map| |table| |thenBranch| + |factors| |f02awf| |polyPart| |unitNormal| |stronglyReduce| |iisqrt2| + |empty?| |power| |new| |OMgetApp| |setMinPoints| |rootOf| |iilog| + |areEquivalent?| |infieldint| |alphabetic?| |iiabs| |subSet| + |internalAugment| |ffactor| |radicalSolve| |substitute| |lex| + |supRittWu?| |nextNormalPoly| |f01qcf| |sinh2csch| |commutative?| + |retract| |constantLeft| |drawStyle| |constant?| |shape| |nil| + |partialDenominators| |setButtonValue| |palginfieldint| |computeInt| + |sizeLess?| |ellipticCylindrical| |mainMonomials| |variable?| + |factor1| |leftUnit| |OMopenFile| |infLex?| |LyndonBasis| |convert| + |symmetricDifference| |randnum| |sinhcosh| |irForm| |matrixGcd| + |extractIfCan| |factorAndSplit| |createMultiplicationMatrix| |d02ejf| + |colorFunction| |nonSingularModel| |limitedIntegrate| |mkIntegral| + |setRealSteps| |approximate| |cothIfCan| |rspace| |dominantTerm| + |roughBase?| |c06fpf| |numberOfComposites| |merge| |box| + |mapMatrixIfCan| |e02bcf| |complex| |stop| |resultantnaif| + |factorSquareFreeByRecursion| |rightFactorIfCan| |GospersMethod| + |rightExactQuotient| |lyndon?| |allRootsOf| |distdfact| + |ScanFloatIgnoreSpaces| |lfunc| |factorSquareFreePolynomial| + |exponential| |rightMinimalPolynomial| |ODESolve| |OMgetObject| + |nodeOf?| |mkAnswer| |discriminant| |stopMusserTrials| |ListOfTerms| + |subResultantChain| |commonDenominator| |pointPlot| |primlimitedint| + |rational| |socf2socdf| |key?| |failed| |stopTableInvSet!| + |associatedSystem| |BumInSepFFE| |unitCanonical| |left| + |doubleResultant| |reducedContinuedFraction| |shade| |hasoln| + |denominator| |putProperty| |ignore?| |possiblyInfinite?| |f07fdf| + |right| |antisymmetricTensors| |infinite?| |commaSeparate| + |rischNormalize| |forLoop| |getPickedPoints| |OMgetBVar| |makeop| + |newSubProgram| |printTypes| |rowEchelonLocal| |LazardQuotient2| + |approxSqrt| |changeThreshhold| |initial| |groebgen| |aQuartic| + |gderiv| |leadingIndex| |bezoutDiscriminant| |heap| |open?| |e01bgf| + |wronskianMatrix| |doublyTransitive?| |high| |expandPower| + |generalSqFr| |scalarTypeOf| |octon| |uniform01| |leftNorm| |padecf| + |nonLinearPart| |finiteBasis| |lieAdmissible?| |defineProperty| + |iiasec| |inverseLaplace| |leastMonomial| |cSec| |create3Space| |next| + |diagonal?| |sdf2lst| |permutationRepresentation| |f01brf| + |ScanArabic| |separateFactors| |indiceSubResultant| |idealSimplify| + |nativeModuleExtension| |splitConstant| |pdf2ef| |f07adf| + |lieAlgebra?| |cyclePartition| |irreducible?| |mainVariable?| |swap| + |symbol?| |certainlySubVariety?| |f01qdf| |subResultantsChain| + |minGbasis| |headReduce| |chebyshevT| |radicalEigenvalues| + |univariate?| |fortranTypeOf| |listOfMonoms| |lazyPseudoRemainder| + |unprotectedRemoveRedundantFactors| |approximants| |attributeData| + |basisOfMiddleNucleus| |zerosOf| |rootOfIrreduciblePoly| + |extendedResultant| |taylorIfCan| |e04ucf| |minrank| + |halfExtendedSubResultantGcd2| |key| |elliptic| |s17ahf| |normalize| + |vconcat| |max| |pointColorPalette| |partialQuotients| + |physicalLength| |sorted?| |lfinfieldint| |clipParametric| + |selectSumOfSquaresRoutines| |returns| |decomposeFunc| + |genericLeftTraceForm| |belong?| |finite?| |inputBinaryFile| + |filename| |intersect| |maximumExponent| |concat!| + |selectOptimizationRoutines| |parametersOf| |composite| |fortranReal| + |expt| |pack!| |bernoulli| |s17dlf| |errorInfo| |outputMeasure| |hue| + |infinityNorm| |quadraticNorm| |s18adf| |Frobenius| |parse| + |countable?| |orbit| |inverseColeman| |taylorQuoByVar| |transcendent?| + |internalLastSubResultant| |iisin| |pureLex| |addmod| |super| + |nextNormalPrimitivePoly| |modularFactor| |roman| |normFactors| + |numericalIntegration| |redPol| |zeroOf| |PDESolve| |f04arf| |solid?| + |Ei| |cCosh| |subNodeOf?| |tail| |resize| |reducedDiscriminant| + |f01rdf| |addMatch| |f04axf| |double?| |corrPoly| |lineColorDefault| + |parabolicCylindrical| |sech2cosh| |f01rcf| |blankSeparate| |csubst| + |OMgetAtp| |po| |linearMatrix| |refine| |opeval| |drawCurves| + |resetVariableOrder| |xCoord| |cycleLength| |readLine!| + |basisOfCentroid| FG2F |calcRanges| |OMencodingBinary| |predicates| + |entry| |optpair| |cSin| |dimensionsOf| |say| |currentCategoryFrame| + |cross| |decimal| |s17acf| |basisOfLeftNucleus| |negative?| |arg1| + |removeCosSq| |exprHasAlgebraicWeight| |complexIntegrate| + |genericLeftNorm| |green| |convergents| |showScalarValues| + |arrayStack| |rowEchelon| |sPol| |arg2| |polygon| |OMgetType| |reset| + |options| |cCot| |completeHensel| |OMputString| |trunc| |cAcot| + |graphCurves| |dom| |sum| |setLength!| |monicLeftDivide| + |mainSquareFreePart| |LiePoly| |inc| |supDimElseRittWu?| |e01bef| + |relativeApprox| |bipolarCylindrical| |physicalLength!| |conditions| + |complexRoots| |failed?| |completeEchelonBasis| |write| |leftPower| + |karatsubaDivide| |nil| |infinite| |arbitraryExponent| |approximate| + |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 3cb3c9ab..4f792e95 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5422 +1,5422 @@ -(3263500 . 3486554186) -((-1812 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-4065 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3731 ((|#2| $ (-576) |#2|) NIL) ((|#2| $ (-1253 (-576)) |#2|) 44)) (-2518 (($ $) 80)) (-2521 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-3584 (((-576) (-1 (-112) |#2|) $) 27) (((-576) |#2| $) NIL) (((-576) |#2| $ (-576)) 96)) (-3826 (((-656 |#2|) $) 13)) (-1678 (($ (-1 (-112) |#2| |#2|) $ $) 64) (($ $ $) NIL)) (-1763 (($ 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1221)) ((-95) |has| |#1| (-1221)) ((-102) . T) ((-111 #0# #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2835 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2835 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-874)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1041)) ((-626 (-171 (-390))) |has| |#1| (-1041)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-905 (-390))) |has| |#1| (-626 (-905 (-390)))) ((-626 (-905 (-576))) |has| |#1| (-626 (-905 (-576)))) ((-626 #1=(-1191 |#1|)) . 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T) ((-464) -2835 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1221)) ((-526 (-1195) |#1|) |has| |#1| (-526 (-1195) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-909 $ #3=(-1195)) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #3#) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) |has| |#1| (-899 (-390))) ((-899 (-576)) |has| |#1| (-899 (-576))) ((-897 |#1|) . T) ((-926) -12 (|has| |#1| (-317)) (|has| |#1| (-926))) ((-937) -2835 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1021) -12 (|has| |#1| (-1021)) (|has| |#1| (-1221))) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1070 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1070 |#1|) . T) ((-1070 $) . T) ((-1075 #0#) -2835 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1075 |#1|) . T) ((-1075 $) . T) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-360)) ((-1221) |has| |#1| (-1221)) ((-1224) |has| |#1| (-1221)) ((-1236) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1221)) ((-95) |has| |#1| (-1221)) ((-102) . T) ((-111 #0# #0#) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2781 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2781 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-874)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1041)) ((-626 (-171 (-390))) |has| |#1| (-1041)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-905 (-390))) |has| |#1| (-626 (-905 (-390)))) ((-626 (-905 (-576))) |has| |#1| (-626 (-905 (-576)))) ((-626 #1=(-1191 |#1|)) . 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T) ((-464) -2781 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1221)) ((-526 (-1195) |#1|) |has| |#1| (-526 (-1195) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2781 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-909 $ #3=(-1195)) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #3#) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) |has| |#1| (-899 (-390))) ((-899 (-576)) |has| |#1| (-899 (-576))) ((-897 |#1|) . T) ((-926) -12 (|has| |#1| (-317)) (|has| |#1| (-926))) ((-937) -2781 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1021) -12 (|has| |#1| (-1021)) (|has| |#1| (-1221))) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1070 #0#) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1070 |#1|) . T) ((-1070 $) . T) ((-1075 #0#) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1075 |#1|) . T) ((-1075 $) . T) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-360)) ((-1221) |has| |#1| (-1221)) ((-1224) |has| |#1| (-1221)) ((-1236) . 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(-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2835 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2835 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-628 (-576)) -2835 (|has| |#2| (-1068)) (-12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119)))) ((-628 |#2|) |has| |#2| (-1119)) ((-625 (-874)) -2835 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-874))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1286 |#2|)) . T) ((-234 $) -2835 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-232 |#2|) |has| |#2| (-1068)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1068))) ((-237) -2835 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-272 |#2|) |has| |#2| (-1068)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1068)) ((-423 |#2|) |has| |#2| (-1119)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-658 (-576)) -2835 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1068)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-660 |#2|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1068)) ((-652 |#2|) -2835 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-651 |#2|) |has| |#2| (-1068)) ((-729 |#2|) -2835 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1068)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-862) -2835 (|has| |#2| (-862)) (|has| |#2| (-805))) ((-909 $ #3=(-1195)) -2835 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-915 (-1195)) -12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) ((-917 #3#) -2835 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-1057 #0#) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-1057 (-576)) -12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) ((-1057 |#2|) |has| |#2| (-1119)) ((-1070 |#2|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1075 |#2|) -2835 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1068) |has| |#2| (-1068)) ((-1077) |has| |#2| (-1068)) ((-1131) |has| |#2| (-1068)) ((-1119) -2835 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1236) . T) ((-1293 |#2|) |has| |#2| (-374))) -((-1488 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-2521 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-1630 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) -(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -1488 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2521 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -1630 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1236) (-1236)) (T -244)) -((-1630 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1236)) (-4 *7 (-1236)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-2521 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1236)) (-4 *2 (-1236)) (-5 *1 (-244 *5 *6 *2)))) (-1488 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1236)) (-4 *5 (-1236)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) -(-10 -7 (-15 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(-21)) |%noBranch|) (IF (|has| |t#2| (-738)) (-6 (-652 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-379)) (-6 (-379)) |%noBranch|) (IF (|has| |t#2| (-174)) (-6 (-729 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4459)) (-6 -4459) |%noBranch|) (IF (|has| |t#2| (-862)) (-6 (-862)) |%noBranch|) (IF (|has| |t#2| (-805)) (-6 (-805)) |%noBranch|) (IF (|has| |t#2| (-374)) (-6 (-1293 |t#2|)) |%noBranch|))) +(((-21) -2781 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-23) -2781 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -2781 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2781 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2781 (|has| |#2| (-1068)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-628 (-576)) -2781 (|has| |#2| (-1068)) (-12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119)))) ((-628 |#2|) |has| |#2| (-1119)) ((-625 (-874)) -2781 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-874))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1286 |#2|)) . T) ((-234 $) -2781 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-232 |#2|) |has| |#2| (-1068)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1068))) ((-237) -2781 (-12 (|has| |#2| (-237)) (|has| |#2| (-1068))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1068)))) ((-272 |#2|) |has| |#2| (-1068)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1068)) ((-423 |#2|) |has| |#2| (-1119)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1119))) ((-658 (-576)) -2781 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1068)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-660 |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1068)) ((-652 |#2|) -2781 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068))) ((-651 |#2|) |has| |#2| (-1068)) ((-729 |#2|) -2781 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1068)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-862) -2781 (|has| |#2| (-862)) (|has| |#2| (-805))) ((-909 $ #3=(-1195)) -2781 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-915 (-1195)) -12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068))) ((-917 #3#) -2781 (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068))) (-12 (|has| |#2| (-915 (-1195))) (|has| |#2| (-1068)))) ((-1057 #0#) -12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119))) ((-1057 (-576)) -12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) ((-1057 |#2|) |has| |#2| (-1119)) ((-1070 |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1075 |#2|) -2781 (|has| |#2| (-1068)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1068) |has| |#2| (-1068)) ((-1077) |has| |#2| (-1068)) ((-1131) |has| |#2| (-1068)) ((-1119) -2781 (|has| |#2| (-1119)) (|has| |#2| (-1068)) (|has| |#2| (-862)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1236) . T) ((-1293 |#2|) |has| |#2| (-374))) +((-2645 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-2488 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4096 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) +(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -2645 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2488 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4096 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1236) (-1236)) (T -244)) +((-4096 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1236)) (-4 *7 (-1236)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-2488 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1236)) (-4 *2 (-1236)) (-5 *1 (-244 *5 *6 *2)))) (-2645 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1236)) (-4 *5 (-1236)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) +(-10 -7 (-15 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(|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119)))) ((|#2| $) 28 (|has| |#2| (-1119)))) (-2797 (((-701 (-576)) (-701 $)) NIL (-12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068)))) (((-2 (|:| -3199 (-701 (-576))) (|:| |vec| (-1286 (-576)))) (-701 $) (-1286 $)) NIL (-12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1068)))) (((-2 (|:| -3199 (-701 |#2|)) (|:| |vec| (-1286 |#2|))) (-701 $) (-1286 $)) NIL (|has| |#2| (-1068))) (((-701 |#2|) (-701 $)) NIL (|has| |#2| (-1068)))) (-3684 (((-3 $ "failed") $) 58 (|has| |#2| (-1068)))) (-1765 (($) NIL (|has| |#2| (-379)))) (-1736 ((|#2| $ (-576) |#2|) NIL (|has| $ (-6 -4463)))) (-1669 ((|#2| $ (-576)) 56)) (-3904 (((-656 |#2|) $) 14 (|has| $ (-6 -4462)))) (-2137 (((-112) $) NIL (|has| |#2| (-1068)))) (-2431 (((-112) $ (-783)) NIL)) (-3329 (((-576) $) 19 (|has| (-576) (-862)))) (-2406 (($ $ $) NIL (|has| |#2| (-862)))) (-3896 (((-656 |#2|) $) NIL (|has| $ (-6 -4462)))) (-2802 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4462)) (|has| |#2| (-1119))))) 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NIL (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068)))) (($ $ (-1195)) NIL (-12 (|has| |#2| (-917 (-1195))) (|has| |#2| (-1068)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1068))) (($ $ (-1 |#2| |#2|) (-783)) NIL (|has| |#2| (-1068)))) (-1434 (((-783) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4462))) (((-783) |#2| $) NIL (-12 (|has| $ (-6 -4462)) (|has| |#2| (-1119))))) (-1873 (($ $) NIL)) (-3581 (((-1286 |#2|) $) 9) (($ (-576)) NIL (-2781 (-12 (|has| |#2| (-1057 (-576))) (|has| |#2| (-1119))) (|has| |#2| (-1068)))) (($ (-419 (-576))) NIL (-12 (|has| |#2| (-1057 (-419 (-576)))) (|has| |#2| (-1119)))) (($ |#2|) 12 (|has| |#2| (-1119))) (((-874) $) NIL (|has| |#2| (-625 (-874))))) (-1425 (((-783)) NIL (|has| |#2| (-1068)) CONST)) (-2784 (((-112) $ $) NIL (|has| |#2| (-1119)))) (-1944 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4462)))) (-2748 (($) 36 (|has| |#2| (-23)) CONST)) (-2758 (($) 40 (|has| |#2| (-1068)) CONST)) (-1992 (($ $ (-783)) NIL (-12 (|has| |#2| (-237)) (|has| |#2| 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T) ((-174) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| |#1| (-626 (-548))) (|has| |#3| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| |#1| (-626 (-905 (-390)))) (|has| |#3| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| |#1| (-626 (-905 (-576)))) (|has| |#3| (-626 (-905 (-576))))) ((-234 $) -2835 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2835 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-300) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-319 $) . T) ((-336 |#1| |#4|) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2835 (|has| |#1| (-926)) (|has| |#1| (-464))) ((-526 |#2| |#1|) |has| |#1| (-238)) ((-526 |#2| $) |has| |#1| (-238)) ((-526 |#3| |#1|) . T) ((-526 |#3| $) . T) ((-526 $ $) . T) ((-568) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-658 #0#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-576)))) ((-660 #1=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-651 #1#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-738) . T) ((-909 $ #2=(-1195)) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-909 $ |#3|) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-915 |#3|) . T) ((-917 #2#) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-917 |#3|) . T) ((-899 (-390)) -12 (|has| |#1| (-899 (-390))) (|has| |#3| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-899 (-576))) (|has| |#3| (-899 (-576)))) ((-966 |#1| |#4| |#3|) . T) ((-926) |has| |#1| (-926)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1057 |#2|) . T) ((-1057 |#3|) . T) ((-1070 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1075 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1236) . T) ((-1240) |has| |#1| (-926))) -((-3474 (((-112) $ $) 20 (|has| |#1| (-102)))) (-2547 ((|#1| $) 55)) (-1347 ((|#1| $) 45)) (-2904 (((-112) $ (-783)) 8)) (-4209 (($) 7 T CONST)) (-2479 (($ $) 61)) (-2518 (($ $) 49)) (-3465 ((|#1| |#1| $) 47)) (-3725 ((|#1| $) 46)) (-3826 (((-656 |#1|) $) 31 (|has| $ (-6 -4461)))) (-3910 (((-112) $ (-783)) 9)) (-1938 (((-656 |#1|) $) 30 (|has| $ (-6 -4461)))) (-4241 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4461))))) (-1763 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4462)))) (-1630 (($ (-1 |#1| |#1|) $) 36)) (-1561 (((-112) $ (-783)) 10)) (-4260 (((-783) $) 62)) (-2971 (((-1177) $) 22 (|has| |#1| (-1119)))) (-2063 ((|#1| $) 40)) (-3912 ((|#1| |#1| $) 53)) (-3553 ((|#1| |#1| $) 52)) (-3711 (($ |#1| $) 41)) (-2331 (((-783) $) 56)) (-1445 (((-1139) $) 21 (|has| |#1| (-1119)))) (-3707 ((|#1| $) 63)) (-2013 ((|#1| $) 51)) (-2281 ((|#1| $) 50)) (-2700 ((|#1| $) 42)) (-2400 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4461)))) (-3306 (($ $ (-656 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-656 |#1|) (-656 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119))))) (-3354 (((-112) $ $) 14)) (-4211 ((|#1| |#1| $) 59)) (-1557 (((-112) $) 11)) (-1580 (($) 12)) (-2819 ((|#1| $) 60)) (-2841 (($) 58) (($ (-656 |#1|)) 57)) (-4329 (((-783) $) 44)) (-1456 (((-783) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4461))) (((-783) |#1| $) 29 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4461))))) (-1954 (($ $) 13)) (-3563 (((-874) $) 18 (|has| |#1| (-625 (-874))))) (-2625 ((|#1| $) 54)) (-1856 (((-112) $ $) 23 (|has| |#1| (-1119)))) (-3269 (($ (-656 |#1|)) 43)) (-4166 ((|#1| $) 64)) (-3161 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4461)))) (-2988 (((-112) $ $) 19 (|has| |#1| (-102)))) (-3485 (((-783) $) 6 (|has| $ (-6 -4461))))) +((-1770 (*1 *2 *3) (-12 (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-1 *1 (-783))) (-4 *1 (-260 *4 *3 *5 *6)))) (-3892 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-656 *4)))) (-3624 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-3624 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-783)))) (-2269 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-3659 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-656 (-783))))) (-3577 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-783)))) (-3659 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-656 (-783))))) (-3577 (*1 *2 *1 *3) (-12 (-4 *1 (-260 *4 *3 *5 *6)) (-4 *4 (-1068)) (-4 *3 (-862)) (-4 *5 (-275 *3)) (-4 *6 (-805)) (-5 *2 (-783)))) (-2484 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *5 *6)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-112)))) (-3976 (*1 *2 *1) (-12 (-4 *1 (-260 *3 *4 *2 *5)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-805)) (-4 *2 (-275 *4)))) (-4231 (*1 *1 *1) (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1068)) (-4 *3 (-862)) (-4 *4 (-275 *3)) (-4 *5 (-805)))) (-2927 (*1 *1 *1) (-12 (-4 *1 (-260 *2 *3 *4 *5)) (-4 *2 (-1068)) (-4 *3 (-862)) (-4 *4 (-275 *3)) (-4 *5 (-805)))) (-1770 (*1 *2 *1) (-12 (-4 *3 (-238)) (-4 *3 (-1068)) (-4 *4 (-862)) (-4 *5 (-275 *4)) (-4 *6 (-805)) (-5 *2 (-1 *1 (-783))) (-4 *1 (-260 *3 *4 *5 *6))))) +(-13 (-966 |t#1| |t#4| |t#3|) (-232 |t#1|) (-1057 |t#2|) (-10 -8 (-15 -1770 ((-1 $ (-783)) |t#2|)) (-15 -3892 ((-656 |t#2|) $)) (-15 -3624 ((-783) $ |t#2|)) (-15 -3624 ((-783) $)) (-15 -2269 ((-783) $ |t#2|)) (-15 -3659 ((-656 (-783)) $)) (-15 -3577 ((-783) $)) (-15 -3659 ((-656 (-783)) $ |t#2|)) (-15 -3577 ((-783) $ |t#2|)) (-15 -2484 ((-112) $)) (-15 -3976 (|t#3| $)) (-15 -4231 ($ $)) (-15 -2927 ($ $)) (IF (|has| |t#1| (-238)) (PROGN (-6 (-526 |t#2| |t#1|)) (-6 (-526 |t#2| $)) (-6 (-319 $)) (-15 -1770 ((-1 $ (-783)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) -2781 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 |#2|) . T) ((-628 |#3|) . T) ((-628 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-625 (-874)) . T) ((-174) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| |#1| (-626 (-548))) (|has| |#3| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| |#1| (-626 (-905 (-390)))) (|has| |#3| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| |#1| (-626 (-905 (-576)))) (|has| |#3| (-626 (-905 (-576))))) ((-234 $) -2781 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2781 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-300) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-319 $) . T) ((-336 |#1| |#4|) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2781 (|has| |#1| (-926)) (|has| |#1| (-464))) ((-526 |#2| |#1|) |has| |#1| (-238)) ((-526 |#2| $) |has| |#1| (-238)) ((-526 |#3| |#1|) . T) ((-526 |#3| $) . T) ((-526 $ $) . T) ((-568) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-658 #0#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) |has| |#1| (-38 (-419 (-576)))) ((-660 #1=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-651 #1#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-738) . T) ((-909 $ #2=(-1195)) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-909 $ |#3|) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-915 |#3|) . T) ((-917 #2#) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-917 |#3|) . T) ((-899 (-390)) -12 (|has| |#1| (-899 (-390))) (|has| |#3| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-899 (-576))) (|has| |#3| (-899 (-576)))) ((-966 |#1| |#4| |#3|) . T) ((-926) |has| |#1| (-926)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1057 |#2|) . T) ((-1057 |#3|) . T) ((-1070 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1075 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1236) . T) ((-1240) |has| |#1| (-926))) +((-3488 (((-112) $ $) 20 (|has| |#1| (-102)))) (-3619 ((|#1| $) 55)) (-1371 ((|#1| $) 45)) (-2627 (((-112) $ (-783)) 8)) (-3763 (($) 7 T CONST)) (-2901 (($ $) 61)) (-3717 (($ $) 49)) (-3616 ((|#1| |#1| $) 47)) (-2686 ((|#1| $) 46)) (-3904 (((-656 |#1|) $) 31 (|has| $ (-6 -4462)))) (-2431 (((-112) $ (-783)) 9)) (-3896 (((-656 |#1|) $) 30 (|has| $ (-6 -4462)))) (-2802 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-1726 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4463)))) (-4096 (($ (-1 |#1| |#1|) $) 36)) (-1373 (((-112) $ (-783)) 10)) (-1750 (((-783) $) 62)) (-3343 (((-1177) $) 22 (|has| |#1| (-1119)))) (-2653 ((|#1| $) 40)) (-2623 ((|#1| |#1| $) 53)) (-3798 ((|#1| |#1| $) 52)) (-1870 (($ |#1| $) 41)) (-2282 (((-783) $) 56)) (-1423 (((-1139) $) 21 (|has| |#1| (-1119)))) (-1575 ((|#1| $) 63)) (-1510 ((|#1| $) 51)) (-1694 ((|#1| $) 50)) (-2244 ((|#1| $) 42)) (-3942 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4462)))) (-3290 (($ $ (-656 (-304 |#1|))) 27 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-304 |#1|)) 26 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119)))) (($ $ (-656 |#1|) (-656 |#1|)) 24 (-12 (|has| |#1| (-319 |#1|)) (|has| |#1| (-1119))))) (-3793 (((-112) $ $) 14)) (-2926 ((|#1| |#1| $) 59)) (-4105 (((-112) $) 11)) (-2630 (($) 12)) (-1430 ((|#1| $) 60)) (-2989 (($) 58) (($ (-656 |#1|)) 57)) (-1814 (((-783) $) 44)) (-1434 (((-783) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4462))) (((-783) |#1| $) 29 (-12 (|has| |#1| (-1119)) (|has| $ (-6 -4462))))) (-1873 (($ $) 13)) (-3581 (((-874) $) 18 (|has| |#1| (-625 (-874))))) (-3414 ((|#1| $) 54)) (-2784 (((-112) $ $) 23 (|has| |#1| (-1119)))) (-2277 (($ (-656 |#1|)) 43)) (-1512 ((|#1| $) 64)) (-1944 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4462)))) (-2942 (((-112) $ $) 19 (|has| |#1| (-102)))) (-3500 (((-783) $) 6 (|has| $ (-6 -4462))))) (((-261 |#1|) (-141) (-1236)) (T -261)) -((-2841 (*1 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-2841 (*1 *1 *2) (-12 (-5 *2 (-656 *3)) (-4 *3 (-1236)) (-4 *1 (-261 *3)))) (-2331 (*1 *2 *1) (-12 (-4 *1 (-261 *3)) (-4 *3 (-1236)) (-5 *2 (-783)))) (-2547 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-2625 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-3912 (*1 *2 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-3553 (*1 *2 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-2013 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-2281 (*1 *2 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236)))) (-2518 (*1 *1 *1) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1236))))) -(-13 (-1140 |t#1|) (-1014 |t#1|) (-10 -8 (-15 -2841 ($)) (-15 -2841 ($ (-656 |t#1|))) (-15 -2331 ((-783) $)) (-15 -2547 (|t#1| $)) (-15 -2625 (|t#1| $)) (-15 -3912 (|t#1| |t#1| $)) (-15 -3553 (|t#1| |t#1| $)) (-15 -2013 (|t#1| $)) (-15 -2281 (|t#1| $)) (-15 -2518 ($ $)))) -(((-34) . 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T) ((-312) . T) ((-374) |has| |#1| (-568)) ((-388 |#1|) |has| |#1| (-1068)) ((-412 |#1|) . T) ((-423 |#1|) . T) ((-464) |has| |#1| (-568)) ((-485) |has| |#1| (-485)) ((-526 (-624 $) $) . T) ((-526 $ $) . 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"failed") (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) 34)) (-3126 (((-656 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) $) 31)) (-1870 (($ (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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"))))))) 28)) (-3098 (($ (-656 (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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")))))))) 26)) (-4391 (((-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 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|upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -1870 ($ (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both 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(-15 -3618 ((-656 (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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"))))))) $)) (-15 -4391 ((-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))))) (T -571)) +((-4391 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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 (-571)))) (-3618 (*1 *2 *1) (-12 (-5 *2 (-656 (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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 (-571)))) (-2624 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *2 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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 (-571)))) (-1870 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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 (-571)))) (-3098 (*1 *1 *2) (-12 (-5 *2 (-656 (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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 (-571)))) (-3126 (*1 *2 *1) (-12 (-5 *2 (-656 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-5 *1 (-571)))) (-2459 (*1 *2) (-12 (-5 *2 (-1291)) (-5 *1 (-571)))) (-3529 (*1 *1) (-5 *1 (-571)))) +(-10 -8 (-15 -3529 ($)) (-15 -2459 ((-1291))) (-15 -3126 ((-656 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) $)) (-15 -3098 ($ (-656 (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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"))))))))) (-15 -1870 ($ (-2 (|:| -4300 (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| -4391 (-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| (-1176 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1951 (-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")))))))) (-15 -2624 ((-3 (-2 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-102) . T) ((-111 #0# #0#) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2781 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2781 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2781 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) . T) ((-626 |#2|) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #0#) . T) ((-628 (-576)) . T) ((-628 #1=(-1195)) |has| |#1| (-1057 (-1195))) ((-628 |#1|) . T) ((-628 $) . T) ((-625 (-874)) . T) ((-174) . T) ((-626 (-227)) |has| |#1| (-1041)) ((-626 (-390)) |has| |#1| (-1041)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-905 (-390))) |has| |#1| (-626 (-905 (-390)))) ((-626 (-905 (-576))) |has| |#1| (-626 (-905 (-576)))) ((-234 $) -2781 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -2781 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-272 |#1|) . T) ((-248) . T) ((-296 |#1| $) |has| |#1| (-296 |#1| |#1|)) ((-300) . T) ((-317) . T) ((-319 |#1|) |has| |#1| (-319 |#1|)) ((-374) . T) ((-349 |#1|) . T) ((-388 |#1|) . T) ((-412 |#1|) . T) ((-464) . 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T) ((-660 #0#) |has| |#1| (-38 (-419 (-576)))) ((-660 #1=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-651 #1#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464))) ((-738) . T) ((-909 $ |#3|) . T) ((-915 |#3|) . T) ((-917 |#3|) . T) ((-899 (-390)) -12 (|has| |#1| (-899 (-390))) (|has| |#3| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-899 (-576))) (|has| |#3| (-899 (-576)))) ((-966 |#1| |#2| |#3|) . T) ((-926) |has| |#1| (-926)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 |#1|) . T) ((-1057 |#3|) . T) ((-1070 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1075 #0#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1236) . 