Annotation of OpenXM/src/k097/help.k, Revision 1.1
1.1 ! maekawa 1:
! 2: if (K00_verbose)
! 3: Println("help.k (help.ccc). 8/6, 1996 --- 8/7, 1996. 3/6, 1997 --- 12/21, 1997.");
! 4:
! 5: def help(x) {
! 6: if (Length(Arglist) < 1) {
! 7: ShowKeyWords(" ");
! 8: } else {
! 9: Help(x);
! 10: }
! 11: }
! 12:
! 13:
! 14: def Help(key) {
! 15: local n,i,item,m,item1,j;
! 16: if (Length(Arglist) < 1) {
! 17: ShowKeyWords(" ");
! 18: return( [ ] );
! 19: }
! 20:
! 21: if (key == "ALL") {
! 22: ShowKeyWords("ALL"); return(0);
! 23: }
! 24: n = Length(Helplist);
! 25: PSfor (i=0; i<n; i++) {
! 26: item = Helplist[i];
! 27: if (item[0] == key) {
! 28: if (IsArray(item[1])) {
! 29: item1 = item[1];
! 30: m = Length(item1);
! 31: for (j=0; j<m; j++) {
! 32: Println(item1[j]);
! 33: }
! 34: }else{
! 35: Println(item[1]);
! 36: }
! 37: return(item);
! 38: }
! 39: }
! 40: Print("The key word <<"); Print(key); Println(">> could not be found.");
! 41: return([ ]);
! 42: }
! 43:
! 44:
! 45: def ShowKeyWords(ss) {
! 46: local i,j,n,keys,max,width,m,k,kk,tmp0;
! 47: Ln();
! 48: n = Length(Helplist);
! 49: keys = [" " ]; /* This is a gate keeper for shell. */
! 50: PSfor (i=0; i< n; i++ ) {
! 51: keys = Append(keys,Helplist[i,0]);
! 52: }
! 53: keys = sm1(keys," shell ");
! 54: n = Length(keys);
! 55: if (ss == "ALL") {
! 56: PSfor (i=1; i<n; i++) {
! 57: Print("# "); Print(keys[i]); Ln();
! 58: Help(keys[i]); Ln();
! 59: }
! 60: return(0);
! 61: }
! 62: max = 0;
! 63: PSfor (i=1; i<n; i++) {
! 64: if (Length(keys[i]) > max) {
! 65: max = Length(keys[i]);
! 66: }
! 67: }
! 68: /* Println(max); */
! 69: max = max+3;
! 70: width = 80;
! 71: m = 0;
! 72: while ((m*max) < 80) {
! 73: m = m+1;
! 74: }
! 75: if (m > 1) m = m-1;
! 76: k = 0; kk = 0;
! 77: PSfor (i=1; i<n; i++) {
! 78: Print(keys[i]); kk = kk+1;
! 79: k = k+Length(keys[i]);
! 80: tmp0 = max-Length(keys[i]);
! 81: /*for (j=0; j < tmp0 ; j++) {
! 82: k = k+1;
! 83: if (kk < m) {Print(" ");}
! 84: }*/
! 85: k = k+tmp0;
! 86: if (kk < m) {
! 87: sm1(" [ 0 1 ", tmp0, " (integer) dc 1 sub { pop $ $ } for ] aload length cat_n messagen ");
! 88: }
! 89: if (kk >= m) {
! 90: kk = 0; k=0; Ln();
! 91: }
! 92: }
! 93: Ln();
! 94: Println("Type in Help(keyword); to see a help message (string keyword).");
! 95:
! 96: /* Println(keys); */
! 97: }
! 98:
! 99: def ShowKeyWordsOfSm1(ss) {
! 100: local i,j,n,keys,max,width,m,k,kk,tmp0;
! 101: Ln();
! 102: sm1(" /help_Sm1Macro @.usages def ");
! 103: n = Length(help_Sm1Macro);
! 104: keys = [" " ];
! 105: for (i=0; i< n; i++ ) {
! 106: keys = Append(keys,help_Sm1Macro[i,0]);
! 107: }
! 108: keys = sm1(keys," shell ");
! 109: n = Length(keys);
! 110: if (ss == "ALL") {
! 111: for (i=1; i<n; i++) {
! 112: tmp0 = keys[i];
! 113: Print("# "); Print(tmp0); Ln();
! 114: sm1(tmp0," usage "); Ln();
! 115: }
! 116: return(0);
! 117: }
! 118:
! 119: max = 0;
