Annotation of OpenXM/src/kan96xx/Doc/tower.sm1, Revision 1.1
1.1 ! maekawa 1: %% It is used to check the mmLarger_tower, 1997, 10/26 at Heidelberg.
! 2: %% It is used to check the mmLarger_tower, 1997, 10/27 -- 29 at Oberwolfach.
! 3: %% 1997, 11/7 s_ring_of_differential_operators at Kobe
! 4: %% 1998, 1/28 Homogenize_vec = 0;
! 5: %% 1998, 11/5 Doc/tower.sm1
! 6: %%
! 7: %% tower.sm1 is kept in this directory for the compatibility to
! 8: %% old demo programs and packages. It is being merged to
! 9: %% resol0.sm1 cf. r-interface.sm1, tower.sm1, tower-sugar.sm1
! 10: %%
! 11: /tower.version (2.981105) def
! 12: tower.version [(Version)] system_variable gt
! 13: { (This package requires the latest version of kan/sm1) message
! 14: (Please get it from http://www.math.kobe-u.ac.jp/KAN) message
! 15: error
! 16: } { } ifelse
! 17:
! 18: /debug.res0 0 def
! 19: /debug.sResolution 0 def
! 20: /stat.tower 0 def
! 21: /tower.verbose 0 def
! 22: %(tower-test.sm1) run
! 23: tower.verbose
! 24: { (Doc/tower.sm1 is still under construction.) message } { } ifelse
! 25:
! 26: [(sResolution)
! 27: [( sResolution constructs the Schreyer resolution.)
! 28: ( depth f sResolution r where )
! 29: ( r = [starting Groebner basis g, [ s1, s2 , s3, ...], order-def].)
! 30: ( g is the reduced Groebner basis for f, )
! 31: ( s1 is the syzygy of f,)
! 32: ( s2 is the syzygy of s1,)
! 33: ( s3 is the syzygy of s2 and so on.)
! 34: (Note that es and ES are reserved for schreyer ordering.)
! 35: (Note also that schreyer order causes troubles for other computations)
! 36: (except sResolution in kan/sm1.)
! 37: (Example:)
! 38: $ [(x,y) s_ring_of_differential_operators$
! 39: $ [[(Dx) 1 (x) -1]] s_weight_vector$
! 40: $ 0 [(schreyer) 1]] define_ring$
! 41: $ $
! 42: $ [( x^3-y^2 ) tparse$
! 43: $ ( 2 x Dx + 3 y Dy + 6 ) tparse$
! 44: $ ( 2 y Dx + 3 x^2 Dy) tparse$
! 45: $ ] sResolution /ans set ; $
! 46: ]] putUsages
! 47:
! 48: /offTower {
! 49: [(AvoidTheSameRing)] pushEnv
! 50: [ [(AvoidTheSameRing) 0] system_variable
! 51: [(gbListTower) [[ ]] (list) dc] system_variable
! 52: ] pop popEnv
! 53: } def
! 54:
! 55:
! 56: /tparse {
! 57: /arg1 set
! 58: [/f /ans /fhead /val] pushVariables
! 59: [
! 60: /f arg1 def
! 61: (report) (mmLarger) switch_function /val set
! 62: f isString { } { f toString /f set } ifelse
! 63: (mmLarger) (matrix) switch_function
! 64: f expand /f set
! 65: [(AvoidTheSameRing)] pushEnv [ [(AvoidTheSameRing) 0] system_variable (mmLarger) (tower) switch_function ] pop popEnv
! 66: /ans (0). def
! 67: {
! 68: f (0). eq {exit} { } ifelse
! 69: (mmLarger) (matrix) switch_function
! 70: f init /fhead set f fhead sub /f set
! 71: [(AvoidTheSameRing)] pushEnv [ [(AvoidTheSameRing) 0] system_variable (mmLarger) (tower) switch_function ] pop popEnv
! 72: ans fhead add /ans set
! 73: } loop
! 74: (mmLarger) val switch_function
! 75: /arg1 ans def
! 76: ] pop
! 77: popVariables
! 78: arg1
! 79: } def
! 80:
! 81:
! 82: /toes {
! 83: %% [x+2, y x ] ===> x + 2 + y x es (sorted by the schreyer order.)
! 84: /arg1 set
! 85: [/vec] pushVariables
! 86: [
! 87: /vec arg1 def
! 88: vec isPolynomial { /vec [vec] def } { } ifelse
! 89: [(toes) vec] gbext /arg1 set
! 90: ] pop
! 91: popVariables
! 92: arg1
! 93: } def
! 94:
! 95: /toE {
! 96: %% [x+2, y x ] ===> x e + 2 e + y s e (sorted by the schreyer order.)
