Annotation of OpenXM/src/k097/help.k, Revision 1.6
1.6 ! takayama 1: /* $OpenXM: OpenXM/src/k097/help.k,v 1.5 2000/12/28 00:08:13 takayama Exp $ */
1.1 maekawa 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:
1.6 ! takayama 273: HelpAdd(["IsRing",
! 274: ["IsRing(obj) returns true if << obj >> is a ring (object obj)."
! 275: ]]);
! 276:
1.1 maekawa 277:
278: HelpAdd(["IsSm1Integer",
279: ["IsSm1Integer(obj) returns true if << obj >> is an integer of sm1(object obj)."]]);
280:
281: HelpAdd(["sm1",
282: ["sm1(arg1,arg2,...) is used to embed sm1 native code in the kxx program.",
283: "Example: sm1( 2, 2, \" add print \"); ",
284: "Example: def myadd(a,b) { sm1(a,b,\" add /FunctionValue set \"); }" ]]);
285:
286: HelpAdd(["DC",
287: ["DC(obj,key) converts << obj >> to a new object in the primitive",
288: "class << key >> (object obj, string key)",
289: "Example: DC(\" (x+1)^10 \", \"polynomial\"): "]]);
290:
291: HelpAdd(["Length",
292: ["Length(vec) returns the length of the array << vec >>",
293: "(array vec)"]]);
294:
295: HelpAdd(["Transpose",
296: ["Transpose(m) return the transpose of the matrix << m >>",
297: "(array of array m)."]]);
298:
299: HelpAdd(["Save",
300: ["Save(obj) appends << obj >> to the file sm1out.txt (object obj)."]]);
301:
302: HelpAdd(["Coefficients",
303: ["Coefficients(f,v) returns [exponents, coefficients] of << f >>",
304: "with respect to the variable << v >>",
305: "(polynomial f,v).",
306: "Example: Coefficients(Poly(\"(x+1)^2\"),Poly(\"x\")): "]]);
307:
308: HelpAdd(["System",
309: ["System(comm) executes the unix system command << comm >>",
310: "(string comm)",
311: "Example: System(\"ls\");"]]);
312:
313: HelpAdd(["Exponent",
314: ["Expoent(f,vars) returns the vector of exponents of the polynomial f",
315: "Ex. Exponent( x^2*y-1,[x,y])"]]);
316:
317: HelpAdd(["Protect",
318: ["Protect(name) protects the symbol <<name>> (string)",
319: "Protect(name,level) protects the symbol <<name>> (string) with ",
320: "<<level>> "]]);
321:
322: HelpAdd(["IsPolynomial",
323: ["IsPolynomial(f) returns true if <<f>> (object) is a polynomial."]]);
324:
325:
326:
327: /* -----------------------------------------------
328: functions on tests. */
329: /* ------------ Developping functions --------------------- */
330:
331: def RingPoly(vList,weightMatrix,pp) {
332: local new0,tmp,size,n,i,j,newtmp,ringpp,argsize;
333: argsize = Length(Arglist);
334: if (argsize == 1) {
335: sm1("[", vList,
336: "ring_of_polynomials ( ) elimination_order 0 ] define_ring
337: /tmp set ");
1.3 takayama 338: SetRingVariables();
1.1 maekawa 339: return(tmp);
340: } else ;
341: if (argsize == 2) {
342: pp = 0;
343: }
344: pp = IntegerToSm1Integer(pp);
345: size = Length(weightMatrix);
346: new0 = NewVector(size);
347: sm1(" /@@@.indexMode.flag.save @@@.indexMode.flag def ");
348: sm1(" 0 @@@.indexMode ");
349: for (i=0; i<size; i++) {
350: tmp = weightMatrix[i];
351: n = Length(tmp);
352: newtmp = NewVector(n);
353: for (j=1; j<n; j = j+2) {
354: newtmp[j-1] = tmp[j-1];
355: newtmp[j] = IntegerToSm1Integer( tmp[j] );
356: }
357: new0[i] = newtmp;
358: }
1.3 takayama 359: SetRingVariables();
1.1 maekawa 360: ringpp =
361: sm1("[", vList,
362: "ring_of_polynomials ", new0, " weight_vector", pp, " ] define_ring");
363: sm1(" @@@.indexMode.flag.save @@@.indexMode ");
364: return( ringpp );
365: }
366:
367: def IsString(ob) {
368: sm1(ob , " isString /FunctionValue set ");
369: }
370:
371: def IsSm1Integer(ob) {
372: sm1(ob , " isInteger /FunctionValue set ");