! 120: for (i=1; i<n; i++) {
! 121: if (Length(keys[i]) > max) {
! 122: max = Length(keys[i]);
! 123: }
! 124: }
! 125: /* Println(max); */
! 126: max = max+3;
! 127: width = 80;
! 128: m = 0;
! 129: while ((m*max) < 80) {
! 130: m = m+1;
! 131: }
! 132: k = 0; kk = 0;
! 133: for (i=1; i<n; i++) {
! 134: Print(keys[i]); kk = kk+1;
! 135: k = k+Length(keys[i]);
! 136: tmp0 = max-Length(keys[i]);
! 137: if (kk >= m) {
! 138: }else {
! 139: for (j=0; j < tmp0 ; j++) {
! 140: k = k+1;
! 141: Print(" ");
! 142: }
! 143: }
! 144: if (kk >= m) {
! 145: kk = 0; k=0; Ln();
! 146: }
! 147: }
! 148: Ln();
! 149: Ln();
! 150: Println("Type in (keyword) usage ; to see a help message.");
! 151:
! 152: /* Println(keys); */
! 153: }
! 154:
! 155: HelpAdd(["Help", "Help(key) shows an explanation on the key (string key)."]);
! 156: HelpAdd(["HelpAdd",
! 157: ["HelpAdd([key,explanation]) (string key, string explanation)",
! 158: " or (string key, array explanation)."]]);
! 159: HelpAdd(["load",
! 160: ["load(fname) loads the file << fname >>(string fname).",
! 161: "load fname loads the file << fname >>.",
! 162: "load[fname] loads the file << fname >> with the preprocessing by /lib/cpp."
! 163: ]]);
! 164: HelpAdd(["Ln","Ln() newline."]);
! 165: HelpAdd(["Println","Println(f) prints f and goes to the new line."]);
! 166: HelpAdd(["Print","Print(f) prints f."]);
! 167: HelpAdd(["Poly",
! 168: "Poly(name) returns the polynomial name in the current ring
! 169: (string name)."]);
! 170: HelpAdd(["PolyR",
! 171: "PolyR(name,r) returns the polynomial name in the ring r
! 172: (string name, ring r).
! 173: Ex. r = RingD(\"x,y\"); y = PolyR(\"y\",r); "]);
! 174: HelpAdd(["RingD",
! 175: ["RingD(names) defines a new ring (string names).",
! 176: "RingD(names,weight_vector) defines a new ring with the weight vector",
! 177: "(string names, array weight_vector).",
! 178: "RingD(names,weight_vector,characteristic)",
! 179: " Ex. RingD(\"x,y\",[[\"x\",2,\"y\",1]]) "]]);
! 180: HelpAdd(["Reduction","Reduction(f,G) returns the remainder and sygygies when
! 181: f is devided by G (polynomial f, array G)."]);
! 182: HelpAdd(["AddString","AddString(list) returns the concatnated string (array list)."]);
! 183: HelpAdd(["AsciiToString","AsciiToString(ascii_code) returns the string of which
! 184: ascii code is ascii_code (integer ascii_code)."]);
! 185: HelpAdd(["ToString","ToString(obj) transforms the <<obj>> to a string."]);
! 186: HelpAdd(["Numerator","Numerator(f) returns the numerator of <<f>> (rational f)."]);
! 187: HelpAdd(["Denominator","Denominator(f) returns the denominator of <<f>> (rational f)."]);
! 188: HelpAdd(["Replace","Replace(f,rule) (polynomial f, array rule).
! 189: Ex. Replace( (x+y)^3, [[x,Poly(\"1\")]])"]);
! 190: HelpAdd(["SetRingVariables",
! 191: "SetRingVariables()
! 192: Set the generators of the current ring as global variables.
