1: # The LearningOnline Network with CAPA - LON-CAPA
2: # Parsed tree node
3: #
4: # Copyright (C) 2014 Michigan State University Board of Trustees
5: #
6: # This program is free software: you can redistribute it and/or modify
7: # it under the terms of the GNU General Public License as published by
8: # the Free Software Foundation, either version 3 of the License, or
9: # (at your option) any later version.
10: #
11: # This program is distributed in the hope that it will be useful,
12: # but WITHOUT ANY WARRANTY; without even the implied warranty of
13: # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14: # GNU General Public License for more details.
15: #
16: # You should have received a copy of the GNU General Public License
17: # along with this program. If not, see <http://www.gnu.org/licenses/>.
18: #
19:
20: ##
21: # Parsed tree node. ENode.toMathML(hcolors) contains the code for the transformation into MathML.
22: ##
23: package Apache::math_parser::ENode;
24:
25: use strict;
26: use warnings;
27: use utf8;
28:
29: use Switch 'Perl6';
30:
31: use aliased 'Apache::math_parser::CalcException';
32: use aliased 'Apache::math_parser::Operator';
33: use aliased 'Apache::math_parser::ParseException';
34: use aliased 'Apache::math_parser::QMatrix';
35: use aliased 'Apache::math_parser::Quantity';
36: use aliased 'Apache::math_parser::QVector';
37: use aliased 'Apache::math_parser::QInterval';
38: use aliased 'Apache::math_parser::QIntervalUnion';
39: use aliased 'Apache::math_parser::QSet';
40: use aliased 'Apache::math_parser::Units';
41:
42: use enum qw(UNKNOWN NAME NUMBER OPERATOR FUNCTION VECTOR INTERVAL SET SUBSCRIPT);
43: use enum qw(NOT_AN_INTERVAL OPEN_OPEN OPEN_CLOSED CLOSED_OPEN CLOSED_CLOSED);
44:
45: ##
46: # @param {integer} type - UNKNOWN | NAME | NUMBER | OPERATOR | FUNCTION | VECTOR | INTERVAL | SET | SUBSCRIPT
47: # @param {Operator} op - The operator
48: # @param {string} value - Node value as a string, undef for type VECTOR
49: # @param {ENode[]} children - The children nodes, only for types OPERATOR, FUNCTION, VECTOR, INTERVAL, SET, SUBSCRIPT
50: # @param {interval_type} - The interval type, NOT_AN_INTERVAL | OPEN_OPEN | OPEN_CLOSED | CLOSED_OPEN | CLOSED_CLOSED
51: ##
52: sub new {
53: my $class = shift;
54: my $self = {
55: _type => shift,
56: _op => shift,
57: _value => shift,
58: _children => shift,
59: _interval_type => shift // NOT_AN_INTERVAL,
60: };
61: bless $self, $class;
62: return $self;
63: }
64:
65: # Attribute helpers
66:
67: ##
68: # Node type
69: # @returns {int} UNKNOWN | NAME | NUMBER | OPERATOR | FUNCTION | VECTOR | INTERVAL | SET | SUBSCRIPT
70: ##
71: sub type {
72: my $self = shift;
73: return $self->{_type};
74: }
75:
76: ##
77: # Operator
78: # @returns {Operator}
79: ##
80: sub op {
81: my $self = shift;
82: return $self->{_op};
83: }
84:
85: ##
86: # Node value as a string, undef for type VECTOR.
87: # @returns {string}
88: ##
89: sub value {
90: my $self = shift;
91: return $self->{_value};
92: }
93:
94: ##
95: # The children nodes, only for types OPERATOR, FUNCTION, VECTOR, INTERVAL, SET, SUBSCRIPT
96: # @returns {ENode[]}
97: ##
98: sub children {
99: my $self = shift;
100: return $self->{_children};
101: }
102:
103: ##
104: # The interval type, NOT_AN_INTERVAL | OPEN_OPEN | OPEN_CLOSED | CLOSED_OPEN | CLOSED_CLOSED
105: # @returns {int}
106: ##
107: sub interval_type {
108: my $self = shift;
109: return $self->{_interval_type};
110: }
111:
112:
113: ##
114: # Returns the node as a string, for debug
115: # @returns {string}
116: ##
117: sub toString {
118: my ( $self ) = @_;
119: my $s = '(';
120: given ($self->type) {
121: when (UNKNOWN) { $s .= "UNKNOWN"; }
122: when (NAME) { $s .= "NAME"; }
123: when (NUMBER) { $s .= "NUMBER"; }
124: when (OPERATOR) { $s .= "OPERATOR"; }
125: when (FUNCTION) { $s .= "FUNCTION"; }
126: when (VECTOR) { $s .= "VECTOR"; }
127: when (INTERVAL) { $s .= "INTERVAL"; }
128: when (SET) { $s .= "SET"; }
129: when (SUBSCRIPT) { $s .= "SUBSCRIPT"; }
130: }
131: if (defined $self->op) {
132: $s .= " '" . $self->op->id . "'";
133: }
134: if (defined $self->value) {
135: $s .= " '" . $self->value . "'";
136: }
137: if (defined $self->{_children}) {
138: $s .= ' [';
139: for (my $i = 0; $i < scalar(@{$self->children}); $i++) {
140: $s .= $self->children->[$i]->toString();
141: if ($i != scalar(@{$self->children}) - 1) {
142: $s .= ',';
143: }
144: }
145: $s .= ']';
146: }
147: if (defined $self->interval_type) {
148: $s .= " " . $self->interval_type;
149: }
150: $s.= ')';
151: return $s;
152: }
153:
154: ##
155: # Evaluates the node, returning a quantity or an object from a more complex class using quantities as base components.