1.6 ! takayama 373: }
! 374:
! 375: def IsRing(ob) {
! 376: sm1(ob , " isRing /FunctionValue set ");
1.1 maekawa 377: }
378:
379:
380: def CancelNumber(rn) {
381: local tmp;
382: sm1(" [(cancel) ",rn," ] mpzext /tmp set ");
383: if (IsInteger(tmp)) return(tmp);
384: sm1(" tmp (denominator) dc (1).. eq { /FunctionValue tmp (numerator) dc def} { /FunctionValue tmp def } ifelse ");
385: }
386:
1.5 takayama 387: def DC_polynomial(obj) {
388: return(DC(obj,"polynomial"));
389: }
1.1 maekawa 390: def DC(obj,key) {
1.5 takayama 391: if (IsArray(obj) && key=="polynomial") {
392: return(Map(obj,"DC_polynomial"));
393: }
1.1 maekawa 394: if (key == "string") { return(ToString(obj)); }
395: else if (key == "integer") { key = "universalNumber"; }
396: else if (key == "sm1integer") { key = "integer"; }
397: else if (key == "polynomial") { key = "poly"; }
398: else ;
399: sm1( obj , key, " data_conversion /FunctionValue set ");
400: }
401:
402: def Transpose(m) {
403: sm1(m, " transpose /FunctionValue set ");
404: }
405:
406: def Save(obj) {
407: sm1(obj, " output ");
408: }
409:
410:
411: def void System(comm) {
412: sm1(comm, " system ");
413: }
414:
415:
416: def IsReducible(f,g) {
417: sm1("[ (isReducible) ",f,g," ] gbext /FunctionValue set ");
418: }
419:
420: def IsPolynomial(f) {
421: sm1(" f isPolynomial /FunctionValue set ");
422: }
423: sm1(" /k00.toric0.mydegree {2 1 roll degree} def ");
424: def Exponent(f,vars) {
425: local n,i,ans;
426: if (f == Poly("0")) return([ ] );
427: sm1(f," /ff.tmp set ", vars ,
428: " {ff.tmp k00.toric0.mydegree (universalNumber) dc }map /FunctionValue set ");
429: }
430: def void Protect(name,level) {
431: local n,str;
432: n = Length(Arglist);
433: if (n == 1) {
434: level = 1;
435: str = AddString(["[(chattr) ",ToString(level)," /",name," ",
436: " ] extension pop "]);
437: /* Println(str); */
438: sm1(" [(parse) ",str ," ] extension pop ");
439: } else if (n ==2) {
440: str = AddString(["[(chattr) ",ToString(level)," /",name," ",
441: " ] extension pop "]);
442: /* Println(str); */
443: sm1(" [(parse) ",str ," ] extension pop ");
444: } else {
445: k00_error("Protect","Arguments must be one or two. ");sm1(" error ");
446: }
447: }
448:
449: def void k00_error(name,msg) {
450: Print("Error in "); Print(name); Print(". ");
451: Println(msg);
452: }
453:
454: def Init(f) {
455: if (IsArray(f)) {
456: return(Map(f,"Init"));
457: } else if (IsPolynomial(f)) {
458: sm1(f," init /FunctionValue set ");
459: } else {
460: k00_error("Init","Argment must be polynomial or an array of polynomials");
461: sm1(" error ");
462: }
463: }
464: HelpAdd(["Init",
465: ["Init(f) returns the initial term of the polynomial <<f>> (polynomial)",
466: "Init(list) returns the array of initial terms of the array of polynomials",
467: "<< list >> (array)"]]);
468:
469: HelpAdd(["NewMatrix",
470: ["NewMatrix(m,n) returns the (m,n)-matrix (array) with the entries 0."]]);
471:
472: def Eliminatev(list,var) /* [(x-y). (y-z).] [(z) ] */
473: {
474: sm1(list, var, " eliminatev /FunctionValue set ");
475: }
476: HelpAdd(["Eliminatev",
477: ["Eliminatev(list,var) prunes polynomials in << list >>(array of polynomials)",
478: "which contains the variables in << var >> ( array of strings )",
479: "Example: Eliminatev([Poly(\" x+h \"),Poly(\" x \")],[ \"h\" ]): "]]);
480:
481: def ReducedBase(base) {
482: sm1( base, " reducedBase /FunctionValue set ");
483: }
484: HelpAdd(["ReducedBase",
485: ["ReducedBase[base] prunes redundant elements in the Grobner basis <<base>> (array)."