! 193: cf. RingD(), Poly(), PolyR()"]);
! 194: HelpAdd(["Append","Append([f1,...,fn],g) returns the list [f1,...,fn,g]"]);
! 195: HelpAdd(["Join",
! 196: "Join([f1,...,fn],[g1,...,gm]) returns the list
! 197: [f1,...,fn,g1,...,gm]"]);
! 198: HelpAdd(["Indexed",
! 199: "Indexed(name,i) returns the string name[i]
! 200: (string name, integer i)"]);
! 201:
! 202: HelpAdd(["-ReservedName1",
! 203: ["The names k00*, K00*, sm1* , arg1,arg2,arg3,arg4,....," ,
! 204: "Helplist, Arglist, FunctionValue,",
! 205: "@@@*, db.*, k.*, tmp002*, tmp00* are used for system functions."]]);
! 206:
! 207: HelpAdd(["IntegerToSm1Integer",
! 208: "IntegerToSm1Integer(i) translates integer i
! 209: to sm1.integer (integer i)."]);
! 210: HelpAdd(["true","true returns sm1.integer 1."]);
! 211: HelpAdd(["false","false returns sm1.integer 0."]);
! 212: HelpAdd(["IsArray",
! 213: ["If f is the array object, then IsArray(f) returns true,",
! 214: "else IsArray(f) returns false."]]);
! 215:
! 216:
! 217:
! 218: HelpAdd(["Init_w",
! 219: ["Init_w(f,vars,w) returns the initial terms with respect to the",
! 220: "weight vector <<w>> (array of integer) of the polynomial <<f>>",
! 221: "(polynomial). Here, <<f>> is regarded as a polynomial with respect",
! 222: "to the variables <<vars>> (array of polynomials).",
! 223: "Example: Init_w(x^2+y^2+x,[x,y],[1,1]):"]]);
! 224:
! 225: HelpAdd(["RingDonIndexedVariables",
! 226: ["RingDonIndexedVariables(name,n) defines and returns the ring of",
! 227: "homogenized differential operators",
! 228: "Q<h, name[0], ..., name[n-1], Dname[0], ..., Dname[n-1]>",
! 229: "where <<name>> is a string and <<n>> is an integer.",
! 230: "Note that this function defines global variables",
! 231: "h, name[0], ..., name[n-1], Dname[0], ..., Dname[n-1].",
! 232: "Example: RingDonIndexedVariables(\"x\",3).",
! 233: "RingDonIndexedVariables(name,n,w) defines and returns the ring of",
! 234: "homogenized differential operators with the ordering defined by ",
! 235: "the weight vector <<w>> (array)",
! 236: "Example: RingDonIndexedVariables(\"x\",3,[[\"x[0]\",1,\"x[2]\",3]])."]]);
! 237:
! 238: HelpAdd(["Groebner",
! 239: ["Groebner(input) returns Groebner basis of the left module (or ideal)",
! 240: "defined by <<input>> (array of polynomials)",
! 241: "The order is that of the ring to which each element of <<input>>",
! 242: "belongs.",
! 243: "The input is automatically homogenized.",
! 244: "Example: RingD(\"x,y\",[[\"x\", 10, \"y\", 1]]);",
! 245: " Groebner([Poly(\" x^2+y^2-4\"),Poly(\" x*y-1 \")]):",
! 246: "cf. RingD, Homogenize"]]);
! 247:
! 248:
! 249: HelpAdd(["RingPoly",
! 250: ["RingPoly(names) defines a Ring of Polyomials (string names).",
! 251: "The names of variables of that ring are <<names>> and ",
! 252: "the homogenization variable h.",
! 253: "cf. SetRingVariables, RingD",
! 254: "Example: R=RingPoly(\"x,y\");",
! 255: " ",
! 256: "RingPoly(names,weight_vector) defines a Ring of Polynomials",
! 257: "with the order defined by the << weight_vector >>",
! 258: "(string names, array of array weight_vector).",
! 259: "RingPoly(names,weight_vector,characteristic)",
! 260: "Example: R=RingPoly(\"x,y\",[[\"x\",10,\"y\",1]]);",
! 261: " (x+y)^10: "]]);
! 262:
! 263:
! 264: HelpAdd(["CancelNumber",
! 265: ["CancelNumber(rn) reduces the rational number <<rn>>",
! 266: "(rational rn).",
! 267: "Example: CancelNumber( 2/6 ) : "]]);
! 268:
! 269: HelpAdd(["IsString",