! 97: /arg1 set
! 98: [/n /vec /oures /i /ppp] pushVariables
! 99: [
! 100: /vec arg1 def
! 101: /oures @@@.esymbol . def
! 102: vec isPolynomial { /vec [vec] def } { } ifelse
! 103: vec isArray
! 104: { } {(error: vec toE, vec must be an array) message error} ifelse
! 105: /n vec length def
! 106: 0 1 n 1 sub
! 107: { /i set
! 108: vec i get oures degree 0 eq
! 109: { }
! 110: {(error: vec toE, vec must not contain the variable e) message error}
! 111: ifelse
! 112: } for
! 113:
! 114: [ 0 1 n 1 sub { /i set oures i power } for ] /ppp set
! 115: %% ppp message
! 116: vec ppp mul /arg1 set
! 117: ] pop
! 118: popVariables
! 119: arg1
! 120: } def
! 121:
! 122: /res0 {
! 123: /arg1 set
! 124: [/g /t.syz /nexttower /m /t.gb /skel /betti /gg
! 125: /k /i /j /pair /tmp /si /sj /grG /syzAll] pushVariables
! 126: [
! 127: /g arg1 def %% g = [g_1, ..., g_m] g_i does not contain h and es.
! 128: [(Homogenize)] system_variable 0 eq
! 129: { tower.verbose {
! 130: (Warning: Homogenization option is automatically turned on. ReduceLowerTerms = 1) message
! 131: } { } ifelse
! 132: [(Homogenize) 1] system_variable
! 133: [(ReduceLowerTerms) 1] system_variable
! 134: } { } ifelse
! 135: g length 0 eq { (error: [ ] argument to res0.) message error } { } ifelse
! 136: g { toes } map /g set
! 137: stat.tower { (Size of g is ) messagen g length messagen } { } ifelse
! 138: stat.tower { (, sizes of each element in g are ) messagen
! 139: g { length } map message } { } ifelse
! 140: debug.res0 {(es expression of g: ) messagen g message } { } ifelse
! 141: stat.tower { (Computing the skelton.) message } { } ifelse
! 142: [(schreyerSkelton) g] gbext /skel set
! 143: /betti skel length def
! 144: stat.tower { (Done. Number of skelton is ) messagen betti message } { } ifelse
! 145:
! 146: debug.res0
! 147: { (init of original g : ) messagen g {init} map message
! 148: (length of skelton ) messagen betti message
! 149: (schreyerSkelton g : ) messagen skel message
! 150: (Doing reduction ) messagen
! 151: } { } ifelse
! 152:
! 153: %(red@) (debug) switch_function
! 154: %(red@) (module1v) switch_function
! 155:
! 156: /grG g (gradedPolySet) dc def
! 157: [ 0 1 betti 1 sub { pop 0 } for ] /syzAll set
! 158: 0 1 betti 1 sub {
! 159: /k set
! 160: [
! 161: /pair skel k get def
! 162: pair 0 get 0 get /i set
! 163: pair 0 get 1 get /j set
! 164: pair 1 get 0 get /si set
! 165: pair 1 get 1 get /sj set
! 166: si g i get mul
! 167: sj g j get mul add
! 168: grG reduction /tmp set % si g[i] + sj g[j] + \sum tmp[2][k] g[k] = 0.
! 169: tmp 0 get (0). eq {
! 170: tower.verbose { (.) messagen [(flush)] extension pop } { } ifelse
! 171: }
! 172: {
! 173: (Error: the result of resolution is not zero) message
! 174: ( [i,j], [si,sj] = ) messagen [ [ i j ] [si sj ]] message
! 175: error
! 176: } ifelse
! 177: /t.syz tmp 2 get def
! 178: << tmp 1 get >> si mul << t.syz i get >> add /si set
! 179: << tmp 1 get >> sj mul << t.syz j get >> add /sj set
! 180: t.syz i si put
! 181: t.syz j sj put
! 182: ] pop
! 183: syzAll k t.syz put
! 184: } for
! 185:
! 186: /t.syz syzAll def
! 187: tower.verbose {
! 188: ( Done. betti=) messagen betti message
! 189: } { } ifelse
! 190:
! 191: /nexttower g {init } map def
! 192: /arg1 [t.syz nexttower] def
! 193: ] pop
! 194: popVariables
! 195: arg1
! 196: } def
! 197:
! 198: /sResolution {
! 199: /arg1 set
! 200: /arg2 set %% optional parameter.