156: # Can throw a CalcException if a result cannot be calculated.
157: # @param {CalcEnv} env - Calculation environment.
158: # @returns {Quantity|QVector|QMatrix|QSet|QInterval|QIntervalUnion}
159: ##
160: sub calc {
161: my ( $self, $env ) = @_;
162:
163: given ($self->type) {
164: when (UNKNOWN) {
165: die CalcException->new("Unknown node type: [_1].", $self->value);
166: }
167: when (NAME) {
168: my $name = $self->value;
169: if ($name =~ /^inf$/i) {
170: return Quantity->new(9**9**9);
171: } elsif ($name =~ /^nan$/i) {
172: return Quantity->new(-sin(9**9**9));
173: }
174: if ($env->unit_mode) {
175: my $cst = $env->getConstant($name);
176: if (defined $cst) {
177: return $cst;
178: }
179: return $env->convertToSI($name);
180: } else {
181: my $q = $env->getVariable($name);
182: if (!defined $q) {
183: my $cst = $env->getConstant($name);
184: if (defined $cst) {
185: return $cst;
186: }
187: die CalcException->new("Variable has undefined value: [_1].", $name);
188: }
189: return $q;
190: }
191: }
192: when (NUMBER) {
193: return Quantity->new($self->value);
194: }
195: when (OPERATOR) {
196: my @children = @{$self->children};
197: my ($q1, $q2);
198: if (defined $children[0]) {
199: $q1 = $children[0]->calc($env);
200: }
201: if (defined $children[1]) {
202: $q2 = $children[1]->calc($env);
203: }
204: given ($self->value) {
205: when ("+") {
206: if (!overload::Method($q1, '+')) {
207: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
208: }
209: return($q1 + $q2);
210: }
211: when ("-") {
212: if (!defined $q2) {
213: if (!$q1->can('qneg')) {
214: die CalcException->new("Negation is not implemented for this type.");
215: }
216: return($q1->qneg());
217: } else {
218: if (!overload::Method($q1, '-')) {
219: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
220: }
221: return($q1 - $q2);
222: }
223: }
224: when ("*") {
225: if (!overload::Method($q1, '*')) {
226: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
227: }
228: return($q1 * $q2);
229: }
230: when ("/") {
231: if (!overload::Method($q1, '/')) {
232: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
233: }
234: return($q1 / $q2);
235: }
236: when ("^") {
237: if (!overload::Method($q1, '^')) {
238: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
239: }
240: return($q1 ^ $q2);
241: }
242: when ("!") {
243: if (!$q1->can('qfact')) {
244: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
245: }
246: return $q1->qfact();
247: }
248: when ("%") {
249: if (!$q1->isa(Quantity) || !$q2->isa(Quantity)) {
250: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
251: }
252: return(($q1 / Quantity->new(100)) * $q2);
253: }
254: when (".") {
255: # scalar product for vectors, multiplication for matrices
256: if (!$q1->can('qdot')) {
257: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
258: }
259: return($q1->qdot($children[1]->calc($env)));
260: }
261: when ("`") {
262: if (!overload::Method($q1, '*')) {
263: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
264: }
265: return($q1 * $q2);
266: }
267: when ("=") {
268: if (!$q1->can('qeq')) {
269: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
270: }
271: return($q1->qeq($q2, $env->tolerance));
272: }
273: when ("<") {
274: if (!overload::Method($q1, '<')) {
275: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
276: }
277: return($q1 < $q2);
278: }
279: when ("<=") {
280: if (!overload::Method($q1, '<=')) {
281: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
282: }
283: return($q1 <= $q2);
284: }
285: when (">") {
286: if (!overload::Method($q1, '>')) {
287: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
288: }
289: return($q1 > $q2);
290: }
291: when (">=") {
292: if (!overload::Method($q1, '>=')) {
293: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
294: }
295: return($q1 >= $q2);
296: }
297: default {
298: die CalcException->new("Unknown operator: [_1].", $self->value);
299: }
300: }
301: }
302: when (FUNCTION) {