! 270: ["IsString(obj) returns true if << obj >> is a string (object obj).",
! 271: "Example: if (IsString(\"abc\")) Println(\"Hello\"); ;"]]);
! 272:
! 273:
! 274: HelpAdd(["IsSm1Integer",
! 275: ["IsSm1Integer(obj) returns true if << obj >> is an integer of sm1(object obj)."]]);
! 276:
! 277: HelpAdd(["sm1",
! 278: ["sm1(arg1,arg2,...) is used to embed sm1 native code in the kxx program.",
! 279: "Example: sm1( 2, 2, \" add print \"); ",
! 280: "Example: def myadd(a,b) { sm1(a,b,\" add /FunctionValue set \"); }" ]]);
! 281:
! 282: HelpAdd(["DC",
! 283: ["DC(obj,key) converts << obj >> to a new object in the primitive",
! 284: "class << key >> (object obj, string key)",
! 285: "Example: DC(\" (x+1)^10 \", \"polynomial\"): "]]);
! 286:
! 287: HelpAdd(["Length",
! 288: ["Length(vec) returns the length of the array << vec >>",
! 289: "(array vec)"]]);
! 290:
! 291: HelpAdd(["Transpose",
! 292: ["Transpose(m) return the transpose of the matrix << m >>",
! 293: "(array of array m)."]]);
! 294:
! 295: HelpAdd(["Save",
! 296: ["Save(obj) appends << obj >> to the file sm1out.txt (object obj)."]]);
! 297:
! 298: HelpAdd(["Coefficients",
! 299: ["Coefficients(f,v) returns [exponents, coefficients] of << f >>",
! 300: "with respect to the variable << v >>",
! 301: "(polynomial f,v).",
! 302: "Example: Coefficients(Poly(\"(x+1)^2\"),Poly(\"x\")): "]]);
! 303:
! 304: HelpAdd(["System",
! 305: ["System(comm) executes the unix system command << comm >>",
! 306: "(string comm)",
! 307: "Example: System(\"ls\");"]]);
! 308:
! 309: HelpAdd(["Exponent",
! 310: ["Expoent(f,vars) returns the vector of exponents of the polynomial f",
! 311: "Ex. Exponent( x^2*y-1,[x,y])"]]);
! 312:
! 313: HelpAdd(["Protect",
! 314: ["Protect(name) protects the symbol <<name>> (string)",
! 315: "Protect(name,level) protects the symbol <<name>> (string) with ",
! 316: "<<level>> "]]);
! 317:
! 318: HelpAdd(["IsPolynomial",
! 319: ["IsPolynomial(f) returns true if <<f>> (object) is a polynomial."]]);
! 320:
! 321:
! 322:
! 323: /* -----------------------------------------------
! 324: functions on tests. */
! 325: /* ------------ Developping functions --------------------- */
! 326:
! 327: def RingPoly(vList,weightMatrix,pp) {
! 328: local new0,tmp,size,n,i,j,newtmp,ringpp,argsize;
! 329: argsize = Length(Arglist);
! 330: if (argsize == 1) {
! 331: sm1("[", vList,
! 332: "ring_of_polynomials ( ) elimination_order 0 ] define_ring
! 333: /tmp set ");
! 334: return(tmp);
! 335: } else ;
! 336: if (argsize == 2) {
! 337: pp = 0;
! 338: }
! 339: pp = IntegerToSm1Integer(pp);
! 340: size = Length(weightMatrix);
! 341: new0 = NewVector(size);
! 342: sm1(" /@@@.indexMode.flag.save @@@.indexMode.flag def ");
! 343: sm1(" 0 @@@.indexMode ");
! 344: for (i=0; i<size; i++) {
! 345: tmp = weightMatrix[i];
! 346: n = Length(tmp);
! 347: newtmp = NewVector(n);
! 348: for (j=1; j<n; j = j+2) {
! 349: newtmp[j-1] = tmp[j-1];
! 350: newtmp[j] = IntegerToSm1Integer( tmp[j] );
! 351: }
! 352: new0[i] = newtmp;
! 353: }
! 354: ringpp =
! 355: sm1("[", vList,
! 356: "ring_of_polynomials ", new0, " weight_vector", pp, " ] define_ring");
! 357: sm1(" @@@.indexMode.flag.save @@@.indexMode ");
! 358: return( ringpp );
! 359: }
! 360:
! 361: def IsString(ob) {
! 362: sm1(ob , " isString /FunctionValue set ");
! 363: }
! 364:
! 365: def IsSm1Integer(ob) {
! 366: sm1(ob , " isInteger /FunctionValue set ");