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T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-803) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-806) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-832) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-860) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-862) -2835 (-12 (|has| |#1| (-374)) (|has| |#2| (-862))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-909 $ #4=(-1195)) -2835 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-915 (-1195)) -2835 (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-917 #4#) -2835 (-12 (|has| |#1| (-374)) (|has| |#2| (-917 (-1195)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-915 (-1195)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-915 (-1195))))) ((-899 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-390)))) ((-899 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-899 (-576)))) ((-897 |#2|) |has| |#1| (-374)) ((-926) -12 (|has| |#1| (-374)) (|has| |#2| (-926))) ((-992 |#1| #0# (-1101)) . T) ((-937) |has| |#1| (-374)) ((-1011 |#2|) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1041) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-1057 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-576)))) ((-1057 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-1057 |#2|) . T) ((-1070 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 |#2|) |has| |#1| (-374)) ((-1070 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 |#2|) |has| |#1| (-374)) ((-1075 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) -12 (|has| |#1| (-374)) (|has| |#2| (-1171))) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1240) |has| |#1| (-374)) ((-1246 |#1|) . T) ((-1264 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2781 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2781 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1195)) -12 (|has| |#1| (-374)) (|has| |#2| (-1057 (-1195)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2781 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1041))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-905 (-576))))) ((-234 $) -2781 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -2781 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -2781 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1131)) ((-300) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1195) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1195) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2835 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1101)) . T) ((-628 |#1|) . T) ((-628 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| (-1101) (-626 (-548))) (|has| |#1| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| (-1101) (-626 (-905 (-390)))) (|has| |#1| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| (-1101) (-626 (-905 (-576)))) (|has| |#1| (-626 (-905 (-576))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-272 |#1|) . T) ((-296 (-419 $) (-419 $)) |has| |#1| (-568)) ((-296 |#1| |#1|) . T) ((-296 $ $) . T) ((-300) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 $) . T) ((-336 |#1| #0#) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2835 (|has| |#1| (-926)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-568) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-658 #1#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-576)))) ((-660 #3=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-651 #3#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #1#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2#) . T) ((-909 $ #4=(-1195)) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #2#) . T) ((-917 #4#) -2835 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) -12 (|has| (-1101) (-899 (-390))) (|has| |#1| (-899 (-390)))) ((-899 (-576)) -12 (|has| (-1101) (-899 (-576))) (|has| |#1| (-899 (-576)))) ((-966 |#1| #0# #2#) . T) ((-926) |has| |#1| (-926)) ((-937) |has| |#1| (-374)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 #2#) . T) ((-1057 |#1|) . T) ((-1070 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2835 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-1171)) ((-1236) . T) ((-1240) |has| |#1| (-926))) -((-1992 (((-656 (-1101)) $) 34)) (-2166 (($ $) 31)) (-1969 (($ |#2| |#3|) NIL) (($ $ (-1101) |#3|) 28) (($ $ (-656 (-1101)) (-656 |#3|)) 27)) (-2129 (($ $) 14)) (-2142 ((|#2| $) 12)) (-1546 ((|#3| $) 10))) -(((-1263 |#1| |#2| |#3|) (-10 -8 (-15 -1992 ((-656 (-1101)) |#1|)) (-15 -1969 (|#1| |#1| (-656 (-1101)) (-656 |#3|))) (-15 -1969 (|#1| |#1| (-1101) |#3|)) (-15 -2166 (|#1| |#1|)) (-15 -1969 (|#1| |#2| |#3|)) (-15 -1546 (|#3| |#1|)) (-15 -2129 (|#1| |#1|)) (-15 -2142 (|#2| |#1|))) (-1264 |#2| |#3|) (-1068) (-804)) (T -1263)) -NIL -(-10 -8 (-15 -1992 ((-656 (-1101)) |#1|)) (-15 -1969 (|#1| |#1| (-656 (-1101)) (-656 |#3|))) (-15 -1969 (|#1| |#1| (-1101) |#3|)) (-15 -2166 (|#1| |#1|)) (-15 -1969 (|#1| |#2| |#3|)) (-15 -1546 (|#3| |#1|)) (-15 -2129 (|#1| |#1|)) (-15 -2142 (|#2| |#1|))) -((-3474 (((-112) $ $) 6)) (-1949 (((-112) $) 17)) (-1992 (((-656 (-1101)) $) 86)) (-3022 (((-1195) $) 118)) (-4283 (((-2 (|:| -4302 $) (|:| -4448 $) (|:| |associate| $)) 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(-576))))))) +(-13 (-966 |t#1| (-783) (-1101)) (-296 |t#1| |t#1|) (-296 $ $) (-238) (-232 |t#1|) (-10 -8 (-15 -1772 ((-1286 |t#1|) $ (-783))) (-15 -2386 ((-1191 |t#1|) $)) (-15 -1709 ($ (-1191 |t#1|))) (-15 -1458 ($ $ (-783))) (-15 -2495 ((-3 $ "failed") $ (-783))) (-15 -2712 ((-2 (|:| -1482 $) (|:| -1509 $)) $ $)) (-15 -4442 ((-2 (|:| -1482 $) (|:| -1509 $)) $ (-783))) (-15 -3022 ($ $ (-783))) (-15 -3855 ($ $ (-783))) (-15 -2514 ($ $ $)) (-15 -2711 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1171)) (-6 (-1171)) |%noBranch|) (IF (|has| |t#1| (-174)) (PROGN (-15 -4191 (|t#1| $)) (-15 -3960 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-568)) (PROGN (-6 (-296 (-419 $) (-419 $))) (-15 -2816 ((-419 $) (-419 $) (-419 $))) (-15 -3624 ((-783) $ $)) (-15 -3679 ($ $ $)) (-15 -4325 ((-3 $ "failed") $ $)) (-15 -4325 ((-3 (-419 $) "failed") (-419 $) $)) (-15 -3112 ($ $ $)) (-15 -1984 ((-2 (|:| -1677 |t#1|) (|:| -1482 $) (|:| -1509 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-464)) (-15 -2518 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-374)) (PROGN (-6 (-317)) (-6 -4458) (-15 -2816 (|t#1| (-419 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-419 (-576)))) (-15 -3009 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2781 (|has| |#1| (-1057 (-419 (-576)))) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1101)) . T) ((-628 |#1|) . T) ((-628 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-548)) -12 (|has| (-1101) (-626 (-548))) (|has| |#1| (-626 (-548)))) ((-626 (-905 (-390))) -12 (|has| (-1101) (-626 (-905 (-390)))) (|has| |#1| (-626 (-905 (-390))))) ((-626 (-905 (-576))) -12 (|has| (-1101) (-626 (-905 (-576)))) (|has| |#1| (-626 (-905 (-576))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-272 |#1|) . T) ((-296 (-419 $) (-419 $)) |has| |#1| (-568)) ((-296 |#1| |#1|) . T) ((-296 $ $) . T) ((-300) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 $) . T) ((-336 |#1| #0#) . T) ((-388 |#1|) . T) ((-423 |#1|) . T) ((-464) -2781 (|has| |#1| (-926)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-526 #2# |#1|) . T) ((-526 #2# $) . T) ((-526 $ $) . T) ((-568) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-658 #1#) |has| |#1| (-38 (-419 (-576)))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-576)))) ((-660 #3=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) |has| |#1| (-38 (-419 (-576)))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-651 #3#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #1#) |has| |#1| (-38 (-419 (-576)))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2#) . T) ((-909 $ #4=(-1195)) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) . T) ((-915 (-1195)) |has| |#1| (-915 (-1195))) ((-917 #2#) . T) ((-917 #4#) -2781 (|has| |#1| (-917 (-1195))) (|has| |#1| (-915 (-1195)))) ((-899 (-390)) -12 (|has| (-1101) (-899 (-390))) (|has| |#1| (-899 (-390)))) ((-899 (-576)) -12 (|has| (-1101) (-899 (-576))) (|has| |#1| (-899 (-576)))) ((-966 |#1| #0# #2#) . T) ((-926) |has| |#1| (-926)) ((-937) |has| |#1| (-374)) ((-1057 (-419 (-576))) |has| |#1| (-1057 (-419 (-576)))) ((-1057 (-576)) |has| |#1| (-1057 (-576))) ((-1057 #2#) . T) ((-1057 |#1|) . T) ((-1070 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1070 |#1|) . T) ((-1070 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1075 |#1|) . T) ((-1075 $) -2781 (|has| |#1| (-926)) (|has| |#1| (-568)) (|has| |#1| (-464)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1171) |has| |#1| (-1171)) ((-1236) . 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T) ((-652 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-729 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2=(-1195)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-917 #2#) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-992 |#1| #0# (-1101)) . T) ((-937) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1070 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2781 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 $) -2781 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1240) |has| |#1| (-374)) ((-1264 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-419 (-576))) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-874)) . T) ((-174) -2835 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-234 $) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) ((-238) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) ((-237) |has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 $ $) |has| (-419 (-576)) (-1131)) ((-300) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-374) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-568) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-729 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-909 $ #2=(-1195)) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-915 #2#) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-917 #2#) -12 (|has| |#1| (-15 * (|#1| (-419 (-576)) |#1|))) (|has| |#1| (-915 (-1195)))) ((-992 |#1| #0# (-1101)) . T) ((-937) |has| |#1| (-374)) ((-1021) |has| |#1| (-38 (-419 (-576)))) ((-1057 |#2|) . T) ((-1070 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1070 |#1|) . T) ((-1070 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1075 #1#) -2835 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1075 |#1|) . T) ((-1075 $) -2835 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1068) . T) ((-1077) . T) ((-1131) . T) ((-1119) . T) ((-1221) |has| |#1| (-38 (-419 (-576)))) ((-1224) |has| |#1| (-38 (-419 (-576)))) ((-1236) . T) ((-1240) |has| |#1| (-374)) ((-1264 |#1| #0#) . T) ((-1267 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) |has| |#1| (-568)) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2835 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) |has| |#1| (-38 (-419 (-576)))) ((-628 (-576)) . T) ((-628 |#1|) |has| |#1| (-174)) ((-628 $) |has| |#1| (-568)) ((-625 (-874)) . T) ((-174) -2835 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-234 $) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-238) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-237) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . 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NIL NIL NIL) (-1301 3223400 3225141 3225237 "XDPOLY" 3225242 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3222193 3222793 3222836 "XALG" 3222841 NIL XALG (NIL T) -9 NIL 3222952 NIL) (-1299 3215635 3220170 3220664 "WUTSET" 3221785 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1298 3213891 3214687 3215010 "WP" 3215446 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1297 3213493 3213713 3213783 "WHILEAST" 3213843 T WHILEAST (NIL) -8 NIL NIL NIL) (-1296 3212965 3213210 3213304 "WHEREAST" 3213421 T WHEREAST (NIL) -8 NIL NIL NIL) (-1295 3211851 3212049 3212344 "WFFINTBS" 3212762 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1294 3209755 3210182 3210644 "WEIER" 3211423 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1293 3208787 3209237 3209279 "VSPACE" 3209415 NIL VSPACE (NIL T) -9 NIL 3209489 NIL) (-1292 3208625 3208652 3208743 "VSPACE-" 3208748 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1291 3208434 3208476 3208544 "VOID" 3208579 T VOID (NIL) -8 NIL NIL NIL) (-1290 3206570 3206929 3207335 "VIEW" 3208050 T VIEW (NIL) -7 NIL NIL NIL) (-1289 3202994 3203633 3204370 "VIEWDEF" 3205855 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1288 3192298 3194542 3196715 "VIEW3D" 3200843 T VIEW3D (NIL) -8 NIL NIL NIL) (-1287 3184549 3186209 3187788 "VIEW2D" 3190741 T VIEW2D (NIL) -8 NIL NIL NIL) (-1286 3179904 3184319 3184411 "VECTOR" 3184492 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1285 3178481 3178740 3179058 "VECTOR2" 3179634 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1284 3171905 3176212 3176255 "VECTCAT" 3177250 NIL VECTCAT (NIL T) -9 NIL 3177837 NIL) (-1283 3170919 3171173 3171563 "VECTCAT-" 3171568 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1282 3170373 3170570 3170690 "VARIABLE" 3170834 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1281 3170306 3170311 3170341 "UTYPE" 3170346 T UTYPE (NIL) -9 NIL NIL NIL) (-1280 3169136 3169290 3169552 "UTSODETL" 3170132 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1279 3166576 3167036 3167560 "UTSODE" 3168677 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1278 3158524 3164337 3164817 "UTS" 3166154 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3149088 3154458 3154501 "UTSCAT" 3155613 NIL UTSCAT (NIL T) -9 NIL 3156371 NIL) (-1276 3146436 3147158 3148147 "UTSCAT-" 3148152 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1275 3146063 3146106 3146239 "UTS2" 3146387 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1274 3140263 3142873 3142916 "URAGG" 3144986 NIL URAGG (NIL T) -9 NIL 3145709 NIL) (-1273 3137202 3138065 3139188 "URAGG-" 3139193 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1272 3132911 3135837 3136302 "UPXSSING" 3136866 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1271 3125087 3132293 3132557 "UPXS" 3132705 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1270 3118160 3124991 3125063 "UPXSCONS" 3125068 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1269 3107567 3114363 3114425 "UPXSCCA" 3114999 NIL UPXSCCA (NIL T T) -9 NIL 3115232 NIL) (-1268 3107205 3107290 3107464 "UPXSCCA-" 3107469 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1267 3096464 3103033 3103076 "UPXSCAT" 3103724 NIL UPXSCAT (NIL T) -9 NIL 3104333 NIL) (-1266 3095894 3095973 3096152 "UPXS2" 3096379 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1265 3094548 3094801 3095152 "UPSQFREE" 3095637 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1264 3087756 3090816 3090871 "UPSCAT" 3091951 NIL UPSCAT (NIL T T) -9 NIL 3092716 NIL) (-1263 3086960 3087167 3087494 "UPSCAT-" 3087499 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1262 3072050 3080087 3080130 "UPOLYC" 3082231 NIL UPOLYC (NIL T) -9 NIL 3083452 NIL) (-1261 3063378 3065804 3068951 "UPOLYC-" 3068956 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1260 3063005 3063048 3063181 "UPOLYC2" 3063329 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1259 3054548 3062688 3062817 "UP" 3062924 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1258 3053887 3053994 3054158 "UPMP" 3054437 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1257 3053440 3053521 3053660 "UPDIVP" 3053800 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1256 3052008 3052257 3052573 "UPDECOMP" 3053189 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1255 3051239 3051351 3051537 "UPCDEN" 3051892 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1254 3050758 3050827 3050976 "UP2" 3051164 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1253 3049225 3049962 3050239 "UNISEG" 3050516 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1252 3048440 3048567 3048772 "UNISEG2" 3049068 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1251 3047500 3047680 3047906 "UNIFACT" 3048256 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1250 3030260 3046812 3047054 "ULS" 3047316 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1249 3017898 3030164 3030236 "ULSCONS" 3030241 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1248 2998734 3011086 3011148 "ULSCCAT" 3011786 NIL ULSCCAT (NIL T T) -9 NIL 3012075 NIL) (-1247 2997784 2998029 2998417 "ULSCCAT-" 2998422 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1246 2986848 2993331 2993374 "ULSCAT" 2994237 NIL ULSCAT (NIL T) -9 NIL 2994968 NIL) (-1245 2986278 2986357 2986536 "ULS2" 2986763 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1244 2985397 2985907 2986014 "UINT8" 2986125 T UINT8 (NIL) -8 NIL NIL 2986210) (-1243 2984515 2985025 2985132 "UINT64" 2985243 T UINT64 (NIL) -8 NIL NIL 2985328) (-1242 2983633 2984143 2984250 "UINT32" 2984361 T UINT32 (NIL) -8 NIL NIL 2984446) (-1241 2982751 2983261 2983368 "UINT16" 2983479 T UINT16 (NIL) -8 NIL NIL 2983564) (-1240 2981040 2981997 2982027 "UFD" 2982239 T UFD (NIL) -9 NIL 2982353 NIL) (-1239 2980834 2980880 2980975 "UFD-" 2980980 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1238 2979916 2980099 2980315 "UDVO" 2980640 T UDVO (NIL) -7 NIL NIL NIL) (-1237 2977732 2978141 2978612 "UDPO" 2979480 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1236 2977665 2977670 2977700 "TYPE" 2977705 T TYPE (NIL) -9 NIL NIL NIL) (-1235 2977425 2977620 2977651 "TYPEAST" 2977656 T TYPEAST (NIL) -8 NIL NIL NIL) (-1234 2976396 2976598 2976838 "TWOFACT" 2977219 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1233 2975419 2975805 2976040 "TUPLE" 2976196 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1232 2973110 2973629 2974168 "TUBETOOL" 2974902 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1231 2971959 2972164 2972405 "TUBE" 2972903 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1230 2966688 2970931 2971214 "TS" 2971711 NIL TS (NIL T) -8 NIL NIL NIL) (-1229 2955328 2959447 2959544 "TSETCAT" 2964813 NIL TSETCAT (NIL T T T T) -9 NIL 2966344 NIL) (-1228 2950060 2951660 2953551 "TSETCAT-" 2953556 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1227 2944699 2945546 2946475 "TRMANIP" 2949196 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1226 2944140 2944203 2944366 "TRIMAT" 2944631 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1225 2942006 2942243 2942600 "TRIGMNIP" 2943889 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1224 2941526 2941639 2941669 "TRIGCAT" 2941882 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1223 2941195 2941274 2941415 "TRIGCAT-" 2941420 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1222 2938042 2940053 2940334 "TREE" 2940949 NIL TREE (NIL T) -8 NIL NIL NIL) (-1221 2937316 2937844 2937874 "TRANFUN" 2937909 T TRANFUN (NIL) -9 NIL 2937975 NIL) (-1220 2936595 2936786 2937066 "TRANFUN-" 2937071 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1219 2936399 2936431 2936492 "TOPSP" 2936556 T TOPSP (NIL) -7 NIL NIL NIL) (-1218 2935747 2935862 2936016 "TOOLSIGN" 2936280 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1217 2934381 2934924 2935163 "TEXTFILE" 2935530 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1216 2932293 2932834 2933263 "TEX" 2933974 T TEX (NIL) -8 NIL NIL NIL) (-1215 2932074 2932105 2932177 "TEX1" 2932256 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1214 2931722 2931785 2931875 "TEMUTL" 2932006 T TEMUTL (NIL) -7 NIL NIL NIL) (-1213 2929876 2930156 2930481 "TBCMPPK" 2931445 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1212 2921583 2927962 2928018 "TBAGG" 2928418 NIL TBAGG (NIL T T) -9 NIL 2928629 NIL) (-1211 2916653 2918141 2919895 "TBAGG-" 2919900 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1210 2916037 2916144 2916289 "TANEXP" 2916542 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1209 2915548 2915812 2915902 "TALGOP" 2915982 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1208 2908942 2915405 2915498 "TABLE" 2915503 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1207 2908354 2908453 2908591 "TABLEAU" 2908839 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1206 2902962 2904182 2905430 "TABLBUMP" 2907140 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1205 2902184 2902331 2902512 "SYSTEM" 2902803 T SYSTEM (NIL) -8 NIL NIL NIL) (-1204 2898643 2899342 2900125 "SYSSOLP" 2901435 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1203 2898441 2898598 2898629 "SYSPTR" 2898634 T SYSPTR (NIL) -8 NIL NIL NIL) (-1202 2897477 2897982 2898101 "SYSNNI" 2898287 NIL SYSNNI (NIL NIL) -8 NIL NIL 2898372) (-1201 2896776 2897235 2897314 "SYSINT" 2897374 NIL SYSINT (NIL NIL) -8 NIL NIL 2897419) (-1200 2893108 2894054 2894764 "SYNTAX" 2896088 T SYNTAX (NIL) -8 NIL NIL NIL) (-1199 2890266 2890868 2891500 "SYMTAB" 2892498 T SYMTAB (NIL) -8 NIL NIL NIL) (-1198 2885515 2886417 2887400 "SYMS" 2889305 T SYMS (NIL) -8 NIL NIL NIL) (-1197 2882750 2884973 2885203 "SYMPOLY" 2885320 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1196 2882267 2882342 2882465 "SYMFUNC" 2882662 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1195 2878287 2879579 2880392 "SYMBOL" 2881476 T SYMBOL (NIL) -8 NIL NIL NIL) (-1194 2871826 2873515 2875235 "SWITCH" 2876589 T SWITCH (NIL) -8 NIL NIL NIL) (-1193 2865170 2870782 2871076 "SUTS" 2871590 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2857346 2864552 2864816 "SUPXS" 2864964 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2848837 2856964 2857090 "SUP" 2857255 NIL SUP (NIL T) -8 NIL NIL NIL) (-1190 2847996 2848123 2848340 "SUPFRACF" 2848705 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1189 2847617 2847676 2847789 "SUP2" 2847931 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1188 2846065 2846339 2846695 "SUMRF" 2847316 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1187 2845400 2845466 2845658 "SUMFS" 2845986 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1186 2828195 2844712 2844954 "SULS" 2845216 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2827797 2828017 2828087 "SUCHTAST" 2828147 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1184 2827092 2827322 2827462 "SUCH" 2827705 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1183 2820959 2821998 2822957 "SUBSPACE" 2826180 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1182 2820389 2820479 2820643 "SUBRESP" 2820847 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1181 2813757 2815054 2816365 "STTF" 2819125 NIL STTF (NIL T) -7 NIL NIL NIL) (-1180 2807930 2809050 2810197 "STTFNC" 2812657 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1179 2799243 2801112 2802906 "STTAYLOR" 2806171 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1178 2792377 2799107 2799190 "STRTBL" 2799195 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1177 2787337 2792086 2792185 "STRING" 2792300 T STRING (NIL) -8 NIL NIL NIL) (-1176 2780092 2784956 2785567 "STREAM" 2786761 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2779602 2779679 2779823 "STREAM3" 2780009 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1174 2778584 2778767 2779002 "STREAM2" 2779415 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1173 2778272 2778324 2778417 "STREAM1" 2778526 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1172 2777288 2777469 2777700 "STINPROD" 2778088 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1171 2776826 2777036 2777066 "STEP" 2777146 T STEP (NIL) -9 NIL 2777224 NIL) (-1170 2776013 2776315 2776463 "STEPAST" 2776700 T STEPAST (NIL) -8 NIL NIL NIL) (-1169 2769449 2775912 2775989 "STBL" 2775994 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1168 2764518 2768612 2768655 "STAGG" 2768808 NIL STAGG (NIL T) -9 NIL 2768897 NIL) (-1167 2762220 2762822 2763694 "STAGG-" 2763699 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1166 2760369 2761990 2762082 "STACK" 2762163 NIL STACK (NIL T) -8 NIL NIL NIL) (-1165 2753064 2758510 2758966 "SREGSET" 2759999 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1164 2745489 2746858 2748371 "SRDCMPK" 2751670 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1163 2738354 2742877 2742907 "SRAGG" 2744210 T SRAGG (NIL) -9 NIL 2744818 NIL) (-1162 2737371 2737626 2738005 "SRAGG-" 2738010 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1161 2731563 2736318 2736739 "SQMATRIX" 2736997 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1160 2725250 2728281 2729008 "SPLTREE" 2730908 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1159 2721213 2721906 2722552 "SPLNODE" 2724676 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1158 2720260 2720493 2720523 "SPFCAT" 2720967 T SPFCAT (NIL) -9 NIL NIL NIL) (-1157 2718997 2719207 2719471 "SPECOUT" 2720018 T SPECOUT (NIL) -7 NIL NIL NIL) (-1156 2710093 2711965 2711995 "SPADXPT" 2716671 T SPADXPT (NIL) -9 NIL 2718835 NIL) (-1155 2709854 2709894 2709963 "SPADPRSR" 2710046 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1154 2707903 2709809 2709840 "SPADAST" 2709845 T SPADAST (NIL) -8 NIL NIL NIL) (-1153 2699834 2701607 2701650 "SPACEC" 2706023 NIL SPACEC (NIL T) -9 NIL 2707839 NIL) (-1152 2697964 2699766 2699815 "SPACE3" 2699820 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1151 2696716 2696887 2697178 "SORTPAK" 2697769 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1150 2694808 2695111 2695523 "SOLVETRA" 2696380 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1149 2693858 2694080 2694341 "SOLVESER" 2694581 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1148 2689162 2690050 2691045 "SOLVERAD" 2692910 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1147 2684977 2685586 2686315 "SOLVEFOR" 2688529 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1146 2679247 2684326 2684423 "SNTSCAT" 2684428 NIL SNTSCAT (NIL T T T T) -9 NIL 2684498 NIL) (-1145 2673353 2677570 2677961 "SMTS" 2678937 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1144 2667770 2673241 2673318 "SMP" 2673323 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1143 2665929 2666230 2666628 "SMITH" 2667467 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1142 2658041 2662508 2662611 "SMATCAT" 2663962 NIL SMATCAT (NIL NIL T T T) -9 NIL 2664512 NIL) (-1141 2654255 2655292 2656726 "SMATCAT-" 2656731 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1140 2651895 2653463 2653506 "SKAGG" 2653767 NIL SKAGG (NIL T) -9 NIL 2653902 NIL) (-1139 2648093 2651368 2651552 "SINT" 2651704 T SINT (NIL) -8 NIL NIL 2651866) (-1138 2647865 2647903 2647969 "SIMPAN" 2648049 T SIMPAN (NIL) -7 NIL NIL NIL) (-1137 2647144 2647400 2647540 "SIG" 2647747 T SIG (NIL) -8 NIL NIL NIL) (-1136 2645982 2646203 2646478 "SIGNRF" 2646903 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1135 2644815 2644966 2645250 "SIGNEF" 2645811 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1134 2644121 2644398 2644522 "SIGAST" 2644713 T SIGAST (NIL) -8 NIL NIL NIL) (-1133 2641811 2642265 2642771 "SHP" 2643662 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1132 2635647 2641712 2641788 "SHDP" 2641793 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1131 2635206 2635398 2635428 "SGROUP" 2635521 T SGROUP (NIL) -9 NIL 2635583 NIL) (-1130 2635064 2635090 2635163 "SGROUP-" 2635168 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1129 2631855 2632553 2633276 "SGCF" 2634363 T SGCF (NIL) -7 NIL NIL NIL) (-1128 2626223 2631302 2631399 "SFRTCAT" 2631404 NIL SFRTCAT (NIL T T T T) -9 NIL 2631443 NIL) (-1127 2619644 2620662 2621798 "SFRGCD" 2625206 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1126 2612770 2613843 2615029 "SFQCMPK" 2618577 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1125 2612390 2612479 2612590 "SFORT" 2612711 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1124 2611508 2612230 2612351 "SEXOF" 2612356 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1123 2610615 2611389 2611457 "SEX" 2611462 T SEX (NIL) -8 NIL NIL NIL) (-1122 2606396 2607111 2607206 "SEXCAT" 2609828 NIL SEXCAT (NIL T T T T T) -9 NIL 2610388 NIL) (-1121 2603549 2606330 2606378 "SET" 2606383 NIL SET (NIL T) -8 NIL NIL NIL) (-1120 2601773 2602262 2602567 "SETMN" 2603290 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1119 2601255 2601407 2601437 "SETCAT" 2601613 T SETCAT (NIL) -9 NIL 2601723 NIL) (-1118 2600947 2601025 2601155 "SETCAT-" 2601160 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1117 2597308 2599408 2599451 "SETAGG" 2600321 NIL SETAGG (NIL T) -9 NIL 2600661 NIL) (-1116 2596766 2596882 2597119 "SETAGG-" 2597124 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1115 2596209 2596462 2596563 "SEQAST" 2596687 T SEQAST (NIL) -8 NIL NIL NIL) (-1114 2595408 2595702 2595763 "SEGXCAT" 2596049 NIL SEGXCAT (NIL T T) -9 NIL 2596169 NIL) (-1113 2594414 2595074 2595256 "SEG" 2595261 NIL SEG (NIL T) -8 NIL NIL NIL) (-1112 2593393 2593607 2593650 "SEGCAT" 2594172 NIL SEGCAT (NIL T) -9 NIL 2594393 NIL) (-1111 2592325 2592756 2592964 "SEGBIND" 2593220 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1110 2591946 2592005 2592118 "SEGBIND2" 2592260 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1109 2591519 2591747 2591824 "SEGAST" 2591891 T SEGAST (NIL) -8 NIL NIL NIL) (-1108 2590738 2590864 2591068 "SEG2" 2591363 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1107 2590109 2590673 2590720 "SDVAR" 2590725 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1106 2582368 2589879 2590009 "SDPOL" 2590014 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1105 2580961 2581227 2581546 "SCPKG" 2582083 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1104 2580125 2580297 2580489 "SCOPE" 2580791 T SCOPE (NIL) -8 NIL NIL NIL) (-1103 2579345 2579479 2579658 "SCACHE" 2579980 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1102 2578977 2579163 2579193 "SASTCAT" 2579198 T SASTCAT (NIL) -9 NIL 2579211 NIL) (-1101 2578464 2578812 2578888 "SAOS" 2578923 T SAOS (NIL) -8 NIL NIL NIL) (-1100 2578029 2578064 2578237 "SAERFFC" 2578423 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1099 2571700 2577926 2578006 "SAE" 2578011 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2571293 2571328 2571487 "SAEFACT" 2571659 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1097 2569614 2569928 2570329 "RURPK" 2570959 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1096 2568251 2568557 2568862 "RULESET" 2569448 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1095 2565474 2566004 2566462 "RULE" 2567932 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2565086 2565268 2565351 "RULECOLD" 2565426 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1093 2564876 2564904 2564975 "RTVALUE" 2565037 T RTVALUE (NIL) -8 NIL NIL NIL) (-1092 2564347 2564593 2564687 "RSTRCAST" 2564804 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1091 2559195 2559990 2560910 "RSETGCD" 2563546 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1090 2548425 2553504 2553601 "RSETCAT" 2557720 NIL RSETCAT (NIL T T T T) -9 NIL 2558817 NIL) (-1089 2546352 2546891 2547715 "RSETCAT-" 2547720 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1088 2538738 2540114 2541634 "RSDCMPK" 2544951 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1087 2536703 2537170 2537244 "RRCC" 2538330 NIL RRCC (NIL T T) -9 NIL 2538674 NIL) (-1086 2536054 2536228 2536507 "RRCC-" 2536512 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1085 2535497 2535750 2535851 "RPTAST" 2535975 T RPTAST (NIL) -8 NIL NIL NIL) (-1084 2508981 2518609 2518676 "RPOLCAT" 2529342 NIL RPOLCAT (NIL T T T) -9 NIL 2532502 NIL) (-1083 2500479 2502819 2505941 "RPOLCAT-" 2505946 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1082 2491414 2498690 2499172 "ROUTINE" 2500019 T ROUTINE (NIL) -8 NIL NIL NIL) (-1081 2488083 2491040 2491180 "ROMAN" 2491296 T ROMAN (NIL) -8 NIL NIL NIL) (-1080 2486327 2486943 2487203 "ROIRC" 2487888 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1079 2482545 2484829 2484859 "RNS" 2485163 T RNS (NIL) -9 NIL 2485437 NIL) (-1078 2481054 2481437 2481971 "RNS-" 2482046 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1077 2480443 2480851 2480881 "RNG" 2480886 T RNG (NIL) -9 NIL 2480907 NIL) (-1076 2479446 2479808 2480010 "RNGBIND" 2480294 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1075 2478831 2479219 2479262 "RMODULE" 2479267 NIL RMODULE (NIL T) -9 NIL 2479294 NIL) (-1074 2477667 2477761 2478097 "RMCAT2" 2478732 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1073 2474517 2477013 2477310 "RMATRIX" 2477429 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1072 2467344 2469604 2469719 "RMATCAT" 2473078 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2474060 NIL) (-1071 2466719 2466866 2467173 "RMATCAT-" 2467178 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1070 2466334 2466506 2466549 "RLINSET" 2466611 NIL RLINSET (NIL T) -9 NIL 2466655 NIL) (-1069 2465901 2465976 2466104 "RINTERP" 2466253 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1068 2464945 2465499 2465529 "RING" 2465585 T RING (NIL) -9 NIL 2465677 NIL) (-1067 2464737 2464781 2464878 "RING-" 2464883 NIL RING- (NIL T) -8 NIL NIL NIL) (-1066 2463578 2463815 2464073 "RIDIST" 2464501 T RIDIST (NIL) -7 NIL NIL NIL) (-1065 2454867 2463046 2463252 "RGCHAIN" 2463426 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1064 2454203 2454609 2454650 "RGBCSPC" 2454708 NIL RGBCSPC (NIL T) -9 NIL 2454760 NIL) (-1063 2453347 2453728 2453769 "RGBCMDL" 2454001 NIL RGBCMDL (NIL T) -9 NIL 2454115 NIL) (-1062 2450341 2450955 2451625 "RF" 2452711 NIL RF (NIL T) -7 NIL NIL NIL) (-1061 2449987 2450050 2450153 "RFFACTOR" 2450272 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1060 2449712 2449747 2449844 "RFFACT" 2449946 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1059 2447829 2448193 2448575 "RFDIST" 2449352 T RFDIST (NIL) -7 NIL NIL NIL) (-1058 2447282 2447374 2447537 "RETSOL" 2447731 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1057 2446918 2446998 2447041 "RETRACT" 2447174 NIL RETRACT (NIL T) -9 NIL 2447261 NIL) (-1056 2446767 2446792 2446879 "RETRACT-" 2446884 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1055 2446369 2446589 2446659 "RETAST" 2446719 T RETAST (NIL) -8 NIL NIL NIL) (-1054 2439111 2446022 2446149 "RESULT" 2446264 T RESULT (NIL) -8 NIL NIL NIL) (-1053 2437702 2438380 2438579 "RESRING" 2439014 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1052 2437338 2437387 2437485 "RESLATC" 2437639 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1051 2437043 2437078 2437185 "REPSQ" 2437297 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1050 2434465 2435045 2435647 "REP" 2436463 T REP (NIL) -7 NIL NIL NIL) (-1049 2434162 2434197 2434308 "REPDB" 2434424 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1048 2428062 2429451 2430674 "REP2" 2432974 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1047 2424439 2425120 2425928 "REP1" 2427289 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1046 2417135 2422580 2423036 "REGSET" 2424069 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1045 2415900 2416283 2416533 "REF" 2416920 NIL REF (NIL T) -8 NIL NIL NIL) (-1044 2415277 2415380 2415547 "REDORDER" 2415784 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1043 2411245 2414490 2414717 "RECLOS" 2415105 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1042 2410297 2410478 2410693 "REALSOLV" 2411052 T REALSOLV (NIL) -7 NIL NIL NIL) (-1041 2410143 2410184 2410214 "REAL" 2410219 T REAL (NIL) -9 NIL 2410254 NIL) (-1040 2406626 2407428 2408312 "REAL0Q" 2409308 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1039 2402227 2403215 2404276 "REAL0" 2405607 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1038 2401698 2401944 2402038 "RDUCEAST" 2402155 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1037 2401103 2401175 2401382 "RDIV" 2401620 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1036 2400171 2400345 2400558 "RDIST" 2400925 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1035 2398768 2399055 2399427 "RDETRS" 2399879 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1034 2396580 2397034 2397572 "RDETR" 2398310 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1033 2395205 2395483 2395880 "RDEEFS" 2396296 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1032 2393714 2394020 2394445 "RDEEF" 2394893 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1031 2387761 2390681 2390711 "RCFIELD" 2392006 T RCFIELD (NIL) -9 NIL 2392737 NIL) (-1030 2385825 2386329 2387025 "RCFIELD-" 2387100 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1029 2382068 2383898 2383941 "RCAGG" 2385025 NIL RCAGG (NIL T) -9 NIL 2385490 NIL) (-1028 2381696 2381790 2381953 "RCAGG-" 2381958 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1027 2381031 2381143 2381308 "RATRET" 2381580 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1026 2380584 2380651 2380772 "RATFACT" 2380959 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1025 2379892 2380012 2380164 "RANDSRC" 2380454 T RANDSRC (NIL) -7 NIL NIL NIL) (-1024 2379626 2379670 2379743 "RADUTIL" 2379841 T RADUTIL (NIL) -7 NIL NIL NIL) (-1023 2372462 2378457 2378768 "RADIX" 2379349 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1022 2362930 2372304 2372434 "RADFF" 2372439 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1021 2362577 2362652 2362682 "RADCAT" 2362842 T RADCAT (NIL) -9 NIL NIL NIL) (-1020 2362359 2362407 2362507 "RADCAT-" 2362512 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1019 2360459 2362129 2362221 "QUEUE" 2362302 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1018 2356728 2360392 2360440 "QUAT" 2360445 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1017 2356359 2356402 2356533 "QUATCT2" 2356679 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1016 2349193 2352809 2352851 "QUATCAT" 2353642 NIL QUATCAT (NIL T) -9 NIL 2354408 NIL) (-1015 2345332 2346369 2347759 "QUATCAT-" 2347855 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1014 2342771 2344380 2344423 "QUAGG" 2344804 NIL QUAGG (NIL T) -9 NIL 2344979 NIL) (-1013 2342373 2342593 2342663 "QQUTAST" 2342723 T QQUTAST (NIL) -8 NIL NIL NIL) (-1012 2341386 2341886 2342051 "QFORM" 2342254 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1011 2331781 2337288 2337330 "QFCAT" 2337998 NIL QFCAT (NIL T) -9 NIL 2338999 NIL) (-1010 2326622 2328037 2329887 "QFCAT-" 2329983 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1009 2326253 2326296 2326427 "QFCAT2" 2326573 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2325708 2325818 2325950 "QEQUAT" 2326143 T QEQUAT (NIL) -8 NIL NIL NIL) (-1007 2318834 2319907 2321093 "QCMPACK" 2324641 