Annotation of OpenXM/src/k097/help.k, Revision 1.5
1.5 ! takayama 1: /* $OpenXM: OpenXM/src/k097/help.k,v 1.4 2000/12/12 13:58:21 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:
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 ");
1.3 takayama 334: SetRingVariables();
1.1 maekawa 335: return(tmp);
336: } else ;
337: if (argsize == 2) {
338: pp = 0;
339: }
340: pp = IntegerToSm1Integer(pp);
341: size = Length(weightMatrix);
342: new0 = NewVector(size);
343: sm1(" /@@@.indexMode.flag.save @@@.indexMode.flag def ");
344: sm1(" 0 @@@.indexMode ");
345: for (i=0; i<size; i++) {
346: tmp = weightMatrix[i];
347: n = Length(tmp);
348: newtmp = NewVector(n);
349: for (j=1; j<n; j = j+2) {
350: newtmp[j-1] = tmp[j-1];
351: newtmp[j] = IntegerToSm1Integer( tmp[j] );
352: }
353: new0[i] = newtmp;
354: }
1.3 takayama 355: SetRingVariables();
1.1 maekawa 356: ringpp =
357: sm1("[", vList,
358: "ring_of_polynomials ", new0, " weight_vector", pp, " ] define_ring");
359: sm1(" @@@.indexMode.flag.save @@@.indexMode ");
360: return( ringpp );
361: }
362:
363: def IsString(ob) {
364: sm1(ob , " isString /FunctionValue set ");
365: }
366:
367: def IsSm1Integer(ob) {
368: sm1(ob , " isInteger /FunctionValue set ");
369: }
370:
371:
372: def CancelNumber(rn) {
373: local tmp;
374: sm1(" [(cancel) ",rn," ] mpzext /tmp set ");
375: if (IsInteger(tmp)) return(tmp);
376: sm1(" tmp (denominator) dc (1).. eq { /FunctionValue tmp (numerator) dc def} { /FunctionValue tmp def } ifelse ");
377: }
378:
1.5 ! takayama 379: def DC_polynomial(obj) {
! 380: return(DC(obj,"polynomial"));
! 381: }
1.1 maekawa 382: def DC(obj,key) {
1.5 ! takayama 383: if (IsArray(obj) && key=="polynomial") {
! 384: return(Map(obj,"DC_polynomial"));
! 385: }
1.1 maekawa 386: if (key == "string") { return(ToString(obj)); }
387: else if (key == "integer") { key = "universalNumber"; }
388: else if (key == "sm1integer") { key = "integer"; }
389: else if (key == "polynomial") { key = "poly"; }
390: else ;
391: sm1( obj , key, " data_conversion /FunctionValue set ");
392: }
393:
394: def Transpose(m) {
395: sm1(m, " transpose /FunctionValue set ");
396: }
397:
398: def Save(obj) {
399: sm1(obj, " output ");
400: }
401:
402:
403: def void System(comm) {
404: sm1(comm, " system ");
405: }
406:
407:
408: def IsReducible(f,g) {
409: sm1("[ (isReducible) ",f,g," ] gbext /FunctionValue set ");
410: }
411:
412: def IsPolynomial(f) {
413: sm1(" f isPolynomial /FunctionValue set ");
414: }
415: sm1(" /k00.toric0.mydegree {2 1 roll degree} def ");
416: def Exponent(f,vars) {
417: local n,i,ans;
418: if (f == Poly("0")) return([ ] );
419: sm1(f," /ff.tmp set ", vars ,
420: " {ff.tmp k00.toric0.mydegree (universalNumber) dc }map /FunctionValue set ");
421: }
422: def void Protect(name,level) {
423: local n,str;
424: n = Length(Arglist);
425: if (n == 1) {
426: level = 1;
427: str = AddString(["[(chattr) ",ToString(level)," /",name," ",
428: " ] extension pop "]);
429: /* Println(str); */
430: sm1(" [(parse) ",str ," ] extension pop ");
431: } else if (n ==2) {
432: str = AddString(["[(chattr) ",ToString(level)," /",name," ",
433: " ] extension pop "]);
434: /* Println(str); */
435: sm1(" [(parse) ",str ," ] extension pop ");
436: } else {
437: k00_error("Protect","Arguments must be one or two. ");sm1(" error ");
438: }
439: }
440:
441: def void k00_error(name,msg) {
442: Print("Error in "); Print(name); Print(". ");
443: Println(msg);
444: }
445:
446: def Init(f) {
447: if (IsArray(f)) {
448: return(Map(f,"Init"));
449: } else if (IsPolynomial(f)) {
450: sm1(f," init /FunctionValue set ");
451: } else {
452: k00_error("Init","Argment must be polynomial or an array of polynomials");