! 201: [/g /gbTower /ans /ff /opt /count /startingGB /opts /vectorInput
! 202: ] pushVariables
! 203: [ /g arg1 def
! 204: /opt arg2 def
! 205:
! 206: setupEnvForResolution
! 207:
! 208: /count -1 def
! 209: %% optional parameter.
! 210: opt isInteger {
! 211: /count opt def
! 212: } { } ifelse
! 213:
! 214: (mmLarger) (matrix) switch_function
! 215: %% new code of 1999, 5/18
! 216: g 0 get isArray {
! 217: /vectorInput 1 def
! 218: } {
! 219: /vectorInput 0 def
! 220: } ifelse
! 221: vectorInput {
! 222: tower.verbose { (tower.sm1: Vector input is homogenized : ) message
! 223: [g { sHomogenize2 } map ] message } { } ifelse
! 224: [g { sHomogenize2 } map ] groebner 0 get /g set
! 225: } {
! 226: tower.verbose { (tower.sm1: Homogenize the scalar input : ) message
! 227: [g {sHomogenize} map ] message } { } ifelse
! 228: [g {sHomogenize} map ] groebner 0 get /g set
! 229: } ifelse
! 230:
! 231:
! 232: /startingGB g def
! 233: debug.sResolution
! 234: {
! 235: (g is ) messagen g message
! 236: (---------------------------------------------------) message
! 237: } { } ifelse
! 238: /ans [ ] def
! 239: % /gbTower [g {init} map ] def
! 240: /gbTower [ ] def
! 241: [(AvoidTheSameRing)] pushEnv [ [(AvoidTheSameRing) 0] system_variable (mmLarger) (tower) switch_function ] pop popEnv
! 242: {
! 243: g res0 /ff set
! 244: ans ff 0 get append /ans set %% store the syzygy.
! 245: debug.sResolution
! 246: {
! 247: (Syzygy : ) messagen ff 0 get message
! 248: (----------------------------------------------------) message
! 249: } { } ifelse
! 250: [ff 1 get] gbTower join /gbTower set
! 251: /g ff 0 get def
! 252: g length 0 eq { exit } { } ifelse
! 253:
! 254: [(AvoidTheSameRing)] pushEnv
! 255: [ [(AvoidTheSameRing) 0] system_variable
! 256: [(gbListTower) gbTower (list) dc] system_variable
! 257: ] pop popEnv
! 258:
! 259: count 0 eq { (Resolution procedure stoped because counter == 0.) message
! 260: exit }
! 261: { } ifelse
! 262: count 1 sub /count set
! 263:
! 264:
! 265: } loop
! 266:
! 267: restoreEnvAfterResolution
! 268:
! 269: /arg1 [startingGB ans gbTower] def
! 270: ] pop
! 271: popVariables
! 272: arg1
! 273: } def
! 274:
! 275: /sHomogenize {
! 276: /arg1 set
! 277: [/ff ] pushVariables
! 278: [
! 279: /ff arg1 def
! 280: ff homogenize
! 281: toString tparse %% homogenization may destroy the order.
! 282: %% cf. 97feb4.txt 1997, 10/29
! 283: /arg1 set
! 284: ] pop
! 285: popVariables
! 286: arg1
! 287: } def
! 288:
! 289: /sHomogenize2 {
! 290: /arg1 set
! 291: [/ff /vectorInput /f2deg /f2 /tt /f2max /ttdeg] pushVariables
! 292: [
! 293: /ff arg1 def
! 294: ff isArray{
! 295: ff homogenize /f2 set
! 296: f2 {toString tparse} map /f2 set
! 297: f2 {/tt set [(grade) tt] gbext} map /f2deg set
! 298: [-1] f2deg join shell reverse 0 get /f2max set
! 299: f2 { /tt set [(grade) tt] gbext /ttdeg set
! 300: tt [@@@.hsymbol (^) f2max ttdeg sub toString] cat . mul
! 301: } map
! 302: } {
! 303: ff homogenize
! 304: toString tparse %% homogenization may destroy the order.
