Annotation of OpenXM/src/k097/help.k, Revision 1.8
1.8 ! takayama 1: /* $OpenXM: OpenXM/src/k097/help.k,v 1.7 2001/01/04 12:29:31 takayama Exp $ */
1.1 maekawa 2: if (K00_verbose)
1.8 ! takayama 3: Println("help.k: 8/6, 1996 --- 8/7, 1996. 3/6, 1997 --- 12/21, 1997.");
1.1 maekawa 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",
1.7 takayama 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); "]]);
1.1 maekawa 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)."]);
1.7 takayama 188: HelpAdd(["Replace",
189: ["Replace(f,rule) (polynomial f, array rule). ",
190: "Ex. Replace( (x+y)^3, [[x,Poly(\"1\")]])"]]);
1.1 maekawa 191: HelpAdd(["SetRingVariables",
192: "SetRingVariables()
193: Set the generators of the current ring as global variables.
194: cf. RingD(), Poly(), PolyR()"]);
195: HelpAdd(["Append","Append([f1,...,fn],g) returns the list [f1,...,fn,g]"]);
196: HelpAdd(["Join",
197: "Join([f1,...,fn],[g1,...,gm]) returns the list
198: [f1,...,fn,g1,...,gm]"]);
199:
1.8 ! takayama 200: HelpAdd(["!ReservedNames",
1.1 maekawa 201: ["The names k00*, K00*, sm1* , arg1,arg2,arg3,arg4,....," ,
202: "Helplist, Arglist, FunctionValue,",
203: "@@@*, db.*, k.*, tmp002*, tmp00* are used for system functions."]]);
204:
205: HelpAdd(["IntegerToSm1Integer",
206: "IntegerToSm1Integer(i) translates integer i
207: to sm1.integer (integer i)."]);
208: HelpAdd(["true","true returns sm1.integer 1."]);
209: HelpAdd(["false","false returns sm1.integer 0."]);
210: HelpAdd(["IsArray",
211: ["If f is the array object, then IsArray(f) returns true,",
212: "else IsArray(f) returns false."]]);
213:
214:
215:
216: HelpAdd(["Init_w",
217: ["Init_w(f,vars,w) returns the initial terms with respect to the",
218: "weight vector <<w>> (array of integer) of the polynomial <<f>>",
219: "(polynomial). Here, <<f>> is regarded as a polynomial with respect",
220: "to the variables <<vars>> (array of polynomials).",
221: "Example: Init_w(x^2+y^2+x,[x,y],[1,1]):"]]);
222:
223:
224: HelpAdd(["Groebner",
225: ["Groebner(input) returns Groebner basis of the left module (or ideal)",
226: "defined by <<input>> (array of polynomials)",
227: "The order is that of the ring to which each element of <<input>>",
228: "belongs.",
229: "The input is automatically homogenized.",
230: "Example: RingD(\"x,y\",[[\"x\", 10, \"y\", 1]]);",
231: " Groebner([Poly(\" x^2+y^2-4\"),Poly(\" x*y-1 \")]):",
232: "cf. RingD, Homogenize"]]);
233:
234:
235: HelpAdd(["RingPoly",
236: ["RingPoly(names) defines a Ring of Polyomials (string names).",
237: "The names of variables of that ring are <<names>> and ",
238: "the homogenization variable h.",
239: "cf. SetRingVariables, RingD",
240: "Example: R=RingPoly(\"x,y\");",
241: " ",
242: "RingPoly(names,weight_vector) defines a Ring of Polynomials",
243: "with the order defined by the << weight_vector >>",
244: "(string names, array of array weight_vector).",
245: "RingPoly(names,weight_vector,characteristic)",
246: "Example: R=RingPoly(\"x,y\",[[\"x\",10,\"y\",1]]);",
247: " (x+y)^10: "]]);
248:
249:
250: HelpAdd(["CancelNumber",
251: ["CancelNumber(rn) reduces the rational number <<rn>>",
252: "(rational rn).",
253: "Example: CancelNumber( 2/6 ) : "]]);
254:
255: HelpAdd(["IsString",
256: ["IsString(obj) returns true if << obj >> is a string (object obj).",
257: "Example: if (IsString(\"abc\")) Println(\"Hello\"); ;"]]);
258:
1.6 takayama 259: HelpAdd(["IsRing",
260: ["IsRing(obj) returns true if << obj >> is a ring (object obj)."