486: ]]);
487:
488: def IndexedVariables(name,size) {
489: local result,i,result2;
490: result = [ ];
491: for (i=0; i<size-1; i++) {
492: result = Append(result,Indexed(name,i));
493: result = Append(result,",");
494: }
495: if (size-1 >= 0) {
496: result = Append(result,Indexed(name,size-1));
497: }
498: result2 = Join(["{"],result);
499: result2 = Join(result2,["}"]);
500: return(AddString(result2));
501: }
502: HelpAdd(["IndexedVariables",
503: ["IndexedVariables(name,size) returns the string ",
504: " {name[0],name[1],...,name[size-1]} which can be used as inputs to ",
505: " the function RingD (string name, integer size).",
506: " cf. RingDonIndexedVariables.",
507: " Ex. R = RingD(IndexedVariables(\"a\",3)); ",
508: " h = Poly(\"h\");",
509: " a = NewArray(3);",
510: " for (i=0; i<3; i++) {a[i] = Poly(Indexed(\"a\",i));} ;"]]);
511:
512:
513: def RingDonIndexedVariables(vList, size, weightMatrix,pp) {
514: local myring,tmp,k00_i,argsize,vListD;
515: /* You cannot use these local varialbes as a name of global ring
516: variables. Change these names to names that start with k00_ */
517: argsize = Length(Arglist);
518: if (argsize == 1) {
519: Println("Error (IndexedRingD): ");
520: return(null);
521: }
522: if (argsize == 2) {
523: vListD = AddString(["D",vList]);
524: myring = RingD(IndexedVariables(vList,size));
525: tmp = NewArray(size);
526: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
527: sm1(vList, " (literal) dc ", tmp, " def ");
528: tmp = NewArray(size);
529: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}
530: sm1(vListD, " (literal) dc ", tmp, " def ");
531: if (SetRingVariables_Verbose) {
532: Print("Set the global variables ");
533: sm1("[(parse) ",vList," ] extension pop print ");
534: sm1("[(parse) ",vListD," ] extension pop print "); Ln();
535: }else {
536: sm1("[(parse) ",vList," ] extension pop ");
537: sm1("[(parse) ",vListD," ] extension pop ");
538: }
539: return( myring );
540: }
541: if (argsize == 3 || argsize == 4) {
542: if (argsize == 3) { pp = 0; }
543: vListD = AddString(["D",vList]);
544: myring = RingD(IndexedVariables(vList,size),weightMatrix,pp);
545: SetRingVariables();
546: tmp = NewArray(size);
547: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
548: sm1(vList, " (literal) dc ", tmp, " def ");
549: tmp = NewArray(size);
550: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}
551: sm1(vListD, " (literal) dc ", tmp, " def ");
552: if (SetRingVariables_Verbose) {
553: Print("Set the global variables ");
554: sm1("[(parse) ",vList," ] extension pop print ");
555: sm1("[(parse) ",vListD," ] extension pop print "); Ln();
556: } else {
557: sm1("[(parse) ",vList," ] extension pop ");
558: sm1("[(parse) ",vListD," ] extension pop ");
559: }
560: return( myring );
561: }
562: return(-1);
563: }
564:
565: def Ringp(f) {
566: sm1(f, " (ring) dc /FunctionValue set ");
567: }
568: HelpAdd(["Ringp",
569: ["Ringp(f) ( polynomial f ) returns the ring to which the polynomial << f >>",
570: "belongs."]]);
571:
572: def Coefficients(f,v) {
573: local ans,exp;
574: ans = sm1(f,v, " coefficients ");
575: exp = ans[0];
576: exp = sm1(exp," { (universalNumber) dc } map ");
577: return([exp,ans[1]]);
578: }
579:
580: def IsInteger(a) {
581: sm1(a , " isUniversalNumber /FunctionValue set ");
582: }
583: HelpAdd(["IsInteger",
