Annotation of OpenXM/src/k097/help.k, Revision 1.1.1.1
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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