! 367: }
! 368:
! 369:
! 370: def CancelNumber(rn) {
! 371: local tmp;
! 372: sm1(" [(cancel) ",rn," ] mpzext /tmp set ");
! 373: if (IsInteger(tmp)) return(tmp);
! 374: sm1(" tmp (denominator) dc (1).. eq { /FunctionValue tmp (numerator) dc def} { /FunctionValue tmp def } ifelse ");
! 375: }
! 376:
! 377: def DC(obj,key) {
! 378: if (key == "string") { return(ToString(obj)); }
! 379: else if (key == "integer") { key = "universalNumber"; }
! 380: else if (key == "sm1integer") { key = "integer"; }
! 381: else if (key == "polynomial") { key = "poly"; }
! 382: else ;
! 383: sm1( obj , key, " data_conversion /FunctionValue set ");
! 384: }
! 385:
! 386: def Transpose(m) {
! 387: sm1(m, " transpose /FunctionValue set ");
! 388: }
! 389:
! 390: def Save(obj) {
! 391: sm1(obj, " output ");
! 392: }
! 393:
! 394:
! 395: def void System(comm) {
! 396: sm1(comm, " system ");
! 397: }
! 398:
! 399:
! 400: def IsReducible(f,g) {
! 401: sm1("[ (isReducible) ",f,g," ] gbext /FunctionValue set ");
! 402: }
! 403:
! 404: def IsPolynomial(f) {
! 405: sm1(" f isPolynomial /FunctionValue set ");
! 406: }
! 407: sm1(" /k00.toric0.mydegree {2 1 roll degree} def ");
! 408: def Exponent(f,vars) {
! 409: local n,i,ans;
! 410: if (f == Poly("0")) return([ ] );
! 411: sm1(f," /ff.tmp set ", vars ,
! 412: " {ff.tmp k00.toric0.mydegree (universalNumber) dc }map /FunctionValue set ");
! 413: }
! 414: def void Protect(name,level) {
! 415: local n,str;
! 416: n = Length(Arglist);
! 417: if (n == 1) {
! 418: level = 1;
! 419: str = AddString(["[(chattr) ",ToString(level)," /",name," ",
! 420: " ] extension pop "]);
! 421: /* Println(str); */
! 422: sm1(" [(parse) ",str ," ] extension pop ");
! 423: } else if (n ==2) {
! 424: str = AddString(["[(chattr) ",ToString(level)," /",name," ",
! 425: " ] extension pop "]);
! 426: /* Println(str); */
! 427: sm1(" [(parse) ",str ," ] extension pop ");
! 428: } else {
! 429: k00_error("Protect","Arguments must be one or two. ");sm1(" error ");
! 430: }
! 431: }
! 432:
! 433: def void k00_error(name,msg) {
! 434: Print("Error in "); Print(name); Print(". ");
! 435: Println(msg);
! 436: }
! 437:
! 438: def Init(f) {
! 439: if (IsArray(f)) {
! 440: return(Map(f,"Init"));
! 441: } else if (IsPolynomial(f)) {
! 442: sm1(f," init /FunctionValue set ");
! 443: } else {
! 444: k00_error("Init","Argment must be polynomial or an array of polynomials");
! 445: sm1(" error ");
! 446: }
! 447: }
! 448: HelpAdd(["Init",
! 449: ["Init(f) returns the initial term of the polynomial <<f>> (polynomial)",
! 450: "Init(list) returns the array of initial terms of the array of polynomials",
! 451: "<< list >> (array)"]]);
! 452:
! 453: HelpAdd(["NewMatrix",
! 454: ["NewMatrix(m,n) returns the (m,n)-matrix (array) with the entries 0."]]);
! 455:
! 456: def Eliminatev(list,var) /* [(x-y). (y-z).] [(z) ] */
! 457: {
! 458: sm1(list, var, " eliminatev /FunctionValue set ");
! 459: }
! 460: HelpAdd(["Eliminatev",
! 461: ["Eliminatev(list,var) prunes polynomials in << list >>(array of polynomials)",
! 462: "which contains the variables in << var >> ( array of strings )",
! 463: "Example: Eliminatev([Poly(\" x+h \"),Poly(\" x \")],[ \"h\" ]): "]]);
! 464:
! 465: def ReducedBase(base) {
! 466: sm1( base, " reducedBase /FunctionValue set ");
! 467: }
! 468: HelpAdd(["ReducedBase",
! 469: ["ReducedBase[base] prunes redundant elements in the Grobner basis <<base>> (array)."