261: ]]);
262:
1.1 maekawa 263:
264: HelpAdd(["IsSm1Integer",
265: ["IsSm1Integer(obj) returns true if << obj >> is an integer of sm1(object obj)."]]);
266:
267: HelpAdd(["sm1",
268: ["sm1(arg1,arg2,...) is used to embed sm1 native code in the kxx program.",
269: "Example: sm1( 2, 2, \" add print \"); ",
270: "Example: def myadd(a,b) { sm1(a,b,\" add /FunctionValue set \"); }" ]]);
271:
272: HelpAdd(["DC",
273: ["DC(obj,key) converts << obj >> to a new object in the primitive",
274: "class << key >> (object obj, string key)",
275: "Example: DC(\" (x+1)^10 \", \"polynomial\"): "]]);
276:
277: HelpAdd(["Length",
278: ["Length(vec) returns the length of the array << vec >>",
279: "(array vec)"]]);
280:
281: HelpAdd(["Transpose",
282: ["Transpose(m) return the transpose of the matrix << m >>",
283: "(array of array m)."]]);
284:
285: HelpAdd(["Save",
286: ["Save(obj) appends << obj >> to the file sm1out.txt (object obj)."]]);
287:
288: HelpAdd(["Coefficients",
289: ["Coefficients(f,v) returns [exponents, coefficients] of << f >>",
290: "with respect to the variable << v >>",
291: "(polynomial f,v).",
292: "Example: Coefficients(Poly(\"(x+1)^2\"),Poly(\"x\")): "]]);
293:
294: HelpAdd(["System",
295: ["System(comm) executes the unix system command << comm >>",
296: "(string comm)",
297: "Example: System(\"ls\");"]]);
298:
299: HelpAdd(["Exponent",
300: ["Expoent(f,vars) returns the vector of exponents of the polynomial f",
301: "Ex. Exponent( x^2*y-1,[x,y])"]]);
302:
303: HelpAdd(["Protect",
304: ["Protect(name) protects the symbol <<name>> (string)",
305: "Protect(name,level) protects the symbol <<name>> (string) with ",
306: "<<level>> "]]);
307:
308: HelpAdd(["IsPolynomial",
309: ["IsPolynomial(f) returns true if <<f>> (object) is a polynomial."]]);
310:
311:
312:
313: /* -----------------------------------------------
314: functions on tests. */
315: /* ------------ Developping functions --------------------- */
316:
317: def RingPoly(vList,weightMatrix,pp) {
318: local new0,tmp,size,n,i,j,newtmp,ringpp,argsize;
319: argsize = Length(Arglist);
320: if (argsize == 1) {
321: sm1("[", vList,
322: "ring_of_polynomials ( ) elimination_order 0 ] define_ring
323: /tmp set ");
1.3 takayama 324: SetRingVariables();
1.1 maekawa 325: return(tmp);
326: } else ;
327: if (argsize == 2) {
328: pp = 0;
329: }
330: pp = IntegerToSm1Integer(pp);
331: size = Length(weightMatrix);
332: new0 = NewVector(size);
333: sm1(" /@@@.indexMode.flag.save @@@.indexMode.flag def ");
334: sm1(" 0 @@@.indexMode ");
335: for (i=0; i<size; i++) {
336: tmp = weightMatrix[i];
337: n = Length(tmp);
338: newtmp = NewVector(n);
339: for (j=1; j<n; j = j+2) {
340: newtmp[j-1] = tmp[j-1];
341: newtmp[j] = IntegerToSm1Integer( tmp[j] );
342: }
343: new0[i] = newtmp;
344: }
1.3 takayama 345: SetRingVariables();
1.1 maekawa 346: ringpp =
347: sm1("[", vList,
348: "ring_of_polynomials ", new0, " weight_vector", pp, " ] define_ring");
349: sm1(" @@@.indexMode.flag.save @@@.indexMode ");
350: return( ringpp );
351: }
352:
353: def IsString(ob) {
354: sm1(ob , " isString /FunctionValue set ");
355: }
356:
357: def IsSm1Integer(ob) {
358: sm1(ob , " isInteger /FunctionValue set ");
1.6 takayama 359: }
360:
361: def IsRing(ob) {
362: sm1(ob , " isRing /FunctionValue set ");
1.1 maekawa 363: }
364:
365:
366: def CancelNumber(rn) {
367: local tmp;
368: sm1(" [(cancel) ",rn," ] mpzext /tmp set ");
369: if (IsInteger(tmp)) return(tmp);
370: sm1(" tmp (denominator) dc (1).. eq { /FunctionValue tmp (numerator) dc def} { /FunctionValue tmp def } ifelse ");
371: }
372:
1.5 takayama 373: def DC_polynomial(obj) {
374: return(DC(obj,"polynomial"));
375: }
1.1 maekawa 376: def DC(obj,key) {
1.5 takayama 377: if (IsArray(obj) && key=="polynomial") {
378: return(Map(obj,"DC_polynomial"));
379: }
1.1 maekawa 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:
475: def Ringp(f) {
476: sm1(f, " (ring) dc /FunctionValue set ");
477: }
478: HelpAdd(["Ringp",
479: ["Ringp(f) ( polynomial f ) returns the ring to which the polynomial << f >>",
480: "belongs."]]);
481:
482: def Coefficients(f,v) {
483: local ans,exp;
484: ans = sm1(f,v, " coefficients ");
485: exp = ans[0];
486: exp = sm1(exp," { (universalNumber) dc } map ");
487: return([exp,ans[1]]);
488: }
489:
490: def IsInteger(a) {
491: sm1(a , " isUniversalNumber /FunctionValue set ");
492: }
493: HelpAdd(["IsInteger",
494: ["IsInteger(a) returns true if << a >> is an integer (object a).",
495: "It returns false if << a >> is not.",
496: "cf. IsSm1Integer"]]);
497:
498: def IsRational(a) {
499: sm1(a , " isRational /FunctionValue set ");
500: }
501: HelpAdd(["IsRational",
502: ["IsRational(a) returns true if << a >> is a rational (object a).",
503: "It returns false if << a >> is not."]]);
504:
505:
506: def IsDouble(a) {
507: sm1(a , " isDouble /FunctionValue set ");
508: }
509: HelpAdd(["IsDouble",
510: ["IsDouble(a) returns true if << a >> is a double (object a).",
511: "It returns false if << a >> is not."]]);
512:
513:
514: sm1(" /cs { this [ ] Cleards } def ");
515:
516:
517: def Init_w(f,vars,weight) {
518: local w,w2,w3,ans,i,n;
519: if (f == Poly("0")) return( Poly("0") );
520: w = Map(vars,"ToString");
521: w2 = sm1(weight," {$integer$ data_conversion} map ");
522: n = Length(w);
523: w3 = NewArray(n*2);
524: for (i=0; i<n ; i++) {
525: w3[2*i] = w[i]; w3[2*i+1] = w2[i];
526: }
527: ans = sm1(f,w3, " weightv init ");
528: return(ans);
529: }
530:
531: HelpAdd(["Mapto",
532: ["Mapto(obj,ring) parses << obj >> as elements of the << ring >>.",
533: "(ring << ring >>, polynomial << obj >> or array of polynomial << obj >>).",
534: "Ex. R = RingD(\"x,y\"); SetRingVariables();",
535: " f = (x+y)^2; R2 = RingD(\"x,y,z\",[[\"y\",1]]); ",
536: " f2 = Mapto(f,R2); f2: "]]);
537:
538: def Mapto(obj,ring) {
539: local ans,i,n;
540: if (IsArray(obj)) {
541: n = Length(obj);
542: ans = Map(obj,"ToString");
543: for (i=0; i<n; i++) {
544: ans[i] = PolyR(ans[i],ring);
545: }
546: }else{
547: ans = ToString(obj);
548: ans = PolyR(ans,ring);
549: }
550: return(ans);
551: }
552:
553:
554: HelpAdd(["ToDouble",
555: ["ToDouble(f) translates << f >> into double when it is possible",
556: "object << f >>.",
557: "Example: ToDouble([1,1/2,[5]]): "]]);