303: my @children = @{$self->children};
304: my $fname = $children[0]->value;
305:
306: if (!defined $children[1]) {
307: die CalcException->new("Missing parameter for function [_1].", $fname);
308: }
309: my ($q1, $q2);
310: if ($fname ~~ ['pow', 'sqrt', 'abs', 'exp', 'ln', 'log', 'log10', 'factorial',
311: 'mod', 'sgn', 'ceil', 'floor', 'sin', 'cos', 'tan', 'asin', 'acos', 'atan',
312: 'atan2', 'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh']) {
313: $q1 = $children[1]->calc($env);
314: if (!$q1->isa(Quantity)) {
315: die CalcException->new("The [_1] function is not implemented for this type.", $fname);
316: }
317: }
318: if ($fname ~~ ['pow', 'mod', 'atan2']) {
319: if (!defined $children[2]) {
320: die CalcException->new("Missing parameter for function [_1].", $fname);
321: }
322: $q2 = $children[2]->calc($env);
323: if (!$q2->isa(Quantity)) {
324: die CalcException->new("The [_1] function is not implemented for this type.", $fname);
325: }
326: }
327: given ($fname) {
328: when ("matrix") { return $self->createVectorOrMatrix($env); }
329: when ("pow") { return $q1->qpow($q2); }
330: when ("sqrt") { return $q1->qsqrt(); }
331: when ("abs") { return $q1->qabs(); }
332: when ("exp") { return $q1->qexp(); }
333: when ("ln") { return $q1->qln(); }
334: when ("log") { return $q1->qln(); }
335: when ("log10") { return $q1->qlog10(); }
336: when ("factorial") { return $q1->qfact(); }
337: when ("mod") { return $q1->qmod($q2); }
338: when ("sgn") { return $q1->qsgn(); }
339: when ("ceil") { return $q1->qceil(); }
340: when ("floor") { return $q1->qfloor(); }
341: when ("sin") { return $q1->qsin(); }
342: when ("cos") { return $q1->qcos(); }
343: when ("tan") { return $q1->qtan(); }
344: when ("asin") { return $q1->qasin(); }
345: when ("acos") { return $q1->qacos(); }
346: when ("atan") { return $q1->qatan(); }
347: when ("atan2") { return $q1->qatan2($q2); }
348: when ("sinh") { return $q1->qsinh(); }
349: when ("cosh") { return $q1->qcosh(); }
350: when ("tanh") { return $q1->qtanh(); }
351: when ("asinh") { return $q1->qasinh(); }
352: when ("acosh") { return $q1->qacosh(); }
353: when ("atanh") { return $q1->qatanh(); }
354: when (["sum","product"]) {
355: if ($env->unit_mode) {
356: die CalcException->new("[_1] cannot work in unit mode.", $fname);
357: }
358: if (scalar(@children) != 5) {
359: die CalcException->new("[_1] should have four parameters.", $fname);
360: }
361: my $var = "".$children[2]->value;
362: if ($var !~ /^[a-zA-Z_][a-zA-Z_0-9]*$/) {
363: die CalcException->new("[_1]: wrong variable name", $fname);
364: }
365: if ($var eq "i") {
366: die CalcException->new("[_1]: please use another variable name, i is the imaginary number.", $fname);
367: }
368: my $initial = $env->getVariable($var);
369: my $var_value_1 = $children[3]->value;
370: my $var_value_2 = $children[4]->value;
371: if ($var_value_1 !~ /^[0-9]+$/) {
372: die CalcException->new("[_1]: the third parameter should be an integer", $fname);
373: }
374: if ($var_value_2 !~ /^[0-9]+$/) {
375: die CalcException->new("[_1]: the fourth parameter should be an integer", $fname);
376: }
377: if ($var_value_1 > $var_value_2) {
378: die CalcException->new("[_1]: are you trying to make me loop forever?", $fname);
379: }
380: my $result;
381: for (my $var_value=$var_value_1; $var_value <= $var_value_2; $var_value++) {
382: $env->setVariable($var, $var_value);
383: my $nq = $children[1]->calc($env);
384: if (!$nq->isa(Quantity) && !$nq->isa(QVector) && !$nq->isa(QMatrix)) {
385: die CalcException->new("[_1]: wrong type for a calculated value", $fname);
386: }
387: if (!defined $result) {
388: $result = $nq;
389: } elsif ($fname eq "sum") {
390: $result += $nq;
391: } else {
392: $result *= $nq;
393: }
394: }
395: $env->setVariable($var, $initial);
396: return $result;
397: }
398: when ("binomial") {
399: if (scalar(@children) != 3) {
400: die CalcException->new("[_1] should have two parameters.", $fname);