584: ["IsInteger(a) returns true if << a >> is an integer (object a).",
585: "It returns false if << a >> is not.",
586: "cf. IsSm1Integer"]]);
587:
588: def IsRational(a) {
589: sm1(a , " isRational /FunctionValue set ");
590: }
591: HelpAdd(["IsRational",
592: ["IsRational(a) returns true if << a >> is a rational (object a).",
593: "It returns false if << a >> is not."]]);
594:
595:
596: def IsDouble(a) {
597: sm1(a , " isDouble /FunctionValue set ");
598: }
599: HelpAdd(["IsDouble",
600: ["IsDouble(a) returns true if << a >> is a double (object a).",
601: "It returns false if << a >> is not."]]);
602:
603:
604: sm1(" /cs { this [ ] Cleards } def ");
605:
606:
607: def Init_w(f,vars,weight) {
608: local w,w2,w3,ans,i,n;
609: if (f == Poly("0")) return( Poly("0") );
610: w = Map(vars,"ToString");
611: w2 = sm1(weight," {$integer$ data_conversion} map ");
612: n = Length(w);
613: w3 = NewArray(n*2);
614: for (i=0; i<n ; i++) {
615: w3[2*i] = w[i]; w3[2*i+1] = w2[i];
616: }
617: ans = sm1(f,w3, " weightv init ");
618: return(ans);
619: }
620:
621: HelpAdd(["Mapto",
622: ["Mapto(obj,ring) parses << obj >> as elements of the << ring >>.",
623: "(ring << ring >>, polynomial << obj >> or array of polynomial << obj >>).",
624: "Ex. R = RingD(\"x,y\"); SetRingVariables();",
625: " f = (x+y)^2; R2 = RingD(\"x,y,z\",[[\"y\",1]]); ",
626: " f2 = Mapto(f,R2); f2: "]]);
627:
628: def Mapto(obj,ring) {
629: local ans,i,n;
630: if (IsArray(obj)) {
631: n = Length(obj);
632: ans = Map(obj,"ToString");
633: for (i=0; i<n; i++) {
634: ans[i] = PolyR(ans[i],ring);
635: }
636: }else{
637: ans = ToString(obj);
638: ans = PolyR(ans,ring);
639: }
640: return(ans);
641: }
642:
643:
644: HelpAdd(["ToDouble",
645: ["ToDouble(f) translates << f >> into double when it is possible",
646: "object << f >>.",
647: "Example: ToDouble([1,1/2,[5]]): "]]);
648: def k00_toDouble(f) { return(DC(f,"double")); }
649: def ToDouble(f) {
650: if (IsArray(f)) return(Map(f,"ToDouble"));
651: if (IsDouble(f)) return(f);
652: return(k00_toDouble(f));
653: }
654:
655:
656: def RingPonIndexedVariables(vList, size, weightMatrix) {
657: local myring,tmp,k00_i,argsize,vListD;
658: /* You cannot use these local varialbes as a name of global ring
659: variables. Change these names to names that start with k00_ */
660: argsize = Length(Arglist);
661: if (argsize == 1) {
662: Println("Error (RingPonIndexedVariables): ");
663: return(null);
664: }
665: if (argsize == 2) {
666: myring = RingPoly(IndexedVariables(vList,size));
667: SetRingVariables();
668: tmp = NewArray(size);
669: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
670: sm1(vList, " (literal) dc ", tmp, " def ");
671: if (SetRingVariables_Verbose) {
672: Print("Set the global variables ");
673: sm1("[(parse) ",vList," ] extension pop print "); Ln();
674: }else {
675: sm1("[(parse) ",vList," ] extension pop ");
676: }
677: return( myring );
678: }
679: if (argsize == 3) {
680: myring = RingPoly(IndexedVariables(vList,size),weightMatrix);
681: SetRingVariables();
682: tmp = NewArray(size);
683: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
684: sm1(vList, " (literal) dc ", tmp, " def ");
685: if (SetRingVariables_Verbose) {
686: Print("Set the global variables ");
687: sm1("[(parse) ",vList," ] extension pop print "); Ln();
688: } else {
689: sm1("[(parse) ",vList," ] extension pop ");
690: }
