1: # The LearningOnline Network with CAPA - LON-CAPA
2: # Parsed tree node
3: #
4: # $Id: ENode.pm,v 1.6 2023/03/13 22:31:22 raeburn Exp $
5: #
6: # Copyright (C) 2014 Michigan State University Board of Trustees
7: #
8: # This program is free software: you can redistribute it and/or modify
9: # it under the terms of the GNU General Public License as published by
10: # the Free Software Foundation, either version 3 of the License, or
11: # (at your option) any later version.
12: #
13: # This program is distributed in the hope that it will be useful,
14: # but WITHOUT ANY WARRANTY; without even the implied warranty of
15: # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16: # GNU General Public License for more details.
17: #
18: # You should have received a copy of the GNU General Public License
19: # along with this program. If not, see <http://www.gnu.org/licenses/>.
20: #
21:
22: ##
23: # Parsed tree node. ENode.toMathML(hcolors) contains the code for the transformation into MathML.
24: ##
25: package Apache::math_parser::ENode;
26:
27: use strict;
28: use warnings;
29: use utf8;
30:
31: use Switch 'Perl6';
32:
33: use aliased 'Apache::math_parser::CalcException';
34: use aliased 'Apache::math_parser::Operator';
35: use aliased 'Apache::math_parser::ParseException';
36: use aliased 'Apache::math_parser::QMatrix';
37: use aliased 'Apache::math_parser::Quantity';
38: use aliased 'Apache::math_parser::QVector';
39: use aliased 'Apache::math_parser::QInterval';
40: use aliased 'Apache::math_parser::QIntervalUnion';
41: use aliased 'Apache::math_parser::QSet';
42: use aliased 'Apache::math_parser::Units';
43:
44: use enum qw(UNKNOWN NAME NUMBER OPERATOR FUNCTION VECTOR INTERVAL SET SUBSCRIPT);
45: use enum qw(NOT_AN_INTERVAL OPEN_OPEN OPEN_CLOSED CLOSED_OPEN CLOSED_CLOSED);
46:
47: ##
48: # @param {integer} type - UNKNOWN | NAME | NUMBER | OPERATOR | FUNCTION | VECTOR | INTERVAL | SET | SUBSCRIPT
49: # @param {Operator} op - The operator
50: # @param {string} value - Node value as a string, undef for type VECTOR
51: # @param {ENode[]} children - The children nodes, only for types OPERATOR, FUNCTION, VECTOR, INTERVAL, SET, SUBSCRIPT
52: # @param {interval_type} - The interval type, NOT_AN_INTERVAL | OPEN_OPEN | OPEN_CLOSED | CLOSED_OPEN | CLOSED_CLOSED
53: ##
54: sub new {
55: my ($class, $type, $op, $value, $children, $interval_type) = @_;
56: if (!defined $interval_type) {
57: $interval_type = NOT_AN_INTERVAL;
58: }
59: my $self = {
60: _type => $type,
61: _op => $op,
62: _value => $value,
63: _children => $children,
64: _interval_type => $interval_type,
65: };
66: bless $self, $class;
67: return $self;
68: }
69:
70: # Attribute helpers
71:
72: ##
73: # Node type
74: # @returns {int} UNKNOWN | NAME | NUMBER | OPERATOR | FUNCTION | VECTOR | INTERVAL | SET | SUBSCRIPT
75: ##
76: sub type {
77: my $self = shift;
78: return $self->{_type};
79: }
80:
81: ##
82: # Operator
83: # @returns {Operator}
84: ##
85: sub op {
86: my $self = shift;
87: return $self->{_op};
88: }
89:
90: ##
91: # Node value as a string, undef for type VECTOR.
92: # @returns {string}
93: ##
94: sub value {
95: my $self = shift;
96: return $self->{_value};
97: }
98:
99: ##
100: # The children nodes, only for types OPERATOR, FUNCTION, VECTOR, INTERVAL, SET, SUBSCRIPT
101: # @returns {ENode[]}
102: ##
103: sub children {
104: my $self = shift;
105: return $self->{_children};
106: }
107:
108: ##
109: # The interval type, NOT_AN_INTERVAL | OPEN_OPEN | OPEN_CLOSED | CLOSED_OPEN | CLOSED_CLOSED
110: # @returns {int}
111: ##
112: sub interval_type {
113: my $self = shift;
114: return $self->{_interval_type};
115: }
116:
117:
118: ##
119: # Returns the node as a string, for debug
120: # @returns {string}
121: ##
122: sub toString {
123: my ( $self ) = @_;
124: my $s = '(';
125: given ($self->type) {
126: when (UNKNOWN) { $s .= "UNKNOWN"; }
127: when (NAME) { $s .= "NAME"; }
128: when (NUMBER) { $s .= "NUMBER"; }
129: when (OPERATOR) { $s .= "OPERATOR"; }
130: when (FUNCTION) { $s .= "FUNCTION"; }
131: when (VECTOR) { $s .= "VECTOR"; }
132: when (INTERVAL) { $s .= "INTERVAL"; }
133: when (SET) { $s .= "SET"; }
134: when (SUBSCRIPT) { $s .= "SUBSCRIPT"; }
135: }
136: if (defined $self->op) {
137: $s .= " '" . $self->op->id . "'";
138: }
139: if (defined $self->value) {
140: $s .= " '" . $self->value . "'";
141: }
142: if (defined $self->{_children}) {
143: $s .= ' [';
144: for (my $i = 0; $i < scalar(@{$self->children}); $i++) {
145: $s .= $self->children->[$i]->toString();
146: if ($i != scalar(@{$self->children}) - 1) {
147: $s .= ',';
148: }
149: }
150: $s .= ']';
151: }
152: if (defined $self->interval_type) {
153: $s .= " " . $self->interval_type;
154: }
155: $s.= ')';
156: return $s;
157: }
158:
159: ##
160: # Evaluates the node, returning a quantity or an object from a more complex class using quantities as base components.