453: sm1(" error ");
454: }
455: }
456: HelpAdd(["Init",
457: ["Init(f) returns the initial term of the polynomial <<f>> (polynomial)",
458: "Init(list) returns the array of initial terms of the array of polynomials",
459: "<< list >> (array)"]]);
460:
461: HelpAdd(["NewMatrix",
462: ["NewMatrix(m,n) returns the (m,n)-matrix (array) with the entries 0."]]);
463:
464: def Eliminatev(list,var) /* [(x-y). (y-z).] [(z) ] */
465: {
466: sm1(list, var, " eliminatev /FunctionValue set ");
467: }
468: HelpAdd(["Eliminatev",
469: ["Eliminatev(list,var) prunes polynomials in << list >>(array of polynomials)",
470: "which contains the variables in << var >> ( array of strings )",
471: "Example: Eliminatev([Poly(\" x+h \"),Poly(\" x \")],[ \"h\" ]): "]]);
472:
473: def ReducedBase(base) {
474: sm1( base, " reducedBase /FunctionValue set ");
475: }
476: HelpAdd(["ReducedBase",
477: ["ReducedBase[base] prunes redundant elements in the Grobner basis <<base>> (array)."
478: ]]);
479:
480: def IndexedVariables(name,size) {
481: local result,i,result2;
482: result = [ ];
483: for (i=0; i<size-1; i++) {
484: result = Append(result,Indexed(name,i));
485: result = Append(result,",");
486: }
487: if (size-1 >= 0) {
488: result = Append(result,Indexed(name,size-1));
489: }
490: result2 = Join(["{"],result);
491: result2 = Join(result2,["}"]);
492: return(AddString(result2));
493: }
494: HelpAdd(["IndexedVariables",
495: ["IndexedVariables(name,size) returns the string ",
496: " {name[0],name[1],...,name[size-1]} which can be used as inputs to ",
497: " the function RingD (string name, integer size).",
498: " cf. RingDonIndexedVariables.",
499: " Ex. R = RingD(IndexedVariables(\"a\",3)); ",
500: " h = Poly(\"h\");",
501: " a = NewArray(3);",
502: " for (i=0; i<3; i++) {a[i] = Poly(Indexed(\"a\",i));} ;"]]);
503:
504:
505: def RingDonIndexedVariables(vList, size, weightMatrix,pp) {
506: local myring,tmp,k00_i,argsize,vListD;
507: /* You cannot use these local varialbes as a name of global ring
508: variables. Change these names to names that start with k00_ */
509: argsize = Length(Arglist);
510: if (argsize == 1) {
511: Println("Error (IndexedRingD): ");
512: return(null);
513: }
514: if (argsize == 2) {
515: vListD = AddString(["D",vList]);
516: myring = RingD(IndexedVariables(vList,size));
517: tmp = NewArray(size);
518: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
519: sm1(vList, " (literal) dc ", tmp, " def ");
520: tmp = NewArray(size);
521: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}
522: sm1(vListD, " (literal) dc ", tmp, " def ");
523: if (SetRingVariables_Verbose) {
524: Print("Set the global variables ");
525: sm1("[(parse) ",vList," ] extension pop print ");
526: sm1("[(parse) ",vListD," ] extension pop print "); Ln();
527: }else {
528: sm1("[(parse) ",vList," ] extension pop ");
529: sm1("[(parse) ",vListD," ] extension pop ");
530: }
531: return( myring );
532: }
533: if (argsize == 3 || argsize == 4) {
534: if (argsize == 3) { pp = 0; }
535: vListD = AddString(["D",vList]);
536: myring = RingD(IndexedVariables(vList,size),weightMatrix,pp);
537: SetRingVariables();
538: tmp = NewArray(size);
539: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
540: sm1(vList, " (literal) dc ", tmp, " def ");
541: tmp = NewArray(size);
542: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}
543: sm1(vListD, " (literal) dc ", tmp, " def ");
544: if (SetRingVariables_Verbose) {
545: Print("Set the global variables ");
546: sm1("[(parse) ",vList," ] extension pop print ");
547: sm1("[(parse) ",vListD," ] extension pop print "); Ln();
548: } else {
549: sm1("[(parse) ",vList," ] extension pop ");