401: }
402: my $n = $children[1]->calc($env);
403: my $p = $children[2]->calc($env);
404: if (!$n->isa(Quantity) || !$p->isa(Quantity)) {
405: die CalcException->new("Wrong parameter type for function [_1]", $fname);
406: }
407: return $n->qfact() / ($p->qfact() * ($n - $p)->qfact());
408: }
409: when (["union","intersection"]) {
410: if (!defined $children[2]) {
411: die CalcException->new("Missing parameter for function [_1].", $fname);
412: }
413: my $p1 = $children[1]->calc($env);
414: my $p2 = $children[2]->calc($env);
415: if (!$p1->isa(QSet) && !$p1->isa(QInterval) && !$p1->isa(QIntervalUnion)) {
416: die CalcException->new("Wrong type for function [_1] (should be a set or interval).", $fname);
417: }
418: if ($fname eq "union") {
419: return $p1->union($p2);
420: } else {
421: return $p1->intersection($p2);
422: }
423: }
424: default { die CalcException->new("Unknown function: [_1].",$fname); }
425: }
426: }
427: when (VECTOR) {
428: return $self->createVectorOrMatrix($env);
429: }
430: when (INTERVAL) {
431: my @children = @{$self->children};
432: if (scalar(@children) != 2) {
433: die CalcException->new("Interval should have two parameters.");
434: }
435: my $qmin = $children[0]->calc($env);
436: my $qmax = $children[1]->calc($env);
437: my ($qminopen, $qmaxopen);
438: given ($self->interval_type) {
439: when (OPEN_OPEN) { $qminopen = 1; $qmaxopen = 1; }
440: when (OPEN_CLOSED) { $qminopen = 1; $qmaxopen = 0; }
441: when (CLOSED_OPEN) { $qminopen = 0; $qmaxopen = 1; }
442: when (CLOSED_CLOSED) { $qminopen = 0; $qmaxopen = 0; }
443: }
444: return QInterval->new($qmin, $qmax, $qminopen, $qmaxopen);
445: }
446: when (SET) {
447: my @t = ();
448: foreach my $child (@{$self->children}) {
449: push(@t, $child->calc($env));
450: }
451: return QSet->new(\@t);
452: }
453: when (SUBSCRIPT) {
454: die CalcException->new("Subscript cannot be evaluated: [_1].", $self->value);
455: }
456: }
457: }
458:
459: ##
460: # Returns the equation as a string with the Maxima syntax.
461: # @returns {string}
462: ##
463: sub toMaxima {
464: my ( $self, $env ) = @_;
465:
466: given ($self->type) {
467: when (UNKNOWN) {
468: die CalcException->new("Unknown node type: [_1].", $self->value);
469: }
470: when (NAME) {
471: my $name = $self->value;
472: my $cst = $env->getConstant($name);
473: if (defined $cst) {
474: return $cst;
475: }
476: return($name);
477: }
478: when (NUMBER) {
479: if ($self->value eq "i") {
480: return "%i";
481: } else {
482: return $self->value;
483: }
484: }
485: when (OPERATOR) {
486: my @children = @{$self->children};
487: given ($self->value) {
488: when ("+") {
489: if ($children[0]->type == SET && $children[1]->type == SET) {
490: return("union(".$children[0]->toMaxima().", ".$children[1]->toMaxima().")");
491: } else {
492: return("(".$children[0]->toMaxima()."+".$children[1]->toMaxima().")");
493: }
494: }
495: when ("-") {
496: if (!defined $children[1]) {
497: return("(-".$children[0]->toMaxima().")");
498: } else {
499: return("(".$children[0]->toMaxima()."-".$children[1]->toMaxima().")");
500: }
501: }
502: when ("*") {
503: return("(".$children[0]->toMaxima()."*".$children[1]->toMaxima().")");
504: }
505: when ("/") {
506: return("(".$children[0]->toMaxima()."/".$children[1]->toMaxima().")");
507: }
508: when ("^") {
509: return("(".$children[0]->toMaxima()."^".$children[1]->toMaxima().")");
510: }
511: when ("!") {
512: return("factorial(".$children[0]->toMaxima().")");
513: }
514: when ("%") {
515: return("((".$children[0]->toMaxima()."/100)*".$children[1]->toMaxima().")");
516: }
517: when (".") {
518: # scalar product for vectors, multiplication for matrices
519: return("(".$children[0]->toMaxima().".".$children[1]->toMaxima().")");
520: }
521: when ("`") {
522: return("(".$children[0]->toMaxima()."`".$children[1]->toMaxima().")");
523: }
524: when ("=") {
525: # NOTE: should we use is(...) to evaluate the expression ?
