Annotation of OpenXM/src/k097/help.k, Revision 1.4
1.4 ! takayama 1: /* $OpenXM: OpenXM/src/k097/help.k,v 1.3 2000/12/10 09:34:27 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:
379: def DC(obj,key) {
380: if (key == "string") { return(ToString(obj)); }
381: else if (key == "integer") { key = "universalNumber"; }
382: else if (key == "sm1integer") { key = "integer"; }
383: else if (key == "polynomial") { key = "poly"; }
384: else ;
385: sm1( obj , key, " data_conversion /FunctionValue set ");
386: }
387:
388: def Transpose(m) {
389: sm1(m, " transpose /FunctionValue set ");
390: }
391:
392: def Save(obj) {
393: sm1(obj, " output ");
394: }
395:
396:
397: def void System(comm) {
398: sm1(comm, " system ");
399: }
400:
401:
402: def IsReducible(f,g) {
403: sm1("[ (isReducible) ",f,g," ] gbext /FunctionValue set ");
404: }
405:
406: def IsPolynomial(f) {
407: sm1(" f isPolynomial /FunctionValue set ");
408: }
409: sm1(" /k00.toric0.mydegree {2 1 roll degree} def ");
410: def Exponent(f,vars) {
411: local n,i,ans;
412: if (f == Poly("0")) return([ ] );
413: sm1(f," /ff.tmp set ", vars ,
414: " {ff.tmp k00.toric0.mydegree (universalNumber) dc }map /FunctionValue set ");
415: }
416: def void Protect(name,level) {
417: local n,str;
418: n = Length(Arglist);
419: if (n == 1) {
420: level = 1;
421: str = AddString(["[(chattr) ",ToString(level)," /",name," ",
422: " ] extension pop "]);
423: /* Println(str); */
424: sm1(" [(parse) ",str ," ] extension pop ");
425: } else if (n ==2) {
426: str = AddString(["[(chattr) ",ToString(level)," /",name," ",
427: " ] extension pop "]);
428: /* Println(str); */
429: sm1(" [(parse) ",str ," ] extension pop ");
430: } else {
431: k00_error("Protect","Arguments must be one or two. ");sm1(" error ");
432: }
433: }
434:
435: def void k00_error(name,msg) {
436: Print("Error in "); Print(name); Print(". ");
437: Println(msg);
438: }
439:
440: def Init(f) {
441: if (IsArray(f)) {
442: return(Map(f,"Init"));
443: } else if (IsPolynomial(f)) {
444: sm1(f," init /FunctionValue set ");
445: } else {
446: k00_error("Init","Argment must be polynomial or an array of polynomials");
447: sm1(" error ");
448: }
449: }
450: HelpAdd(["Init",
451: ["Init(f) returns the initial term of the polynomial <<f>> (polynomial)",
452: "Init(list) returns the array of initial terms of the array of polynomials",
453: "<< list >> (array)"]]);
454:
455: HelpAdd(["NewMatrix",
456: ["NewMatrix(m,n) returns the (m,n)-matrix (array) with the entries 0."]]);
457:
458: def Eliminatev(list,var) /* [(x-y). (y-z).] [(z) ] */
459: {
460: sm1(list, var, " eliminatev /FunctionValue set ");
461: }
462: HelpAdd(["Eliminatev",
463: ["Eliminatev(list,var) prunes polynomials in << list >>(array of polynomials)",
464: "which contains the variables in << var >> ( array of strings )",
465: "Example: Eliminatev([Poly(\" x+h \"),Poly(\" x \")],[ \"h\" ]): "]]);
466:
467: def ReducedBase(base) {
468: sm1( base, " reducedBase /FunctionValue set ");
469: }
470: HelpAdd(["ReducedBase",
471: ["ReducedBase[base] prunes redundant elements in the Grobner basis <<base>> (array)."