! 305: %% cf. 97feb4.txt 1997, 10/29
! 306: } ifelse
! 307: /arg1 set
! 308: ] pop
! 309: popVariables
! 310: arg1
! 311: } def
! 312:
! 313:
! 314:
! 315: /s_ring_of_differential_operators {
! 316: /arg1 set
! 317: [/vars /n /i /xList /dList /param] pushVariables
! 318: [
! 319: (mmLarger) (matrix) switch_function
! 320: (mpMult) (diff) switch_function
! 321: (red@) (module1) switch_function
! 322: (groebner) (standard) switch_function
! 323: (grade) (module1v) switch_function
! 324: (isSameComponent) (x) switch_function
! 325:
! 326: [arg1 to_records pop] /vars set %[x y z]
! 327: vars reverse /xList set %[z y x]
! 328: vars {@@@.Dsymbol 2 1 roll 2 cat_n} map
! 329: reverse /dList set %[Dz Dy Dx]
! 330: [(H)] xList join [(es) @@@.esymbol ] join /xList set
! 331: %% You cannot change the order of es and e, because
! 332: %% mmLarger_tower automatically assumes es is at the bottom
! 333: %% of [nn,n-1] variables.
! 334: [(h)] dList join [(ES) @@@.Esymbol ] join /dList set
! 335: [0 1 1 1 << xList length >>
! 336: 1 1 1 << xList length 2 sub >> ] /param set
! 337: [ xList dList param ] /arg1 set
! 338: ] pop
! 339: popVariables
! 340: arg1
! 341: } def
! 342:
! 343: /s_weight_vector {
! 344: /arg2 set /arg1 set
! 345: [/vars /univ /w-vectors /www /k /order1 /order2] pushVariables
! 346: /vars arg1 def /w-vectors arg2 def
! 347: [
! 348: /univ vars 0 get reverse
! 349: vars 1 get reverse join
! 350: def
! 351: [
! 352: 0 1 << w-vectors length 1 sub >>
! 353: {
! 354: /k set
! 355: univ w-vectors k get w_to_vec
! 356: } for
! 357: ] /order1 set
! 358: %% order1 ::
! 359:
! 360: vars s_reverse_lex_order 3 get /order2 set
! 361: vars [ << order1 order2 join >> ] join /arg1 set
! 362: ] pop
! 363: popVariables
! 364: arg1
! 365: } def
! 366:
! 367: /s_reverse_lex_order {
! 368: %% [x-list d-list params] elimination_order
! 369: %% vars
! 370: %% [x-list d-list params order]
! 371: /arg1 set
! 372: [/vars /univ /order /perm /univ0 /compl] pushVariables
! 373: /vars arg1 def
! 374: [
! 375: /univ vars 0 get reverse
! 376: vars 1 get reverse join
! 377: def
! 378:
! 379: << univ length 3 sub >>
! 380: 0
! 381: eliminationOrderTemplate /order set
! 382:
! 383: [[1]] [[1]] oplus order oplus [[1]] oplus /order set
! 384:
! 385: vars [order] join /arg1 set
! 386: ] pop
! 387: popVariables
! 388: arg1
! 389: } def
! 390:
! 391:
! 392: /setupEnvForResolution {
! 393: getOptions /opts set
! 394: [(Homogenize_vec)] system_variable 1 eq
! 395: { [(Homogenize_vec) 0] system_variable
! 396: (grade) (module1v) switch_function
! 397: tower.verbose {
! 398: (Homogenize_vec is automatically set to 0. grade is set to module1v) message
! 399: } { } ifelse
! 400: } { } ifelse
! 401:
! 402: [(Schreyer)] system_variable 1 eq
! 403: { }
! 404: {(Error: You can compute resolutions only in the ring defined with) message
! 405: $the [(schreyer) 1] option. cf. s_ring_of_differential_operators$ message
! 406: error
! 407: } ifelse
! 408:
! 409: (report) (mmLarger) switch_function (tower) eq
! 410: { }
! 411: { tower.verbose {
! 412: $Warning: (mmLarger) (tower) switch_function is executed.$ message
! 413: } { } ifelse
! 414: [(AvoidTheSameRing)] pushEnv [ [(AvoidTheSameRing) 0] system_variable (mmLarger) (tower) switch_function ] pop popEnv
! 415: } ifelse
! 416:
! 417: } def
! 418:
! 419: /restoreEnvAfterResolution {
! 420: [(AvoidTheSameRing)] pushEnv
! 421: [ [(AvoidTheSameRing) 0] system_variable
! 422: [(gbListTower) [[ ]] (list) dc] system_variable
! 423: ] pop popEnv
! 424: opts restoreOptions
! 425: } def
! 426:
! 427: %%%%% 1998, 4/11. To get frame for homogenized resolutions.