! 470: ]]);
! 471:
! 472: def IndexedVariables(name,size) {
! 473: local result,i,result2;
! 474: result = [ ];
! 475: for (i=0; i<size-1; i++) {
! 476: result = Append(result,Indexed(name,i));
! 477: result = Append(result,",");
! 478: }
! 479: if (size-1 >= 0) {
! 480: result = Append(result,Indexed(name,size-1));
! 481: }
! 482: result2 = Join(["{"],result);
! 483: result2 = Join(result2,["}"]);
! 484: return(AddString(result2));
! 485: }
! 486: HelpAdd(["IndexedVariables",
! 487: ["IndexedVariables(name,size) returns the string ",
! 488: " {name[0],name[1],...,name[size-1]} which can be used as inputs to ",
! 489: " the function RingD (string name, integer size).",
! 490: " cf. RingDonIndexedVariables.",
! 491: " Ex. R = RingD(IndexedVariables(\"a\",3)); ",
! 492: " h = Poly(\"h\");",
! 493: " a = NewArray(3);",
! 494: " for (i=0; i<3; i++) {a[i] = Poly(Indexed(\"a\",i));} ;"]]);
! 495:
! 496:
! 497: def RingDonIndexedVariables(vList, size, weightMatrix,pp) {
! 498: local myring,tmp,k00_i,argsize,vListD;
! 499: /* You cannot use these local varialbes as a name of global ring
! 500: variables. Change these names to names that start with k00_ */
! 501: argsize = Length(Arglist);
! 502: if (argsize == 1) {
! 503: Println("Error (IndexedRingD): ");
! 504: return(null);
! 505: }
! 506: if (argsize == 2) {
! 507: vListD = AddString(["D",vList]);
! 508: myring = RingD(IndexedVariables(vList,size));
! 509: SetRingVariables();
! 510: tmp = NewArray(size);
! 511: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
! 512: sm1(vList, " (literal) dc ", tmp, " def ");
! 513: tmp = NewArray(size);
! 514: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}
! 515: sm1(vListD, " (literal) dc ", tmp, " def ");
! 516: if (SetRingVariables_Verbose) {
! 517: Print("Set the global variables ");
! 518: sm1("[(parse) ",vList," ] extension pop print ");
! 519: sm1("[(parse) ",vListD," ] extension pop print "); Ln();
! 520: }else {
! 521: sm1("[(parse) ",vList," ] extension pop ");
! 522: sm1("[(parse) ",vListD," ] extension pop ");
! 523: }
! 524: return( myring );
! 525: }
! 526: if (argsize == 3 || argsize == 4) {
! 527: if (argsize == 3) { pp = 0; }
! 528: vListD = AddString(["D",vList]);
! 529: myring = RingD(IndexedVariables(vList,size),weightMatrix,pp);
! 530: SetRingVariables();
! 531: tmp = NewArray(size);
! 532: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
! 533: sm1(vList, " (literal) dc ", tmp, " def ");
! 534: tmp = NewArray(size);
! 535: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}
! 536: sm1(vListD, " (literal) dc ", tmp, " def ");
! 537: if (SetRingVariables_Verbose) {
! 538: Print("Set the global variables ");
! 539: sm1("[(parse) ",vList," ] extension pop print ");
! 540: sm1("[(parse) ",vListD," ] extension pop print "); Ln();
! 541: } else {
! 542: sm1("[(parse) ",vList," ] extension pop ");
! 543: sm1("[(parse) ",vListD," ] extension pop ");
! 544: }
! 545: return( myring );
! 546: }
! 547: return(-1);
! 548: }
! 549:
! 550: def Ringp(f) {
! 551: sm1(f, " (ring) dc /FunctionValue set ");
! 552: }
! 553: HelpAdd(["Ringp",
! 554: ["Ringp(f) ( polynomial f ) returns the ring to which the polynomial << f >>",
! 555: "belongs."]]);
! 556:
! 557: def Coefficients(f,v) {
! 558: local ans,exp;
! 559: ans = sm1(f,v, " coefficients ");
! 560: exp = ans[0];
! 561: exp = sm1(exp," { (universalNumber) dc } map ");
! 562: return([exp,ans[1]]);
! 563: }
! 564:
! 565: def IsInteger(a) {
! 566: sm1(a , " isUniversalNumber /FunctionValue set ");