472: ]]);
473:
474: def IndexedVariables(name,size) {
475: local result,i,result2;
476: result = [ ];
477: for (i=0; i<size-1; i++) {
478: result = Append(result,Indexed(name,i));
479: result = Append(result,",");
480: }
481: if (size-1 >= 0) {
482: result = Append(result,Indexed(name,size-1));
483: }
484: result2 = Join(["{"],result);
485: result2 = Join(result2,["}"]);
486: return(AddString(result2));
487: }
488: HelpAdd(["IndexedVariables",
489: ["IndexedVariables(name,size) returns the string ",
490: " {name[0],name[1],...,name[size-1]} which can be used as inputs to ",
491: " the function RingD (string name, integer size).",
492: " cf. RingDonIndexedVariables.",
493: " Ex. R = RingD(IndexedVariables(\"a\",3)); ",
494: " h = Poly(\"h\");",
495: " a = NewArray(3);",
496: " for (i=0; i<3; i++) {a[i] = Poly(Indexed(\"a\",i));} ;"]]);
497:
498:
499: def RingDonIndexedVariables(vList, size, weightMatrix,pp) {
500: local myring,tmp,k00_i,argsize,vListD;
501: /* You cannot use these local varialbes as a name of global ring
502: variables. Change these names to names that start with k00_ */
503: argsize = Length(Arglist);
504: if (argsize == 1) {
505: Println("Error (IndexedRingD): ");
506: return(null);
507: }
508: if (argsize == 2) {
509: vListD = AddString(["D",vList]);
510: myring = RingD(IndexedVariables(vList,size));
511: tmp = NewArray(size);
512: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
513: sm1(vList, " (literal) dc ", tmp, " def ");
514: tmp = NewArray(size);
515: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}
516: sm1(vListD, " (literal) dc ", tmp, " def ");
517: if (SetRingVariables_Verbose) {
518: Print("Set the global variables ");
519: sm1("[(parse) ",vList," ] extension pop print ");
520: sm1("[(parse) ",vListD," ] extension pop print "); Ln();
521: }else {
522: sm1("[(parse) ",vList," ] extension pop ");
523: sm1("[(parse) ",vListD," ] extension pop ");
524: }
525: return( myring );
526: }
527: if (argsize == 3 || argsize == 4) {
528: if (argsize == 3) { pp = 0; }
529: vListD = AddString(["D",vList]);
530: myring = RingD(IndexedVariables(vList,size),weightMatrix,pp);
531: SetRingVariables();
532: tmp = NewArray(size);
533: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
534: sm1(vList, " (literal) dc ", tmp, " def ");
535: tmp = NewArray(size);
536: for (k00_i=0;k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vListD,k00_i));}
537: sm1(vListD, " (literal) dc ", tmp, " def ");
538: if (SetRingVariables_Verbose) {
539: Print("Set the global variables ");
540: sm1("[(parse) ",vList," ] extension pop print ");
541: sm1("[(parse) ",vListD," ] extension pop print "); Ln();
542: } else {
543: sm1("[(parse) ",vList," ] extension pop ");
544: sm1("[(parse) ",vListD," ] extension pop ");
545: }
546: return( myring );
547: }
548: return(-1);
549: }
550:
551: def Ringp(f) {
552: sm1(f, " (ring) dc /FunctionValue set ");
553: }
554: HelpAdd(["Ringp",
555: ["Ringp(f) ( polynomial f ) returns the ring to which the polynomial << f >>",
556: "belongs."]]);
557:
558: def Coefficients(f,v) {
559: local ans,exp;
560: ans = sm1(f,v, " coefficients ");
561: exp = ans[0];
562: exp = sm1(exp," { (universalNumber) dc } map ");
563: return([exp,ans[1]]);
564: }
565:
566: def IsInteger(a) {