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1006 2316372 2316820 2317250 "QALGSET" 2318489 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2315607 2315783 2316019 "QALGSET2" 2316190 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1004 2314292 2314516 2314835 "PWFFINTB" 2315380 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1003 2312467 2312635 2312991 "PUSHVAR" 2314106 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1002 2308356 2309410 2309453 "PTRANFN" 2311364 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1001 2306747 2307038 2307362 "PTPACK" 2308067 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1000 2306376 2306433 2306544 "PTFUNC2" 2306684 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-999 2300803 2305198 2305239 "PTCAT" 2305535 NIL PTCAT (NIL T) -9 NIL 2305688 NIL) (-998 2300461 2300496 2300620 "PSQFR" 2300762 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-997 2299056 2299354 2299688 "PSEUDLIN" 2300159 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-996 2285819 2288190 2290514 "PSETPK" 2296816 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-995 2278837 2281577 2281673 "PSETCAT" 2284694 NIL PSETCAT (NIL T T T T) -9 NIL 2285508 NIL) (-994 2276673 2277307 2278128 "PSETCAT-" 2278133 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-993 2276022 2276187 2276215 "PSCURVE" 2276483 T PSCURVE (NIL) -9 NIL 2276650 NIL) (-992 2272006 2273522 2273587 "PSCAT" 2274431 NIL PSCAT (NIL T T T) -9 NIL 2274671 NIL) (-991 2271069 2271285 2271685 "PSCAT-" 2271690 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-990 2269428 2270138 2270401 "PRTITION" 2270826 T PRTITION (NIL) -8 NIL NIL NIL) (-989 2268903 2269149 2269241 "PRTDAST" 2269356 T PRTDAST (NIL) -8 NIL NIL NIL) (-988 2257993 2260207 2262395 "PRS" 2266765 NIL PRS (NIL T T) -7 NIL NIL NIL) (-987 2255778 2257315 2257355 "PRQAGG" 2257538 NIL PRQAGG (NIL T) -9 NIL 2257640 NIL) (-986 2255114 2255419 2255447 "PROPLOG" 2255586 T PROPLOG (NIL) -9 NIL 2255701 NIL) (-985 2254718 2254775 2254898 "PROPFUN2" 2255037 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-984 2254033 2254154 2254326 "PROPFUN1" 2254579 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-983 2252214 2252780 2253077 "PROPFRML" 2253769 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-982 2251683 2251790 2251918 "PROPERTY" 2252106 T PROPERTY (NIL) -8 NIL NIL NIL) (-981 2245741 2249849 2250669 "PRODUCT" 2250909 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-980 2243019 2245199 2245433 "PR" 2245552 NIL PR (NIL T T) -8 NIL NIL NIL) (-979 2242815 2242847 2242906 "PRINT" 2242980 T PRINT (NIL) -7 NIL NIL NIL) (-978 2242155 2242272 2242424 "PRIMES" 2242695 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-977 2240220 2240621 2241087 "PRIMELT" 2241734 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-976 2239949 2239998 2240026 "PRIMCAT" 2240150 T PRIMCAT (NIL) -9 NIL NIL NIL) (-975 2236066 2239887 2239932 "PRIMARR" 2239937 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-974 2235073 2235251 2235479 "PRIMARR2" 2235884 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-973 2234716 2234772 2234883 "PREASSOC" 2235011 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-972 2234191 2234324 2234352 "PPCURVE" 2234557 T PPCURVE (NIL) -9 NIL 2234693 NIL) (-971 2233786 2233986 2234069 "PORTNUM" 2234128 T PORTNUM (NIL) -8 NIL NIL NIL) (-970 2231145 2231544 2232136 "POLYROOT" 2233367 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-969 2225059 2230749 2230909 "POLY" 2231018 NIL POLY (NIL T) -8 NIL NIL NIL) (-968 2224442 2224500 2224734 "POLYLIFT" 2224995 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-967 2220717 2221166 2221795 "POLYCATQ" 2223987 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-966 2207067 2212464 2212529 "POLYCAT" 2216043 NIL POLYCAT (NIL T T T) -9 NIL 2217921 NIL) (-965 2199790 2201866 2204506 "POLYCAT-" 2204511 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2199377 2199445 2199565 "POLY2UP" 2199716 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-963 2199009 2199066 2199175 "POLY2" 2199314 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-962 2197694 2197933 2198209 "POLUTIL" 2198783 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-961 2196049 2196326 2196657 "POLTOPOL" 2197416 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-960 2191516 2195985 2196031 "POINT" 2196036 NIL POINT (NIL T) -8 NIL NIL NIL) (-959 2189703 2190060 2190435 "PNTHEORY" 2191161 T PNTHEORY (NIL) -7 NIL NIL NIL) (-958 2188161 2188458 2188857 "PMTOOLS" 2189401 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-957 2187754 2187832 2187949 "PMSYM" 2188077 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-956 2187262 2187331 2187506 "PMQFCAT" 2187679 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-955 2186617 2186727 2186883 "PMPRED" 2187139 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2186010 2186096 2186258 "PMPREDFS" 2186518 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-953 2184674 2184882 2185260 "PMPLCAT" 2185772 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-952 2184206 2184285 2184437 "PMLSAGG" 2184589 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-951 2183679 2183755 2183937 "PMKERNEL" 2184124 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-950 2183296 2183371 2183484 "PMINS" 2183598 NIL PMINS (NIL T) -7 NIL NIL NIL) (-949 2182738 2182807 2183016 "PMFS" 2183221 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-948 2181966 2182084 2182289 "PMDOWN" 2182615 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-947 2181133 2181291 2181472 "PMASS" 2181805 T PMASS (NIL) -7 NIL NIL NIL) (-946 2180406 2180516 2180679 "PMASSFS" 2181020 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-945 2180061 2180129 2180223 "PLOTTOOL" 2180332 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-944 2174668 2175872 2177020 "PLOT" 2178933 T PLOT (NIL) -8 NIL NIL NIL) (-943 2170472 2171516 2172437 "PLOT3D" 2173767 T PLOT3D (NIL) -8 NIL NIL NIL) (-942 2169384 2169561 2169796 "PLOT1" 2170276 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-941 2144775 2149450 2154301 "PLEQN" 2164650 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-940 2144093 2144215 2144395 "PINTERP" 2144640 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2143786 2143833 2143936 "PINTERPA" 2144040 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-938 2143002 2143550 2143637 "PI" 2143677 T PI (NIL) -8 NIL NIL 2143744) (-937 2141285 2142260 2142288 "PID" 2142470 T PID (NIL) -9 NIL 2142604 NIL) (-936 2141036 2141073 2141148 "PICOERCE" 2141242 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-935 2140356 2140495 2140671 "PGROEB" 2140892 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-934 2135943 2136757 2137662 "PGE" 2139471 T PGE (NIL) -7 NIL NIL NIL) (-933 2134066 2134313 2134679 "PGCD" 2135660 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-932 2133404 2133507 2133668 "PFRPAC" 2133950 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-931 2130044 2131952 2132305 "PFR" 2133083 NIL PFR (NIL T) -8 NIL NIL NIL) (-930 2128433 2128677 2129002 "PFOTOOLS" 2129791 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-929 2126966 2127205 2127556 "PFOQ" 2128190 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-928 2125467 2125679 2126035 "PFO" 2126750 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-927 2122020 2125356 2125425 "PF" 2125430 NIL PF (NIL NIL) -8 NIL NIL NIL) (-926 2119340 2120611 2120639 "PFECAT" 2121224 T PFECAT (NIL) -9 NIL 2121608 NIL) (-925 2118785 2118939 2119153 "PFECAT-" 2119158 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-924 2117388 2117640 2117941 "PFBRU" 2118534 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-923 2115254 2115606 2116038 "PFBR" 2117039 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-922 2111300 2112766 2113413 "PERM" 2114640 NIL PERM (NIL T) -8 NIL NIL NIL) (-921 2106534 2107507 2108377 "PERMGRP" 2110463 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-920 2104653 2105613 2105654 "PERMCAT" 2106054 NIL PERMCAT (NIL T) -9 NIL 2106352 NIL) (-919 2104306 2104347 2104471 "PERMAN" 2104606 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-918 2101796 2103971 2104093 "PENDTREE" 2104217 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-917 2100725 2100940 2100981 "PDSPC" 2101514 NIL PDSPC (NIL T) -9 NIL 2101759 NIL) (-916 2099828 2100046 2100408 "PDSPC-" 2100413 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-915 2098710 2099478 2099519 "PDRING" 2099524 NIL PDRING (NIL T) -9 NIL 2099552 NIL) (-914 2097597 2098215 2098269 "PDMOD" 2098274 NIL PDMOD (NIL T T) -9 NIL 2098378 NIL) (-913 2094812 2095590 2096258 "PDEPROB" 2096949 T PDEPROB (NIL) -8 NIL NIL NIL) (-912 2092357 2092861 2093416 "PDEPACK" 2094277 T PDEPACK (NIL) -7 NIL NIL NIL) (-911 2091269 2091459 2091710 "PDECOMP" 2092156 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-910 2088834 2089677 2089705 "PDECAT" 2090492 T PDECAT (NIL) -9 NIL 2091205 NIL) (-909 2088463 2088518 2088572 "PDDOM" 2088737 NIL PDDOM (NIL T T) -9 NIL 2088817 NIL) (-908 2088282 2088312 2088419 "PDDOM-" 2088424 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-907 2088033 2088066 2088156 "PCOMP" 2088243 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-906 2086211 2086834 2087131 "PBWLB" 2087762 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-905 2078684 2080284 2081622 "PATTERN" 2084894 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2078316 2078373 2078482 "PATTERN2" 2078621 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-903 2076073 2076461 2076918 "PATTERN1" 2077905 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-902 2073441 2074022 2074503 "PATRES" 2075638 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 2073005 2073072 2073204 "PATRES2" 2073368 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-900 2070888 2071293 2071700 "PATMATCH" 2072672 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-899 2070384 2070593 2070634 "PATMAB" 2070741 NIL PATMAB (NIL T) -9 NIL 2070824 NIL) (-898 2068902 2069238 2069496 "PATLRES" 2070189 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-897 2068448 2068571 2068612 "PATAB" 2068617 NIL PATAB (NIL T) -9 NIL 2068789 NIL) (-896 2066630 2067025 2067448 "PARTPERM" 2068045 T PARTPERM (NIL) -7 NIL NIL NIL) (-895 2066251 2066314 2066416 "PARSURF" 2066561 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-894 2065883 2065940 2066049 "PARSU2" 2066188 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-893 2065647 2065687 2065754 "PARSER" 2065836 T PARSER (NIL) -7 NIL NIL NIL) (-892 2065268 2065331 2065433 "PARSCURV" 2065578 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-891 2064900 2064957 2065066 "PARSC2" 2065205 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-890 2064539 2064597 2064694 "PARPCURV" 2064836 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-889 2064171 2064228 2064337 "PARPC2" 2064476 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-888 2063232 2063544 2063726 "PARAMAST" 2064009 T PARAMAST (NIL) -8 NIL NIL NIL) (-887 2062752 2062838 2062957 "PAN2EXPR" 2063133 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-886 2061529 2061873 2062101 "PALETTE" 2062544 T PALETTE (NIL) -8 NIL NIL NIL) (-885 2059922 2060534 2060894 "PAIR" 2061215 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-884 2053522 2059179 2059374 "PADICRC" 2059776 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-883 2046446 2052866 2053051 "PADICRAT" 2053369 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-882 2044761 2046383 2046428 "PADIC" 2046433 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 2041857 2043421 2043461 "PADICCT" 2044042 NIL PADICCT (NIL NIL) -9 NIL 2044324 NIL) (-880 2040814 2041014 2041282 "PADEPAC" 2041644 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-879 2040026 2040159 2040365 "PADE" 2040676 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-878 2038413 2039234 2039514 "OWP" 2039830 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-877 2037906 2038119 2038216 "OVERSET" 2038336 T OVERSET (NIL) -8 NIL NIL NIL) (-876 2036952 2037511 2037683 "OVAR" 2037774 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-875 2036216 2036337 2036498 "OUT" 2036811 T OUT (NIL) -7 NIL NIL NIL) (-874 2025088 2027325 2029525 "OUTFORM" 2034036 T OUTFORM (NIL) -8 NIL NIL NIL) (-873 2024424 2024685 2024812 "OUTBFILE" 2024981 T OUTBFILE (NIL) -8 NIL NIL NIL) (-872 2023731 2023896 2023924 "OUTBCON" 2024242 T OUTBCON (NIL) -9 NIL 2024408 NIL) (-871 2023332 2023444 2023601 "OUTBCON-" 2023606 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-870 2022712 2023061 2023150 "OSI" 2023263 T OSI (NIL) -8 NIL NIL NIL) (-869 2022228 2022566 2022594 "OSGROUP" 2022599 T OSGROUP (NIL) -9 NIL 2022621 NIL) (-868 2020973 2021200 2021485 "ORTHPOL" 2021975 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-867 2018524 2020808 2020929 "OREUP" 2020934 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-866 2015927 2018215 2018342 "ORESUP" 2018466 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-865 2013455 2013955 2014516 "OREPCTO" 2015416 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-864 2007127 2009328 2009369 "OREPCAT" 2011717 NIL OREPCAT (NIL T) -9 NIL 2012821 NIL) (-863 2004274 2005056 2006114 "OREPCAT-" 2006119 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-862 2003411 2003709 2003737 "ORDSET" 2004046 T ORDSET (NIL) -9 NIL 2004210 NIL) (-861 2002842 2002990 2003214 "ORDSET-" 2003219 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 2001393 2002184 2002212 "ORDRING" 2002414 T ORDRING (NIL) -9 NIL 2002539 NIL) (-859 2001038 2001132 2001276 "ORDRING-" 2001281 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 2000404 2000867 2000895 "ORDMON" 2000900 T ORDMON (NIL) -9 NIL 2000921 NIL) (-857 1999566 1999713 1999908 "ORDFUNS" 2000253 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1998890 1999309 1999337 "ORDFIN" 1999402 T ORDFIN (NIL) -9 NIL 1999476 NIL) (-855 1995449 1997476 1997885 "ORDCOMP" 1998514 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1994715 1994842 1995028 "ORDCOMP2" 1995309 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1991296 1992206 1993020 "OPTPROB" 1993921 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1988098 1988737 1989441 "OPTPACK" 1990612 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1985771 1986537 1986565 "OPTCAT" 1987384 T OPTCAT (NIL) -9 NIL 1988034 NIL) (-850 1985155 1985448 1985553 "OPSIG" 1985686 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1984923 1984962 1985028 "OPQUERY" 1985109 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1982054 1983234 1983738 "OP" 1984452 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1981414 1981640 1981681 "OPERCAT" 1981893 NIL OPERCAT (NIL T) -9 NIL 1981990 NIL) (-846 1981169 1981225 1981342 "OPERCAT-" 1981347 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1977982 1979966 1980335 "ONECOMP" 1980833 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1977287 1977402 1977576 "ONECOMP2" 1977854 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1976706 1976812 1976942 "OMSERVER" 1977177 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1973568 1976146 1976186 "OMSAGG" 1976247 NIL OMSAGG (NIL T) -9 NIL 1976311 NIL) (-841 1972191 1972454 1972736 "OMPKG" 1973306 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1971621 1971724 1971752 "OM" 1972051 T OM (NIL) -9 NIL NIL NIL) (-839 1970168 1971170 1971339 "OMLO" 1971502 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1969128 1969275 1969495 "OMEXPR" 1969994 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1968419 1968674 1968810 "OMERR" 1969012 T OMERR (NIL) -8 NIL NIL NIL) (-836 1967570 1967840 1968000 "OMERRK" 1968279 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1967021 1967247 1967355 "OMENC" 1967482 T OMENC (NIL) -8 NIL NIL NIL) (-834 1960916 1962101 1963272 "OMDEV" 1965870 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1959985 1960156 1960350 "OMCONN" 1960742 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1958492 1959468 1959496 "OINTDOM" 1959501 T OINTDOM (NIL) -9 NIL 1959522 NIL) (-831 1955830 1957180 1957517 "OFMONOID" 1958187 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1955202 1955767 1955812 "ODVAR" 1955817 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1952625 1954947 1955102 "ODR" 1955107 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1944938 1952401 1952527 "ODPOL" 1952532 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1938744 1944810 1944915 "ODP" 1944920 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1937510 1937725 1938000 "ODETOOLS" 1938518 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1934477 1935135 1935851 "ODESYS" 1936843 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1929359 1930267 1931292 "ODERTRIC" 1933552 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1928785 1928867 1929061 "ODERED" 1929271 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1925673 1926221 1926898 "ODERAT" 1928208 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1922632 1923097 1923694 "ODEPRRIC" 1925202 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1920575 1921171 1921657 "ODEPROB" 1922166 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1917095 1917580 1918227 "ODEPRIM" 1920054 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1916344 1916446 1916706 "ODEPAL" 1916987 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1912506 1913297 1914161 "ODEPACK" 1915500 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1911567 1911674 1911896 "ODEINT" 1912395 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1905668 1907093 1908540 "ODEIFTBL" 1910140 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1901066 1901852 1902804 "ODEEF" 1904827 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1900415 1900504 1900727 "ODECONST" 1900971 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1898526 1899187 1899215 "ODECAT" 1899820 T ODECAT (NIL) -9 NIL 1900351 NIL) (-811 1895381 1898231 1898353 "OCT" 1898436 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1895019 1895062 1895189 "OCTCT2" 1895332 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1889654 1892089 1892129 "OC" 1893226 NIL OC (NIL T) -9 NIL 1894084 NIL) (-808 1886881 1887629 1888619 "OC-" 1888713 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1886219 1886687 1886715 "OCAMON" 1886720 T OCAMON (NIL) -9 NIL 1886741 NIL) (-806 1885736 1886077 1886105 "OASGP" 1886110 T OASGP (NIL) -9 NIL 1886130 NIL) (-805 1884983 1885472 1885500 "OAMONS" 1885540 T OAMONS (NIL) -9 NIL 1885583 NIL) (-804 1884383 1884816 1884844 "OAMON" 1884849 T OAMON (NIL) -9 NIL 1884869 NIL) (-803 1883627 1884145 1884173 "OAGROUP" 1884178 T OAGROUP (NIL) -9 NIL 1884198 NIL) (-802 1883317 1883367 1883455 "NUMTUBE" 1883571 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1876890 1878408 1879944 "NUMQUAD" 1881801 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1872646 1873634 1874659 "NUMODE" 1875885 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1869987 1870867 1870895 "NUMINT" 1871818 T NUMINT (NIL) -9 NIL 1872582 NIL) (-798 1868935 1869132 1869350 "NUMFMT" 1869789 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1855294 1858239 1860771 "NUMERIC" 1866442 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1849664 1854743 1854838 "NTSCAT" 1854843 NIL NTSCAT (NIL T T T T) -9 NIL 1854882 NIL) (-795 1848858 1849023 1849216 "NTPOLFN" 1849503 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1836667 1845683 1846495 "NSUP" 1848079 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1836299 1836356 1836465 "NSUP2" 1836604 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1826257 1836073 1836206 "NSMP" 1836211 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1824689 1824990 1825347 "NREP" 1825945 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1823280 1823532 1823890 "NPCOEF" 1824432 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1822346 1822461 1822677 "NORMRETR" 1823161 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1820387 1820677 1821086 "NORMPK" 1822054 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1820072 1820100 1820224 "NORMMA" 1820353 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1819872 1820029 1820058 "NONE" 1820063 T NONE (NIL) -8 NIL NIL NIL) (-785 1819661 1819690 1819759 "NONE1" 1819836 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1819158 1819220 1819399 "NODE1" 1819593 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1817439 1818290 1818545 "NNI" 1818892 T NNI (NIL) -8 NIL NIL 1819127) (-782 1815859 1816172 1816536 "NLINSOL" 1817107 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1812100 1813095 1813994 "NIPROB" 1814980 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1810857 1811091 1811393 "NFINTBAS" 1811862 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1810031 1810507 1810548 "NETCLT" 1810720 NIL NETCLT (NIL T) -9 NIL 1810802 NIL) (-778 1808739 1808970 1809251 "NCODIV" 1809799 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1808501 1808538 1808613 "NCNTFRAC" 1808696 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1806681 1807045 1807465 "NCEP" 1808126 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1805518 1806291 1806319 "NASRING" 1806429 T NASRING (NIL) -9 NIL 1806509 NIL) (-774 1805313 1805357 1805451 "NASRING-" 1805456 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1804406 1804931 1804959 "NARNG" 1805076 T NARNG (NIL) -9 NIL 1805167 NIL) (-772 1804098 1804165 1804299 "NARNG-" 1804304 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1802977 1803184 1803419 "NAGSP" 1803883 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1794249 1795933 1797606 "NAGS" 1801324 T NAGS (NIL) -7 NIL NIL NIL) (-769 1792797 1793105 1793436 "NAGF07" 1793938 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1787335 1788626 1789933 "NAGF04" 1791510 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1780303 1781917 1783550 "NAGF02" 1785722 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1775527 1776627 1777744 "NAGF01" 1779206 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1769155 1770721 1772306 "NAGE04" 1773962 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1760324 1762445 1764575 "NAGE02" 1767045 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1756277 1757224 1758188 "NAGE01" 1759380 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1754072 1754606 1755164 "NAGD03" 1755739 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1745822 1747750 1749704 "NAGD02" 1752138 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1739633 1741058 1742498 "NAGD01" 1744402 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1735842 1736664 1737501 "NAGC06" 1738816 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1734307 1734639 1734995 "NAGC05" 1735506 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1733683 1733802 1733946 "NAGC02" 1734183 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1732628 1733211 1733251 "NAALG" 1733330 NIL NAALG (NIL T) -9 NIL 1733391 NIL) (-755 1732463 1732492 1732582 "NAALG-" 1732587 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1726413 1727521 1728708 "MULTSQFR" 1731359 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1725732 1725807 1725991 "MULTFACT" 1726325 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1718403 1722317 1722370 "MTSCAT" 1723440 NIL MTSCAT (NIL T T) -9 NIL 1723955 NIL) (-751 1718115 1718169 1718261 "MTHING" 1718343 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1717907 1717940 1718000 "MSYSCMD" 1718075 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1713989 1716662 1716982 "MSET" 1717620 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1711058 1713550 1713591 "MSETAGG" 1713596 NIL MSETAGG (NIL T) -9 NIL 1713630 NIL) (-747 1706900 1708437 1709182 "MRING" 1710358 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1706466 1706533 1706664 "MRF2" 1706827 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1706084 1706119 1706263 "MRATFAC" 1706425 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1703696 1703991 1704422 "MPRFF" 1705789 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1697725 1703550 1703647 "MPOLY" 1703652 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1697215 1697250 1697458 "MPCPF" 1697684 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1696729 1696772 1696956 "MPC3" 1697166 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695924 1696005 1696226 "MPC2" 1696644 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1694225 1694562 1694952 "MONOTOOL" 1695584 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1693436 1693753 1693781 "MONOID" 1694000 T MONOID (NIL) -9 NIL 1694147 NIL) (-737 1692982 1693101 1693282 "MONOID-" 1693287 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1682580 1688802 1688861 "MONOGEN" 1689535 NIL MONOGEN (NIL T T) -9 NIL 1689991 NIL) (-735 1679798 1680533 1681533 "MONOGEN-" 1681652 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1678617 1679063 1679091 "MONADWU" 1679483 T MONADWU (NIL) -9 NIL 1679721 NIL) (-733 1677989 1678148 1678396 "MONADWU-" 1678401 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1677334 1677578 1677606 "MONAD" 1677813 T MONAD (NIL) -9 NIL 1677925 NIL) (-731 1677019 1677097 1677229 "MONAD-" 1677234 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1675308 1675932 1676211 "MOEBIUS" 1676772 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1674572 1674976 1675016 "MODULE" 1675021 NIL MODULE (NIL T) -9 NIL 1675060 NIL) (-728 1674140 1674236 1674426 "MODULE-" 1674431 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1671820 1672504 1672831 "MODRING" 1673964 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1668764 1669925 1670446 "MODOP" 1671349 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1667352 1667831 1668108 "MODMONOM" 1668627 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1657128 1665643 1666057 "MODMON" 1666989 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1654284 1655972 1656248 "MODFIELD" 1657003 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1653261 1653565 1653755 "MMLFORM" 1654114 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1652787 1652830 1653009 "MMAP" 1653212 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1650852 1651619 1651660 "MLO" 1652083 NIL MLO (NIL T) -9 NIL 1652325 NIL) (-719 1648218 1648734 1649336 "MLIFT" 1650333 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1647609 1647693 1647847 "MKUCFUNC" 1648129 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1647208 1647278 1647401 "MKRECORD" 1647532 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1646255 1646417 1646645 "MKFUNC" 1647019 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1645643 1645747 1645903 "MKFLCFN" 1646138 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1644920 1645022 1645207 "MKBCFUNC" 1645536 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1641517 1644474 1644610 "MINT" 1644804 T MINT (NIL) -8 NIL NIL NIL) (-712 1640329 1640572 1640849 "MHROWRED" 1641272 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1635709 1638864 1639269 "MFLOAT" 1639944 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1635066 1635142 1635313 "MFINFACT" 1635621 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1631381 1632229 1633113 "MESH" 1634202 T MESH (NIL) -7 NIL NIL NIL) (-708 1629771 1630083 1630436 "MDDFACT" 1631068 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1626540 1628902 1628943 "MDAGG" 1629198 NIL MDAGG (NIL T) -9 NIL 1629341 NIL) (-706 1615242 1625833 1626040 "MCMPLX" 1626353 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1614379 1614525 1614726 "MCDEN" 1615091 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1612269 1612539 1612919 "MCALCFN" 1614109 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1611194 1611434 1611667 "MAYBE" 1612075 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1608806 1609329 1609891 "MATSTOR" 1610665 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1604765 1608178 1608426 "MATRIX" 1608591 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1600531 1601238 1601974 "MATLIN" 1604122 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1590611 1593795 1593872 "MATCAT" 1598752 NIL MATCAT (NIL T T T) -9 NIL 1600169 NIL) (-698 1586967 1587988 1589344 "MATCAT-" 1589349 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1585561 1585714 1586047 "MATCAT2" 1586802 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1583673 1583997 1584381 "MAPPKG3" 1585236 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1582654 1582827 1583049 "MAPPKG2" 1583497 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1581153 1581437 1581764 "MAPPKG1" 1582360 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1580232 1580559 1580736 "MAPPAST" 1580996 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1579843 1579901 1580024 "MAPHACK3" 1580168 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1579435 1579496 1579610 "MAPHACK2" 1579775 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1578873 1578976 1579118 "MAPHACK1" 1579326 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1576952 1577573 1577877 "MAGMA" 1578601 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1576431 1576676 1576767 "MACROAST" 1576881 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1572851 1574670 1575131 "M3D" 1576003 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1566900 1571162 1571203 "LZSTAGG" 1571985 NIL LZSTAGG (NIL T) -9 NIL 1572280 NIL) (-685 1562858 1564031 1565488 "LZSTAGG-" 1565493 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1559945 1560749 1561236 "LWORD" 1562403 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1559521 1559749 1559824 "LSTAST" 1559890 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1552419 1559292 1559426 "LSQM" 1559431 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1551643 1551782 1552010 "LSPP" 1552274 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1549455 1549756 1550212 "LSMP" 1551332 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1546234 1546908 1547638 "LSMP1" 1548757 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1540062 1545351 1545392 "LSAGG" 1545454 NIL LSAGG (NIL T) -9 NIL 1545532 NIL) (-677 1536757 1537681 1538894 "LSAGG-" 1538899 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1534356 1535901 1536150 "LPOLY" 1536552 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1533938 1534023 1534146 "LPEFRAC" 1534265 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1532259 1533032 1533285 "LO" 1533770 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1531897 1532009 1532037 "LOGIC" 1532148 T LOGIC (NIL) -9 NIL 1532229 NIL) (-672 1531759 1531782 1531853 "LOGIC-" 1531858 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1530952 1531092 1531285 "LODOOPS" 1531615 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1528375 1530868 1530934 "LODO" 1530939 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1526913 1527148 1527501 "LODOF" 1528122 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1523117 1525548 1525589 "LODOCAT" 1526027 NIL LODOCAT (NIL T) -9 NIL 1526238 NIL) (-667 1522850 1522908 1523035 "LODOCAT-" 1523040 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1520170 1522691 1522809 "LODO2" 1522814 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1517605 1520107 1520152 "LODO1" 1520157 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1516486 1516651 1516956 "LODEEF" 1517428 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1511763 1514652 1514693 "LNAGG" 1515555 NIL LNAGG (NIL T) -9 NIL 1515990 NIL) (-662 1510910 1511124 1511466 "LNAGG-" 1511471 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1507046 1507835 1508474 "LMOPS" 1510325 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1506435 1506823 1506864 "LMODULE" 1506869 NIL LMODULE (NIL T) -9 NIL 1506895 NIL) (-659 1503635 1506080 1506203 "LMDICT" 1506345 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1503253 1503425 1503466 "LLINSET" 1503527 NIL LLINSET (NIL T) -9 NIL 1503571 NIL) (-657 1502952 1503161 1503221 "LITERAL" 1503226 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1496117 1501886 1502190 "LIST" 1502681 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1495642 1495716 1495855 "LIST3" 1496037 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1494649 1494827 1495055 "LIST2" 1495460 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1492783 1493095 1493494 "LIST2MAP" 1494296 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1492414 1492602 1492643 "LINSET" 1492648 NIL LINSET (NIL T) -9 NIL 1492682 NIL) (-651 1490835 1491441 1491482 "LINEXP" 1491972 NIL LINEXP (NIL T) -9 NIL 1492245 NIL) (-650 1489412 1489672 1489983 "LINDEP" 1490587 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1486179 1486898 1487675 "LIMITRF" 1488667 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1484482 1484778 1485187 "LIMITPS" 1485874 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1478910 1483993 1484221 "LIE" 1484303 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1477844 1478313 1478353 "LIECAT" 1478493 NIL LIECAT (NIL T) -9 NIL 1478644 NIL) (-645 1477685 1477712 1477800 "LIECAT-" 1477805 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1470276 1477225 1477381 "LIB" 1477549 T LIB (NIL) -8 NIL NIL NIL) (-643 1465911 1466794 1467729 "LGROBP" 1469393 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1463909 1464183 1464533 "LF" 1465632 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1462749 1463441 1463469 "LFCAT" 1463676 T LFCAT (NIL) -9 NIL 1463815 NIL) (-640 1459651 1460281 1460969 "LEXTRIPK" 1462113 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1456395 1457221 1457724 "LEXP" 1459231 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1455871 1456116 1456208 "LETAST" 1456323 T LETAST (NIL) -8 NIL NIL NIL) (-637 1454269 1454582 1454983 "LEADCDET" 1455553 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1453459 1453533 1453762 "LAZM3PK" 1454190 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1448376 1451536 1452074 "LAUPOL" 1452971 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1447955 1447999 1448160 "LAPLACE" 1448326 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1445894 1447056 1447307 "LA" 1447788 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1444874 1445458 1445499 "LALG" 1445561 NIL LALG (NIL T) -9 NIL 1445620 NIL) (-631 1444588 1444647 1444783 "LALG-" 1444788 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1444423 1444447 1444488 "KVTFROM" 1444550 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1443346 1443790 1443975 "KTVLOGIC" 1444258 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1443181 1443205 1443246 "KRCFROM" 1443308 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1442085 1442272 1442571 "KOVACIC" 1442981 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1441920 1441944 1441985 "KONVERT" 1442047 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1441755 1441779 1441820 "KOERCE" 1441882 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1439586 1440348 1440725 "KERNEL" 1441411 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1439082 1439163 1439295 "KERNEL2" 1439500 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1432792 1437559 1437613 "KDAGG" 1437990 NIL KDAGG (NIL T T) -9 NIL 1438196 NIL) (-621 1432321 1432445 1432650 "KDAGG-" 1432655 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1425469 1431982 1432137 "KAFILE" 1432199 