! 428: /sResolutionFrame {
! 429: /arg1 set
! 430: /arg2 set %% optional parameter.
! 431: [/g /gbTower /ans /ff /opt /count /startingGB /opts] pushVariables
! 432: [ /g arg1 def
! 433: /opt arg2 def
! 434:
! 435:
! 436: stat.tower { [(Statistics) 1] system_variable } { } ifelse
! 437: /count -1 def
! 438: %% optional parameter.
! 439: opt isInteger {
! 440: /count opt def
! 441: } { } ifelse
! 442:
! 443: (mmLarger) (matrix) switch_function
! 444: [g {sHomogenize} map ] groebner 0 get /g set
! 445: g { init } map /g set
! 446:
! 447: setupEnvForResolution-sugar
! 448:
! 449: /startingGB g def
! 450: debug.sResolution
! 451: {
! 452: (g is ) messagen g message
! 453: (---------------------------------------------------) message
! 454: } { } ifelse
! 455: /ans [ ] def
! 456: % /gbTower [g {init} map ] def
! 457: /gbTower [ ] def
! 458: [(AvoidTheSameRing)] pushEnv [ [(AvoidTheSameRing) 0] system_variable (mmLarger) (tower) switch_function ] pop popEnv
! 459: {
! 460: g res0Frame /ff set
! 461: ans ff 0 get append /ans set %% store the syzygy.
! 462: debug.sResolution
! 463: {
! 464: (Syzygy : ) messagen ff 0 get message
! 465: (----------------------------------------------------) message
! 466: } { } ifelse
! 467: [ff 1 get] gbTower join /gbTower set
! 468: /g ff 0 get def
! 469: g length 0 eq { exit } { } ifelse
! 470:
! 471: [(AvoidTheSameRing)] pushEnv
! 472: [ [(AvoidTheSameRing) 0] system_variable
! 473: [(gbListTower) gbTower (list) dc] system_variable
! 474: ] pop popEnv
! 475:
! 476: count 0 eq { (Resolution prodecure stoped because counter == 0.) message
! 477: exit }
! 478: { } ifelse
! 479: count 1 sub /count set
! 480:
! 481:
! 482: } loop
! 483:
! 484: restoreEnvAfterResolution-sugar
! 485:
! 486: /arg1 [startingGB ans gbTower] def
! 487: ] pop
! 488: popVariables
! 489: arg1
! 490: } def
! 491:
! 492: /newPolyVector {
! 493: /arg1 set
! 494: /arg2 (0). def
! 495: [ 1 1 arg1 { pop arg2 } for ]
! 496: } def
! 497:
! 498: /res0Frame {
! 499: /arg1 set
! 500: [/g /t.syz /nexttower /m /t.gb /skel /betti /gg
! 501: /k /i /j /pair /tmp /si /sj /grG /syzAll /gLength] pushVariables
! 502: [
! 503: /g arg1 def %% g = [g_1, ..., g_m] g_i does not contain h and es.
! 504: [(Homogenize)] system_variable 1 eq
! 505: { (Warning: Homogenization and ReduceLowerTerms options are automatically turned off.) message
! 506: [(Homogenize) 0] system_variable
! 507: [(ReduceLowerTerms) 0] system_variable
! 508: } { } ifelse
! 509: g length 0 eq { (error: [ ] argument to res0.) message error } { } ifelse
! 510: g { toes } map /g set
! 511: stat.tower { (Size of g is ) messagen g length messagen } { } ifelse
! 512: stat.tower { (, sizes of each element in g are ) messagen
! 513: g { length } map message } { } ifelse
! 514: debug.res0 {(es expression of g: ) messagen g message } { } ifelse
! 515: stat.tower { (Computing the skelton.) message } { } ifelse
! 516: [(schreyerSkelton) g] gbext /skel set
! 517: /betti skel length def
! 518: stat.tower { (Done. Number of skelton is ) messagen betti message } { } ifelse
! 519:
! 520: debug.res0
! 521: { (init of original g : ) messagen g {init} map message
! 522: (length of skelton ) messagen betti message
! 523: (schreyerSkelton g : ) messagen skel message
! 524: (Doing reduction ) messagen
! 525: } { } ifelse
! 526:
! 527: g length /gLength set
! 528: /grG g (gradedPolySet) dc def
! 529: [ 0 1 betti 1 sub { pop 0 } for ] /syzAll set
! 530: 0 1 betti 1 sub {
! 531: /k set
! 532: [
! 533: /pair skel k get def
! 534: pair 0 get 0 get /i set
! 535: pair 0 get 1 get /j set
! 536: pair 1 get 0 get /si set
! 537: pair 1 get 1 get /sj set
! 538: % si g[i] + sj g[j] + \sum tmp[2][k] g[k] = 0.