550: sm1("[(parse) ",vListD," ] extension pop ");
551: }
552: return( myring );
553: }
554: return(-1);
555: }
556:
557: def Ringp(f) {
558: sm1(f, " (ring) dc /FunctionValue set ");
559: }
560: HelpAdd(["Ringp",
561: ["Ringp(f) ( polynomial f ) returns the ring to which the polynomial << f >>",
562: "belongs."]]);
563:
564: def Coefficients(f,v) {
565: local ans,exp;
566: ans = sm1(f,v, " coefficients ");
567: exp = ans[0];
568: exp = sm1(exp," { (universalNumber) dc } map ");
569: return([exp,ans[1]]);
570: }
571:
572: def IsInteger(a) {
573: sm1(a , " isUniversalNumber /FunctionValue set ");
574: }
575: HelpAdd(["IsInteger",
576: ["IsInteger(a) returns true if << a >> is an integer (object a).",
577: "It returns false if << a >> is not.",
578: "cf. IsSm1Integer"]]);
579:
580: def IsRational(a) {
581: sm1(a , " isRational /FunctionValue set ");
582: }
583: HelpAdd(["IsRational",
584: ["IsRational(a) returns true if << a >> is a rational (object a).",
585: "It returns false if << a >> is not."]]);
586:
587:
588: def IsDouble(a) {
589: sm1(a , " isDouble /FunctionValue set ");
590: }
591: HelpAdd(["IsDouble",
592: ["IsDouble(a) returns true if << a >> is a double (object a).",
593: "It returns false if << a >> is not."]]);
594:
595:
596: sm1(" /cs { this [ ] Cleards } def ");
597:
598:
599: def Init_w(f,vars,weight) {
600: local w,w2,w3,ans,i,n;
601: if (f == Poly("0")) return( Poly("0") );
602: w = Map(vars,"ToString");
603: w2 = sm1(weight," {$integer$ data_conversion} map ");
604: n = Length(w);
605: w3 = NewArray(n*2);
606: for (i=0; i<n ; i++) {
607: w3[2*i] = w[i]; w3[2*i+1] = w2[i];
608: }
609: ans = sm1(f,w3, " weightv init ");
610: return(ans);
611: }
612:
613: HelpAdd(["Mapto",
614: ["Mapto(obj,ring) parses << obj >> as elements of the << ring >>.",
615: "(ring << ring >>, polynomial << obj >> or array of polynomial << obj >>).",
616: "Ex. R = RingD(\"x,y\"); SetRingVariables();",
617: " f = (x+y)^2; R2 = RingD(\"x,y,z\",[[\"y\",1]]); ",
618: " f2 = Mapto(f,R2); f2: "]]);
619:
620: def Mapto(obj,ring) {
621: local ans,i,n;
622: if (IsArray(obj)) {
623: n = Length(obj);
624: ans = Map(obj,"ToString");
625: for (i=0; i<n; i++) {
626: ans[i] = PolyR(ans[i],ring);
627: }
628: }else{
629: ans = ToString(obj);
630: ans = PolyR(ans,ring);
631: }
632: return(ans);
633: }
634:
635:
636: HelpAdd(["ToDouble",
637: ["ToDouble(f) translates << f >> into double when it is possible",
638: "object << f >>.",
639: "Example: ToDouble([1,1/2,[5]]): "]]);
640: def k00_toDouble(f) { return(DC(f,"double")); }
641: def ToDouble(f) {
642: if (IsArray(f)) return(Map(f,"ToDouble"));
643: if (IsDouble(f)) return(f);
644: return(k00_toDouble(f));
645: }
646:
647:
648: def RingPonIndexedVariables(vList, size, weightMatrix) {
649: local myring,tmp,k00_i,argsize,vListD;
650: /* You cannot use these local varialbes as a name of global ring
651: variables. Change these names to names that start with k00_ */
652: argsize = Length(Arglist);
653: if (argsize == 1) {
654: Println("Error (RingPonIndexedVariables): ");
655: return(null);
656: }
657: if (argsize == 2) {
658: myring = RingPoly(IndexedVariables(vList,size));
659: SetRingVariables();
660: tmp = NewArray(size);
661: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
662: sm1(vList, " (literal) dc ", tmp, " def ");
663: if (SetRingVariables_Verbose) {
664: Print("Set the global variables ");
665: sm1("[(parse) ",vList," ] extension pop print "); Ln();
666: }else {
667: sm1("[(parse) ",vList," ] extension pop ");
668: }
669: return( myring );
670: }
671: if (argsize == 3) {
672: myring = RingPoly(IndexedVariables(vList,size),weightMatrix);
673: SetRingVariables();
674: tmp = NewArray(size);