526: return("(".$children[0]->toMaxima()."=".$children[1]->toMaxima().")");
527: }
528: when ("<") {
529: return("(".$children[0]->toMaxima()."<".$children[1]->toMaxima().")");
530: }
531: when (">") {
532: return("(".$children[0]->toMaxima().">".$children[1]->toMaxima().")");
533: }
534: when ("<=") {
535: return("(".$children[0]->toMaxima()."<=".$children[1]->toMaxima().")");
536: }
537: when (">=") {
538: return("(".$children[0]->toMaxima().">=".$children[1]->toMaxima().")");
539: }
540: default {
541: die CalcException->new("Unknown operator: [_1].", $self->value);
542: }
543: }
544: }
545: when (FUNCTION) {
546: my @children = @{$self->children};
547: my $fname = $children[0]->value;
548:
549: given ($fname) {
550: when ("log10") { return "log(".$children[1]->toMaxima().")/log(10)"; }
551: when ("sgn") { return "signum(".$children[1]->toMaxima().")"; }
552: when ("ceil") { return "ceiling(".$children[1]->toMaxima().")"; }
553: default {
554: my $s = $fname."(";
555: for (my $i=1; $i<scalar(@children); $i++) {
556: if ($i != 1) {
557: $s .= ", ";
558: }
559: $s .= $children[$i]->toMaxima();
560: }
561: $s .= ")";
562: return($s);
563: }
564: }
565: }
566: when (VECTOR) {
567: my @children = @{$self->children};
568: my $s;
569: if ($children[0]->type == VECTOR) {
570: $s = "matrix(";
571: } else {
572: $s = "[";
573: }
574: for (my $i=0; $i<scalar(@children); $i++) {
575: if ($i != 0) {
576: $s .= ", ";
577: }
578: $s .= $children[$i]->toMaxima();
579: }
580: if ($children[0]->type == VECTOR) {
581: $s .= ")";
582: } else {
583: $s .= "]";
584: }
585: return($s);
586: }
587: when (INTERVAL) {
588: die CalcException->new("Maxima syntax: intervals are not implemented.");
589: # see http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=5959544
590: # "New Package in Maxima for Single-Valued Interval Computation on Real Numbers"
591: }
592: when (SET) {
593: my @children = @{$self->children};
594: my $s = "{";
595: for (my $i=0; $i<scalar(@children); $i++) {
596: if ($i != 0) {
597: $s .= ", ";
598: }
599: $s .= $children[$i]->toMaxima();
600: }
601: $s .= "}";
602: return($s);
603: }
604: when (SUBSCRIPT) {
605: my @children = @{$self->children};
606: return("(".$children[0]->toMaxima()."_".$children[1]->toMaxima().")");
607: }
608: }
609: }
610:
611: ##
612: # Returns the equation as a string with the TeX syntax.