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1419897 1424980 1425208 "JORDAN" 1425290 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1419276 1419546 1419667 "JOINAST" 1419796 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1419122 1419181 1419236 "JAVACODE" 1419241 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1415348 1417299 1417353 "IXAGG" 1418282 NIL IXAGG (NIL T T) -9 NIL 1418741 NIL) (-615 1414267 1414573 1414992 "IXAGG-" 1414997 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1409799 1414189 1414248 "IVECTOR" 1414253 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1408565 1408802 1409068 "ITUPLE" 1409566 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1407067 1407244 1407539 "ITRIGMNP" 1408387 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1405812 1406016 1406299 "ITFUN3" 1406843 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1405444 1405501 1405610 "ITFUN2" 1405749 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1404603 1404924 1405098 "ITFORM" 1405290 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1402564 1403623 1403901 "ITAYLOR" 1404358 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1391509 1396701 1397864 "ISUPS" 1401434 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1390613 1390753 1390989 "ISUMP" 1391356 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385990 1390558 1390599 "ISTRING" 1390604 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1385466 1385711 1385803 "ISAST" 1385918 T ISAST (NIL) -8 NIL NIL NIL) (-603 1384675 1384757 1384973 "IRURPK" 1385380 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1383611 1383812 1384052 "IRSN" 1384455 T IRSN (NIL) -7 NIL NIL NIL) (-601 1381682 1382037 1382466 "IRRF2F" 1383249 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1381429 1381467 1381543 "IRREDFFX" 1381638 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1380044 1380303 1380602 "IROOT" 1381162 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1376648 1377728 1378420 "IR" 1379384 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1375853 1376141 1376292 "IRFORM" 1376517 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1373466 1373961 1374527 "IR2" 1375331 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1372566 1372679 1372893 "IR2F" 1373349 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1372357 1372391 1372451 "IPRNTPK" 1372526 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1368938 1372246 1372315 "IPF" 1372320 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1367265 1368863 1368920 "IPADIC" 1368925 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1366577 1366825 1366955 "IP4ADDR" 1367155 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365951 1366206 1366338 "IOMODE" 1366465 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1365024 1365548 1365675 "IOBFILE" 1365844 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1364512 1364928 1364956 "IOBCON" 1364961 T IOBCON (NIL) -9 NIL 1364982 NIL) (-587 1364023 1364081 1364264 "INVLAPLA" 1364448 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1353671 1356025 1358411 "INTTR" 1361687 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1350006 1350748 1351613 "INTTOOLS" 1352856 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1349592 1349683 1349800 "INTSLPE" 1349909 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1347545 1349515 1349574 "INTRVL" 1349579 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1345147 1345659 1346234 "INTRF" 1347030 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1344558 1344655 1344797 "INTRET" 1345045 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1342555 1342944 1343414 "INTRAT" 1344166 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1339818 1340401 1341020 "INTPM" 1342040 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1336563 1337162 1337900 "INTPAF" 1339204 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1331742 1332704 1333755 "INTPACK" 1335532 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1328562 1331539 1331648 "INT" 1331653 T INT (NIL) -8 NIL NIL NIL) (-575 1327814 1327966 1328174 "INTHERTR" 1328404 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1327253 1327333 1327521 "INTHERAL" 1327728 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1325099 1325542 1325999 "INTHEORY" 1326816 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1316505 1318126 1319898 "INTG0" 1323451 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1297078 1301868 1306678 "INTFTBL" 1311715 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1296327 1296465 1296638 "INTFACT" 1296937 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1293754 1294200 1294757 "INTEF" 1295881 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1292107 1292846 1292874 "INTDOM" 1293175 T INTDOM (NIL) -9 NIL 1293382 NIL) (-567 1291476 1291650 1291892 "INTDOM-" 1291897 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1287850 1289778 1289832 "INTCAT" 1290631 NIL INTCAT (NIL T) -9 NIL 1290952 NIL) (-565 1287322 1287425 1287553 "INTBIT" 1287742 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1286021 1286175 1286482 "INTALG" 1287167 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1285504 1285594 1285751 "INTAF" 1285925 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1278851 1285314 1285454 "INTABL" 1285459 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1278184 1278650 1278715 "INT8" 1278749 T INT8 (NIL) -8 NIL NIL 1278794) (-560 1277516 1277982 1278047 "INT64" 1278081 T INT64 (NIL) -8 NIL NIL 1278126) (-559 1276848 1277314 1277379 "INT32" 1277413 T INT32 (NIL) -8 NIL NIL 1277458) (-558 1276180 1276646 1276711 "INT16" 1276745 T INT16 (NIL) -8 NIL NIL 1276790) (-557 1270897 1273741 1273769 "INS" 1274703 T INS (NIL) -9 NIL 1275368 NIL) (-556 1268137 1268908 1269882 "INS-" 1269955 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1266912 1267139 1267437 "INPSIGN" 1267890 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1266030 1266147 1266344 "INPRODPF" 1266792 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264924 1265041 1265278 "INPRODFF" 1265910 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263924 1264076 1264336 "INNMFACT" 1264760 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1263121 1263218 1263406 "INMODGCD" 1263823 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1261629 1261874 1262198 "INFSP" 1262866 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1260813 1260930 1261113 "INFPROD0" 1261509 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1257668 1258878 1259393 "INFORM" 1260306 T INFORM (NIL) -8 NIL NIL NIL) (-547 1257278 1257338 1257436 "INFORM1" 1257603 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1256801 1256890 1257004 "INFINITY" 1257184 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255977 1256521 1256622 "INETCLTS" 1256720 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1254593 1254843 1255164 "INEP" 1255725 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1253842 1254490 1254555 "INDE" 1254560 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1253406 1253474 1253591 "INCRMAPS" 1253769 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1252224 1252675 1252881 "INBFILE" 1253220 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1247523 1248460 1249404 "INBFF" 1251312 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1246431 1246700 1246728 "INBCON" 1247241 T INBCON (NIL) -9 NIL 1247507 NIL) (-538 1245683 1245906 1246182 "INBCON-" 1246187 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1245162 1245407 1245498 "INAST" 1245612 T INAST (NIL) -8 NIL NIL NIL) (-536 1244589 1244841 1244947 "IMPTAST" 1245076 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1241037 1244433 1244537 "IMATRIX" 1244542 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1239745 1239868 1240184 "IMATQF" 1240893 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1237965 1238192 1238529 "IMATLIN" 1239501 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1232545 1237889 1237947 "ILIST" 1237952 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1230452 1232405 1232518 "IIARRAY2" 1232523 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1225850 1230363 1230427 "IFF" 1230432 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1225197 1225467 1225583 "IFAST" 1225754 T IFAST (NIL) -8 NIL NIL NIL) (-528 1220194 1224489 1224677 "IFARRAY" 1225054 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1219374 1220098 1220171 "IFAMON" 1220176 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1218958 1219023 1219077 "IEVALAB" 1219284 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1218633 1218701 1218861 "IEVALAB-" 1218866 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1218264 1218547 1218610 "IDPO" 1218615 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1217514 1218153 1218228 "IDPOAMS" 1218233 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1216821 1217403 1217478 "IDPOAM" 1217483 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1215866 1216142 1216195 "IDPC" 1216608 NIL IDPC (NIL T T) -9 NIL 1216757 NIL) (-520 1215335 1215758 1215831 "IDPAM" 1215836 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1214711 1215227 1215300 "IDPAG" 1215305 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1214356 1214547 1214622 "IDENT" 1214656 T IDENT (NIL) -8 NIL NIL NIL) (-517 1210611 1211459 1212354 "IDECOMP" 1213513 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1203448 1204534 1205581 "IDEAL" 1209647 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1202608 1202720 1202920 "ICDEN" 1203332 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1201679 1202088 1202235 "ICARD" 1202481 T ICARD (NIL) -8 NIL NIL NIL) (-513 1199739 1200052 1200457 "IBPTOOLS" 1201356 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1195346 1199359 1199472 "IBITS" 1199658 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1192069 1192645 1193340 "IBATOOL" 1194763 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1189848 1190310 1190843 "IBACHIN" 1191604 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1187679 1189694 1189797 "IARRAY2" 1189802 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1183787 1187605 1187662 "IARRAY1" 1187667 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1177655 1182199 1182680 "IAN" 1183326 T IAN (NIL) -8 NIL NIL NIL) (-506 1177166 1177223 1177396 "IALGFACT" 1177592 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1176694 1176807 1176835 "HYPCAT" 1177042 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1176232 1176349 1176535 "HYPCAT-" 1176540 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1175827 1176027 1176110 "HOSTNAME" 1176169 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1175672 1175709 1175750 "HOMOTOP" 1175755 NIL HOMOTOP (NIL T) -9 NIL 1175788 NIL) (-501 1172228 1173604 1173645 "HOAGG" 1174626 NIL HOAGG (NIL T) -9 NIL 1175355 NIL) (-500 1170822 1171221 1171747 "HOAGG-" 1171752 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1164546 1170415 1170565 "HEXADEC" 1170692 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1163294 1163516 1163779 "HEUGCD" 1164323 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1162370 1163131 1163261 "HELLFDIV" 1163266 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1160551 1162147 1162235 "HEAP" 1162314 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1159814 1160103 1160237 "HEADAST" 1160437 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1153664 1159729 1159791 "HDP" 1159796 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1147384 1153299 1153451 "HDMP" 1153565 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1146708 1146848 1147012 "HB" 1147240 T HB (NIL) -7 NIL NIL NIL) (-491 1140098 1146554 1146658 "HASHTBL" 1146663 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1139574 1139819 1139911 "HASAST" 1140026 T HASAST (NIL) -8 NIL NIL NIL) (-489 1137352 1139196 1139378 "HACKPI" 1139412 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1133020 1137205 1137318 "GTSET" 1137323 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1126439 1132898 1132996 "GSTBL" 1133001 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1118826 1125604 1125860 "GSERIES" 1126239 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1117953 1118370 1118398 "GROUP" 1118601 T GROUP (NIL) -9 NIL 1118735 NIL) (-484 1117319 1117478 1117729 "GROUP-" 1117734 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1115686 1116007 1116394 "GROEBSOL" 1116996 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1114586 1114874 1114925 "GRMOD" 1115454 NIL GRMOD (NIL T T) -9 NIL 1115622 NIL) (-481 1114354 1114390 1114518 "GRMOD-" 1114523 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1109644 1110708 1111708 "GRIMAGE" 1113374 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1108110 1108371 1108695 "GRDEF" 1109340 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1107554 1107670 1107811 "GRAY" 1107989 T GRAY (NIL) -7 NIL NIL NIL) (-477 1106727 1107133 1107184 "GRALG" 1107337 NIL GRALG (NIL T T) -9 NIL 1107430 NIL) (-476 1106388 1106461 1106624 "GRALG-" 1106629 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1103165 1105973 1106151 "GPOLSET" 1106295 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1102519 1102576 1102834 "GOSPER" 1103102 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1098251 1098957 1099483 "GMODPOL" 1102218 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1097256 1097440 1097678 "GHENSEL" 1098063 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1091412 1092255 1093275 "GENUPS" 1096340 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1091109 1091160 1091249 "GENUFACT" 1091355 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1090521 1090598 1090763 "GENPGCD" 1091027 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1089995 1090030 1090243 "GENMFACT" 1090480 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1088561 1088818 1089125 "GENEEZ" 1089738 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1082441 1088172 1088334 "GDMP" 1088484 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1071784 1076212 1077318 "GCNAALG" 1081424 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1070097 1070959 1070987 "GCDDOM" 1071242 T GCDDOM (NIL) -9 NIL 1071399 NIL) (-463 1069567 1069694 1069909 "GCDDOM-" 1069914 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1068239 1068424 1068728 "GB" 1069346 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1056855 1059185 1061577 "GBINTERN" 1065930 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1054692 1054984 1055405 "GBF" 1056530 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1053473 1053638 1053905 "GBEUCLID" 1054508 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1052822 1052947 1053096 "GAUSSFAC" 1053344 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1051189 1051491 1051805 "GALUTIL" 1052541 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1049497 1049771 1050095 "GALPOLYU" 1050916 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1046862 1047152 1047559 "GALFACTU" 1049194 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1038668 1040167 1041775 "GALFACT" 1045294 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1036056 1036714 1036742 "FVFUN" 1037898 T FVFUN (NIL) -9 NIL 1038618 NIL) (-452 1035322 1035504 1035532 "FVC" 1035823 T FVC (NIL) -9 NIL 1036006 NIL) (-451 1034965 1035147 1035215 "FUNDESC" 1035274 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1034580 1034762 1034843 "FUNCTION" 1034917 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1032324 1032902 1033368 "FT" 1034134 T FT (NIL) -8 NIL NIL NIL) (-448 1031115 1031625 1031828 "FTEM" 1032141 T FTEM (NIL) -8 NIL NIL NIL) (-447 1029406 1029695 1030092 "FSUPFACT" 1030806 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1027803 1028092 1028424 "FST" 1029094 T FST (NIL) -8 NIL NIL NIL) (-445 1027002 1027108 1027296 "FSRED" 1027685 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1025701 1025957 1026304 "FSPRMELT" 1026717 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1023007 1023445 1023931 "FSPECF" 1025264 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1004080 1012781 1012822 "FS" 1016706 NIL FS (NIL T) -9 NIL 1018995 NIL) (-441 992723 995716 999773 "FS-" 1000073 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 992251 992305 992475 "FSINT" 992664 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 990543 991244 991547 "FSERIES" 992030 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 989585 989701 989925 "FSCINT" 990423 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 985793 988529 988570 "FSAGG" 988940 NIL FSAGG (NIL T) -9 NIL 989199 NIL) (-436 983555 984156 984952 "FSAGG-" 985047 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 982597 982740 982967 "FSAGG2" 983408 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 980275 980555 981103 "FS2UPS" 982315 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 979909 979952 980081 "FS2" 980226 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 978787 978958 979260 "FS2EXPXP" 979734 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 978213 978328 978480 "FRUTIL" 978667 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 969626 973708 975066 "FR" 976887 NIL FR (NIL T) -8 NIL NIL NIL) (-429 964640 967315 967355 "FRNAALG" 968675 NIL FRNAALG (NIL T) -9 NIL 969273 NIL) (-428 960313 961389 962664 "FRNAALG-" 963414 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 959951 959994 960121 "FRNAAF2" 960264 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 958326 958800 959096 "FRMOD" 959763 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 956069 956701 957019 "FRIDEAL" 958117 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 955260 955347 955638 "FRIDEAL2" 955976 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 954393 954807 954848 "FRETRCT" 954853 NIL FRETRCT (NIL T) -9 NIL 955029 NIL) (-422 953505 953736 954087 "FRETRCT-" 954092 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 950579 951789 951848 "FRAMALG" 952730 NIL FRAMALG (NIL T T) -9 NIL 953022 NIL) (-420 948713 949168 949798 "FRAMALG-" 950021 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 942364 948186 948463 "FRAC" 948468 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 942000 942057 942164 "FRAC2" 942301 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 941636 941693 941800 "FR2" 941937 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 936135 939028 939056 "FPS" 940175 T FPS (NIL) -9 NIL 940732 NIL) (-415 935584 935693 935857 "FPS-" 936003 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 932872 934541 934569 "FPC" 934794 T FPC (NIL) -9 NIL 934936 NIL) (-413 932665 932705 932802 "FPC-" 932807 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 931455 932153 932194 "FPATMAB" 932199 NIL FPATMAB (NIL T) -9 NIL 932351 NIL) (-411 929694 930197 930544 "FPARFRAC" 931171 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 925088 925586 926268 "FORTRAN" 929126 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 922804 923304 923843 "FORT" 924569 T FORT (NIL) -7 NIL NIL NIL) (-408 920480 921042 921070 "FORTFN" 922130 T FORTFN (NIL) -9 NIL 922754 NIL) (-407 920244 920294 920322 "FORTCAT" 920381 T FORTCAT (NIL) -9 NIL 920443 NIL) (-406 918350 918860 919250 "FORMULA" 919874 T FORMULA (NIL) -8 NIL NIL NIL) (-405 918138 918168 918237 "FORMULA1" 918314 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 917661 917713 917886 "FORDER" 918080 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 916757 916921 917114 "FOP" 917488 T FOP (NIL) -7 NIL NIL NIL) (-402 915338 916037 916211 "FNLA" 916639 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 914053 914468 914496 "FNCAT" 914956 T FNCAT (NIL) -9 NIL 915216 NIL) (-400 913592 914012 914040 "FNAME" 914045 T FNAME (NIL) -8 NIL NIL NIL) (-399 912141 913104 913132 "FMTC" 913137 T FMTC (NIL) -9 NIL 913173 NIL) (-398 910887 912077 912123 "FMONOID" 912128 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 907701 908869 908910 "FMONCAT" 910127 NIL FMONCAT (NIL T) -9 NIL 910732 NIL) (-396 906893 907443 907592 "FM" 907597 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 904317 904963 904991 "FMFUN" 906135 T FMFUN (NIL) -9 NIL 906843 NIL) (-394 903586 903767 903795 "FMC" 904085 T FMC (NIL) -9 NIL 904267 NIL) (-393 900651 901511 901565 "FMCAT" 902760 NIL FMCAT (NIL T T) -9 NIL 903255 NIL) (-392 899517 900417 900517 "FM1" 900596 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 897291 897707 898201 "FLOATRP" 899068 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 890869 895020 895641 "FLOAT" 896690 T FLOAT (NIL) -8 NIL NIL NIL) (-389 888307 888807 889385 "FLOATCP" 890336 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 886963 887899 887940 "FLINEXP" 887945 NIL FLINEXP (NIL T) -9 NIL 888038 NIL) (-387 885391 885840 886424 "FLINEXP-" 886429 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 884467 884611 884835 "FLASORT" 885243 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 881569 882437 882489 "FLALG" 883716 NIL FLALG (NIL T T) -9 NIL 884183 NIL) (-384 875255 879005 879046 "FLAGG" 880308 NIL FLAGG (NIL T) -9 NIL 880960 NIL) (-383 873981 874320 874810 "FLAGG-" 874815 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 873023 873166 873393 "FLAGG2" 873834 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869860 870868 870927 "FINRALG" 872055 NIL FINRALG (NIL T T) -9 NIL 872563 NIL) (-380 869020 869249 869588 "FINRALG-" 869593 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 868386 868625 868653 "FINITE" 868849 T FINITE (NIL) -9 NIL 868956 NIL) (-378 860729 862916 862956 "FINAALG" 866623 NIL FINAALG (NIL T) -9 NIL 868076 NIL) (-377 856061 857111 858255 "FINAALG-" 859634 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 855429 855816 855919 "FILE" 855991 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 854073 854411 854465 "FILECAT" 855149 NIL FILECAT (NIL T T) -9 NIL 855365 NIL) (-374 851775 853303 853331 "FIELD" 853371 T FIELD (NIL) -9 NIL 853451 NIL) (-373 850395 850780 851291 "FIELD-" 851296 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 848245 849030 849377 "FGROUP" 850081 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 847335 847499 847719 "FGLMICPK" 848077 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 843167 847260 847317 "FFX" 847322 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 842768 842829 842964 "FFSLPE" 843100 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 838758 839540 840336 "FFPOLY" 842004 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 838262 838298 838507 "FFPOLY2" 838716 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 834108 838181 838244 "FFP" 838249 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 829506 834019 834083 "FF" 834088 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 824632 828849 829039 "FFNBX" 829360 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 819560 823767 824025 "FFNBP" 824486 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 814193 818844 819055 "FFNB" 819393 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 813025 813223 813538 "FFINTBAS" 813990 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 809051 811272 811300 "FFIELDC" 811920 T FFIELDC (NIL) -9 NIL 812296 NIL) (-359 807713 808084 808581 "FFIELDC-" 808586 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 807282 807328 807452 "FFHOM" 807655 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804977 805464 805981 "FFF" 806797 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 800595 804719 804820 "FFCGX" 804920 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 796217 800327 800434 "FFCGP" 800538 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 791400 795944 796052 "FFCG" 796153 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770937 781132 781218 "FFCAT" 786383 NIL FFCAT (NIL T T T) -9 NIL 787834 NIL) (-352 766134 767182 768496 "FFCAT-" 769726 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 765545 765588 765823 "FFCAT2" 766085 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754868 758517 759737 "FEXPR" 764397 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 753830 754265 754306 "FEVALAB" 754390 NIL FEVALAB (NIL T) -9 NIL 754651 NIL) (-348 752989 753199 753537 "FEVALAB-" 753542 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 751555 752372 752575 "FDIV" 752888 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 748561 749302 749417 "FDIVCAT" 750985 NIL FDIVCAT (NIL T T T T) -9 NIL 751422 NIL) (-345 748323 748350 748520 "FDIVCAT-" 748525 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 747543 747630 747907 "FDIV2" 748230 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 746517 746838 747040 "FCTRDATA" 747361 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 745203 745462 745751 "FCPAK1" 746248 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 744302 744703 744844 "FCOMP" 745094 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 728007 731452 734990 "FC" 740784 T FC (NIL) -8 NIL NIL NIL) (-339 720300 724328 724368 "FAXF" 726170 NIL FAXF (NIL T) -9 NIL 726862 NIL) (-338 717577 718234 719059 "FAXF-" 719524 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 712631 716953 717129 "FARRAY" 717434 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 707511 709578 709631 "FAMR" 710654 NIL FAMR (NIL T T) -9 NIL 711114 NIL) (-335 706401 706703 707138 "FAMR-" 707143 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 705570 706323 706376 "FAMONOID" 706381 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 703342 704052 704105 "FAMONC" 705046 NIL FAMONC (NIL T T) -9 NIL 705432 NIL) (-332 702006 703096 703233 "FAGROUP" 703238 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 699801 700120 700523 "FACUTIL" 701687 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698900 699085 699307 "FACTFUNC" 699611 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 691322 698203 698402 "EXPUPXS" 698756 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 688805 689345 689931 "EXPRTUBE" 690756 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 685076 685668 686398 "EXPRODE" 688144 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 670568 683725 684154 "EXPR" 684680 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 665122 665709 666515 "EXPR2UPS" 669866 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 664754 664811 664920 "EXPR2" 665059 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 655759 663905 664196 "EXPEXPAN" 664590 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 655559 655716 655745 "EXIT" 655750 T EXIT (NIL) -8 NIL NIL NIL) (-321 655039 655283 655374 "EXITAST" 655488 T EXITAST (NIL) -8 NIL NIL NIL) (-320 654666 654728 654841 "EVALCYC" 654971 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 654207 654325 654366 "EVALAB" 654536 NIL EVALAB (NIL T) -9 NIL 654640 NIL) (-318 653688 653810 654031 "EVALAB-" 654036 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 651042 652344 652372 "EUCDOM" 652927 T EUCDOM (NIL) -9 NIL 653277 NIL) (-316 649447 649889 650479 "EUCDOM-" 650484 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636986 639745 642495 "ESTOOLS" 646717 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 636618 636675 636784 "ESTOOLS2" 636923 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 636369 636411 636491 "ESTOOLS1" 636570 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 630392 632000 632028 "ES" 634796 T ES (NIL) -9 NIL 636206 NIL) (-311 625339 626626 628443 "ES-" 628607 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 621713 622474 623254 "ESCONT" 624579 T ESCONT (NIL) -7 NIL NIL NIL) (-309 621458 621490 621572 "ESCONT1" 621675 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 621133 621183 621283 "ES2" 621402 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 620763 620821 620930 "ES1" 621069 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619979 620108 620284 "ERROR" 620607 T ERROR (NIL) -7 NIL NIL NIL) (-305 613375 619838 619929 "EQTBL" 619934 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605878 608689 610138 "EQ" 611959 NIL -2149 (NIL T) -8 NIL NIL NIL) (-303 605510 605567 605676 "EQ2" 605815 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 600801 601848 602941 "EP" 604449 NIL EP (NIL T) -7 NIL NIL NIL) (-301 599401 599692 599998 "ENV" 600515 T ENV (NIL) -8 NIL NIL NIL) (-300 598481 599035 599063 "ENTIRER" 599068 T ENTIRER (NIL) -9 NIL 599114 NIL) (-299 595175 596663 597024 "EMR" 598289 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 594305 594490 594544 "ELTAGG" 594924 NIL ELTAGG (NIL T T) -9 NIL 595135 NIL) (-297 594024 594086 594227 "ELTAGG-" 594232 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 593788 593817 593871 "ELTAB" 593955 NIL ELTAB (NIL T T) -9 NIL 594007 NIL) (-295 592914 593060 593259 "ELFUTS" 593639 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 592656 592712 592740 "ELEMFUN" 592845 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 592526 592547 592615 "ELEMFUN-" 592620 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 587314 590568 590609 "ELAGG" 591549 NIL ELAGG (NIL T) -9 NIL 592012 NIL) (-291 585599 586033 586696 "ELAGG-" 586701 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584911 585048 585204 "ELABOR" 585463 T ELABOR (NIL) -8 NIL NIL NIL) (-289 583572 583851 584145 "ELABEXPR" 584637 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 576406 578209 579038 "EFUPXS" 582847 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 569854 571655 572466 "EFULS" 575681 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 567339 567697 568169 "EFSTRUC" 569486 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 557130 558696 560244 "EF" 565854 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 556204 556615 556764 "EAB" 557001 T EAB (NIL) -8 NIL NIL NIL) (-283 555386 556163 556191 "E04UCFA" 556196 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 554568 555345 555373 "E04NAFA" 555378 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 553750 554527 554555 "E04MBFA" 554560 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552932 553709 553737 "E04JAFA" 553742 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 552116 552891 552919 "E04GCFA" 552924 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 551300 552075 552103 "E04FDFA" 552108 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 550482 551259 551287 "E04DGFA" 551292 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 544655 546007 547371 "E04AGNT" 549138 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 543426 543969 544009 "DVARCAT" 544350 NIL DVARCAT (NIL T) -9 NIL 544513 NIL) (-274 542630 542842 543156 "DVARCAT-" 543161 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 535499 542429 542558 "DSMP" 542563 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533922 534641 534682 "DSEXT" 535045 NIL DSEXT (NIL T) -9 NIL 535339 NIL) (-271 532207 532635 533301 "DSEXT-" 533306 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526988 528152 529220 "DROPT" 531159 T DROPT (NIL) -8 NIL NIL NIL) (-269 526653 526712 526810 "DROPT1" 526923 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 521768 522894 524031 "DROPT0" 525536 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 520113 520438 520824 "DRAWPT" 521402 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 514700 515623 516702 "DRAW" 519087 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 514333 514386 514504 "DRAWHACK" 514641 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 513064 513333 513624 "DRAWCX" 514062 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 512579 512648 512799 "DRAWCURV" 512990 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 503047 505009 507124 "DRAWCFUN" 510484 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 499785 501712 501753 "DQAGG" 502382 NIL DQAGG (NIL T) -9 NIL 502656 NIL) (-260 487258 493996 494079 "DPOLCAT" 495931 NIL DPOLCAT (NIL T T T T) -9 NIL 496476 NIL) (-259 482095 483443 485401 "DPOLCAT-" 485406 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 475450 481956 482054 "DPMO" 482059 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 468708 475230 475397 "DPMM" 475402 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 468278 468492 468581 "DOMTMPLT" 468639 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 467711 468080 468160 "DOMCTOR" 468218 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466923 467191 467342 "DOMAIN" 467580 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 460643 466558 466710 "DMP" 466824 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 458588 459710 459751 "DMEXT" 459756 NIL DMEXT (NIL T) -9 NIL 459932 NIL) (-251 458188 458244 458388 "DLP" 458526 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 452012 457515 457705 "DLIST" 458030 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 448783 450837 450878 "DLAGG" 451428 NIL DLAGG (NIL T) -9 NIL 451658 NIL) (-248 447445 448109 448137 "DIVRING" 448229 T DIVRING (NIL) -9 NIL 448312 NIL) (-247 446682 446872 447172 "DIVRING-" 447177 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 444784 445141 445547 "DISPLAY" 446296 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 438654 444698 444761 "DIRPROD" 444766 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 437502 437705 437970 "DIRPROD2" 438447 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 426239 432268 432321 "DIRPCAT" 432579 NIL DIRPCAT (NIL NIL T) -9 NIL 433454 NIL) (-242 422839 423695 424832 "DIRPCAT-" 425169 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 422126 422286 422472 "DIOSP" 422673 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418755 421010 421051 "DIOPS" 421485 NIL DIOPS (NIL T) -9 NIL 421714 NIL) (-239 418304 418418 418609 "DIOPS-" 418614 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 417355 417983 418011 "DIFRING" 418016 T DIFRING (NIL) -9 NIL 418038 NIL) (-237 417027 417101 417129 "DIFFSPC" 417248 T DIFFSPC (NIL) -9 NIL 417323 NIL) (-236 416672 416750 416902 "DIFFSPC-" 416907 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415728 416206 416247 "DIFFMOD" 416252 NIL DIFFMOD (NIL T) -9 NIL 416350 NIL) (-234 415436 415481 415522 "DIFFDOM" 415643 NIL DIFFDOM (NIL T) -9 NIL 415711 NIL) (-233 415289 415313 415397 "DIFFDOM-" 415402 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 413221 414493 414534 "DIFEXT" 414539 NIL DIFEXT (NIL T) -9 NIL 414692 NIL) (-231 410470 412725 412766 "DIAGG" 412771 NIL DIAGG (NIL T) -9 NIL 412791 NIL) (-230 409854 410011 410263 "DIAGG-" 410268 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 405273 408813 409090 "DHMATRIX" 409623 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400885 401794 402804 "DFSFUN" 404283 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395963 399816 400128 "DFLOAT" 400593 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 394226 394507 394896 "DFINTTLS" 395671 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 391255 392247 392647 "DERHAM" 393892 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 389058 391030 391119 "DEQUEUE" 391199 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 388312 388445 388628 "DEGRED" 388920 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384742 385487 386333 "DEFINTRF" 387540 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 382297 382766 383358 "DEFINTEF" 384261 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381647 381917 382032 "DEFAST" 382202 T DEFAST (NIL) -8 NIL NIL NIL) (-219 375371 381240 381390 "DECIMAL" 381517 