691: return( myring );
692: }
693: return(-1);
694: }
695:
696: HelpAdd(["RingPonIndexedVariables",
697: ["RingPonIndexedVariables(name,n) defines and returns the ring of",
698: "polynomials",
699: "Q<h, name[0], ..., name[n-1] >",
700: "where <<name>> is a string and <<n>> is an integer.",
701: "Note that this function defines global variables",
702: "h, name[0], ..., name[n-1].",
703: "Example: RingPonIndexedVariables(\"x\",3).",
704: "RingPonIndexedVariables(name,n,w) defines and returns the ring of",
705: "polynomials with the ordering defined by ",
706: "the weight vector <<w>> (array)",
707: "Example: RingPonIndexedVariables(\"x\",3,[[\"x[0]\",1,\"x[2]\",3]])."]]);
708:
709:
710: def Mod(f,n) {
711: if (IsPolynomial(f)) {
712: sm1("[(mod) ",f,n,"] gbext /FunctionValue set ");
713: } else if (IsInteger(f)) { return( Gmp.Mod(f,n) ); }
714: }
715: HelpAdd(["Mod",
716: ["Mod(f,p) returns f modulo n where << f >> (polynomial) and",
717: " << p >> (integer). "]]);
718:
719:
720:
721:
722: def Characteristic(ringp) {
723: local r,p;
724: r = sm1(" [(CurrentRingp)] system_variable ");
725: sm1("[(CurrentRingp) ",ringp, " ] system_variable ");
726: p = sm1("[(P)] system_variable (universalNumber) dc ");
727: sm1("[(CurrentRingp) ",r, " ] system_variable ");
728: return(p);
729: }
730: HelpAdd(["Characteristic",
731: ["Characteristic(ring) returns the characteristic of the << ring >>."
732: ]]);
733:
734: def IsConstant(f) {
735: if (Length(f) > 1) return(false);
736: sm1("[(isConstant) ", f," ] gbext /FunctionValue set ");
737: }
738: HelpAdd(["IsConstant",
739: ["IsConstant(f) returns true if the polynomial << f >> is a constant."
740: ]]);
741:
742: Println("Default ring is Z[x,h]."); x = Poly("x"); h = Poly("h");
743:
744: def Substitute(f,xx,g) {
745: local tmp, coeff0,ex,i,n,newex;
746: if (IsInteger(f)) return(f);
747: if (! IsPolynomial(f)) {
748: k00_error("Substitute","The first argument must be polynomial.");
749: }
750: tmp = Coefficients(f,xx);
751: coeff0 = tmp[1];
752: ex = tmp[0]; /* [3, 2, 0] */
753: n = Length(ex);
754: newex = NewVector(n);
755: if (n>0) { newex[n-1] = g^ex[n-1]; }
756: for (i=n-2; i>=0; i--) {
757: newex[i] = newex[i+1]*(g^(ex[i]-ex[i+1]));
758: }
759: return(Cancel(coeff0*newex));
760: }
761: HelpAdd(["Substitute",
762: ["Substitute(f,xx,g) replaces << xx >> in << f >> by << g >>.",
763: "This function takes coeffients of << f >> with respect to << xx >>",
764: "and returns the inner product of the vector of coefficients and the vector",
765: "of which elements are g^(corresponding exponent).",
766: "Note that it may cause an unexpected result in non-commutative rings."
767: ]]);
768:
769: def Tag(f) {
770: local ans;
771: if (IsArray(f)) {
772: return(Map(f,"Tag"));
773: }else {
1.4 takayama 774: ans = sm1(f," etag (universalNumber) dc ");
1.1 maekawa 775: return(ans);
776: }
777: }
778: HelpAdd(["Tag",
779: ["Tag(f) returns the datatype tags of f where",
780: "5: string, 9: polynomial, 15: integer(big-num), 16: rational, ",
1.4 takayama 781: "18:double, 257: Error ",
1.1 maekawa 782: "Ex. Tag([Poly(\"0\"), 0]):"
783: ]]);
784:
1.4 takayama 785: def Error(s) {
786: sm1(" s error ");
787: }
788: HelpAdd(["Error",
789: ["Error(s) causes an error and outputs a message s."]]);
1.1 maekawa 790:
791: OutputPrompt ;
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