! 539: (.) messagen [(flush)] extension pop
! 540:
! 541: /t.syz gLength newPolyVector def
! 542: t.syz i si put
! 543: t.syz j sj put
! 544: ] pop
! 545: syzAll k t.syz put
! 546: } for
! 547:
! 548: /t.syz syzAll def
! 549: ( Done. betti=) messagen betti message
! 550:
! 551:
! 552: /nexttower g {init } map def
! 553: /arg1 [t.syz nexttower] def
! 554: %% clear all unnecessary variables to save memory.
! 555: /g 0 def /t.syz 0 def /nexttower 0 def /t.gb 0 def /skel 0 def /gg 0 def
! 556: /k 0 def /tmp 0 def /grG 0 def /syzAll 0 def
! 557: ] pop
! 558: popVariables
! 559: arg1
! 560: } def
! 561:
! 562: /s_ring_of_polynomials {
! 563: /arg1 set
! 564: [/vars /n /i /xList /dList /param] pushVariables
! 565: [
! 566: (mmLarger) (matrix) switch_function
! 567: (mpMult) (poly) switch_function
! 568: (red@) (module1) switch_function
! 569: (groebner) (standard) switch_function
! 570: (isSameComponent) (x) switch_function
! 571:
! 572: [arg1 to_records pop] /vars set
! 573: vars length evenQ
! 574: { }
! 575: { vars [(PAD)] join /vars set }
! 576: ifelse
! 577: vars length 2 idiv /n set
! 578: [ << n 1 sub >> -1 0
! 579: { /i set
! 580: vars i get
! 581: } for
! 582: ] /xList set
! 583: [ << n 1 sub >> -1 0
! 584: { /i set
! 585: vars << i n add >> get
! 586: } for
! 587: ] /dList set
! 588:
! 589: [(H)] xList join [(es) @@@.esymbol ] join /xList set
! 590: %% You cannot change the order of es and e, because
! 591: %% mmLarger_tower automatically assumes es is at the bottom
! 592: %% of [nn,n-1] variables.
! 593: [(h)] dList join [(ES) @@@.Esymbol ] join /dList set
! 594: [0 %% dummy characteristic
! 595: << xList length 2 sub >> << xList length 2 sub >>
! 596: << xList length 2 sub >> << xList length >>
! 597: %% c l m n
! 598: << xList length 2 sub >> << xList length 2 sub >>
! 599: << xList length 2 sub >> << xList length 2 sub >>
! 600: %% cc ll mm nn es must belong to differential variables.
! 601: ] /param set
! 602: [xList dList param] /arg1 set
! 603: ] pop
! 604: popVariables
! 605: arg1
! 606: } def
! 607:
! 608: /setupEnvForResolution-sugar {
! 609: getOptions /opts set
! 610: [(Homogenize)] system_variable 1 eq
! 611: { (Warning: Homogenization and ReduceLowerTerms options are automatically turned off.) message
! 612: [(Homogenize) 0] system_variable
! 613: [(ReduceLowerTerms) 0] system_variable
! 614: } { } ifelse
! 615:
! 616: [(Schreyer)] system_variable 1 eq
! 617: { }
! 618: {(Error: You can compute resolutions only in the ring defined with) message
! 619: $the [(schreyer) 1] option. cf. s_ring_of_differential_operators$ message
! 620: error
! 621: } ifelse
! 622:
! 623: (report) (mmLarger) switch_function (tower) eq
! 624: { }
! 625: { $Warning: (mmLarger) (tower) switch_function is executed.$ message
! 626: [(AvoidTheSameRing)] pushEnv [ [(AvoidTheSameRing) 0] system_variable (mmLarger) (tower) switch_function ] pop popEnv
! 627: } ifelse
! 628:
! 629: } def
! 630:
! 631: /restoreEnvAfterResolution-sugar {
! 632: %% Turn off tower by (mmLarger) (tower) switch_function
! 633: %% and clear the tower of orders by [(gbListTower) [[]] (list) dc] system_variable
! 634: [(AvoidTheSameRing)] pushEnv
! 635: [ [(AvoidTheSameRing) 0] system_variable
! 636: [(gbListTower) [[]] (list) dc] system_variable
! 637: ] pop popEnv
! 638: opts restoreOptions
! 639: } def
! 640:
! 641:
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