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372883 373341 373847 "DDFACT" 374915 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372479 372522 372673 "DBLRESP" 372834 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 370347 370709 371070 "DBASE" 372245 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369589 369827 369973 "DATAARY" 370246 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368695 369548 369576 "D03FAFA" 369581 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367802 368654 368682 "D03EEFA" 368687 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365752 366218 366707 "D03AGNT" 367333 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 365041 365711 365739 "D02EJFA" 365744 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364330 365000 365028 "D02CJFA" 365033 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363619 364289 364317 "D02BHFA" 364322 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362908 363578 363606 "D02BBFA" 363611 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 356105 357694 359300 "D02AGNT" 361322 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353873 354396 354942 "D01WGTS" 355579 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352940 353832 353860 "D01TRNS" 353865 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 352008 352899 352927 "D01GBFA" 352932 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 351076 351967 351995 "D01FCFA" 352000 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 350144 351035 351063 "D01ASFA" 351068 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 349212 350103 350131 "D01AQFA" 350136 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 348280 349171 349199 "D01APFA" 349204 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347348 348239 348267 "D01ANFA" 348272 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346416 347307 347335 "D01AMFA" 347340 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345484 346375 346403 "D01ALFA" 346408 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344552 345443 345471 "D01AKFA" 345476 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343620 344511 344539 "D01AJFA" 344544 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336915 338468 340029 "D01AGNT" 342079 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 336252 336380 336532 "CYCLOTOM" 336783 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332985 333700 334427 "CYCLES" 335545 T CYCLES (NIL) -7 NIL NIL NIL) (-191 332297 332431 332602 "CVMP" 332846 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 330138 330396 330765 "CTRIGMNP" 332025 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329574 329932 330005 "CTOR" 330085 T CTOR (NIL) -8 NIL NIL NIL) (-188 329083 329305 329406 "CTORKIND" 329493 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328360 328676 328704 "CTORCAT" 328886 T CTORCAT (NIL) -9 NIL 328999 NIL) (-186 327958 328069 328228 "CTORCAT-" 328233 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327420 327632 327740 "CTORCALL" 327882 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326794 326893 327046 "CSTTOOLS" 327317 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322593 323250 324008 "CRFP" 326106 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 322068 322314 322406 "CRCEAST" 322521 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 321115 321300 321528 "CRAPACK" 321872 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320499 320600 320804 "CPMATCH" 320991 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 320224 320252 320358 "CPIMA" 320465 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316572 317244 317963 "COORDSYS" 319559 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315984 316105 316247 "CONTOUR" 316450 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311875 313987 314479 "CONTFRAC" 315524 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311755 311776 311804 "CONDUIT" 311841 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310829 311383 311411 "COMRING" 311416 T COMRING (NIL) -9 NIL 311468 NIL) (-173 309883 310187 310371 "COMPPROP" 310665 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309544 309579 309707 "COMPLPAT" 309842 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298855 309353 309462 "COMPLEX" 309467 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298491 298548 298655 "COMPLEX2" 298792 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297830 297951 298111 "COMPILER" 298351 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297548 297583 297681 "COMPFACT" 297789 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279835 291252 291292 "COMPCAT" 292296 NIL COMPCAT (NIL T) -9 NIL 293644 NIL) (-166 268621 271762 275645 "COMPCAT-" 276001 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268350 268378 268481 "COMMUPC" 268587 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268144 268178 268237 "COMMONOP" 268311 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 267700 267895 267982 "COMM" 268077 T COMM (NIL) -8 NIL NIL NIL) (-162 267276 267504 267579 "COMMAAST" 267645 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266525 266719 266747 "COMBOPC" 267085 T COMBOPC (NIL) -9 NIL 267260 NIL) (-160 265421 265631 265873 "COMBINAT" 266315 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 261878 262452 263079 "COMBF" 264843 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 260636 260994 261229 "COLOR" 261663 T COLOR (NIL) -8 NIL NIL NIL) (-157 260112 260357 260449 "COLONAST" 260564 T COLONAST (NIL) -8 NIL NIL NIL) (-156 259752 259799 259924 "CMPLXRT" 260059 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259200 259452 259551 "CLLCTAST" 259673 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 254702 255730 256810 "CLIP" 258140 T CLIP (NIL) -7 NIL NIL NIL) (-153 253043 253803 254043 "CLIF" 254529 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249192 251161 251202 "CLAGG" 252131 NIL CLAGG (NIL T) -9 NIL 252667 NIL) (-151 247614 248071 248654 "CLAGG-" 248659 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247158 247243 247383 "CINTSLPE" 247523 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 244659 245130 245678 "CHVAR" 246686 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 243819 244373 244401 "CHARZ" 244406 T CHARZ (NIL) -9 NIL 244421 NIL) (-147 243573 243613 243691 "CHARPOL" 243773 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 242617 243204 243232 "CHARNZ" 243279 T CHARNZ (NIL) -9 NIL 243335 NIL) (-145 240523 241271 241624 "CHAR" 242284 T CHAR (NIL) -8 NIL NIL NIL) (-144 240249 240310 240338 "CFCAT" 240449 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239490 239601 239784 "CDEN" 240133 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235455 238643 238923 "CCLASS" 239230 T CCLASS (NIL) -8 NIL NIL NIL) (-141 234706 234863 235040 "CATEGORY" 235298 T -10 (NIL) -8 NIL NIL NIL) (-140 234279 234625 234673 "CATCTOR" 234678 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 233730 233982 234080 "CATAST" 234201 T CATAST (NIL) -8 NIL NIL NIL) (-138 233206 233451 233543 "CASEAST" 233658 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228344 229363 230107 "CARTEN" 232518 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227452 227600 227821 "CARTEN2" 228191 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 225768 226602 226859 "CARD" 227215 T CARD (NIL) -8 NIL NIL NIL) (-134 225344 225572 225647 "CAPSLAST" 225713 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 224834 225042 225070 "CACHSET" 225202 T CACHSET (NIL) -9 NIL 225280 NIL) (-132 224290 224612 224640 "CABMON" 224690 T CABMON (NIL) -9 NIL 224746 NIL) (-131 223763 223994 224104 "BYTEORD" 224200 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 222740 223292 223434 "BYTE" 223597 T BYTE (NIL) -8 NIL NIL 223719) (-129 218092 222245 222417 "BYTEBUF" 222588 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 215603 217784 217891 "BTREE" 218018 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213054 215251 215373 "BTOURN" 215513 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210398 212496 212537 "BTCAT" 212605 NIL BTCAT (NIL T) -9 NIL 212682 NIL) (-125 210065 210145 210294 "BTCAT-" 210299 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205444 209324 209352 "BTAGG" 209466 T BTAGG (NIL) -9 NIL 209576 NIL) (-123 204934 205059 205265 "BTAGG-" 205270 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 201931 204212 204427 "BSTREE" 204751 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201069 201195 201379 "BRILL" 201787 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 197695 199767 199808 "BRAGG" 200457 NIL BRAGG (NIL T) -9 NIL 200715 NIL) (-119 196224 196630 197185 "BRAGG-" 197190 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189148 195568 195753 "BPADICRT" 196071 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187463 189085 189130 "BPADIC" 189135 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187161 187191 187305 "BOUNDZRO" 187427 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182389 183587 184499 "BOP" 186269 T BOP (NIL) -8 NIL NIL NIL) (-114 180170 180574 181049 "BOP1" 181947 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 179871 179932 179960 "BOOLE" 180071 T BOOLE (NIL) -9 NIL 180153 NIL) (-112 178696 179445 179594 "BOOLEAN" 179742 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 177961 178365 178419 "BMODULE" 178424 NIL BMODULE (NIL T T) -9 NIL 178489 NIL) (-110 173762 177759 177832 "BITS" 177908 T BITS (NIL) -8 NIL NIL NIL) (-109 173183 173302 173442 "BINDING" 173642 T BINDING (NIL) -8 NIL NIL NIL) (-108 166910 172778 172927 "BINARY" 173054 T BINARY (NIL) -8 NIL NIL NIL) (-107 164664 166137 166178 "BGAGG" 166438 NIL BGAGG (NIL T) -9 NIL 166575 NIL) (-106 164495 164527 164618 "BGAGG-" 164623 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163566 163879 164084 "BFUNCT" 164310 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162256 162434 162722 "BEZOUT" 163390 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 158727 161108 161438 "BBTREE" 161959 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158436 158489 158517 "BASTYPE" 158636 T BASTYPE (NIL) -9 NIL 158710 NIL) (-101 158288 158317 158390 "BASTYPE-" 158395 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157722 157798 157950 "BALFACT" 158199 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156578 157137 157323 "AUTOMOR" 157567 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156304 156309 156335 "ATTREG" 156340 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154556 155001 155353 "ATTRBUT" 155970 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154164 154384 154450 "ATTRAST" 154508 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153700 153813 153839 "ATRIG" 154040 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153509 153550 153637 "ATRIG-" 153642 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153140 153326 153352 "ASTCAT" 153357 T ASTCAT (NIL) -9 NIL 153387 NIL) (-92 152867 152926 153045 "ASTCAT-" 153050 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151018 152643 152731 "ASTACK" 152810 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149523 149820 150185 "ASSOCEQ" 150700 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148555 149182 149306 "ASP9" 149430 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148318 148503 148542 "ASP8" 148547 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147186 147923 148065 "ASP80" 148207 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146084 146821 146953 "ASP7" 147085 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145038 145761 145879 "ASP78" 145997 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144007 144718 144835 "ASP77" 144952 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 142919 143645 143776 "ASP74" 143907 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141819 142554 142686 "ASP73" 142818 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 140923 141645 141745 "ASP6" 141750 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139870 140600 140718 "ASP55" 140836 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138819 139544 139663 "ASP50" 139782 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 137907 138520 138630 "ASP4" 138740 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 136995 137608 137718 "ASP49" 137828 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135779 136534 136702 "ASP42" 136884 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134556 135312 135482 "ASP41" 135666 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133506 134233 134351 "ASP35" 134469 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133271 133454 133493 "ASP34" 133498 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133008 133075 133151 "ASP33" 133226 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 131902 132643 132775 "ASP31" 132907 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131667 131850 131889 "ASP30" 131894 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131402 131471 131547 "ASP29" 131622 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131167 131350 131389 "ASP28" 131394 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 130932 131115 131154 "ASP27" 131159 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130016 130630 130741 "ASP24" 130852 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129093 129818 129930 "ASP20" 129935 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128181 128794 128904 "ASP1" 129014 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127124 127855 127974 "ASP19" 128093 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126861 126928 127004 "ASP12" 127079 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125713 126460 126604 "ASP10" 126748 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123566 125557 125648 "ARRAY2" 125653 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119333 123214 123328 "ARRAY1" 123483 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118365 118538 118759 "ARRAY12" 119156 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112651 114567 114642 "ARR2CAT" 117272 NIL ARR2CAT (NIL T T T) -9 NIL 118030 NIL) (-56 110085 110829 111783 "ARR2CAT-" 111788 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109402 109712 109837 "ARITY" 109978 T ARITY (NIL) -8 NIL NIL NIL) (-54 108178 108330 108629 "APPRULE" 109238 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107829 107877 107996 "APPLYORE" 108124 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107183 107422 107542 "ANY" 107727 T ANY (NIL) -8 NIL NIL NIL) (-51 106461 106584 106741 "ANY1" 107057 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 103991 104898 105225 "ANTISYM" 106185 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103483 103698 103794 "ANON" 103913 T ANON (NIL) -8 NIL NIL NIL) (-48 97491 102022 102476 "AN" 103047 T AN (NIL) -8 NIL NIL NIL) (-47 93375 94763 94814 "AMR" 95562 NIL AMR (NIL T T) -9 NIL 96162 NIL) (-46 92487 92708 93071 "AMR-" 93076 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76930 92404 92465 "ALIST" 92470 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73735 76524 76693 "ALGSC" 76848 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70291 70845 71452 "ALGPKG" 73175 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69568 69669 69853 "ALGMFACT" 70177 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65603 66182 66776 "ALGMANIP" 69152 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55822 65229 65379 "ALGFF" 65536 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55018 55149 55328 "ALGFACT" 55680 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53945 54545 54583 "ALGEBRA" 54588 NIL ALGEBRA (NIL T) -9 NIL 54629 NIL) (-37 53663 53722 53854 "ALGEBRA-" 53859 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35658 51561 51613 "ALAGG" 51749 NIL ALAGG (NIL T T) -9 NIL 51910 NIL) (-35 35194 35307 35333 "AHYP" 35534 T AHYP (NIL) -9 NIL NIL NIL) (-34 34125 34373 34399 "AGG" 34898 T AGG (NIL) -9 NIL 35177 NIL) (-33 33559 33721 33935 "AGG-" 33940 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31365 31788 32193 "AF" 33201 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30845 31090 31180 "ADDAST" 31293 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30113 30372 30528 "ACPLOT" 30707 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18744 27045 27083 "ACFS" 27690 NIL ACFS (NIL T) -9 NIL 27929 NIL) (-28 16771 17261 18023 "ACFS-" 18028 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12875 14804 14830 "ACF" 15709 T ACF (NIL) -9 NIL 16122 NIL) (-26 11579 11913 12406 "ACF-" 12411 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11137 11332 11358 "ABELSG" 11450 T ABELSG (NIL) -9 NIL 11515 NIL) (-24 11004 11029 11095 "ABELSG-" 11100 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10333 10620 10646 "ABELMON" 10816 T ABELMON (NIL) -9 NIL 10928 NIL) (-22 9997 10081 10219 "ABELMON-" 10224 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9331 9703 9729 "ABELGRP" 9801 T ABELGRP (NIL) -9 NIL 9876 NIL) (-20 8794 8923 9139 "ABELGRP-" 9144 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) \ No newline at end of file +((-3 3259641 3259646 3259651 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3259626 3259631 3259636 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3259611 3259616 3259621 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3259596 3259601 3259606 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1315 3258739 3259471 3259548 "ZMOD" 3259553 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1314 3257793 3257957 3258180 "ZLINDEP" 3258571 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1313 3247093 3248861 3250833 "ZDSOLVE" 3255923 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1312 3246339 3246480 3246669 "YSTREAM" 3246939 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1311 3245767 3246013 3246126 "YDIAGRAM" 3246248 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1310 3243541 3245068 3245272 "XRPOLY" 3245610 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1309 3240094 3241412 3241987 "XPR" 3243013 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1308 3237815 3239425 3239629 "XPOLY" 3239925 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1307 3235454 3236822 3236877 "XPOLYC" 3237165 NIL XPOLYC (NIL T T) -9 NIL 3237278 NIL) (-1306 3231830 3233971 3234359 "XPBWPOLY" 3235112 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1305 3227511 3229806 3229848 "XF" 3230469 NIL XF (NIL T) -9 NIL 3230869 NIL) (-1304 3227132 3227220 3227389 "XF-" 3227394 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1303 3222314 3223603 3223658 "XFALG" 3225830 NIL XFALG (NIL T T) -9 NIL 3226619 NIL) (-1302 3221447 3221551 3221756 "XEXPPKG" 3222206 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1301 3219556 3221297 3221393 "XDPOLY" 3221398 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3218349 3218949 3218992 "XALG" 3218997 NIL XALG (NIL T) -9 NIL 3219108 NIL) (-1299 3211791 3216326 3216820 "WUTSET" 3217941 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1298 3210047 3210843 3211166 "WP" 3211602 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1297 3209649 3209869 3209939 "WHILEAST" 3209999 T WHILEAST (NIL) -8 NIL NIL NIL) (-1296 3209121 3209366 3209460 "WHEREAST" 3209577 T WHEREAST (NIL) -8 NIL NIL NIL) (-1295 3208007 3208205 3208500 "WFFINTBS" 3208918 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1294 3205911 3206338 3206800 "WEIER" 3207579 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1293 3204943 3205393 3205435 "VSPACE" 3205571 NIL VSPACE (NIL T) -9 NIL 3205645 NIL) (-1292 3204781 3204808 3204899 "VSPACE-" 3204904 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1291 3204590 3204632 3204700 "VOID" 3204735 T VOID (NIL) -8 NIL NIL NIL) (-1290 3202726 3203085 3203491 "VIEW" 3204206 T VIEW (NIL) -7 NIL NIL NIL) (-1289 3199150 3199789 3200526 "VIEWDEF" 3202011 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1288 3188454 3190698 3192871 "VIEW3D" 3196999 T VIEW3D (NIL) -8 NIL NIL NIL) (-1287 3180705 3182365 3183944 "VIEW2D" 3186897 T VIEW2D (NIL) -8 NIL NIL NIL) (-1286 3176060 3180475 3180567 "VECTOR" 3180648 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1285 3174637 3174896 3175214 "VECTOR2" 3175790 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1284 3168061 3172368 3172411 "VECTCAT" 3173406 NIL VECTCAT (NIL T) -9 NIL 3173993 NIL) (-1283 3167075 3167329 3167719 "VECTCAT-" 3167724 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1282 3166529 3166726 3166846 "VARIABLE" 3166990 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1281 3166462 3166467 3166497 "UTYPE" 3166502 T UTYPE (NIL) -9 NIL NIL NIL) (-1280 3165292 3165446 3165708 "UTSODETL" 3166288 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1279 3162732 3163192 3163716 "UTSODE" 3164833 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1278 3154680 3160493 3160973 "UTS" 3162310 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3145244 3150614 3150657 "UTSCAT" 3151769 NIL UTSCAT (NIL T) -9 NIL 3152527 NIL) (-1276 3142592 3143314 3144303 "UTSCAT-" 3144308 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1275 3142219 3142262 3142395 "UTS2" 3142543 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1274 3136419 3139029 3139072 "URAGG" 3141142 NIL URAGG (NIL T) -9 NIL 3141865 NIL) (-1273 3133358 3134221 3135344 "URAGG-" 3135349 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1272 3129067 3131993 3132458 "UPXSSING" 3133022 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1271 3121243 3128449 3128713 "UPXS" 3128861 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1270 3114316 3121147 3121219 "UPXSCONS" 3121224 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1269 3103723 3110519 3110581 "UPXSCCA" 3111155 NIL UPXSCCA (NIL T T) -9 NIL 3111388 NIL) (-1268 3103361 3103446 3103620 "UPXSCCA-" 3103625 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1267 3092620 3099189 3099232 "UPXSCAT" 3099880 NIL UPXSCAT (NIL T) -9 NIL 3100489 NIL) (-1266 3092050 3092129 3092308 "UPXS2" 3092535 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1265 3090704 3090957 3091308 "UPSQFREE" 3091793 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1264 3083912 3086972 3087027 "UPSCAT" 3088107 NIL UPSCAT (NIL T T) -9 NIL 3088872 NIL) (-1263 3083116 3083323 3083650 "UPSCAT-" 3083655 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1262 3068198 3076243 3076286 "UPOLYC" 3078387 NIL UPOLYC (NIL T) -9 NIL 3079608 NIL) (-1261 3059526 3061952 3065099 "UPOLYC-" 3065104 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1260 3059153 3059196 3059329 "UPOLYC2" 3059477 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1259 3050688 3058836 3058965 "UP" 3059072 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1258 3050027 3050134 3050298 "UPMP" 3050577 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1257 3049580 3049661 3049800 "UPDIVP" 3049940 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1256 3048148 3048397 3048713 "UPDECOMP" 3049329 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1255 3047379 3047491 3047677 "UPCDEN" 3048032 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1254 3046898 3046967 3047116 "UP2" 3047304 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1253 3045365 3046102 3046379 "UNISEG" 3046656 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1252 3044580 3044707 3044912 "UNISEG2" 3045208 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1251 3043640 3043820 3044046 "UNIFACT" 3044396 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1250 3026392 3042952 3043194 "ULS" 3043456 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1249 3014022 3026296 3026368 "ULSCONS" 3026373 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1248 2994850 3007210 3007272 "ULSCCAT" 3007910 NIL ULSCCAT (NIL T T) -9 NIL 3008199 NIL) (-1247 2993900 2994145 2994533 "ULSCCAT-" 2994538 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1246 2982964 2989447 2989490 "ULSCAT" 2990353 NIL ULSCAT (NIL T) -9 NIL 2991084 NIL) (-1245 2982394 2982473 2982652 "ULS2" 2982879 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1244 2981513 2982023 2982130 "UINT8" 2982241 T UINT8 (NIL) -8 NIL NIL 2982326) (-1243 2980631 2981141 2981248 "UINT64" 2981359 T UINT64 (NIL) -8 NIL NIL 2981444) (-1242 2979749 2980259 2980366 "UINT32" 2980477 T UINT32 (NIL) -8 NIL NIL 2980562) (-1241 2978867 2979377 2979484 "UINT16" 2979595 T UINT16 (NIL) -8 NIL NIL 2979680) (-1240 2977156 2978113 2978143 "UFD" 2978355 T UFD (NIL) -9 NIL 2978469 NIL) (-1239 2976950 2976996 2977091 "UFD-" 2977096 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1238 2976032 2976215 2976431 "UDVO" 2976756 T UDVO (NIL) -7 NIL NIL NIL) (-1237 2973848 2974257 2974728 "UDPO" 2975596 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1236 2973781 2973786 2973816 "TYPE" 2973821 T TYPE (NIL) -9 NIL NIL NIL) (-1235 2973541 2973736 2973767 "TYPEAST" 2973772 T TYPEAST (NIL) -8 NIL NIL NIL) (-1234 2972512 2972714 2972954 "TWOFACT" 2973335 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1233 2971535 2971921 2972156 "TUPLE" 2972312 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1232 2969226 2969745 2970284 "TUBETOOL" 2971018 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1231 2968075 2968280 2968521 "TUBE" 2969019 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1230 2962804 2967047 2967330 "TS" 2967827 NIL TS (NIL T) -8 NIL NIL NIL) (-1229 2951444 2955563 2955660 "TSETCAT" 2960929 NIL TSETCAT (NIL T T T T) -9 NIL 2962460 NIL) (-1228 2946176 2947776 2949667 "TSETCAT-" 2949672 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1227 2940815 2941662 2942591 "TRMANIP" 2945312 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1226 2940256 2940319 2940482 "TRIMAT" 2940747 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1225 2938122 2938359 2938716 "TRIGMNIP" 2940005 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1224 2937642 2937755 2937785 "TRIGCAT" 2937998 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1223 2937311 2937390 2937531 "TRIGCAT-" 2937536 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1222 2934158 2936169 2936450 "TREE" 2937065 NIL TREE (NIL T) -8 NIL NIL NIL) (-1221 2933432 2933960 2933990 "TRANFUN" 2934025 T TRANFUN (NIL) -9 NIL 2934091 NIL) (-1220 2932711 2932902 2933182 "TRANFUN-" 2933187 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1219 2932515 2932547 2932608 "TOPSP" 2932672 T TOPSP (NIL) -7 NIL NIL NIL) (-1218 2931863 2931978 2932132 "TOOLSIGN" 2932396 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1217 2930497 2931040 2931279 "TEXTFILE" 2931646 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1216 2928409 2928950 2929379 "TEX" 2930090 T TEX (NIL) -8 NIL NIL NIL) (-1215 2928190 2928221 2928293 "TEX1" 2928372 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1214 2927838 2927901 2927991 "TEMUTL" 2928122 T TEMUTL (NIL) -7 NIL NIL NIL) (-1213 2925992 2926272 2926597 "TBCMPPK" 2927561 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1212 2917699 2924078 2924134 "TBAGG" 2924534 NIL TBAGG (NIL T T) -9 NIL 2924745 NIL) (-1211 2912769 2914257 2916011 "TBAGG-" 2916016 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1210 2912153 2912260 2912405 "TANEXP" 2912658 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1209 2911664 2911928 2912018 "TALGOP" 2912098 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1208 2905058 2911521 2911614 "TABLE" 2911619 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1207 2904470 2904569 2904707 "TABLEAU" 2904955 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1206 2899078 2900298 2901546 "TABLBUMP" 2903256 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1205 2898300 2898447 2898628 "SYSTEM" 2898919 T SYSTEM (NIL) -8 NIL NIL NIL) (-1204 2894759 2895458 2896241 "SYSSOLP" 2897551 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1203 2894557 2894714 2894745 "SYSPTR" 2894750 T SYSPTR (NIL) -8 NIL NIL NIL) (-1202 2893593 2894098 2894217 "SYSNNI" 2894403 NIL SYSNNI (NIL NIL) -8 NIL NIL 2894488) (-1201 2892892 2893351 2893430 "SYSINT" 2893490 NIL SYSINT (NIL NIL) -8 NIL NIL 2893535) (-1200 2889224 2890170 2890880 "SYNTAX" 2892204 T SYNTAX (NIL) -8 NIL NIL NIL) (-1199 2886382 2886984 2887616 "SYMTAB" 2888614 T SYMTAB (NIL) -8 NIL NIL NIL) (-1198 2881631 2882533 2883516 "SYMS" 2885421 T SYMS (NIL) -8 NIL NIL NIL) (-1197 2878866 2881089 2881319 "SYMPOLY" 2881436 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1196 2878383 2878458 2878581 "SYMFUNC" 2878778 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1195 2874403 2875695 2876508 "SYMBOL" 2877592 T SYMBOL (NIL) -8 NIL NIL NIL) (-1194 2867942 2869631 2871351 "SWITCH" 2872705 T SWITCH (NIL) -8 NIL NIL NIL) (-1193 2861286 2866898 2867192 "SUTS" 2867706 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2853462 2860668 2860932 "SUPXS" 2861080 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2844945 2853080 2853206 "SUP" 2853371 NIL SUP (NIL T) -8 NIL NIL NIL) (-1190 2844104 2844231 2844448 "SUPFRACF" 2844813 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1189 2843725 2843784 2843897 "SUP2" 2844039 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1188 2842173 2842447 2842803 "SUMRF" 2843424 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1187 2841508 2841574 2841766 "SUMFS" 2842094 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1186 2824295 2840820 2841062 "SULS" 2841324 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2823897 2824117 2824187 "SUCHTAST" 2824247 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1184 2823192 2823422 2823562 "SUCH" 2823805 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1183 2817059 2818098 2819057 "SUBSPACE" 2822280 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1182 2816489 2816579 2816743 "SUBRESP" 2816947 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1181 2809857 2811154 2812465 "STTF" 2815225 NIL STTF (NIL T) -7 NIL NIL NIL) (-1180 2804030 2805150 2806297 "STTFNC" 2808757 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1179 2795343 2797212 2799006 "STTAYLOR" 2802271 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1178 2788477 2795207 2795290 "STRTBL" 2795295 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1177 2783437 2788186 2788285 "STRING" 2788400 T STRING (NIL) -8 NIL NIL NIL) (-1176 2776192 2781056 2781667 "STREAM" 2782861 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2775702 2775779 2775923 "STREAM3" 2776109 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1174 2774684 2774867 2775102 "STREAM2" 2775515 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1173 2774372 2774424 2774517 "STREAM1" 2774626 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1172 2773388 2773569 2773800 "STINPROD" 2774188 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1171 2772926 2773136 2773166 "STEP" 2773246 T STEP (NIL) -9 NIL 2773324 NIL) (-1170 2772113 2772415 2772563 "STEPAST" 2772800 T STEPAST (NIL) -8 NIL NIL NIL) (-1169 2765549 2772012 2772089 "STBL" 2772094 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1168 2760618 2764712 2764755 "STAGG" 2764908 NIL STAGG (NIL T) -9 NIL 2764997 NIL) (-1167 2758320 2758922 2759794 "STAGG-" 2759799 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1166 2756469 2758090 2758182 "STACK" 2758263 NIL STACK (NIL T) -8 NIL NIL NIL) (-1165 2749164 2754610 2755066 "SREGSET" 2756099 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1164 2741589 2742958 2744471 "SRDCMPK" 2747770 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1163 2734454 2738977 2739007 "SRAGG" 2740310 T SRAGG (NIL) -9 NIL 2740918 NIL) (-1162 2733471 2733726 2734105 "SRAGG-" 2734110 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1161 2727655 2732418 2732839 "SQMATRIX" 2733097 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1160 2721342 2724373 2725100 "SPLTREE" 2727000 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1159 2717305 2717998 2718644 "SPLNODE" 2720768 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1158 2716352 2716585 2716615 "SPFCAT" 2717059 T SPFCAT (NIL) -9 NIL NIL NIL) (-1157 2715089 2715299 2715563 "SPECOUT" 2716110 T SPECOUT (NIL) -7 NIL NIL NIL) (-1156 2706185 2708057 2708087 "SPADXPT" 2712763 T SPADXPT (NIL) -9 NIL 2714927 NIL) (-1155 2705946 2705986 2706055 "SPADPRSR" 2706138 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1154 2703995 2705901 2705932 "SPADAST" 2705937 T SPADAST (NIL) -8 NIL NIL NIL) (-1153 2695926 2697699 2697742 "SPACEC" 2702115 NIL SPACEC (NIL T) -9 NIL 2703931 NIL) (-1152 2694056 2695858 2695907 "SPACE3" 2695912 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1151 2692808 2692979 2693270 "SORTPAK" 2693861 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1150 2690900 2691203 2691615 "SOLVETRA" 2692472 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1149 2689950 2690172 2690433 "SOLVESER" 2690673 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1148 2685254 2686142 2687137 "SOLVERAD" 2689002 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1147 2681069 2681678 2682407 "SOLVEFOR" 2684621 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1146 2675339 2680418 2680515 "SNTSCAT" 2680520 NIL SNTSCAT (NIL T T T T) -9 NIL 2680590 NIL) (-1145 2669445 2673662 2674053 "SMTS" 2675029 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1144 2663854 2669333 2669410 "SMP" 2669415 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1143 2662013 2662314 2662712 "SMITH" 2663551 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1142 2654117 2658592 2658695 "SMATCAT" 2660046 NIL SMATCAT (NIL NIL T T T) -9 NIL 2660596 NIL) (-1141 2651057 2651880 2653058 "SMATCAT-" 2653063 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1140 2648697 2650265 2650308 "SKAGG" 2650569 NIL SKAGG (NIL T) -9 NIL 2650704 NIL) (-1139 2644887 2648170 2648354 "SINT" 2648506 T SINT (NIL) -8 NIL NIL 2648668) (-1138 2644659 2644697 2644763 "SIMPAN" 2644843 T SIMPAN (NIL) -7 NIL NIL NIL) (-1137 2643938 2644194 2644334 "SIG" 2644541 T SIG (NIL) -8 NIL NIL NIL) (-1136 2642776 2642997 2643272 "SIGNRF" 2643697 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1135 2641609 2641760 2642044 "SIGNEF" 2642605 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1134 2640915 2641192 2641316 "SIGAST" 2641507 T SIGAST (NIL) -8 NIL NIL NIL) (-1133 2638605 2639059 2639565 "SHP" 2640456 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1132 2632433 2638506 2638582 "SHDP" 2638587 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1131 2631992 2632184 2632214 "SGROUP" 2632307 T SGROUP (NIL) -9 NIL 2632369 NIL) (-1130 2631850 2631876 2631949 "SGROUP-" 2631954 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1129 2628641 2629339 2630062 "SGCF" 2631149 T SGCF (NIL) -7 NIL NIL NIL) (-1128 2623009 2628088 2628185 "SFRTCAT" 2628190 NIL SFRTCAT (NIL T T T T) -9 NIL 2628229 NIL) (-1127 2616430 2617448 2618584 "SFRGCD" 2621992 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1126 2609556 2610629 2611815 "SFQCMPK" 2615363 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1125 2609176 2609265 2609376 "SFORT" 2609497 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1124 2608294 2609016 2609137 "SEXOF" 2609142 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1123 2607401 2608175 2608243 "SEX" 2608248 T SEX (NIL) -8 NIL NIL NIL) (-1122 2603182 2603897 2603992 "SEXCAT" 2606614 NIL SEXCAT (NIL T T T T T) -9 NIL 2607174 NIL) (-1121 2600335 2603116 