567: sm1(a , " isUniversalNumber /FunctionValue set ");
568: }
569: HelpAdd(["IsInteger",
570: ["IsInteger(a) returns true if << a >> is an integer (object a).",
571: "It returns false if << a >> is not.",
572: "cf. IsSm1Integer"]]);
573:
574: def IsRational(a) {
575: sm1(a , " isRational /FunctionValue set ");
576: }
577: HelpAdd(["IsRational",
578: ["IsRational(a) returns true if << a >> is a rational (object a).",
579: "It returns false if << a >> is not."]]);
580:
581:
582: def IsDouble(a) {
583: sm1(a , " isDouble /FunctionValue set ");
584: }
585: HelpAdd(["IsDouble",
586: ["IsDouble(a) returns true if << a >> is a double (object a).",
587: "It returns false if << a >> is not."]]);
588:
589:
590: sm1(" /cs { this [ ] Cleards } def ");
591:
592:
593: def Init_w(f,vars,weight) {
594: local w,w2,w3,ans,i,n;
595: if (f == Poly("0")) return( Poly("0") );
596: w = Map(vars,"ToString");
597: w2 = sm1(weight," {$integer$ data_conversion} map ");
598: n = Length(w);
599: w3 = NewArray(n*2);
600: for (i=0; i<n ; i++) {
601: w3[2*i] = w[i]; w3[2*i+1] = w2[i];
602: }
603: ans = sm1(f,w3, " weightv init ");
604: return(ans);
605: }
606:
607: HelpAdd(["Mapto",
608: ["Mapto(obj,ring) parses << obj >> as elements of the << ring >>.",
609: "(ring << ring >>, polynomial << obj >> or array of polynomial << obj >>).",
610: "Ex. R = RingD(\"x,y\"); SetRingVariables();",
611: " f = (x+y)^2; R2 = RingD(\"x,y,z\",[[\"y\",1]]); ",
612: " f2 = Mapto(f,R2); f2: "]]);
613:
614: def Mapto(obj,ring) {
615: local ans,i,n;
616: if (IsArray(obj)) {
617: n = Length(obj);
618: ans = Map(obj,"ToString");
619: for (i=0; i<n; i++) {
620: ans[i] = PolyR(ans[i],ring);
621: }
622: }else{
623: ans = ToString(obj);
624: ans = PolyR(ans,ring);
625: }
626: return(ans);
627: }
628:
629:
630: HelpAdd(["ToDouble",
631: ["ToDouble(f) translates << f >> into double when it is possible",
632: "object << f >>.",
633: "Example: ToDouble([1,1/2,[5]]): "]]);
634: def k00_toDouble(f) { return(DC(f,"double")); }
635: def ToDouble(f) {
636: if (IsArray(f)) return(Map(f,"ToDouble"));
637: if (IsDouble(f)) return(f);
638: return(k00_toDouble(f));
639: }
640:
641:
642: def RingPonIndexedVariables(vList, size, weightMatrix) {
643: local myring,tmp,k00_i,argsize,vListD;
644: /* You cannot use these local varialbes as a name of global ring
645: variables. Change these names to names that start with k00_ */
646: argsize = Length(Arglist);
647: if (argsize == 1) {
648: Println("Error (RingPonIndexedVariables): ");
649: return(null);
650: }
651: if (argsize == 2) {
652: myring = RingPoly(IndexedVariables(vList,size));
653: SetRingVariables();
654: tmp = NewArray(size);
655: for (k00_i=0; k00_i<size; k00_i++) {tmp[k00_i]=Poly(Indexed(vList,k00_i));}
656: sm1(vList, " (literal) dc ", tmp, " def ");
657: if (SetRingVariables_Verbose) {
658: Print("Set the global variables ");
659: sm1("[(parse) ",vList," ] extension pop print "); Ln();
660: }else {
661: sm1("[(parse) ",vList," ] extension pop ");
662: }
663: return( myring );
664: }
665: if (argsize == 3) {
666: myring = RingPoly(IndexedVariables(vList,size),weightMatrix);
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: return(-1);
680: }
681:
682: HelpAdd(["RingPonIndexedVariables",