675: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
676: sm1(vList, " (literal) dc ", tmp, " def ");
677: if (SetRingVariables_Verbose) {
678: Print("Set the global variables ");
679: sm1("[(parse) ",vList," ] extension pop print "); Ln();
680: } else {
681: sm1("[(parse) ",vList," ] extension pop ");
682: }
683: return( myring );
684: }
685: return(-1);
686: }
687:
688: HelpAdd(["RingPonIndexedVariables",
689: ["RingPonIndexedVariables(name,n) defines and returns the ring of",
690: "polynomials",
691: "Q<h, name[0], ..., name[n-1] >",
692: "where <<name>> is a string and <<n>> is an integer.",
693: "Note that this function defines global variables",
694: "h, name[0], ..., name[n-1].",
695: "Example: RingPonIndexedVariables(\"x\",3).",
696: "RingPonIndexedVariables(name,n,w) defines and returns the ring of",
697: "polynomials with the ordering defined by ",
698: "the weight vector <<w>> (array)",
699: "Example: RingPonIndexedVariables(\"x\",3,[[\"x[0]\",1,\"x[2]\",3]])."]]);
700:
701:
702: def Mod(f,n) {
703: if (IsPolynomial(f)) {
704: sm1("[(mod) ",f,n,"] gbext /FunctionValue set ");
705: } else if (IsInteger(f)) { return( Gmp.Mod(f,n) ); }
706: }
707: HelpAdd(["Mod",
708: ["Mod(f,p) returns f modulo n where << f >> (polynomial) and",
709: " << p >> (integer). "]]);
710:
711:
712:
713:
714: def Characteristic(ringp) {
715: local r,p;
716: r = sm1(" [(CurrentRingp)] system_variable ");
717: sm1("[(CurrentRingp) ",ringp, " ] system_variable ");
718: p = sm1("[(P)] system_variable (universalNumber) dc ");
719: sm1("[(CurrentRingp) ",r, " ] system_variable ");
720: return(p);
721: }
722: HelpAdd(["Characteristic",
723: ["Characteristic(ring) returns the characteristic of the << ring >>."
724: ]]);
725:
726: def IsConstant(f) {
727: if (Length(f) > 1) return(false);
728: sm1("[(isConstant) ", f," ] gbext /FunctionValue set ");
729: }
730: HelpAdd(["IsConstant",
731: ["IsConstant(f) returns true if the polynomial << f >> is a constant."
732: ]]);
733:
734: Println("Default ring is Z[x,h]."); x = Poly("x"); h = Poly("h");
735:
736: def Substitute(f,xx,g) {
737: local tmp, coeff0,ex,i,n,newex;
738: if (IsInteger(f)) return(f);
739: if (! IsPolynomial(f)) {
740: k00_error("Substitute","The first argument must be polynomial.");
741: }
742: tmp = Coefficients(f,xx);
743: coeff0 = tmp[1];
744: ex = tmp[0]; /* [3, 2, 0] */
745: n = Length(ex);
746: newex = NewVector(n);
747: if (n>0) { newex[n-1] = g^ex[n-1]; }
748: for (i=n-2; i>=0; i--) {
749: newex[i] = newex[i+1]*(g^(ex[i]-ex[i+1]));
750: }
751: return(Cancel(coeff0*newex));
752: }
753: HelpAdd(["Substitute",
754: ["Substitute(f,xx,g) replaces << xx >> in << f >> by << g >>.",
755: "This function takes coeffients of << f >> with respect to << xx >>",
756: "and returns the inner product of the vector of coefficients and the vector",
757: "of which elements are g^(corresponding exponent).",
758: "Note that it may cause an unexpected result in non-commutative rings."
759: ]]);
760:
761: def Tag(f) {
762: local ans;
763: if (IsArray(f)) {
764: return(Map(f,"Tag"));
765: }else {
1.4 takayama 766: ans = sm1(f," etag (universalNumber) dc ");
1.1 maekawa 767: return(ans);
768: }
769: }
770: HelpAdd(["Tag",
771: ["Tag(f) returns the datatype tags of f where",
772: "5: string, 9: polynomial, 15: integer(big-num), 16: rational, ",
1.4 takayama 773: "18:double, 257: Error ",
1.1 maekawa 774: "Ex. Tag([Poly(\"0\"), 0]):"
775: ]]);
776:
1.4 takayama 777: def Error(s) {
778: sm1(" s error ");
779: }
780: HelpAdd(["Error",
781: ["Error(s) causes an error and outputs a message s."]]);
1.1 maekawa 782:
783: OutputPrompt ;
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