! 567: }
! 568: HelpAdd(["IsInteger",
! 569: ["IsInteger(a) returns true if << a >> is an integer (object a).",
! 570: "It returns false if << a >> is not.",
! 571: "cf. IsSm1Integer"]]);
! 572:
! 573: def IsRational(a) {
! 574: sm1(a , " isRational /FunctionValue set ");
! 575: }
! 576: HelpAdd(["IsRational",
! 577: ["IsRational(a) returns true if << a >> is a rational (object a).",
! 578: "It returns false if << a >> is not."]]);
! 579:
! 580:
! 581: def IsDouble(a) {
! 582: sm1(a , " isDouble /FunctionValue set ");
! 583: }
! 584: HelpAdd(["IsDouble",
! 585: ["IsDouble(a) returns true if << a >> is a double (object a).",
! 586: "It returns false if << a >> is not."]]);
! 587:
! 588:
! 589: sm1(" /cs { this [ ] Cleards } def ");
! 590:
! 591:
! 592: def Init_w(f,vars,weight) {
! 593: local w,w2,w3,ans,i,n;
! 594: if (f == Poly("0")) return( Poly("0") );
! 595: w = Map(vars,"ToString");
! 596: w2 = sm1(weight," {$integer$ data_conversion} map ");
! 597: n = Length(w);
! 598: w3 = NewArray(n*2);
! 599: for (i=0; i<n ; i++) {
! 600: w3[2*i] = w[i]; w3[2*i+1] = w2[i];
! 601: }
! 602: ans = sm1(f,w3, " weightv init ");
! 603: return(ans);
! 604: }
! 605:
! 606: HelpAdd(["Mapto",
! 607: ["Mapto(obj,ring) parses << obj >> as elements of the << ring >>.",
! 608: "(ring << ring >>, polynomial << obj >> or array of polynomial << obj >>).",
! 609: "Ex. R = RingD(\"x,y\"); SetRingVariables();",
! 610: " f = (x+y)^2; R2 = RingD(\"x,y,z\",[[\"y\",1]]); ",
! 611: " f2 = Mapto(f,R2); f2: "]]);
! 612:
! 613: def Mapto(obj,ring) {
! 614: local ans,i,n;
! 615: if (IsArray(obj)) {
! 616: n = Length(obj);
! 617: ans = Map(obj,"ToString");
! 618: for (i=0; i<n; i++) {
! 619: ans[i] = PolyR(ans[i],ring);
! 620: }
! 621: }else{
! 622: ans = ToString(obj);
! 623: ans = PolyR(ans,ring);
! 624: }
! 625: return(ans);
! 626: }
! 627:
! 628:
! 629: HelpAdd(["ToDouble",
! 630: ["ToDouble(f) translates << f >> into double when it is possible",
! 631: "object << f >>.",
! 632: "Example: ToDouble([1,1/2,[5]]): "]]);
! 633: def k00_toDouble(f) { return(DC(f,"double")); }
! 634: def ToDouble(f) {
! 635: if (IsArray(f)) return(Map(f,"ToDouble"));
! 636: if (IsDouble(f)) return(f);
! 637: return(k00_toDouble(f));
! 638: }
! 639:
! 640:
! 641: def RingPonIndexedVariables(vList, size, weightMatrix) {
! 642: local myring,tmp,k00_i,argsize,vListD;
! 643: /* You cannot use these local varialbes as a name of global ring
! 644: variables. Change these names to names that start with k00_ */
! 645: argsize = Length(Arglist);
! 646: if (argsize == 1) {
! 647: Println("Error (RingPonIndexedVariables): ");
! 648: return(null);
! 649: }
! 650: if (argsize == 2) {
! 651: myring = RingPoly(IndexedVariables(vList,size));
! 652: SetRingVariables();
! 653: tmp = NewArray(size);
! 654: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
! 655: sm1(vList, " (literal) dc ", tmp, " def ");
! 656: if (SetRingVariables_Verbose) {
! 657: Print("Set the global variables ");
! 658: sm1("[(parse) ",vList," ] extension pop print "); Ln();
! 659: }else {
! 660: sm1("[(parse) ",vList," ] extension pop ");
! 661: }
! 662: return( myring );
! 663: }
! 664: if (argsize == 3) {
! 665: myring = RingPoly(IndexedVariables(vList,size),weightMatrix);
! 666: SetRingVariables();
! 667: tmp = NewArray(size);
! 668: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
! 669: sm1(vList, " (literal) dc ", tmp, " def ");
! 670: if (SetRingVariables_Verbose) {
! 671: Print("Set the global variables ");