613: # @returns {string}
614: ##
615: sub toTeX {
616: my ( $self ) = @_;
617:
618: given ($self->type) {
619: when (UNKNOWN) {
620: die CalcException->new("Unknown node type: [_1].", $self->value);
621: }
622: when (NAME) {
623: my $name = $self->value;
624: if ($name =~ /^([a-zA-Z]+)([0-9]+)$/) {
625: return($1."_{".$2."}");
626: }
627: my @greek = (
628: "alpha", "beta", "gamma", "delta", "epsilon", "zeta",
629: "eta", "theta", "iota", "kappa", "lambda", "mu",
630: "nu", "xi", "omicron", "pi", "rho", "sigma",
631: "tau", "upsilon", "phi", "chi", "psi", "omega",
632: "Alpha", "Beta", "Gamma", "Delta", "Epsilon", "Zeta",
633: "Eta", "Theta", "Iota", "Kappa", "Lambda", "Mu",
634: "Nu", "Xi", "Omicron", "Pi", "Rho", "Sigma",
635: "Tau", "Upsilon", "Phi", "Chi", "Psi", "Omega",
636: );
637: if ($name ~~ @greek) {
638: return('\\'.$name);
639: } elsif ($name eq "hbar") {
640: return("\\hbar");
641: } elsif ($name eq "inf") {
642: return("\\infty");
643: } elsif ($name eq "minf") {
644: return("-\\infty");
645: } else {
646: return($name);
647: }
648: }
649: when (NUMBER) {
650: return $self->value;
651: }
652: when (OPERATOR) {
653: my @children = @{$self->children};
654: my $c0 = $children[0];
655: my $c1 = $children[1];
656: given ($self->value) {
657: when ("+") {
658: # should we add parenthesis ? We need to check if there is a '-' to the left of c1
659: my $par = 0;
660: my $first = $c1;
661: while ($first->type == OPERATOR) {
662: if ($first->value eq "-" && scalar(@{$first->children}) == 1) {
663: $par = 1;
664: last;
665: } elsif ($first->value eq "+" || $first->value eq "-" || $first->value eq "*") {
666: $first = $first->children->[0];
667: } else {
668: last;
669: }
670: }
671: my $s = $c0->toTeX()." + ".$c1->toTeX();
672: if ($par) {
673: $s = "(".$s.")";
674: }
675: return $s;
676: }
677: when ("-") {
678: if (!defined $c1) {
679: return("-".$c0->toTeX());
680: } else {
681: my $s = $c0->toTeX()." - ";
682: my $par = ($c1->type == OPERATOR &&
683: ($c1->value eq "+" || $c1->value eq "-"));
684: if ($par) {
685: $s .= "(".$c1->toTeX().")";
686: } else {
687: $s .= $c1->toTeX();
688: }
689: return $s;
690: }
691: }
692: when ("*") {
693: my $par = ($c0->type == OPERATOR && ($c0->value eq "+" || $c0->value eq "-"));
694: my $s = $c0->toTeX();
695: if ($par) {
696: $s = "(".$s.")";
697: }
698: # should the x operator be visible ? We need to check if there is a number to the left of c1
699: my $firstinc1 = $c1;
700: while ($firstinc1->type == OPERATOR) {
701: $firstinc1 = $firstinc1->children->[0];
702: }
703: # ... and if it's an operation between vectors/matrices, the * operator should be displayed
704: # (it is ambiguous otherwise)
705: # note: this will not work if the matrix is calculated, for instance with 2[1;2]*[3;4]
706: if ($c0->type == VECTOR && $c1->type == VECTOR) {
707: $s .= " * ";
708: } elsif ($firstinc1->type == NUMBER) {
709: $s .= " \\times ";
710: } else {
711: $s .= " ";
712: }
713: $par = ($c1->type == OPERATOR && ($c1->value eq "+" || $c1->value eq "-"));
714: if ($par) {
715: $s .= "(".$c1->toTeX().")";
716: } else {
717: $s .= $c1->toTeX();
718: }
719: return $s;
720: }
721: when ("/") {
722: # NOTE: cfrac would be better but tth does not handle it
723: return("\\frac{".$c0->toTeX()."}{".$c1->toTeX()."}");
724: }
725: when ("^") {
726: my $par;
727: if ($c0->type == FUNCTION) {
728: if ($c0->value eq "sqrt" || $c0->value eq "abs" || $c0->value eq "matrix" ||
729: $c0->value eq "diff") {
730: $par = 0;
731: } else {
732: $par = 1;
733: }
734: } elsif ($c0->type == OPERATOR) {
735: $par = 1;
736: } else {
737: $par = 0;
738: }
739: if ($par) {
740: return("(".$c0->toTeX().")^{".$c1->toTeX()."}");
741: } else {