2603164 "SET" 2603169 NIL SET (NIL T) -8 NIL NIL NIL) (-1120 2598559 2599048 2599353 "SETMN" 2600076 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1119 2598041 2598193 2598223 "SETCAT" 2598399 T SETCAT (NIL) -9 NIL 2598509 NIL) (-1118 2597733 2597811 2597941 "SETCAT-" 2597946 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1117 2594094 2596194 2596237 "SETAGG" 2597107 NIL SETAGG (NIL T) -9 NIL 2597447 NIL) (-1116 2593552 2593668 2593905 "SETAGG-" 2593910 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1115 2592995 2593248 2593349 "SEQAST" 2593473 T SEQAST (NIL) -8 NIL NIL NIL) (-1114 2592194 2592488 2592549 "SEGXCAT" 2592835 NIL SEGXCAT (NIL T T) -9 NIL 2592955 NIL) (-1113 2591200 2591860 2592042 "SEG" 2592047 NIL SEG (NIL T) -8 NIL NIL NIL) (-1112 2590179 2590393 2590436 "SEGCAT" 2590958 NIL SEGCAT (NIL T) -9 NIL 2591179 NIL) (-1111 2589111 2589542 2589750 "SEGBIND" 2590006 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1110 2588732 2588791 2588904 "SEGBIND2" 2589046 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1109 2588305 2588533 2588610 "SEGAST" 2588677 T SEGAST (NIL) -8 NIL NIL NIL) (-1108 2587524 2587650 2587854 "SEG2" 2588149 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1107 2586895 2587459 2587506 "SDVAR" 2587511 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1106 2579146 2586665 2586795 "SDPOL" 2586800 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1105 2577739 2578005 2578324 "SCPKG" 2578861 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1104 2576903 2577075 2577267 "SCOPE" 2577569 T SCOPE (NIL) -8 NIL NIL NIL) (-1103 2576123 2576257 2576436 "SCACHE" 2576758 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1102 2575755 2575941 2575971 "SASTCAT" 2575976 T SASTCAT (NIL) -9 NIL 2575989 NIL) (-1101 2575242 2575590 2575666 "SAOS" 2575701 T SAOS (NIL) -8 NIL NIL NIL) (-1100 2574807 2574842 2575015 "SAERFFC" 2575201 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1099 2568470 2574704 2574784 "SAE" 2574789 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1098 2568063 2568098 2568257 "SAEFACT" 2568429 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1097 2566384 2566698 2567099 "RURPK" 2567729 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1096 2565021 2565327 2565632 "RULESET" 2566218 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1095 2562244 2562774 2563232 "RULE" 2564702 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1094 2561856 2562038 2562121 "RULECOLD" 2562196 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1093 2561646 2561674 2561745 "RTVALUE" 2561807 T RTVALUE (NIL) -8 NIL NIL NIL) (-1092 2561117 2561363 2561457 "RSTRCAST" 2561574 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1091 2555965 2556760 2557680 "RSETGCD" 2560316 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1090 2545195 2550274 2550371 "RSETCAT" 2554490 NIL RSETCAT (NIL T T T T) -9 NIL 2555587 NIL) (-1089 2543122 2543661 2544485 "RSETCAT-" 2544490 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1088 2535508 2536884 2538404 "RSDCMPK" 2541721 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1087 2533473 2533940 2534014 "RRCC" 2535100 NIL RRCC (NIL T T) -9 NIL 2535444 NIL) (-1086 2532824 2532998 2533277 "RRCC-" 2533282 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1085 2532267 2532520 2532621 "RPTAST" 2532745 T RPTAST (NIL) -8 NIL NIL NIL) (-1084 2505743 2515379 2515446 "RPOLCAT" 2526112 NIL RPOLCAT (NIL T T T) -9 NIL 2529272 NIL) (-1083 2497241 2499581 2502703 "RPOLCAT-" 2502708 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1082 2488176 2495452 2495934 "ROUTINE" 2496781 T ROUTINE (NIL) -8 NIL NIL NIL) (-1081 2484837 2487802 2487942 "ROMAN" 2488058 T ROMAN (NIL) -8 NIL NIL NIL) (-1080 2483081 2483697 2483957 "ROIRC" 2484642 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1079 2479299 2481583 2481613 "RNS" 2481917 T RNS (NIL) -9 NIL 2482191 NIL) (-1078 2477808 2478191 2478725 "RNS-" 2478800 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1077 2477197 2477605 2477635 "RNG" 2477640 T RNG (NIL) -9 NIL 2477661 NIL) (-1076 2476200 2476562 2476764 "RNGBIND" 2477048 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1075 2475585 2475973 2476016 "RMODULE" 2476021 NIL RMODULE (NIL T) -9 NIL 2476048 NIL) (-1074 2474421 2474515 2474851 "RMCAT2" 2475486 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1073 2471271 2473767 2474064 "RMATRIX" 2474183 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1072 2464098 2466358 2466473 "RMATCAT" 2469832 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2470814 NIL) (-1071 2463473 2463620 2463927 "RMATCAT-" 2463932 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1070 2463088 2463260 2463303 "RLINSET" 2463365 NIL RLINSET (NIL T) -9 NIL 2463409 NIL) (-1069 2462655 2462730 2462858 "RINTERP" 2463007 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1068 2461699 2462253 2462283 "RING" 2462339 T RING (NIL) -9 NIL 2462431 NIL) (-1067 2461491 2461535 2461632 "RING-" 2461637 NIL RING- (NIL T) -8 NIL NIL NIL) (-1066 2460332 2460569 2460827 "RIDIST" 2461255 T RIDIST (NIL) -7 NIL NIL NIL) (-1065 2451621 2459800 2460006 "RGCHAIN" 2460180 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1064 2450957 2451363 2451404 "RGBCSPC" 2451462 NIL RGBCSPC (NIL T) -9 NIL 2451514 NIL) (-1063 2450101 2450482 2450523 "RGBCMDL" 2450755 NIL RGBCMDL (NIL T) -9 NIL 2450869 NIL) (-1062 2447095 2447709 2448379 "RF" 2449465 NIL RF (NIL T) -7 NIL NIL NIL) (-1061 2446741 2446804 2446907 "RFFACTOR" 2447026 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1060 2446466 2446501 2446598 "RFFACT" 2446700 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1059 2444583 2444947 2445329 "RFDIST" 2446106 T RFDIST (NIL) -7 NIL NIL NIL) (-1058 2444036 2444128 2444291 "RETSOL" 2444485 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1057 2443672 2443752 2443795 "RETRACT" 2443928 NIL RETRACT (NIL T) -9 NIL 2444015 NIL) (-1056 2443521 2443546 2443633 "RETRACT-" 2443638 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1055 2443123 2443343 2443413 "RETAST" 2443473 T RETAST (NIL) -8 NIL NIL NIL) (-1054 2435865 2442776 2442903 "RESULT" 2443018 T RESULT (NIL) -8 NIL NIL NIL) (-1053 2434456 2435134 2435333 "RESRING" 2435768 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1052 2434092 2434141 2434239 "RESLATC" 2434393 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1051 2433797 2433832 2433939 "REPSQ" 2434051 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1050 2431219 2431799 2432401 "REP" 2433217 T REP (NIL) -7 NIL NIL NIL) (-1049 2430916 2430951 2431062 "REPDB" 2431178 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1048 2424816 2426205 2427428 "REP2" 2429728 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1047 2421193 2421874 2422682 "REP1" 2424043 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1046 2413889 2419334 2419790 "REGSET" 2420823 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1045 2412654 2413037 2413287 "REF" 2413674 NIL REF (NIL T) -8 NIL NIL NIL) (-1044 2412031 2412134 2412301 "REDORDER" 2412538 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1043 2407999 2411244 2411471 "RECLOS" 2411859 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1042 2407051 2407232 2407447 "REALSOLV" 2407806 T REALSOLV (NIL) -7 NIL NIL NIL) (-1041 2406897 2406938 2406968 "REAL" 2406973 T REAL (NIL) -9 NIL 2407008 NIL) (-1040 2403380 2404182 2405066 "REAL0Q" 2406062 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1039 2398981 2399969 2401030 "REAL0" 2402361 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1038 2398452 2398698 2398792 "RDUCEAST" 2398909 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1037 2397857 2397929 2398136 "RDIV" 2398374 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1036 2396925 2397099 2397312 "RDIST" 2397679 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1035 2395522 2395809 2396181 "RDETRS" 2396633 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1034 2393334 2393788 2394326 "RDETR" 2395064 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1033 2391959 2392237 2392634 "RDEEFS" 2393050 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1032 2390468 2390774 2391199 "RDEEF" 2391647 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1031 2384515 2387435 2387465 "RCFIELD" 2388760 T RCFIELD (NIL) -9 NIL 2389491 NIL) (-1030 2382579 2383083 2383779 "RCFIELD-" 2383854 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1029 2378822 2380652 2380695 "RCAGG" 2381779 NIL RCAGG (NIL T) -9 NIL 2382244 NIL) (-1028 2378450 2378544 2378707 "RCAGG-" 2378712 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1027 2377785 2377897 2378062 "RATRET" 2378334 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1026 2377338 2377405 2377526 "RATFACT" 2377713 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1025 2376646 2376766 2376918 "RANDSRC" 2377208 T RANDSRC (NIL) -7 NIL NIL NIL) (-1024 2376380 2376424 2376497 "RADUTIL" 2376595 T RADUTIL (NIL) -7 NIL NIL NIL) (-1023 2369208 2375211 2375522 "RADIX" 2376103 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1022 2359668 2369050 2369180 "RADFF" 2369185 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1021 2359315 2359390 2359420 "RADCAT" 2359580 T RADCAT (NIL) -9 NIL NIL NIL) (-1020 2359097 2359145 2359245 "RADCAT-" 2359250 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1019 2357197 2358867 2358959 "QUEUE" 2359040 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1018 2353458 2357130 2357178 "QUAT" 2357183 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1017 2353089 2353132 2353263 "QUATCT2" 2353409 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1016 2345915 2349539 2349581 "QUATCAT" 2350372 NIL QUATCAT (NIL T) -9 NIL 2351138 NIL) (-1015 2342054 2343091 2344481 "QUATCAT-" 2344577 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1014 2339493 2341102 2341145 "QUAGG" 2341526 NIL QUAGG (NIL T) -9 NIL 2341701 NIL) (-1013 2339095 2339315 2339385 "QQUTAST" 2339445 T QQUTAST (NIL) -8 NIL NIL NIL) (-1012 2338108 2338608 2338773 "QFORM" 2338976 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1011 2328495 2334010 2334052 "QFCAT" 2334720 NIL QFCAT (NIL T) -9 NIL 2335721 NIL) (-1010 2324062 2325263 2326857 "QFCAT-" 2326953 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1009 2323693 2323736 2323867 "QFCAT2" 2324013 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2323148 2323258 2323390 "QEQUAT" 2323583 T QEQUAT (NIL) -8 NIL NIL NIL) (-1007 2316274 2317347 2318533 "QCMPACK" 2322081 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1006 2313812 2314260 2314690 "QALGSET" 2315929 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1005 2313047 2313223 2313459 "QALGSET2" 2313630 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1004 2311732 2311956 2312275 "PWFFINTB" 2312820 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1003 2309907 2310075 2310431 "PUSHVAR" 2311546 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1002 2305796 2306850 2306893 "PTRANFN" 2308804 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1001 2304187 2304478 2304802 "PTPACK" 2305507 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1000 2303816 2303873 2303984 "PTFUNC2" 2304124 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-999 2298243 2302638 2302679 "PTCAT" 2302975 NIL PTCAT (NIL T) -9 NIL 2303128 NIL) (-998 2297901 2297936 2298060 "PSQFR" 2298202 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-997 2296496 2296794 2297128 "PSEUDLIN" 2297599 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-996 2283259 2285630 2287954 "PSETPK" 2294256 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-995 2276277 2279017 2279113 "PSETCAT" 2282134 NIL PSETCAT (NIL T T T T) -9 NIL 2282948 NIL) (-994 2274113 2274747 2275568 "PSETCAT-" 2275573 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-993 2273462 2273627 2273655 "PSCURVE" 2273923 T PSCURVE (NIL) -9 NIL 2274090 NIL) (-992 2269446 2270962 2271027 "PSCAT" 2271871 NIL PSCAT (NIL T T T) -9 NIL 2272111 NIL) (-991 2268509 2268725 2269125 "PSCAT-" 2269130 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-990 2266868 2267578 2267841 "PRTITION" 2268266 T PRTITION (NIL) -8 NIL NIL NIL) (-989 2266343 2266589 2266681 "PRTDAST" 2266796 T PRTDAST (NIL) -8 NIL NIL NIL) (-988 2255433 2257647 2259835 "PRS" 2264205 NIL PRS (NIL T T) -7 NIL NIL NIL) (-987 2253218 2254755 2254795 "PRQAGG" 2254978 NIL PRQAGG (NIL T) -9 NIL 2255080 NIL) (-986 2252554 2252859 2252887 "PROPLOG" 2253026 T PROPLOG (NIL) -9 NIL 2253141 NIL) (-985 2252158 2252215 2252338 "PROPFUN2" 2252477 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-984 2251473 2251594 2251766 "PROPFUN1" 2252019 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-983 2249654 2250220 2250517 "PROPFRML" 2251209 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-982 2249123 2249230 2249358 "PROPERTY" 2249546 T PROPERTY (NIL) -8 NIL NIL NIL) (-981 2243181 2247289 2248109 "PRODUCT" 2248349 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-980 2240459 2242639 2242873 "PR" 2242992 NIL PR (NIL T T) -8 NIL NIL NIL) (-979 2240255 2240287 2240346 "PRINT" 2240420 T PRINT (NIL) -7 NIL NIL NIL) (-978 2239595 2239712 2239864 "PRIMES" 2240135 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-977 2237660 2238061 2238527 "PRIMELT" 2239174 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-976 2237389 2237438 2237466 "PRIMCAT" 2237590 T PRIMCAT (NIL) -9 NIL NIL NIL) (-975 2233506 2237327 2237372 "PRIMARR" 2237377 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-974 2232513 2232691 2232919 "PRIMARR2" 2233324 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-973 2232156 2232212 2232323 "PREASSOC" 2232451 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-972 2231631 2231764 2231792 "PPCURVE" 2231997 T PPCURVE (NIL) -9 NIL 2232133 NIL) (-971 2231226 2231426 2231509 "PORTNUM" 2231568 T PORTNUM (NIL) -8 NIL NIL NIL) (-970 2228585 2228984 2229576 "POLYROOT" 2230807 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-969 2222491 2228189 2228349 "POLY" 2228458 NIL POLY (NIL T) -8 NIL NIL NIL) (-968 2221874 2221932 2222166 "POLYLIFT" 2222427 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-967 2218149 2218598 2219227 "POLYCATQ" 2221419 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-966 2204491 2209896 2209961 "POLYCAT" 2213475 NIL POLYCAT (NIL T T T) -9 NIL 2215353 NIL) (-965 2197940 2199802 2202186 "POLYCAT-" 2202191 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2197527 2197595 2197715 "POLY2UP" 2197866 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-963 2197159 2197216 2197325 "POLY2" 2197464 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-962 2195844 2196083 2196359 "POLUTIL" 2196933 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-961 2194199 2194476 2194807 "POLTOPOL" 2195566 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-960 2189666 2194135 2194181 "POINT" 2194186 NIL POINT (NIL T) -8 NIL NIL NIL) (-959 2187853 2188210 2188585 "PNTHEORY" 2189311 T PNTHEORY (NIL) -7 NIL NIL NIL) (-958 2186311 2186608 2187007 "PMTOOLS" 2187551 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-957 2185904 2185982 2186099 "PMSYM" 2186227 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-956 2185412 2185481 2185656 "PMQFCAT" 2185829 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-955 2184767 2184877 2185033 "PMPRED" 2185289 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-954 2184160 2184246 2184408 "PMPREDFS" 2184668 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-953 2182824 2183032 2183410 "PMPLCAT" 2183922 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-952 2182356 2182435 2182587 "PMLSAGG" 2182739 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-951 2181829 2181905 2182087 "PMKERNEL" 2182274 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-950 2181446 2181521 2181634 "PMINS" 2181748 NIL PMINS (NIL T) -7 NIL NIL NIL) (-949 2180888 2180957 2181166 "PMFS" 2181371 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-948 2180116 2180234 2180439 "PMDOWN" 2180765 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-947 2179283 2179441 2179622 "PMASS" 2179955 T PMASS (NIL) -7 NIL NIL NIL) (-946 2178556 2178666 2178829 "PMASSFS" 2179170 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-945 2178211 2178279 2178373 "PLOTTOOL" 2178482 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-944 2172818 2174022 2175170 "PLOT" 2177083 T PLOT (NIL) -8 NIL NIL NIL) (-943 2168622 2169666 2170587 "PLOT3D" 2171917 T PLOT3D (NIL) -8 NIL NIL NIL) (-942 2167534 2167711 2167946 "PLOT1" 2168426 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-941 2142925 2147600 2152451 "PLEQN" 2162800 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-940 2142243 2142365 2142545 "PINTERP" 2142790 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-939 2141936 2141983 2142086 "PINTERPA" 2142190 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-938 2141152 2141700 2141787 "PI" 2141827 T PI (NIL) -8 NIL NIL 2141894) (-937 2139435 2140410 2140438 "PID" 2140620 T PID (NIL) -9 NIL 2140754 NIL) (-936 2139186 2139223 2139298 "PICOERCE" 2139392 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-935 2138506 2138645 2138821 "PGROEB" 2139042 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-934 2134093 2134907 2135812 "PGE" 2137621 T PGE (NIL) -7 NIL NIL NIL) (-933 2132216 2132463 2132829 "PGCD" 2133810 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-932 2131554 2131657 2131818 "PFRPAC" 2132100 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-931 2128194 2130102 2130455 "PFR" 2131233 NIL PFR (NIL T) -8 NIL NIL NIL) (-930 2126583 2126827 2127152 "PFOTOOLS" 2127941 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-929 2125116 2125355 2125706 "PFOQ" 2126340 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-928 2123617 2123829 2124185 "PFO" 2124900 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-927 2120170 2123506 2123575 "PF" 2123580 NIL PF (NIL NIL) -8 NIL NIL NIL) (-926 2117490 2118761 2118789 "PFECAT" 2119374 T PFECAT (NIL) -9 NIL 2119758 NIL) (-925 2116935 2117089 2117303 "PFECAT-" 2117308 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-924 2115538 2115790 2116091 "PFBRU" 2116684 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-923 2113404 2113756 2114188 "PFBR" 2115189 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-922 2109450 2110916 2111563 "PERM" 2112790 NIL PERM (NIL T) -8 NIL NIL NIL) (-921 2104684 2105657 2106527 "PERMGRP" 2108613 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-920 2102803 2103763 2103804 "PERMCAT" 2104204 NIL PERMCAT (NIL T) -9 NIL 2104502 NIL) (-919 2102456 2102497 2102621 "PERMAN" 2102756 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-918 2099946 2102121 2102243 "PENDTREE" 2102367 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-917 2098875 2099090 2099131 "PDSPC" 2099664 NIL PDSPC (NIL T) -9 NIL 2099909 NIL) (-916 2097978 2098196 2098558 "PDSPC-" 2098563 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-915 2096860 2097628 2097669 "PDRING" 2097674 NIL PDRING (NIL T) -9 NIL 2097702 NIL) (-914 2095747 2096365 2096419 "PDMOD" 2096424 NIL PDMOD (NIL T T) -9 NIL 2096528 NIL) (-913 2092962 2093740 2094408 "PDEPROB" 2095099 T PDEPROB (NIL) -8 NIL NIL NIL) (-912 2090507 2091011 2091566 "PDEPACK" 2092427 T PDEPACK (NIL) -7 NIL NIL NIL) (-911 2089419 2089609 2089860 "PDECOMP" 2090306 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-910 2086984 2087827 2087855 "PDECAT" 2088642 T PDECAT (NIL) -9 NIL 2089355 NIL) (-909 2086613 2086668 2086722 "PDDOM" 2086887 NIL PDDOM (NIL T T) -9 NIL 2086967 NIL) (-908 2086432 2086462 2086569 "PDDOM-" 2086574 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-907 2086183 2086216 2086306 "PCOMP" 2086393 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-906 2084361 2084984 2085281 "PBWLB" 2085912 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-905 2076834 2078434 2079772 "PATTERN" 2083044 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2076466 2076523 2076632 "PATTERN2" 2076771 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-903 2074223 2074611 2075068 "PATTERN1" 2076055 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-902 2071591 2072172 2072653 "PATRES" 2073788 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-901 2071155 2071222 2071354 "PATRES2" 2071518 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-900 2069038 2069443 2069850 "PATMATCH" 2070822 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-899 2068534 2068743 2068784 "PATMAB" 2068891 NIL PATMAB (NIL T) -9 NIL 2068974 NIL) (-898 2067052 2067388 2067646 "PATLRES" 2068339 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-897 2066598 2066721 2066762 "PATAB" 2066767 NIL PATAB (NIL T) -9 NIL 2066939 NIL) (-896 2064780 2065175 2065598 "PARTPERM" 2066195 T PARTPERM (NIL) -7 NIL NIL NIL) (-895 2064401 2064464 2064566 "PARSURF" 2064711 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-894 2064033 2064090 2064199 "PARSU2" 2064338 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-893 2063797 2063837 2063904 "PARSER" 2063986 T PARSER (NIL) -7 NIL NIL NIL) (-892 2063418 2063481 2063583 "PARSCURV" 2063728 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-891 2063050 2063107 2063216 "PARSC2" 2063355 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-890 2062689 2062747 2062844 "PARPCURV" 2062986 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-889 2062321 2062378 2062487 "PARPC2" 2062626 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-888 2061382 2061694 2061876 "PARAMAST" 2062159 T PARAMAST (NIL) -8 NIL NIL NIL) (-887 2060902 2060988 2061107 "PAN2EXPR" 2061283 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-886 2059679 2060023 2060251 "PALETTE" 2060694 T PALETTE (NIL) -8 NIL NIL NIL) (-885 2058072 2058684 2059044 "PAIR" 2059365 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-884 2051664 2057329 2057524 "PADICRC" 2057926 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-883 2044580 2051008 2051193 "PADICRAT" 2051511 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-882 2042895 2044517 2044562 "PADIC" 2044567 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-881 2039991 2041555 2041595 "PADICCT" 2042176 NIL PADICCT (NIL NIL) -9 NIL 2042458 NIL) (-880 2038948 2039148 2039416 "PADEPAC" 2039778 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-879 2038160 2038293 2038499 "PADE" 2038810 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-878 2036547 2037368 2037648 "OWP" 2037964 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-877 2036040 2036253 2036350 "OVERSET" 2036470 T OVERSET (NIL) -8 NIL NIL NIL) (-876 2035086 2035645 2035817 "OVAR" 2035908 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-875 2034350 2034471 2034632 "OUT" 2034945 T OUT (NIL) -7 NIL NIL NIL) (-874 2023222 2025459 2027659 "OUTFORM" 2032170 T OUTFORM (NIL) -8 NIL NIL NIL) (-873 2022558 2022819 2022946 "OUTBFILE" 2023115 T OUTBFILE (NIL) -8 NIL NIL NIL) (-872 2021865 2022030 2022058 "OUTBCON" 2022376 T OUTBCON (NIL) -9 NIL 2022542 NIL) (-871 2021466 2021578 2021735 "OUTBCON-" 2021740 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-870 2020846 2021195 2021284 "OSI" 2021397 T OSI (NIL) -8 NIL NIL NIL) (-869 2020362 2020700 2020728 "OSGROUP" 2020733 T OSGROUP (NIL) -9 NIL 2020755 NIL) (-868 2019107 2019334 2019619 "ORTHPOL" 2020109 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-867 2016658 2018942 2019063 "OREUP" 2019068 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-866 2014061 2016349 2016476 "ORESUP" 2016600 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-865 2011589 2012089 2012650 "OREPCTO" 2013550 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-864 2005261 2007462 2007503 "OREPCAT" 2009851 NIL OREPCAT (NIL T) -9 NIL 2010955 NIL) (-863 2002408 2003190 2004248 "OREPCAT-" 2004253 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-862 2001545 2001843 2001871 "ORDSET" 2002180 T ORDSET (NIL) -9 NIL 2002344 NIL) (-861 2000976 2001124 2001348 "ORDSET-" 2001353 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-860 1999527 2000318 2000346 "ORDRING" 2000548 T ORDRING (NIL) -9 NIL 2000673 NIL) (-859 1999172 1999266 1999410 "ORDRING-" 1999415 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 1998538 1999001 1999029 "ORDMON" 1999034 T ORDMON (NIL) -9 NIL 1999055 NIL) (-857 1997700 1997847 1998042 "ORDFUNS" 1998387 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1997024 1997443 1997471 "ORDFIN" 1997536 T ORDFIN (NIL) -9 NIL 1997610 NIL) (-855 1993583 1995610 1996019 "ORDCOMP" 1996648 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1992849 1992976 1993162 "ORDCOMP2" 1993443 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1989430 1990340 1991154 "OPTPROB" 1992055 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1986232 1986871 1987575 "OPTPACK" 1988746 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1983905 1984671 1984699 "OPTCAT" 1985518 T OPTCAT (NIL) -9 NIL 1986168 NIL) (-850 1983289 1983582 1983687 "OPSIG" 1983820 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1983057 1983096 1983162 "OPQUERY" 1983243 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1980188 1981368 1981872 "OP" 1982586 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1979548 1979774 1979815 "OPERCAT" 1980027 NIL OPERCAT (NIL T) -9 NIL 1980124 NIL) (-846 1979303 1979359 1979476 "OPERCAT-" 1979481 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1976116 1978100 1978469 "ONECOMP" 1978967 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1975421 1975536 1975710 "ONECOMP2" 1975988 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1974840 1974946 1975076 "OMSERVER" 1975311 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1971702 1974280 1974320 "OMSAGG" 1974381 NIL OMSAGG (NIL T) -9 NIL 1974445 NIL) (-841 1970325 1970588 1970870 "OMPKG" 1971440 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1969755 1969858 1969886 "OM" 1970185 T OM (NIL) -9 NIL NIL NIL) (-839 1968302 1969304 1969473 "OMLO" 1969636 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1967262 1967409 1967629 "OMEXPR" 1968128 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1966553 1966808 1966944 "OMERR" 1967146 T OMERR (NIL) -8 NIL NIL NIL) (-836 1965704 1965974 1966134 "OMERRK" 1966413 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1965155 1965381 1965489 "OMENC" 1965616 T OMENC (NIL) -8 NIL NIL NIL) (-834 1959050 1960235 1961406 "OMDEV" 1964004 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1958119 1958290 1958484 "OMCONN" 1958876 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1956626 1957602 1957630 "OINTDOM" 1957635 T OINTDOM (NIL) -9 NIL 1957656 NIL) (-831 1953964 1955314 1955651 "OFMONOID" 1956321 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1953336 1953901 1953946 "ODVAR" 1953951 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1950759 1953081 1953236 "ODR" 1953241 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1943064 1950535 1950661 "ODPOL" 1950666 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1936862 1942936 1943041 "ODP" 1943046 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1935628 1935843 1936118 "ODETOOLS" 1936636 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1932595 1933253 1933969 "ODESYS" 1934961 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1927477 1928385 1929410 "ODERTRIC" 1931670 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1926903 1926985 1927179 "ODERED" 1927389 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1923791 1924339 1925016 "ODERAT" 1926326 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1920750 1921215 1921812 "ODEPRRIC" 1923320 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1918693 1919289 1919775 "ODEPROB" 1920284 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1915213 1915698 1916345 "ODEPRIM" 1918172 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1914462 1914564 1914824 "ODEPAL" 1915105 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1910624 1911415 1912279 "ODEPACK" 1913618 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1909685 1909792 1910014 "ODEINT" 1910513 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1903786 1905211 1906658 "ODEIFTBL" 1908258 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1899184 1899970 1900922 "ODEEF" 1902945 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1898533 1898622 1898845 "ODECONST" 1899089 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1896644 1897305 1897333 "ODECAT" 1897938 T ODECAT (NIL) -9 NIL 1898469 NIL) (-811 1893499 1896349 1896471 "OCT" 1896554 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1893137 1893180 1893307 "OCTCT2" 1893450 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1887772 1890207 1890247 "OC" 1891344 NIL OC (NIL T) -9 NIL 1892202 NIL) (-808 1884999 1885747 1886737 "OC-" 1886831 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1884337 1884805 1884833 "OCAMON" 1884838 T OCAMON (NIL) -9 NIL 1884859 NIL) (-806 1883854 1884195 1884223 "OASGP" 1884228 T OASGP (NIL) -9 NIL 1884248 NIL) (-805 1883101 1883590 1883618 "OAMONS" 1883658 T OAMONS (NIL) -9 NIL 1883701 NIL) (-804 1882501 1882934 1882962 "OAMON" 1882967 T OAMON (NIL) -9 NIL 1882987 NIL) (-803 1881745 1882263 1882291 "OAGROUP" 1882296 T OAGROUP (NIL) -9 NIL 1882316 NIL) (-802 1881435 1881485 1881573 "NUMTUBE" 1881689 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1875008 1876526 1878062 "NUMQUAD" 1879919 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1870764 1871752 1872777 "NUMODE" 1874003 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1868105 1868985 1869013 "NUMINT" 1869936 T NUMINT (NIL) -9 NIL 1870700 NIL) (-798 1867053 1867250 1867468 "NUMFMT" 1867907 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1853412 1856357 1858889 "NUMERIC" 1864560 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1847782 1852861 1852956 "NTSCAT" 1852961 NIL NTSCAT (NIL T T T T) -9 NIL 1853000 NIL) (-795 1846976 1847141 1847334 "NTPOLFN" 1847621 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1834777 1843801 1844613 "NSUP" 1846197 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1834409 1834466 1834575 "NSUP2" 1834714 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1824359 1834183 1834316 "NSMP" 1834321 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1822791 1823092 1823449 "NREP" 1824047 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1821382 1821634 1821992 "NPCOEF" 1822534 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1820448 1820563 1820779 "NORMRETR" 1821263 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1818489 1818779 1819188 "NORMPK" 1820156 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1818174 1818202 1818326 "NORMMA" 1818455 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1817974 1818131 1818160 "NONE" 1818165 T NONE (NIL) -8 NIL NIL NIL) (-785 1817763 1817792 1817861 "NONE1" 1817938 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1817260 1817322 1817501 "NODE1" 1817695 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1815541 1816392 1816647 "NNI" 1816994 T NNI (NIL) -8 NIL NIL 1817229) (-782 1813961 1814274 1814638 "NLINSOL" 1815209 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1810202 1811197 1812096 "NIPROB" 1813082 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1808959 1809193 1809495 "NFINTBAS" 1809964 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1808133 1808609 1808650 "NETCLT" 1808822 NIL NETCLT (NIL T) -9 NIL 1808904 NIL) (-778 1806841 1807072 1807353 "NCODIV" 1807901 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1806603 1806640 1806715 "NCNTFRAC" 1806798 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1804783 1805147 1805567 "NCEP" 1806228 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1803620 1804393 1804421 "NASRING" 1804531 T NASRING (NIL) -9 NIL 1804611 NIL) (-774 1803415 1803459 1803553 "NASRING-" 1803558 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1802508 1803033 1803061 "NARNG" 1803178 T NARNG (NIL) -9 NIL 1803269 NIL) (-772 1802200 1802267 1802401 "NARNG-" 1802406 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1801079 1801286 1801521 "NAGSP" 1801985 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1792351 1794035 1795708 "NAGS" 1799426 T NAGS (NIL) -7 NIL NIL NIL) (-769 1790899 1791207 1791538 "NAGF07" 1792040 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1785437 1786728 1788035 "NAGF04" 1789612 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1778405 1780019 1781652 "NAGF02" 1783824 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1773629 1774729 1775846 "NAGF01" 1777308 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1767257 1768823 1770408 "NAGE04" 1772064 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1758426 1760547 1762677 "NAGE02" 1765147 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1754379 1755326 1756290 "NAGE01" 1757482 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1752174 1752708 1753266 "NAGD03" 1753841 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1743924 1745852 1747806 "NAGD02" 1750240 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1737735 1739160 1740600 "NAGD01" 1742504 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1733944 1734766 1735603 "NAGC06" 1736918 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1732409 1732741 1733097 "NAGC05" 1733608 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1731785 1731904 1732048 "NAGC02" 1732285 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1730730 1731313 1731353 "NAALG" 1731432 NIL NAALG (NIL T) -9 NIL 1731493 NIL) (-755 1730565 1730594 1730684 "NAALG-" 1730689 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1724515 1725623 1726810 "MULTSQFR" 1729461 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1723834 1723909 1724093 "MULTFACT" 1724427 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1716505 1720419 1720472 "MTSCAT" 1721542 NIL MTSCAT (NIL T T) -9 NIL 1722057 NIL) (-751 1716217 1716271 1716363 "MTHING" 1716445 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1716009 1716042 1716102 "MSYSCMD" 1716177 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1712091 1714764 1715084 "MSET" 1715722 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1709160 1711652 1711693 "MSETAGG" 1711698 NIL MSETAGG (NIL T) -9 NIL 1711732 NIL) (-747 1705002 1706539 1707284 "MRING" 1708460 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1704568 1704635 1704766 "MRF2" 1704929 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1704186 1704221 1704365 "MRATFAC" 1704527 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1701798 1702093 1702524 "MPRFF" 1703891 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1695819 1701652 1701749 "MPOLY" 1701754 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1695309 1695344 1695552 "MPCPF" 1695778 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1694823 1694866 1695050 "MPC3" 1695260 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1694018 1694099 1694320 "MPC2" 1694738 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1692319 1692656 1693046 "MONOTOOL" 1693678 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1691530 1691847 1691875 "MONOID" 1692094 T MONOID (NIL) -9 NIL 1692241 NIL) (-737 1691076 1691195 1691376 "MONOID-" 1691381 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1680666 1686896 1686955 "MONOGEN" 1687629 NIL MONOGEN (NIL T T) -9 NIL 1688085 NIL) (-735 1677884 1678619 1679619 "MONOGEN-" 1679738 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1676703 1677149 1677177 "MONADWU" 1677569 T MONADWU (NIL) -9 NIL 1677807 NIL) (-733 1676075 1676234 1676482 "MONADWU-" 1676487 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1675420 1675664 1675692 "MONAD" 1675899 T MONAD (NIL) -9 NIL 1676011 NIL) (-731 1675105 1675183 1675315 "MONAD-" 1675320 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1673394 1674018 1674297 "MOEBIUS" 1674858 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1672658 1673062 1673102 "MODULE" 1673107 NIL MODULE (NIL T) -9 NIL 1673146 NIL) (-728 1672226 1672322 1672512 "MODULE-" 1672517 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1669906 1670590 1670917 "MODRING" 1672050 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1666850 1668011 1668532 "MODOP" 1669435 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1665438 1665917 1666194 "MODMONOM" 1666713 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1655206 1663729 1664143 "MODMON" 1665075 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1652362 1654050 1654326 "MODFIELD" 1655081 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1651339 1651643 1651833 "MMLFORM" 1652192 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1650865 1650908 1651087 "MMAP" 1651290 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1648930 1649697 1649738 "MLO" 1650161 NIL MLO (NIL T) -9 NIL 1650403 NIL) (-719 1646296 1646812 1647414 "MLIFT" 1648411 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1645687 1645771 1645925 "MKUCFUNC" 1646207 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1645286 1645356 1645479 "MKRECORD" 1645610 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1644333 1644495 1644723 "MKFUNC" 1645097 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1643721 1643825 1643981 "MKFLCFN" 1644216 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1642998 1643100 1643285 "MKBCFUNC" 1643614 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1639587 1642552 1642688 "MINT" 1642882 T MINT (NIL) -8 NIL NIL NIL) (-712 1638399 1638642 1638919 "MHROWRED" 1639342 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1633779 1636934 1637339 "MFLOAT" 1638014 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1633136 1633212 1633383 "MFINFACT" 1633691 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1629451 1630299 1631183 "MESH" 1632272 T MESH (NIL) -7 NIL NIL NIL) (-708 1627841 1628153 1628506 "MDDFACT" 1629138 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1624610 1626972 1627013 "MDAGG" 1627268 NIL MDAGG (NIL T) -9 NIL 1627411 NIL) (-706 1613304 1623903 1624110 "MCMPLX" 1624423 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1612441 1612587 1612788 "MCDEN" 1613153 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1610331 1610601 1610981 "MCALCFN" 1612171 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1609256 1609496 1609729 "MAYBE" 1610137 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1606868 1607391 1607953 "MATSTOR" 1608727 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1602827 1606240 1606488 "MATRIX" 1606653 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1598593 1599300 1600036 "MATLIN" 1602184 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1588673 1591857 1591934 "MATCAT" 1596814 NIL MATCAT (NIL T T T) -9 NIL 1598231 NIL) (-698 1585029 1586050 1587406 "MATCAT-" 1587411 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1583623 1583776 1584109 "MATCAT2" 1584864 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1581735 1582059 1582443 "MAPPKG3" 1583298 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1580716 1580889 1581111 "MAPPKG2" 1581559 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1579215 1579499 1579826 "MAPPKG1" 1580422 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1578294 1578621 1578798 "MAPPAST" 1579058 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1577905 1577963 1578086 "MAPHACK3" 1578230 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1577497 1577558 1577672 "MAPHACK2" 1577837 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1576935 1577038 1577180 "MAPHACK1" 1577388 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1575014 1575635 1575939 "MAGMA" 1576663 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1574493 1574738 1574829 "MACROAST" 1574943 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1570913 1572732 1573193 "M3D" 1574065 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1564962 1569224 1569265 "LZSTAGG" 1570047 NIL LZSTAGG (NIL T) -9 NIL 1570342 NIL) (-685 1560920 1562093 1563550 "LZSTAGG-" 1563555 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1558007 1558811 1559298 "LWORD" 1560465 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1557583 1557811 1557886 "LSTAST" 1557952 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1550473 1557354 1557488 "LSQM" 1557493 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1549697 1549836 1550064 "LSPP" 1550328 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1547509 1547810 1548266 "LSMP" 1549386 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1544288 1544962 1545692 "LSMP1" 1546811 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1538116 1543405 1543446 "LSAGG" 1543508 NIL LSAGG (NIL T) -9 NIL 1543586 NIL) (-677 1534811 1535735 1536948 "LSAGG-" 1536953 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1532410 1533955 1534204 "LPOLY" 1534606 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1531992 1532077 1532200 "LPEFRAC" 1532319 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1530313 1531086 1531339 "LO" 1531824 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1529951 1530063 1530091 "LOGIC" 1530202 T LOGIC (NIL) -9 NIL 1530283 NIL) (-672 1529813 1529836 1529907 "LOGIC-" 1529912 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1529006 1529146 1529339 "LODOOPS" 1529669 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1526429 1528922 1528988 "LODO" 1528993 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1524967 1525202 1525555 "LODOF" 1526176 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1521171 1523602 1523643 "LODOCAT" 1524081 NIL LODOCAT (NIL T) -9 NIL 1524292 NIL) (-667 1520904 1520962 1521089 "LODOCAT-" 1521094 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1518224 1520745 1520863 "LODO2" 1520868 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1515659 1518161 1518206 "LODO1" 1518211 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1514540 1514705 1515010 "LODEEF" 1515482 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1509817 1512706 1512747 "LNAGG" 1513609 NIL LNAGG (NIL T) -9 NIL 1514044 NIL) (-662 1508964 1509178 1509520 "LNAGG-" 1509525 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1505100 1505889 1506528 "LMOPS" 1508379 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1504489 1504877 1504918 "LMODULE" 1504923 NIL LMODULE (NIL T) -9 NIL 1504949 NIL) (-659 1501689 1504134 1504257 "LMDICT" 1504399 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1501307 1501479 1501520 "LLINSET" 1501581 NIL LLINSET (NIL T) -9 NIL 1501625 NIL) (-657 1501006 1501215 1501275 "LITERAL" 1501280 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1494171 1499940 1500244 "LIST" 1500735 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1493696 1493770 1493909 "LIST3" 1494091 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1492703 1492881 1493109 "LIST2" 1493514 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1490837 1491149 1491548 "LIST2MAP" 1492350 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1490468 1490656 1490697 "LINSET" 1490702 NIL LINSET (NIL T) -9 NIL 1490736 NIL) (-651 1488881 1489495 1489536 "LINEXP" 1490026 NIL LINEXP (NIL T) -9 NIL 1490299 NIL) (-650 1487458 1487718 1488029 "LINDEP" 1488633 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1484225 1484944 1485721 "LIMITRF" 1486713 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1482528 1482824 1483233 "LIMITPS" 1483920 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1476956 1482039 1482267 "LIE" 1482349 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1475890 1476359 1476399 "LIECAT" 1476539 NIL LIECAT (NIL T) -9 NIL 1476690 NIL) (-645 1475731 1475758 1475846 "LIECAT-" 1475851 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1468322 1475271 1475427 "LIB" 1475595 T LIB (NIL) -8 NIL NIL NIL) (-643 1463957 1464840 1465775 "LGROBP" 1467439 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1461955 1462229 1462579 "LF" 1463678 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1460795 1461487 1461515 "LFCAT" 1461722 T LFCAT (NIL) -9 NIL 1461861 NIL) (-640 1457697 1458327 1459015 "LEXTRIPK" 1460159 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1454441 1455267 1455770 "LEXP" 1457277 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1453917 1454162 1454254 "LETAST" 1454369 T LETAST (NIL) -8 NIL NIL NIL) (-637 1452315 1452628 1453029 "LEADCDET" 1453599 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1451505 1451579 1451808 "LAZM3PK" 1452236 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1446422 1449582 1450120 "LAUPOL" 1451017 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1446001 1446045 1446206 "LAPLACE" 1446372 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1443940 1445102 1445353 "LA" 1445834 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1442920 1443504 1443545 "LALG" 1443607 NIL LALG (NIL T) -9 NIL 1443666 NIL) (-631 1442634 1442693 1442829 "LALG-" 1442834 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1442469 1442493 1442534 "KVTFROM" 1442596 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1441392 1441836 1442021 "KTVLOGIC" 1442304 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1441227 1441251 1441292 "KRCFROM" 1441354 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1440131 1440318 1440617 "KOVACIC" 1441027 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1439966 1439990 1440031 "KONVERT" 1440093 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1439801 1439825 1439866 "KOERCE" 1439928 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1437632 1438394 1438771 "KERNEL" 1439457 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1437128 1437209 1437341 "KERNEL2" 1437546 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1430838 1435605 1435659 "KDAGG" 1436036 NIL KDAGG (NIL T T) -9 NIL 1436242 NIL) (-621 1430367 1430491 1430696 "KDAGG-" 1430701 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1423515 1430028 1430183 "KAFILE" 1430245 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1417943 1423026 1423254 "JORDAN" 1423336 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1417322 1417592 1417713 "JOINAST" 1417842 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1417168 1417227 1417282 "JAVACODE" 1417287 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1413394 1415345 1415399 "IXAGG" 1416328 NIL IXAGG (NIL T T) -9 NIL 1416787 NIL) (-615 1412313 1412619 1413038 "IXAGG-" 1413043 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407845 1412235 1412294 "IVECTOR" 1412299 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1406611 1406848 1407114 "ITUPLE" 1407612 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1405113 1405290 1405585 "ITRIGMNP" 1406433 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1403858 1404062 1404345 "ITFUN3" 1404889 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1403490 1403547 1403656 "ITFUN2" 1403795 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1402649 1402970 1403144 "ITFORM" 1403336 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1400610 1401669 1401947 "ITAYLOR" 1402404 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1389555 1394747 1395910 "ISUPS" 1399480 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1388659 1388799 1389035 "ISUMP" 1389402 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1384036 1388604 1388645 "ISTRING" 1388650 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1383512 1383757 1383849 "ISAST" 1383964 T ISAST (NIL) -8 NIL NIL NIL) (-603 1382721 1382803 1383019 "IRURPK" 1383426 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1381657 1381858 1382098 "IRSN" 1382501 T IRSN (NIL) -7 NIL NIL NIL) (-601 1379728 1380083 1380512 "IRRF2F" 1381295 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1379475 1379513 1379589 "IRREDFFX" 1379684 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1378090 1378349 1378648 "IROOT" 1379208 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1374694 1375774 1376466 "IR" 1377430 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1373899 1374187 1374338 "IRFORM" 1374563 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1371512 1372007 1372573 "IR2" 1373377 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1370612 1370725 1370939 "IR2F" 1371395 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1370403 1370437 1370497 "IPRNTPK" 1370572 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1366984 1370292 1370361 "IPF" 1370366 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1365311 1366909 1366966 "IPADIC" 1366971 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1364623 1364871 1365001 "IP4ADDR" 1365201 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1363997 1364252 1364384 "IOMODE" 1364511 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1363070 1363594 1363721 "IOBFILE" 1363890 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1362558 1362974 1363002 "IOBCON" 1363007 T IOBCON (NIL) -9 NIL 1363028 NIL) (-587 1362069 1362127 1362310 "INVLAPLA" 1362494 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1351717 1354071 1356457 "INTTR" 1359733 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1348052 1348794 1349659 "INTTOOLS" 1350902 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1347638 1347729 1347846 "INTSLPE" 1347955 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1345591 1347561 1347620 "INTRVL" 1347625 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1343193 1343705 1344280 "INTRF" 1345076 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1342604 1342701 1342843 "INTRET" 1343091 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1340601 1340990 1341460 "INTRAT" 1342212 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1337864 1338447 1339066 "INTPM" 1340086 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1334609 1335208 1335946 "INTPAF" 1337250 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1329788 1330750 1331801 "INTPACK" 1333578 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1326600 1329585 1329694 "INT" 1329699 T INT (NIL) -8 NIL NIL NIL) (-575 1325852 1326004 1326212 "INTHERTR" 1326442 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1325291 1325371 1325559 "INTHERAL" 1325766 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1323137 1323580 1324037 "INTHEORY" 1324854 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1314543 1316164 1317936 "INTG0" 1321489 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1295116 1299906 1304716 "INTFTBL" 1309753 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1294365 1294503 1294676 "INTFACT" 1294975 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1291792 1292238 1292795 "INTEF" 1293919 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1290145 1290884 1290912 "INTDOM" 1291213 T INTDOM (NIL) -9 NIL 1291420 NIL) (-567 1289514 1289688 1289930 "INTDOM-" 1289935 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1285888 1287816 1287870 "INTCAT" 1288669 NIL INTCAT (NIL T) -9 NIL 1288990 NIL) (-565 1285360 1285463 1285591 "INTBIT" 1285780 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1284059 1284213 1284520 "INTALG" 1285205 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1283542 1283632 1283789 "INTAF" 1283963 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1276889 1283352 1283492 "INTABL" 1283497 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1276222 1276688 1276753 "INT8" 1276787 T INT8 (NIL) -8 NIL NIL 1276832) (-560 1275554 1276020 1276085 "INT64" 1276119 T INT64 (NIL) -8 NIL NIL 1276164) (-559 1274886 1275352 1275417 "INT32" 1275451 T INT32 (NIL) -8 NIL NIL 1275496) (-558 1274218 1274684 1274749 "INT16" 1274783 T INT16 (NIL) -8 NIL NIL 1274828) (-557 1268927 1271779 1271807 "INS" 1272741 T INS (NIL) -9 NIL 1273406 NIL) (-556 1266167 1266938 1267912 "INS-" 1267985 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1264942 1265169 1265467 "INPSIGN" 1265920 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1264060 1264177 1264374 "INPRODPF" 1264822 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1262954 1263071 1263308 "INPRODFF" 1263940 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1261954 1262106 1262366 "INNMFACT" 1262790 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1261151 1261248 1261436 "INMODGCD" 1261853 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1259659 1259904 1260228 "INFSP" 1260896 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1258843 1258960 1259143 "INFPROD0" 1259539 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1255698 1256908 1257423 "INFORM" 1258336 T INFORM (NIL) -8 NIL NIL NIL) (-547 1255308 1255368 1255466 "INFORM1" 1255633 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1254831 1254920 1255034 "INFINITY" 1255214 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1254007 1254551 1254652 "INETCLTS" 1254750 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1252623 1252873 1253194 "INEP" 1253755 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1251872 1252520 1252585 "INDE" 1252590 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1251436 1251504 1251621 "INCRMAPS" 1251799 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1250254 1250705 1250911 "INBFILE" 1251250 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1245553 1246490 1247434 "INBFF" 1249342 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1244461 1244730 1244758 "INBCON" 1245271 T INBCON (NIL) -9 NIL 1245537 NIL) (-538 1243713 1243936 1244212 "INBCON-" 1244217 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1243192 1243437 1243528 "INAST" 1243642 T INAST (NIL) -8 NIL NIL NIL) (-536 1242619 1242871 1242977 "IMPTAST" 1243106 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1239067 1242463 1242567 "IMATRIX" 1242572 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1237775 1237898 1238214 "IMATQF" 1238923 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1235995 1236222 1236559 "IMATLIN" 1237531 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1230575 1235919 1235977 "ILIST" 1235982 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1228482 1230435 1230548 "IIARRAY2" 1230553 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1223880 1228393 1228457 "IFF" 1228462 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1223227 1223497 1223613 "IFAST" 1223784 T IFAST (NIL) -8 NIL NIL NIL) (-528 1218224 1222519 1222707 "IFARRAY" 1223084 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1217404 1218128 1218201 "IFAMON" 1218206 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1216988 1217053 1217107 "IEVALAB" 1217314 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1216663 1216731 1216891 "IEVALAB-" 1216896 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1216294 1216577 1216640 "IDPO" 1216645 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1215544 1216183 1216258 "IDPOAMS" 1216263 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1214851 1215433 1215508 "IDPOAM" 1215513 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1213896 1214172 1214225 "IDPC" 1214638 NIL IDPC (NIL T T) -9 NIL 1214787 NIL) (-520 1213365 1213788 1213861 "IDPAM" 1213866 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1212741 1213257 1213330 "IDPAG" 1213335 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212386 1212577 1212652 "IDENT" 1212686 T IDENT (NIL) -8 NIL NIL NIL) (-517 1208641 1209489 1210384 "IDECOMP" 1211543 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1201478 1202564 1203611 "IDEAL" 1207677 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1200638 1200750 1200950 "ICDEN" 1201362 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1199709 1200118 1200265 "ICARD" 1200511 T ICARD (NIL) -8 NIL NIL NIL) (-513 1197769 1198082 1198487 "IBPTOOLS" 1199386 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193376 1197389 1197502 "IBITS" 1197688 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190099 1190675 1191370 "IBATOOL" 1192793 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1187878 1188340 1188873 "IBACHIN" 1189634 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1185709 1187724 1187827 "IARRAY2" 1187832 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1181817 1185635 1185692 "IARRAY1" 1185697 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1175677 1180229 1180710 "IAN" 1181356 T IAN (NIL) -8 NIL NIL NIL) (-506 1175188 1175245 1175418 "IALGFACT" 1175614 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1174716 1174829 1174857 "HYPCAT" 1175064 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174254 1174371 1174557 "HYPCAT-" 1174562 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1173849 1174049 1174132 "HOSTNAME" 1174191 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1173694 1173731 1173772 "HOMOTOP" 1173777 NIL HOMOTOP (NIL T) -9 NIL 1173810 NIL) (-501 1170250 1171626 1171667 "HOAGG" 1172648 NIL HOAGG (NIL T) -9 NIL 1173377 NIL) (-500 1168844 1169243 1169769 "HOAGG-" 1169774 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1162560 1168437 1168587 "HEXADEC" 1168714 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161308 1161530 1161793 "HEUGCD" 1162337 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160384 1161145 1161275 "HELLFDIV" 1161280 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1158565 1160161 1160249 "HEAP" 1160328 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1157828 1158117 1158251 "HEADAST" 1158451 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1151670 1157743 1157805 "HDP" 1157810 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145382 1151305 1151457 "HDMP" 1151571 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1144706 1144846 1145010 "HB" 1145238 T HB (NIL) -7 NIL NIL NIL) (-491 1138096 1144552 1144656 "HASHTBL" 1144661 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1137572 1137817 1137909 "HASAST" 1138024 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135350 1137194 1137376 "HACKPI" 1137410 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131018 1135203 1135316 "GTSET" 1135321 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1124437 1130896 1130994 "GSTBL" 1130999 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1116824 1123602 1123858 "GSERIES" 1124237 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1115951 1116368 1116396 "GROUP" 1116599 T GROUP (NIL) -9 NIL 1116733 NIL) (-484 1115317 1115476 1115727 "GROUP-" 1115732 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1113684 1114005 1114392 "GROEBSOL" 1114994 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1112584 1112872 1112923 "GRMOD" 1113452 NIL GRMOD (NIL T T) -9 NIL 1113620 NIL) (-481 1112352 1112388 1112516 "GRMOD-" 1112521 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1107642 1108706 1109706 "GRIMAGE" 1111372 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106108 1106369 1106693 "GRDEF" 1107338 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1105552 1105668 1105809 "GRAY" 1105987 T GRAY (NIL) -7 NIL NIL NIL) (-477 1104725 1105131 1105182 "GRALG" 1105335 NIL GRALG (NIL T T) -9 NIL 1105428 NIL) (-476 1104386 1104459 1104622 "GRALG-" 1104627 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101163 1103971 1104149 "GPOLSET" 1104293 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1100517 1100574 1100832 "GOSPER" 1101100 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096249 1096955 1097481 "GMODPOL" 1100216 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095254 1095438 1095676 "GHENSEL" 1096061 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1089410 1090253 1091273 "GENUPS" 1094338 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089107 1089158 1089247 "GENUFACT" 1089353 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1088519 1088596 1088761 "GENPGCD" 1089025 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1087993 1088028 1088241 "GENMFACT" 1088478 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1086559 1086816 1087123 "GENEEZ" 1087736 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1080431 1086170 1086332 "GDMP" 1086482 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1069774 1074202 1075308 "GCNAALG" 1079414 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068087 1068949 1068977 "GCDDOM" 1069232 T GCDDOM (NIL) -9 NIL 1069389 NIL) (-463 1067557 1067684 1067899 "GCDDOM-" 1067904 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066229 1066414 1066718 "GB" 1067336 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1054845 1057175 1059567 "GBINTERN" 1063920 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1052682 1052974 1053395 "GBF" 1054520 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1051463 1051628 1051895 "GBEUCLID" 1052498 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1050812 1050937 1051086 "GAUSSFAC" 1051334 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049179 1049481 1049795 "GALUTIL" 1050531 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1047487 1047761 1048085 "GALPOLYU" 1048906 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1044852 1045142 1045549 "GALFACTU" 1047184 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1036658 1038157 1039765 "GALFACT" 1043284 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034046 1034704 1034732 "FVFUN" 1035888 T FVFUN (NIL) -9 NIL 1036608 NIL) (-452 1033312 1033494 1033522 "FVC" 1033813 T FVC (NIL) -9 NIL 1033996 NIL) (-451 1032955 1033137 1033205 "FUNDESC" 1033264 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1032570 1032752 1032833 "FUNCTION" 1032907 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030314 1030892 1031358 "FT" 1032124 T FT (NIL) -8 NIL NIL NIL) (-448 1029105 1029615 1029818 "FTEM" 1030131 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027396 1027685 1028082 "FSUPFACT" 1028796 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1025793 1026082 1026414 "FST" 1027084 T FST (NIL) -8 NIL NIL NIL) (-445 1024992 1025098 1025286 "FSRED" 1025675 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1023691 1023947 1024294 "FSPRMELT" 1024707 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1020997 1021435 1021921 "FSPECF" 1023254 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002062 1010771 1010812 "FS" 1014696 NIL FS (NIL T) -9 NIL 1016985 NIL) (-441 990705 993698 997755 "FS-" 998055 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990233 990287 990457 "FSINT" 990646 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 988525 989226 989529 "FSERIES" 990012 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 987567 987683 987907 "FSCINT" 988405 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 983775 986511 986552 "FSAGG" 986922 NIL FSAGG (NIL T) -9 NIL 987181 NIL) (-436 981537 982138 982934 "FSAGG-" 983029 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 980579 980722 980949 "FSAGG2" 981390 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978257 978537 979085 "FS2UPS" 980297 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 977891 977934 978063 "FS2" 978208 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 976769 976940 977242 "FS2EXPXP" 977716 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976195 976310 976462 "FRUTIL" 976649 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 967608 971690 973048 "FR" 974869 NIL FR (NIL T) -8 NIL NIL NIL) (-429 962622 965297 965337 "FRNAALG" 966657 NIL FRNAALG (NIL T) -9 NIL 967255 NIL) (-428 958295 959371 960646 "FRNAALG-" 961396 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 957933 957976 958103 "FRNAAF2" 958246 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956308 956782 957078 "FRMOD" 957745 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954051 954683 955001 "FRIDEAL" 956099 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953242 953329 953620 "FRIDEAL2" 953958 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952375 952789 952830 "FRETRCT" 952835 NIL FRETRCT (NIL T) -9 NIL 953011 NIL) (-422 951487 951718 952069 "FRETRCT-" 952074 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 948561 949771 949830 "FRAMALG" 950712 NIL FRAMALG (NIL T T) -9 NIL 951004 NIL) (-420 946695 947150 947780 "FRAMALG-" 948003 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940338 946168 946445 "FRAC" 946450 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 939974 940031 940138 "FRAC2" 940275 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 939610 939667 939774 "FR2" 939911 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934109 937002 937030 "FPS" 938149 T FPS (NIL) -9 NIL 938706 NIL) (-415 933558 933667 933831 "FPS-" 933977 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 930846 932515 932543 "FPC" 932768 T FPC (NIL) -9 NIL 932910 NIL) (-413 930639 930679 930776 "FPC-" 930781 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 929429 930127 930168 "FPATMAB" 930173 NIL FPATMAB (NIL T) -9 NIL 930325 NIL) (-411 927668 928171 928518 "FPARFRAC" 929145 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923062 923560 924242 "FORTRAN" 927100 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 920778 921278 921817 "FORT" 922543 T FORT (NIL) -7 NIL NIL NIL) (-408 918454 919016 919044 "FORTFN" 920104 T FORTFN (NIL) -9 NIL 920728 NIL) (-407 918218 918268 918296 "FORTCAT" 918355 T FORTCAT (NIL) -9 NIL 918417 NIL) (-406 916324 916834 917224 "FORMULA" 917848 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916112 916142 916211 "FORMULA1" 916288 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 915635 915687 915860 "FORDER" 916054 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 914731 914895 915088 "FOP" 915462 T FOP (NIL) -7 NIL NIL NIL) (-402 913312 914011 914185 "FNLA" 914613 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912027 912442 912470 "FNCAT" 912930 T FNCAT (NIL) -9 NIL 913190 NIL) (-400 911566 911986 912014 "FNAME" 912019 T FNAME (NIL) -8 NIL NIL NIL) (-399 910115 911078 911106 "FMTC" 911111 T FMTC (NIL) -9 NIL 911147 NIL) (-398 908861 910051 910097 "FMONOID" 910102 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 905675 906843 906884 "FMONCAT" 908101 NIL FMONCAT (NIL T) -9 NIL 908706 NIL) (-396 904867 905417 905566 "FM" 905571 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902291 902937 902965 "FMFUN" 904109 T FMFUN (NIL) -9 NIL 904817 NIL) (-394 901560 901741 901769 "FMC" 902059 T FMC (NIL) -9 NIL 902241 NIL) (-393 898625 899485 899539 "FMCAT" 900734 NIL FMCAT (NIL T T) -9 NIL 901229 NIL) (-392 897491 898391 898491 "FM1" 898570 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895265 895681 896175 "FLOATRP" 897042 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 888843 892994 893615 "FLOAT" 894664 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886281 886781 887359 "FLOATCP" 888310 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 884929 885873 885914 "FLINEXP" 885919 NIL FLINEXP (NIL T) -9 NIL 886012 NIL) (-387 884083 884318 884646 "FLINEXP-" 884651 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883159 883303 883527 "FLASORT" 883935 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880261 881129 881181 "FLALG" 882408 NIL FLALG (NIL T T) -9 NIL 882875 NIL) (-384 873947 877697 877738 "FLAGG" 879000 NIL FLAGG (NIL T) -9 NIL 879652 NIL) (-383 872673 873012 873502 "FLAGG-" 873507 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 871715 871858 872085 "FLAGG2" 872526 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 868552 869560 869619 "FINRALG" 870747 NIL FINRALG (NIL T T) -9 NIL 871255 NIL) (-380 867712 867941 868280 "FINRALG-" 868285 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867078 867317 867345 "FINITE" 867541 T FINITE (NIL) -9 NIL 867648 NIL) (-378 859421 861608 861648 "FINAALG" 865315 NIL FINAALG (NIL T) -9 NIL 866768 NIL) (-377 854753 855803 856947 "FINAALG-" 858326 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854121 854508 854611 "FILE" 854683 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 852765 853103 853157 "FILECAT" 853841 NIL FILECAT (NIL T T) -9 NIL 854057 NIL) (-374 850467 851995 852023 "FIELD" 852063 T FIELD (NIL) -9 NIL 852143 NIL) (-373 849087 849472 849983 "FIELD-" 849988 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 846937 847722 848069 "FGROUP" 848773 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846027 846191 846411 "FGLMICPK" 846769 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 841859 845952 846009 "FFX" 846014 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841460 841521 841656 "FFSLPE" 841792 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837450 838232 839028 "FFPOLY" 840696 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 836954 836990 837199 "FFPOLY2" 837408 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 832800 836873 836936 "FFP" 836941 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828198 832711 832775 "FF" 832780 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823324 827541 827731 "FFNBX" 828052 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818252 822459 822717 "FFNBP" 823178 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 812885 817536 817747 "FFNB" 818085 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 811717 811915 812230 "FFINTBAS" 812682 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 807743 809964 809992 "FFIELDC" 810612 T FFIELDC (NIL) -9 NIL 810988 NIL) (-359 806405 806776 807273 "FFIELDC-" 807278 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 805974 806020 806144 "FFHOM" 806347 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 803669 804156 804673 "FFF" 805489 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799287 803411 803512 "FFCGX" 803612 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 794909 799019 799126 "FFCGP" 799230 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790092 794636 794744 "FFCG" 794845 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 769621 779824 779910 "FFCAT" 785075 NIL FFCAT (NIL T T T) -9 NIL 786526 NIL) (-352 764818 765866 767180 "FFCAT-" 768410 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764229 764272 764507 "FFCAT2" 764769 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 753552 757201 758421 "FEXPR" 763081 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752514 752949 752990 "FEVALAB" 753074 NIL FEVALAB (NIL T) -9 NIL 753335 NIL) (-348 751673 751883 752221 "FEVALAB-" 752226 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750239 751056 751259 "FDIV" 751572 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747245 747986 748101 "FDIVCAT" 749669 NIL FDIVCAT (NIL T T T T) -9 NIL 750106 NIL) (-345 747007 747034 747204 "FDIVCAT-" 747209 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746227 746314 746591 "FDIV2" 746914 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745201 745522 745724 "FCTRDATA" 746045 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 743887 744146 744435 "FCPAK1" 744932 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 742986 743387 743528 "FCOMP" 743778 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 726691 730136 733674 "FC" 739468 T FC (NIL) -8 NIL NIL NIL) (-339 718984 723012 723052 "FAXF" 724854 NIL FAXF (NIL T) -9 NIL 725546 NIL) (-338 716261 716918 717743 "FAXF-" 718208 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711315 715637 715813 "FARRAY" 716118 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706195 708262 708315 "FAMR" 709338 NIL FAMR (NIL T T) -9 NIL 709798 NIL) (-335 705085 705387 705822 "FAMR-" 705827 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704254 705007 705060 "FAMONOID" 705065 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702026 702736 702789 "FAMONC" 703730 NIL FAMONC (NIL T T) -9 NIL 704116 NIL) (-332 700690 701780 701917 "FAGROUP" 701922 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698485 698804 699207 "FACUTIL" 700371 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 697584 697769 697991 "FACTFUNC" 698295 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690006 696887 697086 "EXPUPXS" 697440 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687489 688029 688615 "EXPRTUBE" 689440 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 683760 684352 685082 "EXPRODE" 686828 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669244 682409 682838 "EXPR" 683364 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 663798 664385 665191 "EXPR2UPS" 668542 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663430 663487 663596 "EXPR2" 663735 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654427 662581 662872 "EXPEXPAN" 663266 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654227 654384 654413 "EXIT" 654418 T EXIT (NIL) -8 NIL NIL NIL) (-321 653707 653951 654042 "EXITAST" 654156 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653334 653396 653509 "EVALCYC" 653639 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 652875 652993 653034 "EVALAB" 653204 NIL EVALAB (NIL T) -9 NIL 653308 NIL) (-318 652356 652478 652699 "EVALAB-" 652704 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 649710 651012 651040 "EUCDOM" 651595 T EUCDOM (NIL) -9 NIL 651945 NIL) (-316 648115 648557 649147 "EUCDOM-" 649152 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 635654 638413 641163 "ESTOOLS" 645385 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635286 635343 635452 "ESTOOLS2" 635591 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635037 635079 635159 "ESTOOLS1" 635238 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629060 630668 630696 "ES" 633464 T ES (NIL) -9 NIL 634874 NIL) (-311 624007 625294 627111 "ES-" 627275 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620381 621142 621922 "ESCONT" 623247 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620126 620158 620240 "ESCONT1" 620343 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 619801 619851 619951 "ES2" 620070 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619431 619489 619598 "ES1" 619737 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 618647 618776 618952 "ERROR" 619275 T ERROR (NIL) -7 NIL NIL NIL) (-305 612043 618506 618597 "EQTBL" 618602 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 604546 607357 608806 "EQ" 610627 NIL -2054 (NIL T) -8 NIL NIL NIL) (-303 604178 604235 604344 "EQ2" 604483 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599469 600516 601609 "EP" 603117 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598069 598360 598666 "ENV" 599183 T ENV (NIL) -8 NIL NIL NIL) (-300 597149 597703 597731 "ENTIRER" 597736 T ENTIRER (NIL) -9 NIL 597782 NIL) (-299 593843 595331 595692 "EMR" 596957 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 592973 593158 593212 "ELTAGG" 593592 NIL ELTAGG (NIL T T) -9 NIL 593803 NIL) (-297 592692 592754 592895 "ELTAGG-" 592900 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592456 592485 592539 "ELTAB" 592623 NIL ELTAB (NIL T T) -9 NIL 592675 NIL) (-295 591582 591728 591927 "ELFUTS" 592307 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591324 591380 591408 "ELEMFUN" 591513 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591194 591215 591283 "ELEMFUN-" 591288 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 585982 589236 589277 "ELAGG" 590217 NIL ELAGG (NIL T) -9 NIL 590680 NIL) (-291 584267 584701 585364 "ELAGG-" 585369 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 583579 583716 583872 "ELABOR" 584131 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582240 582519 582813 "ELABEXPR" 583305 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575074 576877 577706 "EFUPXS" 581515 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568522 570323 571134 "EFULS" 574349 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566007 566365 566837 "EFSTRUC" 568154 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 555798 557364 558912 "EF" 564522 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 554872 555283 555432 "EAB" 555669 T EAB (NIL) -8 NIL NIL NIL) (-283 554054 554831 554859 "E04UCFA" 554864 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553236 554013 554041 "E04NAFA" 554046 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552418 553195 553223 "E04MBFA" 553228 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 551600 552377 552405 "E04JAFA" 552410 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 550784 551559 551587 "E04GCFA" 551592 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 549968 550743 550771 "E04FDFA" 550776 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549150 549927 549955 "E04DGFA" 549960 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543323 544675 546039 "E04AGNT" 547806 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542094 542637 542677 "DVARCAT" 543018 NIL DVARCAT (NIL T) -9 NIL 543181 NIL) (-274 541298 541510 541824 "DVARCAT-" 541829 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534159 541097 541226 "DSMP" 541231 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 532582 533301 533342 "DSEXT" 533705 NIL DSEXT (NIL T) -9 NIL 533999 NIL) (-271 530867 531295 531961 "DSEXT-" 531966 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 525648 526812 527880 "DROPT" 529819 T DROPT (NIL) -8 NIL NIL NIL) (-269 525313 525372 525470 "DROPT1" 525583 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520428 521554 522691 "DROPT0" 524196 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 518773 519098 519484 "DRAWPT" 520062 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513360 514283 515362 "DRAW" 517747 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 512993 513046 513164 "DRAWHACK" 513301 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 511724 511993 512284 "DRAWCX" 512722 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511239 511308 511459 "DRAWCURV" 511650 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 501707 503669 505784 "DRAWCFUN" 509144 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498445 500372 500413 "DQAGG" 501042 NIL DQAGG (NIL T) -9 NIL 501316 NIL) (-260 485910 492656 492739 "DPOLCAT" 494591 NIL DPOLCAT (NIL T T T T) -9 NIL 495136 NIL) (-259 480747 482095 484053 "DPOLCAT-" 484058 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474094 480608 480706 "DPMO" 480711 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467344 473874 474041 "DPMM" 474046 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 466914 467128 467217 "DOMTMPLT" 467275 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466347 466716 466796 "DOMCTOR" 466854 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 465559 465827 465978 "DOMAIN" 466216 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459271 465194 465346 "DMP" 465460 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457216 458338 458379 "DMEXT" 458384 NIL DMEXT (NIL T) -9 NIL 458560 NIL) (-251 456816 456872 457016 "DLP" 457154 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 450640 456143 456333 "DLIST" 456658 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447411 449465 449506 "DLAGG" 450056 NIL DLAGG (NIL T) -9 NIL 450286 NIL) (-248 446073 446737 446765 "DIVRING" 446857 T DIVRING (NIL) -9 NIL 446940 NIL) (-247 445310 445500 445800 "DIVRING-" 445805 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443412 443769 444175 "DISPLAY" 444924 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437274 443326 443389 "DIRPROD" 443394 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436122 436325 436590 "DIRPROD2" 437067 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 424851 430888 430941 "DIRPCAT" 431199 NIL DIRPCAT (NIL NIL T) -9 NIL 432074 NIL) (-242 422177 422819 423700 "DIRPCAT-" 424037 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421464 421624 421810 "DIOSP" 422011 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418093 420348 420389 "DIOPS" 420823 NIL DIOPS (NIL T) -9 NIL 421052 NIL) (-239 417642 417756 417947 "DIOPS-" 417952 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 416693 417321 417349 "DIFRING" 417354 T DIFRING (NIL) -9 NIL 417376 NIL) (-237 416365 416439 416467 "DIFFSPC" 416586 T DIFFSPC (NIL) -9 NIL 416661 NIL) (-236 416010 416088 416240 "DIFFSPC-" 416245 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415066 415544 415585 "DIFFMOD" 415590 NIL DIFFMOD (NIL T) -9 NIL 415688 NIL) (-234 414774 414819 414860 "DIFFDOM" 414981 NIL DIFFDOM (NIL T) -9 NIL 415049 NIL) (-233 414627 414651 414735 "DIFFDOM-" 414740 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412559 413831 413872 "DIFEXT" 413877 NIL DIFEXT (NIL T) -9 NIL 414030 NIL) (-231 409808 412063 412104 "DIAGG" 412109 NIL DIAGG (NIL T) -9 NIL 412129 NIL) (-230 409192 409349 409601 "DIAGG-" 409606 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404611 408151 408428 "DHMATRIX" 408961 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400223 401132 402142 "DFSFUN" 403621 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395301 399154 399466 "DFLOAT" 399931 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393564 393845 394234 "DFINTTLS" 395009 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390593 391585 391985 "DERHAM" 393230 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388396 390368 390457 "DEQUEUE" 390537 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 387650 387783 387966 "DEGRED" 388258 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384080 384825 385671 "DEFINTRF" 386878 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 381635 382104 382696 "DEFINTEF" 383599 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 380985 381255 381370 "DEFAST" 381540 T DEFAST (NIL) -8 NIL NIL NIL) (-219 374701 380578 380728 "DECIMAL" 380855 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372213 372671 373177 "DDFACT" 374245 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 371809 371852 372003 "DBLRESP" 372164 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 369677 370039 370400 "DBASE" 371575 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 368919 369157 369303 "DATAARY" 369576 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368025 368878 368906 "D03FAFA" 368911 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367132 367984 368012 "D03EEFA" 368017 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365082 365548 366037 "D03AGNT" 366663 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364371 365041 365069 "D02EJFA" 365074 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 363660 364330 364358 "D02CJFA" 364363 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 362949 363619 363647 "D02BHFA" 363652 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362238 362908 362936 "D02BBFA" 362941 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355435 357024 358630 "D02AGNT" 360652 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353203 353726 354272 "D01WGTS" 354909 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352270 353162 353190 "D01TRNS" 353195 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351338 352229 352257 "D01GBFA" 352262 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350406 351297 351325 "D01FCFA" 351330 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349474 350365 350393 "D01ASFA" 350398 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348542 349433 349461 "D01AQFA" 349466 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347610 348501 348529 "D01APFA" 348534 T D01APFA (NIL) -8 NIL NIL NIL) (-199 346678 347569 347597 "D01ANFA" 347602 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 345746 346637 346665 "D01AMFA" 346670 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 344814 345705 345733 "D01ALFA" 345738 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 343882 344773 344801 "D01AKFA" 344806 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 342950 343841 343869 "D01AJFA" 343874 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336245 337798 339359 "D01AGNT" 341409 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335582 335710 335862 "CYCLOTOM" 336113 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332315 333030 333757 "CYCLES" 334875 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331627 331761 331932 "CVMP" 332176 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329468 329726 330095 "CTRIGMNP" 331355 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 328904 329262 329335 "CTOR" 329415 T CTOR (NIL) -8 NIL NIL NIL) (-188 328413 328635 328736 "CTORKIND" 328823 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 327690 328006 328034 "CTORCAT" 328216 T CTORCAT (NIL) -9 NIL 328329 NIL) (-186 327288 327399 327558 "CTORCAT-" 327563 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 326750 326962 327070 "CTORCALL" 327212 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326124 326223 326376 "CSTTOOLS" 326647 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 321923 322580 323338 "CRFP" 325436 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321398 321644 321736 "CRCEAST" 321851 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320445 320630 320858 "CRAPACK" 321202 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 319829 319930 320134 "CPMATCH" 320321 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319554 319582 319688 "CPIMA" 319795 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 315902 316574 317293 "COORDSYS" 318889 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315314 315435 315577 "CONTOUR" 315780 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311205 313317 313809 "CONTFRAC" 314854 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311085 311106 311134 "CONDUIT" 311171 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310159 310713 310741 "COMRING" 310746 T COMRING (NIL) -9 NIL 310798 NIL) (-173 309213 309517 309701 "COMPPROP" 309995 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 308874 308909 309037 "COMPLPAT" 309172 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298177 308683 308792 "COMPLEX" 308797 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 297813 297870 297977 "COMPLEX2" 298114 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297152 297273 297433 "COMPILER" 297673 T COMPILER (NIL) -8 NIL NIL NIL) (-168 296870 296905 297003 "COMPFACT" 297111 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279149 290574 290614 "COMPCAT" 291618 NIL COMPCAT (NIL T) -9 NIL 292966 NIL) (-166 268661 271588 275215 "COMPCAT-" 275571 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268390 268418 268521 "COMMUPC" 268627 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268184 268218 268277 "COMMONOP" 268351 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 267740 267935 268022 "COMM" 268117 T COMM (NIL) -8 NIL NIL NIL) (-162 267316 267544 267619 "COMMAAST" 267685 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266565 266759 266787 "COMBOPC" 267125 T COMBOPC (NIL) -9 NIL 267300 NIL) (-160 265461 265671 265913 "COMBINAT" 266355 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 261918 262492 263119 "COMBF" 264883 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 260676 261034 261269 "COLOR" 261703 T COLOR (NIL) -8 NIL NIL NIL) (-157 260152 260397 260489 "COLONAST" 260604 T COLONAST (NIL) -8 NIL NIL NIL) (-156 259792 259839 259964 "CMPLXRT" 260099 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259240 259492 259591 "CLLCTAST" 259713 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 254742 255770 256850 "CLIP" 258180 T CLIP (NIL) -7 NIL NIL NIL) (-153 253083 253843 254083 "CLIF" 254569 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249232 251201 251242 "CLAGG" 252171 NIL CLAGG (NIL T) -9 NIL 252707 NIL) (-151 247654 248111 248694 "CLAGG-" 248699 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247198 247283 247423 "CINTSLPE" 247563 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 244699 245170 245718 "CHVAR" 246726 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 243859 244413 244441 "CHARZ" 244446 T CHARZ (NIL) -9 NIL 244461 NIL) (-147 243613 243653 243731 "CHARPOL" 243813 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 242657 243244 243272 "CHARNZ" 243319 T CHARNZ (NIL) -9 NIL 243375 NIL) (-145 240563 241311 241664 "CHAR" 242324 T CHAR (NIL) -8 NIL NIL NIL) (-144 240289 240350 240378 "CFCAT" 240489 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239530 239641 239824 "CDEN" 240173 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235495 238683 238963 "CCLASS" 239270 T CCLASS (NIL) -8 NIL NIL NIL) (-141 234746 234903 235080 "CATEGORY" 235338 T -10 (NIL) -8 NIL NIL NIL) (-140 234319 234665 234713 "CATCTOR" 234718 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 233770 234022 234120 "CATAST" 234241 T CATAST (NIL) -8 NIL NIL NIL) (-138 233246 233491 233583 "CASEAST" 233698 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228384 229403 230147 "CARTEN" 232558 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227492 227640 227861 "CARTEN2" 228231 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 225808 226642 226899 "CARD" 227255 T CARD (NIL) -8 NIL NIL NIL) (-134 225384 225612 225687 "CAPSLAST" 225753 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 224874 225082 225110 "CACHSET" 225242 T CACHSET (NIL) -9 NIL 225320 NIL) (-132 224330 224652 224680 "CABMON" 224730 T CABMON (NIL) -9 NIL 224786 NIL) (-131 223803 224034 224144 "BYTEORD" 224240 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 222780 223332 223474 "BYTE" 223637 T BYTE (NIL) -8 NIL NIL 223759) (-129 218132 222285 222457 "BYTEBUF" 222628 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 215643 217824 217931 "BTREE" 218058 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213094 215291 215413 "BTOURN" 215553 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210438 212536 212577 "BTCAT" 212645 NIL BTCAT (NIL T) -9 NIL 212722 NIL) (-125 210105 210185 210334 "BTCAT-" 210339 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205484 209364 209392 "BTAGG" 209506 T BTAGG (NIL) -9 NIL 209616 NIL) (-123 204974 205099 205305 "BTAGG-" 205310 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 201971 204252 204467 "BSTREE" 204791 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201109 201235 201419 "BRILL" 201827 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 197735 199807 199848 "BRAGG" 200497 NIL BRAGG (NIL T) -9 NIL 200755 NIL) (-119 196264 196670 197225 "BRAGG-" 197230 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189180 195608 195793 "BPADICRT" 196111 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187495 189117 189162 "BPADIC" 189167 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187193 187223 187337 "BOUNDZRO" 187459 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182421 183619 184531 "BOP" 186301 T BOP (NIL) -8 NIL NIL NIL) (-114 180202 180606 181081 "BOP1" 181979 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 179903 179964 179992 "BOOLE" 180103 T BOOLE (NIL) -9 NIL 180185 NIL) (-112 178728 179477 179626 "BOOLEAN" 179774 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 177993 178397 178451 "BMODULE" 178456 NIL BMODULE (NIL T T) -9 NIL 178521 NIL) (-110 173794 177791 177864 "BITS" 177940 T BITS (NIL) -8 NIL NIL NIL) (-109 173215 173334 173474 "BINDING" 173674 T BINDING (NIL) -8 NIL NIL NIL) (-108 166934 172810 172959 "BINARY" 173086 T BINARY (NIL) -8 NIL NIL NIL) (-107 164688 166161 166202 "BGAGG" 166462 NIL BGAGG (NIL T) -9 NIL 166599 NIL) (-106 164519 164551 164642 "BGAGG-" 164647 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163590 163903 164108 "BFUNCT" 164334 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162280 162458 162746 "BEZOUT" 163414 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 158751 161132 161462 "BBTREE" 161983 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158460 158513 158541 "BASTYPE" 158660 T BASTYPE (NIL) -9 NIL 158734 NIL) (-101 158312 158341 158414 "BASTYPE-" 158419 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157746 157822 157974 "BALFACT" 158223 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156602 157161 157347 "AUTOMOR" 157591 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156328 156333 156359 "ATTREG" 156364 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154580 155025 155377 "ATTRBUT" 155994 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154188 154408 154474 "ATTRAST" 154532 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153724 153837 153863 "ATRIG" 154064 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153533 153574 153661 "ATRIG-" 153666 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153164 153350 153376 "ASTCAT" 153381 T ASTCAT (NIL) -9 NIL 153411 NIL) (-92 152891 152950 153069 "ASTCAT-" 153074 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151042 152667 152755 "ASTACK" 152834 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149547 149844 150209 "ASSOCEQ" 150724 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148579 149206 149330 "ASP9" 149454 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148342 148527 148566 "ASP8" 148571 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147210 147947 148089 "ASP80" 148231 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146108 146845 146977 "ASP7" 147109 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145062 145785 145903 "ASP78" 146021 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144031 144742 144859 "ASP77" 144976 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 142943 143669 143800 "ASP74" 143931 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141843 142578 142710 "ASP73" 142842 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 140947 141669 141769 "ASP6" 141774 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139894 140624 140742 "ASP55" 140860 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138843 139568 139687 "ASP50" 139806 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 137931 138544 138654 "ASP4" 138764 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 137019 137632 137742 "ASP49" 137852 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135803 136558 136726 "ASP42" 136908 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134580 135336 135506 "ASP41" 135690 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133530 134257 134375 "ASP35" 134493 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133295 133478 133517 "ASP34" 133522 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133032 133099 133175 "ASP33" 133250 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 131926 132667 132799 "ASP31" 132931 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131691 131874 131913 "ASP30" 131918 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131426 131495 131571 "ASP29" 131646 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131191 131374 131413 "ASP28" 131418 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 130956 131139 131178 "ASP27" 131183 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130040 130654 130765 "ASP24" 130876 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129117 129842 129954 "ASP20" 129959 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128205 128818 128928 "ASP1" 129038 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127148 127879 127998 "ASP19" 128117 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126885 126952 127028 "ASP12" 127103 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125737 126484 126628 "ASP10" 126772 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123590 125581 125672 "ARRAY2" 125677 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119357 123238 123352 "ARRAY1" 123507 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118389 118562 118783 "ARRAY12" 119180 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112675 114591 114666 "ARR2CAT" 117296 NIL ARR2CAT (NIL T T T) -9 NIL 118054 NIL) (-56 110109 110853 111807 "ARR2CAT-" 111812 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109426 109736 109861 "ARITY" 110002 T ARITY (NIL) -8 NIL NIL NIL) (-54 108202 108354 108653 "APPRULE" 109262 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107853 107901 108020 "APPLYORE" 108148 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107207 107446 107566 "ANY" 107751 T ANY (NIL) -8 NIL NIL NIL) (-51 106485 106608 106765 "ANY1" 107081 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104015 104922 105249 "ANTISYM" 106209 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103507 103722 103818 "ANON" 103937 T ANON (NIL) -8 NIL NIL NIL) (-48 97507 102046 102500 "AN" 103071 T AN (NIL) -8 NIL NIL NIL) (-47 93391 94779 94830 "AMR" 95578 NIL AMR (NIL T T) -9 NIL 96178 NIL) (-46 92503 92724 93087 "AMR-" 93092 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76946 92420 92481 "ALIST" 92486 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73751 76540 76709 "ALGSC" 76864 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70307 70861 71468 "ALGPKG" 73191 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69584 69685 69869 "ALGMFACT" 70193 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65619 66198 66792 "ALGMANIP" 69168 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55830 65245 65395 "ALGFF" 65552 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55026 55157 55336 "ALGFACT" 55688 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53953 54553 54591 "ALGEBRA" 54596 NIL ALGEBRA (NIL T) -9 NIL 54637 NIL) (-37 53671 53730 53862 "ALGEBRA-" 53867 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35666 51569 51621 "ALAGG" 51757 NIL ALAGG (NIL T T) -9 NIL 51918 NIL) (-35 35202 35315 35341 "AHYP" 35542 T AHYP (NIL) -9 NIL NIL NIL) (-34 34133 34381 34407 "AGG" 34906 T AGG (NIL) -9 NIL 35185 NIL) (-33 33567 33729 33943 "AGG-" 33948 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31373 31796 32201 "AF" 33209 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30853 31098 31188 "ADDAST" 31301 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30121 30380 30536 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b/src/share/algebra/operation.daase index cf707828..ad3c96dd 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,128 +1,10 @@ -(731276 . 3486554164) -(((*1 *2 *3) - (-12 (-14 *4 (-656 (-1195))) (-4 *5 (-464)) - (-5 *2 - (-2 (|:| |glbase| (-656 (-253 *4 *5))) (|:| |glval| (-656 (-576))))) - (-5 *1 (-643 *4 *5)) (-5 *3 (-656 (-253 *4 *5)))))) -(((*1 *2 *1) (-12 (-5 *2 (-1176 *3)) (-5 *1 (-176 *3)) (-4 *3 (-317))))) -(((*1 *2) (-12 (-5 *2 (-1195)) (-5 *1 (-1198))))) -(((*1 *2 *3) - (-12 (-5 *3 (-656 (-624 *5))) (-4 *4 (-1119)) (-5 *2 (-624 *5)) - (-5 *1 (-585 *4 *5)) (-4 *5 (-442 *4))))) -(((*1 *2 *2 *1) - (-12 (-4 *1 (-1229 *3 *4 *5 *2)) (-4 *3 (-568)) (-4 *4 (-805)) - (-4 *5 (-862)) (-4 *2 (-1084 *3 *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-430 *3)) (-5 *1 (-931 *3)) (-4 *3 (-317))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1259 *5 *4)) (-4 *4 (-832)) (-14 *5 (-1195)) - (-5 *2 (-576)) (-5 *1 (-1133 *4 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-1291)) (-5 *1 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(-576) *6 *6)) (-4 *6 (-374)) - (-4 *7 (-1262 *6)) - (-5 *2 (-2 (|:| |answer| (-598 (-419 *7))) (|:| |a0| *6))) - (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) -(((*1 *1 *2) (-12 (-5 *2 (-886)) (-5 *1 (-270)))) - ((*1 *1 *2) (-12 (-5 *2 (-390)) (-5 *1 (-270))))) -(((*1 *1) (-5 *1 (-158))) - ((*1 *2 *1) (-12 (-4 *1 (-1063 *2)) (-4 *2 (-23))))) -(((*1 *2 *3) (-12 (-5 *3 (-1177)) (-5 *2 (-112)) (-5 *1 (-841))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-576)) (-5 *1 (-708 *2)) (-4 *2 (-1262 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 (-1161 *3 *4)) (-14 *3 (-938)) (-4 *4 (-374)) - (-5 *1 (-1012 *3 *4))))) +(731278 . 3486628452) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-783)) (-4 *4 (-1068)) + (-5 *2 (-2 (|:| -1482 *1) (|:| -1509 *1))) (-4 *1 (-1262 *4))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-732)) (-5 *2 (-938)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-734)) (-5 *2 (-783))))) (((*1 *2 *1 *2 *3) (-12 (-5 *3 (-656 (-1177))) (-5 *2 (-1177)) (-5 *1 (-1287)))) ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1287)))) @@ -131,82 +13,66 @@ (-12 (-5 *3 (-656 (-1177))) (-5 *2 (-1177)) (-5 *1 (-1288)))) ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1288)))) ((*1 *2 *1 *2) (-12 (-5 *2 (-1177)) (-5 *1 (-1288))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1284 *2)) (-4 *2 (-1236)) (-4 *2 (-1021)) - (-4 *2 (-1068))))) (((*1 *2 *3) - (-12 (-5 *3 (-783)) (-5 *2 (-1 (-1176 (-969 *4)) (-1176 (-969 *4)))) - (-5 *1 (-1294 *4)) (-4 *4 (-374))))) -(((*1 *2 *3) - (-12 (-5 *3 (-419 *5)) (-4 *5 (-1262 *4)) (-4 *4 (-568)) - (-4 *4 (-1068)) (-4 *2 (-1277 *4)) (-5 *1 (-1280 *4 *5 *6 *2)) - (-4 *6 (-668 *5))))) + (-12 (-5 *3 (-1286 (-1286 *4))) (-4 *4 (-1068)) (-5 *2 (-701 *4)) + (-5 *1 (-1048 *4))))) +(((*1 *2 *1) + (-12 (-4 *4 (-1119)) (-5 *2 (-112)) (-5 *1 (-898 *3 *4 *5)) + (-4 *3 (-1119)) (-4 *5 (-678 *4)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-902 *3 *4)) (-4 *3 (-1119)) + (-4 *4 (-1119))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-419 (-969 (-171 (-576))))) (-5 *2 (-656 (-171 *4))) + (-5 *1 (-389 *4)) (-4 *4 (-13 (-374) (-860))))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-656 (-419 (-969 (-171 (-576)))))) + (-5 *4 (-656 (-1195))) (-5 *2 (-656 (-656 (-171 *5)))) + (-5 *1 (-389 *5)) (-4 *5 (-13 (-374) (-860)))))) (((*1 *2 *1) (-12 (-5 *2 (-656 *4)) (-5 *1 (-1160 *3 *4)) (-4 *3 (-13 (-1119) (-34))) (-4 *4 (-13 (-1119) (-34)))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-337 *3)) (-4 *3 (-1236)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-576)) (-5 *1 (-528 *3 *4)) (-4 *3 (-1236)) (-14 *4 *2)))) (((*1 *2 *3) - (-12 (-5 *3 (-1286 (-326 (-227)))) - (-5 *2 - (-2 (|:| |additions| (-576)) (|:| |multiplications| (-576)) - (|:| |exponentiations| (-576)) (|:| |functionCalls| (-576)))) - (-5 *1 (-315))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1176 (-1176 *4))) (-5 *2 (-1176 *4)) (-5 *1 (-1179 *4)) - (-4 *4 (-1068))))) -(((*1 *1 *1) - (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-576)))) (-4 *2 (-1068))))) -(((*1 *2 *1 *2) (-12 (-5 *1 (-1045 *2)) (-4 *2 (-1236))))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *3 (-576)) (-5 *4 (-701 (-227))) (-5 *5 (-227)) - (-5 *2 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(-860)))))) + (-12 (-4 *4 (-38 (-419 (-576)))) + (-5 *2 (-2 (|:| -3951 (-1176 *4)) (|:| -3961 (-1176 *4)))) + (-5 *1 (-1181 *4)) (-5 *3 (-1176 *4))))) +(((*1 *2) (-12 (-5 *2 (-576)) (-5 *1 (-1025)))) + ((*1 *2 *2) (-12 (-5 *2 (-576)) (-5 *1 (-1025))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1117 *2)) (-4 *2 (-1119))))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-626 *2) (-174))) (-5 *2 (-905 *4)) (-5 *1 (-172 *4 *5 *3)) (-4 *4 (-1119)) (-4 *3 (-167 *5)))) @@ -1933,9 +1332,9 @@ (-12 (-5 *2 (-969 *3)) (-4 *3 (-1068)) (-4 *1 (-1084 *3 *4 *5)) (-4 *5 (-626 (-1195))) (-4 *4 (-805)) (-4 *5 (-862)))) ((*1 *1 *2) - (-2835 + (-2781 (-12 (-5 *2 (-969 (-576))) (-4 *1 (-1084 *3 *4 *5)) - (-12 (-2746 (-4 *3 (-38 (-419 (-576))))) (-4 *3 (-38 (-576))) + (-12 (-2684 (-4 *3 (-38 (-419 (-576))))) (-4 *3 (-38 (-576))) (-4 *5 (-626 (-1195)))) (-4 *3 (-1068)) (-4 *4 (-805)) (-4 *5 (-862))) (-12 (-5 *2 (-969 (-576))) (-4 *1 (-1084 *3 *4 *5)) @@ -1946,12 +1345,12 @@ (-4 *3 (-38 (-419 (-576)))) (-4 *5 (-626 (-1195))) (-4 *3 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(-12 (-4 *4 (-568)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -2101 *4))) - (-5 *1 (-988 *4 *3)) (-4 *3 (-1262 *4))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1031)) (-5 *2 (-874))))) + (-12 (-4 *1 (-1303 *3 *4)) (-4 *3 (-862)) (-4 *4 (-1068)) + (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1309 *3 *4)) (-4 *3 (-1068)) + (-4 *4 (-858))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1177)) (-5 *2 (-1291)) (-5 *1 (-1288))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1119)) (-4 *6 (-1119)) + (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-696 *4 *5 *6)) (-4 *4 (-1119))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1236)))) ((*1 *1 *2) (-12 (-5 *2 (-969 (-390))) (-5 *1 (-350 *3 *4 *5)) @@ -2122,11 +1488,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1195)) (|:| |fn| (-326 (-227))) - (|:| -3586 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| -1951 (-1113 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-227))) - (|:| -3586 (-656 (-1113 (-855 (-227))))) + (|:| -1951 (-656 (-1113 (-855 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-781)))) ((*1 *2 *1) @@ -2142,13 +1508,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-227))) (|:| -1538 (-656 (-227))) + (-2 (|:| |fn| (-326 (-227))) (|:| -3475 (-656 (-227))) (|:| |lb| (-656 (-855 (-227)))) (|:| |cf| (-656 (-326 (-227)))) (|:| |ub| (-656 (-855 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-656 (-326 (-227)))) - (|:| -1538 (-656 (-227))))))) + (|:| -3475 (-656 (-227))))))) (-5 *1 (-853)))) ((*1 *2 *1) (-12 @@ -2167,26 +1533,26 @@ (-4 *4 (-805)) (-4 *5 (-862)) (-4 *1 (-995 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1057 *2)) (-4 *2 (-1236)))) ((*1 *1 *2) - (-2835 + (-2781 (-12 (-5 *2 (-969 *3)) - (-12 (-2746 (-4 *3 (-38 (-419 (-576))))) - (-2746 (-4 *3 (-38 (-576)))) (-4 *5 (-626 (-1195)))) + (-12 (-2684 (-4 *3 (-38 (-419 (-576))))) + (-2684 (-4 *3 (-38 (-576)))) (-4 *5 (-626 (-1195)))) (-4 *3 (-1068)) (-4 *1 (-1084 *3 *4 *5)) (-4 *4 (-805)) (-4 *5 (-862))) (-12 (-5 *2 (-969 *3)) - (-12 (-2746 (-4 *3 (-557))) (-2746 (-4 *3 (-38 (-419 (-576))))) + (-12 (-2684 (-4 *3 (-557))) (-2684 (-4 *3 (-38 (-419 (-576))))) (-4 *3 (-38 (-576))) (-4 *5 (-626 (-1195)))) (-4 *3 (-1068)) (-4 *1 (-1084 *3 *4 *5)) (-4 *4 (-805)) (-4 *5 (-862))) (-12 (-5 *2 (-969 *3)) - (-12 (-2746 (-4 *3 (-1011 (-576)))) (-4 *3 (-38 (-419 (-576)))) + (-12 (-2684 (-4 *3 (-1011 (-576)))) (-4 *3 (-38 (-419 (-576)))) (-4 *5 (-626 (-1195)))) (-4 *3 (-1068)) (-4 *1 (-1084 *3 *4 *5)) (-4 *4 (-805)) (-4 *5 (-862))))) ((*1 *1 *2) - (-2835 + (-2781 (-12 (-5 *2 (-969 (-576))) (-4 *1 (-1084 *3 *4 *5)) - (-12 (-2746 (-4 *3 (-38 (-419 (-576))))) (-4 *3 (-38 (-576))) + (-12 (-2684 (-4 *3 (-38 (-419 (-576))))) (-4 *3 (-38 (-576))) (-4 *5 (-626 (-1195)))) (-4 *3 (-1068)) (-4 *4 (-805)) (-4 *5 (-862))) (-12 (-5 *2 (-969 (-576))) (-4 *1 (-1084 *3 *4 *5)) @@ -2196,99 +1562,108 @@ (-12 (-5 *2 (-969 (-419 (-576)))) (-4 *1 (-1084 *3 *4 *5)) (-4 *3 (-38 (-419 (-576)))) (-4 *5 (-626 (-1195))) (-4 *3 (-1068)) (-4 *4 (-805)) 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