! 672: sm1("[(parse) ",vList," ] extension pop print "); Ln();
! 673: } else {
! 674: sm1("[(parse) ",vList," ] extension pop ");
! 675: }
! 676: return( myring );
! 677: }
! 678: return(-1);
! 679: }
! 680:
! 681: HelpAdd(["RingPonIndexedVariables",
! 682: ["RingPonIndexedVariables(name,n) defines and returns the ring of",
! 683: "polynomials",
! 684: "Q<h, name[0], ..., name[n-1] >",
! 685: "where <<name>> is a string and <<n>> is an integer.",
! 686: "Note that this function defines global variables",
! 687: "h, name[0], ..., name[n-1].",
! 688: "Example: RingPonIndexedVariables(\"x\",3).",
! 689: "RingPonIndexedVariables(name,n,w) defines and returns the ring of",
! 690: "polynomials with the ordering defined by ",
! 691: "the weight vector <<w>> (array)",
! 692: "Example: RingPonIndexedVariables(\"x\",3,[[\"x[0]\",1,\"x[2]\",3]])."]]);
! 693:
! 694:
! 695: def Mod(f,n) {
! 696: if (IsPolynomial(f)) {
! 697: sm1("[(mod) ",f,n,"] gbext /FunctionValue set ");
! 698: } else if (IsInteger(f)) { return( Gmp.Mod(f,n) ); }
! 699: }
! 700: HelpAdd(["Mod",
! 701: ["Mod(f,p) returns f modulo n where << f >> (polynomial) and",
! 702: " << p >> (integer). "]]);
! 703:
! 704:
! 705:
! 706:
! 707: def Characteristic(ringp) {
! 708: local r,p;
! 709: r = sm1(" [(CurrentRingp)] system_variable ");
! 710: sm1("[(CurrentRingp) ",ringp, " ] system_variable ");
! 711: p = sm1("[(P)] system_variable (universalNumber) dc ");
! 712: sm1("[(CurrentRingp) ",r, " ] system_variable ");
! 713: return(p);
! 714: }
! 715: HelpAdd(["Characteristic",
! 716: ["Characteristic(ring) returns the characteristic of the << ring >>."
! 717: ]]);
! 718:
! 719: def IsConstant(f) {
! 720: if (Length(f) > 1) return(false);
! 721: sm1("[(isConstant) ", f," ] gbext /FunctionValue set ");
! 722: }
! 723: HelpAdd(["IsConstant",
! 724: ["IsConstant(f) returns true if the polynomial << f >> is a constant."
! 725: ]]);
! 726:
! 727: Println("Default ring is Z[x,h]."); x = Poly("x"); h = Poly("h");
! 728:
! 729: def Substitute(f,xx,g) {
! 730: local tmp, coeff0,ex,i,n,newex;
! 731: if (IsInteger(f)) return(f);
! 732: if (! IsPolynomial(f)) {
! 733: k00_error("Substitute","The first argument must be polynomial.");
! 734: }
! 735: tmp = Coefficients(f,xx);
! 736: coeff0 = tmp[1];
! 737: ex = tmp[0]; /* [3, 2, 0] */
! 738: n = Length(ex);
! 739: newex = NewVector(n);
! 740: if (n>0) { newex[n-1] = g^ex[n-1]; }
! 741: for (i=n-2; i>=0; i--) {
! 742: newex[i] = newex[i+1]*(g^(ex[i]-ex[i+1]));
! 743: }
! 744: return(Cancel(coeff0*newex));
! 745: }
! 746: HelpAdd(["Substitute",
! 747: ["Substitute(f,xx,g) replaces << xx >> in << f >> by << g >>.",
! 748: "This function takes coeffients of << f >> with respect to << xx >>",
! 749: "and returns the inner product of the vector of coefficients and the vector",
! 750: "of which elements are g^(corresponding exponent).",
! 751: "Note that it may cause an unexpected result in non-commutative rings."
! 752: ]]);
! 753:
! 754: def Tag(f) {
! 755: local ans;
! 756: if (IsArray(f)) {
! 757: return(Map(f,"Tag"));
! 758: }else {
! 759: ans = sm1(f," tag (universalNumber) dc ");
! 760: return(ans);
! 761: }
! 762: }
! 763: HelpAdd(["Tag",
! 764: ["Tag(f) returns the datatype tags of f where",
! 765: "5: string, 9: polynomial, 15: integer(big-num), 16: rational, ",
! 766: "17: object, 18:double.",
! 767: "Ex. Tag([Poly(\"0\"), 0]):"
! 768: ]]);
! 769:
! 770:
! 771:
! 772:
! 773: OutputPrompt ;
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