558: def k00_toDouble(f) { return(DC(f,"double")); }
559: def ToDouble(f) {
560: if (IsArray(f)) return(Map(f,"ToDouble"));
561: if (IsDouble(f)) return(f);
562: return(k00_toDouble(f));
563: }
564:
565:
566:
567: def Mod(f,n) {
568: if (IsPolynomial(f)) {
569: sm1("[(mod) ",f,n,"] gbext /FunctionValue set ");
570: } else if (IsInteger(f)) { return( Gmp.Mod(f,n) ); }
571: }
572: HelpAdd(["Mod",
573: ["Mod(f,p) returns f modulo n where << f >> (polynomial) and",
574: " << p >> (integer). "]]);
575:
576:
577:
578:
579: def Characteristic(ringp) {
580: local r,p;
581: r = sm1(" [(CurrentRingp)] system_variable ");
582: sm1("[(CurrentRingp) ",ringp, " ] system_variable ");
583: p = sm1("[(P)] system_variable (universalNumber) dc ");
584: sm1("[(CurrentRingp) ",r, " ] system_variable ");
585: return(p);
586: }
587: HelpAdd(["Characteristic",
588: ["Characteristic(ring) returns the characteristic of the << ring >>."
589: ]]);
590:
591: def IsConstant(f) {
592: if (Length(f) > 1) return(false);
593: sm1("[(isConstant) ", f," ] gbext /FunctionValue set ");
594: }
595: HelpAdd(["IsConstant",
596: ["IsConstant(f) returns true if the polynomial << f >> is a constant."
597: ]]);
598:
599: Println("Default ring is Z[x,h]."); x = Poly("x"); h = Poly("h");
600:
601: def Substitute(f,xx,g) {
1.7 takayama 602: local tmp, coeff0,ex,i,n,newex,ans;
1.1 maekawa 603: if (IsInteger(f)) return(f);
1.7 takayama 604: if (IsArray(f)) {
605: n = Length(f);
606: ans = NewVector(n);
607: for (i=0; i<n; i++) {
608: ans[i] = Substitute(f[i],xx,g);
609: }
610: return(ans);
611: }
1.1 maekawa 612: if (! IsPolynomial(f)) {
613: k00_error("Substitute","The first argument must be polynomial.");
614: }
615: tmp = Coefficients(f,xx);
616: coeff0 = tmp[1];
617: ex = tmp[0]; /* [3, 2, 0] */
618: n = Length(ex);
619: newex = NewVector(n);
620: if (n>0) { newex[n-1] = g^ex[n-1]; }
621: for (i=n-2; i>=0; i--) {
622: newex[i] = newex[i+1]*(g^(ex[i]-ex[i+1]));
623: }
624: return(Cancel(coeff0*newex));
625: }
626: HelpAdd(["Substitute",
627: ["Substitute(f,xx,g) replaces << xx >> in << f >> by << g >>.",
628: "This function takes coeffients of << f >> with respect to << xx >>",
629: "and returns the inner product of the vector of coefficients and the vector",
630: "of which elements are g^(corresponding exponent).",
631: "Note that it may cause an unexpected result in non-commutative rings."
632: ]]);
633:
634: def Tag(f) {
635: local ans;
636: if (IsArray(f)) {
637: return(Map(f,"Tag"));
638: }else {
1.4 takayama 639: ans = sm1(f," etag (universalNumber) dc ");
1.1 maekawa 640: return(ans);
641: }
642: }
643: HelpAdd(["Tag",
644: ["Tag(f) returns the datatype tags of f where",
645: "5: string, 9: polynomial, 15: integer(big-num), 16: rational, ",
1.4 takayama 646: "18:double, 257: Error ",
1.1 maekawa 647: "Ex. Tag([Poly(\"0\"), 0]):"
648: ]]);
649:
1.4 takayama 650: def Error(s) {
651: sm1(" s error ");
652: }
653: HelpAdd(["Error",
654: ["Error(s) causes an error and outputs a message s."]]);
1.1 maekawa 655:
656: OutputPrompt ;
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