683: ["RingPonIndexedVariables(name,n) defines and returns the ring of",
684: "polynomials",
685: "Q<h, name[0], ..., name[n-1] >",
686: "where <<name>> is a string and <<n>> is an integer.",
687: "Note that this function defines global variables",
688: "h, name[0], ..., name[n-1].",
689: "Example: RingPonIndexedVariables(\"x\",3).",
690: "RingPonIndexedVariables(name,n,w) defines and returns the ring of",
691: "polynomials with the ordering defined by ",
692: "the weight vector <<w>> (array)",
693: "Example: RingPonIndexedVariables(\"x\",3,[[\"x[0]\",1,\"x[2]\",3]])."]]);
694:
695:
696: def Mod(f,n) {
697: if (IsPolynomial(f)) {
698: sm1("[(mod) ",f,n,"] gbext /FunctionValue set ");
699: } else if (IsInteger(f)) { return( Gmp.Mod(f,n) ); }
700: }
701: HelpAdd(["Mod",
702: ["Mod(f,p) returns f modulo n where << f >> (polynomial) and",
703: " << p >> (integer). "]]);
704:
705:
706:
707:
708: def Characteristic(ringp) {
709: local r,p;
710: r = sm1(" [(CurrentRingp)] system_variable ");
711: sm1("[(CurrentRingp) ",ringp, " ] system_variable ");
712: p = sm1("[(P)] system_variable (universalNumber) dc ");
713: sm1("[(CurrentRingp) ",r, " ] system_variable ");
714: return(p);
715: }
716: HelpAdd(["Characteristic",
717: ["Characteristic(ring) returns the characteristic of the << ring >>."
718: ]]);
719:
720: def IsConstant(f) {
721: if (Length(f) > 1) return(false);
722: sm1("[(isConstant) ", f," ] gbext /FunctionValue set ");
723: }
724: HelpAdd(["IsConstant",
725: ["IsConstant(f) returns true if the polynomial << f >> is a constant."
726: ]]);
727:
728: Println("Default ring is Z[x,h]."); x = Poly("x"); h = Poly("h");
729:
730: def Substitute(f,xx,g) {
731: local tmp, coeff0,ex,i,n,newex;
732: if (IsInteger(f)) return(f);
733: if (! IsPolynomial(f)) {
734: k00_error("Substitute","The first argument must be polynomial.");
735: }
736: tmp = Coefficients(f,xx);
737: coeff0 = tmp[1];
738: ex = tmp[0]; /* [3, 2, 0] */
739: n = Length(ex);
740: newex = NewVector(n);
741: if (n>0) { newex[n-1] = g^ex[n-1]; }
742: for (i=n-2; i>=0; i--) {
743: newex[i] = newex[i+1]*(g^(ex[i]-ex[i+1]));
744: }
745: return(Cancel(coeff0*newex));
746: }
747: HelpAdd(["Substitute",
748: ["Substitute(f,xx,g) replaces << xx >> in << f >> by << g >>.",
749: "This function takes coeffients of << f >> with respect to << xx >>",
750: "and returns the inner product of the vector of coefficients and the vector",
751: "of which elements are g^(corresponding exponent).",
752: "Note that it may cause an unexpected result in non-commutative rings."
753: ]]);
754:
755: def Tag(f) {
756: local ans;
757: if (IsArray(f)) {
758: return(Map(f,"Tag"));
759: }else {
1.4 ! takayama 760: ans = sm1(f," etag (universalNumber) dc ");
1.1 maekawa 761: return(ans);
762: }
763: }
764: HelpAdd(["Tag",
765: ["Tag(f) returns the datatype tags of f where",
766: "5: string, 9: polynomial, 15: integer(big-num), 16: rational, ",
1.4 ! takayama 767: "18:double, 257: Error ",
1.1 maekawa 768: "Ex. Tag([Poly(\"0\"), 0]):"
769: ]]);
770:
1.4 ! takayama 771: def Error(s) {
! 772: sm1(" s error ");
! 773: }
! 774: HelpAdd(["Error",
! 775: ["Error(s) causes an error and outputs a message s."]]);
1.1 maekawa 776:
777: OutputPrompt ;
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