742: return($c0->toTeX()."^{".$c1->toTeX()."}");
743: }
744: }
745: when ("!") {
746: return($c0->toTeX()." !");
747: }
748: when ("%") {
749: return($c0->toTeX()." \\% ".$c1->toTeX());
750: }
751: when (".") {
752: # scalar product for vectors, multiplication for matrices
753: my $par = ($c0->type == OPERATOR && ($c0->value eq "+" || $c0->value eq "-"));
754: my $s = $c0->toTeX();
755: if ($par) {
756: $s = "(".$s.")";
757: }
758: $s .= " \\cdot ";
759: $par = ($c1->type == OPERATOR && ($c1->value eq "+" || $c1->value eq "-"));
760: if ($par) {
761: $s .= "(".$c1->toTeX().")";
762: } else {
763: $s .= $c1->toTeX();
764: }
765: return $s;
766: }
767: when ("`") {
768: return($c0->toTeX()." \\mathrm{".$c1->toTeX()."}");
769: }
770: when ("=") {
771: return($c0->toTeX()." = ".$c1->toTeX());
772: }
773: when ("#") {
774: return($c0->toTeX()." \\not ".$c1->toTeX());
775: }
776: when ("<") {
777: return($c0->toTeX()." < ".$c1->toTeX());
778: }
779: when (">") {
780: return($c0->toTeX()." > ".$c1->toTeX());
781: }
782: when ("<=") {
783: return($c0->toTeX()." \\leq ".$c1->toTeX());
784: }
785: when (">=") {
786: return($c0->toTeX()." \\geq ".$c1->toTeX());
787: }
788: default {
789: die CalcException->new("Unknown operator: [_1].", $self->value);
790: }
791: }
792: }
793: when (FUNCTION) {
794: my @children = @{$self->children};
795: my $fname = $children[0]->value;
796: my $c1 = $children[1];
797: my $c2 = $children[2];
798: my $c3 = $children[3];
799: my $c4 = $children[4];
800:
801: given ($fname) {
802: when ("sqrt") { return "\\sqrt{".$c1->toTeX()."}"; }
803: when ("abs") { return "|".$c1->toTeX()."|"; }
804: when ("exp") { return "\\mathrm{e}^{".$c1->toTeX()."}"; }
805: when ("diff") {
806: if (scalar(@children) == 3) {
807: return "\\frac{d}{d".$c2->toTeX()."} ".$c1->toTeX();
808: } else {
809: return "\\frac{d^{".$c3->toTeX()."}}{d ".$c2->toTeX().
810: "^{".$c3->toTeX()."}} ".$c1->toTeX();
811: }
812: }
813: when ("integrate") {
814: if (scalar(@children) == 3) {
815: return "\\int ".$c1->toTeX()." \\ d ".$c2->toTeX();
816: } else {
817: return "\\int_{".$c3->toTeX()."}^{".$c4->toTeX()."} ".
818: $c1->toTeX()." \\ d ".$c2->toTeX();
819: }
820: }
821: when ("sum") {
822: return "\\sum_{".$c2->toTeX()."=".$c3->toTeX().
823: "}^{".$c4->toTeX()."} ".$c1->toTeX();
824: }
825: when ("product") {
826: return "\\prod_{".$c2->toTeX()."=".$c3->toTeX().
827: "}^{".$c4->toTeX()."} ".$c1->toTeX();
828: }
829: when ("limit") {
830: if (scalar(@children) < 4) {
831: return "\\lim ".$c1->toTeX();
832: } elsif (scalar(@children) == 4) {
833: return "\\lim_{".$c2->toTeX()." \\to ".$c3->toTeX().
834: "}".$c1->toTeX();
835: } else {
836: return "\\lim_{".$c2->toTeX()." \\to ".$c3->toTeX().
837: (($c4->value eq "plus") ? "+" : "-").
838: "}".$c1->toTeX();
839: }
840: }
841: when ("binomial") {
842: return "\\binom{".$c1->toTeX()."}{".$c2->toTeX()."}";
843: }
844: when (["union","intersection"]) {
845: if (!defined $children[2]) {
846: die CalcException->new("Missing parameter for function [_1].", $fname);
847: }
848: if ($c1->type != SET && $c1->type != INTERVAL && $c1->type != FUNCTION) {
849: die CalcException->new("Wrong type for function [_1] (should be a set or interval).", $fname);
850: }
851: if ($fname eq "union") {
852: return $c1->toTeX().' \cup '.$c2->toTeX();
853: } else {
854: return $c1->toTeX().' \cap '.$c2->toTeX();
855: }
856: }
857: when ("sin") { return "\\sin ".$c1->toTeX(); }
858: when ("cos") { return "\\cos ".$c1->toTeX(); }
859: when ("tan") { return "\\tan ".$c1->toTeX(); }
860: when ("asin") { return "\\arcsin ".$c1->toTeX(); }
861: when ("acos") { return "\\arccos ".$c1->toTeX(); }
862: when ("atan") { return "\\arctan ".$c1->toTeX(); }
863: when ("sinh") { return "\\sinh ".$c1->toTeX(); }
864: when ("cosh") { return "\\cosh ".$c1->toTeX(); }
865: when ("tanh") { return "\\tanh ".$c1->toTeX(); }
866: default {
867: my $s = $fname."(";
868: for (my $i=1; $i<scalar(@children); $i++) {
869: if ($i != 1) {
870: $s .= ", ";
871: }
872: $s .= $children[$i]->toTeX();
873: }
874: $s .= ")";
875: return($s);
876: }
877: }
878: }
879: when (VECTOR) {
880: my @children = @{$self->children};
881: # my $s = "\\begin{pmatrix}";
882: # NOTE: pmatrix would be easier, but tth does not recognize it
883: my $col;
884: if (scalar(@children) == 0) {
885: $col = 0;
886: } elsif ($children[0]->type == VECTOR) {
887: $col = scalar(@{$children[0]->children});
888: } else {
889: $col = 1;
890: }
891: my $s = "\\left( \\begin{array}{".('c' x $col)."}";
892: for (my $i=0; $i<scalar(@children); $i++) {
893: if ($i != 0) {
894: $s .= " \\\\ ";
895: }
896: if ($children[0]->type == VECTOR) {
897: # matrix
898: for (my $j=0; $j<scalar(@{$children[$i]->children}); $j++) {
899: if ($j != 0) {
900: $s .= " & ";
901: }
902: $s .= $children[$i]->children->[$j]->toTeX();
903: }
904: } else {
905: # vector
906: $s .= $children[$i]->toTeX();
907: }
908: }
909: # $s .= "\\end{pmatrix}";
910: $s .= "\\end{array} \\right)";
911: return($s);
912: }
913: when (INTERVAL) {
914: my @children = @{$self->children};
915: if (scalar(@children) != 2) {
916: die CalcException->new("Interval should have two parameters.");
917: }
918: my ($qminopen, $qmaxopen);
919: given ($self->interval_type) {
920: when (OPEN_OPEN) { $qminopen = 1; $qmaxopen = 1; }
921: when (OPEN_CLOSED) { $qminopen = 1; $qmaxopen = 0; }
922: when (CLOSED_OPEN) { $qminopen = 0; $qmaxopen = 1; }
923: when (CLOSED_CLOSED) { $qminopen = 0; $qmaxopen = 0; }
924: }
925: my $s = "\\left";
926: if ($qminopen) {
927: $s .= "(";
928: } else {
929: $s .= "[";
930: }
931: $s .= $children[0]->toTeX();
932: $s .= ", ";
933: $s .= $children[1]->toTeX();
934: $s .= "\\right";
935: if ($qmaxopen) {
936: $s .= ")";
937: } else {
938: $s .= "]";
939: }
940: return($s);
941: }
942: when (SET) {
943: my @children = @{$self->children};
944: my $s = "\\left\\{ {";
945: for (my $i=0; $i<scalar(@children); $i++) {
946: if ($i != 0) {
947: $s .= ", ";
948: }
949: $s .= $children[$i]->toTeX();
950: }
951: $s .= "}\\right\\}";
952: return($s);
953: }
954: when (SUBSCRIPT) {
955: my @children = @{$self->children};
956: return($children[0]->toTeX()."_{".$children[1]->toTeX()."}");
957: }
958: }
959: }
960: ##
961: # Creates a vector or a matrix with this node
962: # @param {CalcEnv} env - Calculation environment.
963: # @returns {QVector|QMatrix}
964: ##
965: sub createVectorOrMatrix {
966: my ( $self, $env ) = @_;
967: my @children = @{$self->children};
968: my @t = (); # 1d or 2d array of Quantity
969: my $start;
970: if ($self->type == FUNCTION) {
971: $start = 1;
972: } else {
973: $start = 0;
974: }
975: my $nb1;
976: for (my $i=0; $i < scalar(@children) - $start; $i++) {
977: my $qv = $children[$i+$start]->calc($env);
978: my $nb2;
979: if ($qv->isa(Quantity)) {
980: $nb2 = 1;
981: } else {
982: $nb2 = scalar(@{$qv->quantities});
983: }
984: if (!defined $nb1) {
985: $nb1 = $nb2;
986: } elsif ($nb2 != $nb1) {
987: die CalcException->new("Inconsistent number of elements in a matrix.");
988: }
989: if ($qv->isa(Quantity)) {
990: $t[$i] = $qv;
991: } else {
992: $t[$i] = [];
993: for (my $j=0; $j < scalar(@{$qv->quantities}); $j++) {
994: $t[$i][$j] = $qv->quantities->[$j];
995: }
996: }
997: }
998: if (ref($t[0]) eq 'ARRAY') {
999: return QMatrix->new(\@t);
1000: } else {
1001: return QVector->new(\@t);
1002: }
1003: }
1004:
1005: 1;
1006: __END__
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