161: # Can throw a CalcException if a result cannot be calculated.
162: # @param {CalcEnv} env - Calculation environment.
163: # @returns {Quantity|QVector|QMatrix|QSet|QInterval|QIntervalUnion}
164: ##
165: sub calc {
166: my ( $self, $env ) = @_;
167:
168: given ($self->type) {
169: when (UNKNOWN) {
170: die CalcException->new("Unknown node type: [_1].", $self->value);
171: }
172: when (NAME) {
173: my $name = $self->value;
174: if ($name =~ /^inf$/i) {
175: return Quantity->new(9**9**9);
176: } elsif ($name =~ /^nan$/i) {
177: return Quantity->new(-sin(9**9**9));
178: }
179: if ($env->unit_mode) {
180: my $cst = $env->getConstant($name);
181: if (defined $cst) {
182: return $cst;
183: }
184: return $env->convertToSI($name);
185: } else {
186: my $q = $env->getVariable($name);
187: if (!defined $q) {
188: my $cst = $env->getConstant($name);
189: if (defined $cst) {
190: return $cst;
191: }
192: die CalcException->new("Variable has undefined value: [_1].", $name);
193: }
194: return $q;
195: }
196: }
197: when (NUMBER) {
198: return Quantity->new($self->value);
199: }
200: when (OPERATOR) {
201: my @children = @{$self->children};
202: my ($q1, $q2);
203: if (defined $children[0]) {
204: $q1 = $children[0]->calc($env);
205: }
206: if (defined $children[1]) {
207: $q2 = $children[1]->calc($env);
208: }
209: given ($self->value) {
210: when ("+") {
211: if (!overload::Method($q1, '+')) {
212: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
213: }
214: return($q1 + $q2);
215: }
216: when ("-") {
217: if (!defined $q2) {
218: if (!$q1->can('qneg')) {
219: die CalcException->new("Negation is not implemented for this type.");
220: }
221: return($q1->qneg());
222: } else {
223: if (!overload::Method($q1, '-')) {
224: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
225: }
226: return($q1 - $q2);
227: }
228: }
229: when ("*") {
230: if (!overload::Method($q1, '*')) {
231: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
232: }
233: return($q1 * $q2);
234: }
235: when ("/") {
236: if (!overload::Method($q1, '/')) {
237: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
238: }
239: return($q1 / $q2);
240: }
241: when ("^") {
242: if (!overload::Method($q1, '^')) {
243: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
244: }
245: return($q1 ^ $q2);
246: }
247: when ("!") {
248: if (!$q1->can('qfact')) {
249: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
250: }
251: return $q1->qfact();
252: }
253: when ("%") {
254: if (!$q1->isa(Quantity) || !$q2->isa(Quantity)) {
255: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
256: }
257: return(($q1 / Quantity->new(100)) * $q2);
258: }
259: when (".") {
260: # scalar product for vectors, multiplication for matrices
261: if (!$q1->can('qdot')) {
262: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
263: }
264: return($q1->qdot($children[1]->calc($env)));
265: }
266: when ("`") {
267: if (!overload::Method($q1, '*')) {
268: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
269: }
270: return($q1 * $q2);
271: }
272: when ("=") {
273: if (!$q1->can('qeq')) {
274: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
275: }
276: return($q1->qeq($q2, $env->tolerance));
277: }
278: when ("<") {
279: if (!overload::Method($q1, '<')) {
280: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
281: }
282: return($q1 < $q2);
283: }
284: when ("<=") {
285: if (!overload::Method($q1, '<=')) {
286: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
287: }
288: return($q1 <= $q2);
289: }
290: when (">") {
291: if (!overload::Method($q1, '>')) {
292: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
293: }
294: return($q1 > $q2);
295: }
296: when (">=") {
297: if (!overload::Method($q1, '>=')) {
298: die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
299: }
300: return($q1 >= $q2);
301: }
302: default {
303: die CalcException->new("Unknown operator: [_1].", $self->value);
304: }
305: }
306: }
307: when (FUNCTION) {
308: my @children = @{$self->children};
309: my $fname = $children[0]->value;
310:
311: if (!defined $children[1]) {
312: die CalcException->new("Missing parameter for function [_1].", $fname);
313: }
314: my ($q1, $q2);
315: if (string_in_array(['pow', 'sqrt', 'abs', 'exp', 'ln', 'log', 'log10', 'factorial',
316: 'mod', 'sgn', 'ceil', 'floor', 'sin', 'cos', 'tan', 'asin', 'acos', 'atan',
317: 'atan2', 'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh'], $fname)) {
318: $q1 = $children[1]->calc($env);
319: if (!$q1->isa(Quantity)) {
320: die CalcException->new("The [_1] function is not implemented for this type.", $fname);
321: }
322: }
323: if (string_in_array(['pow', 'mod', 'atan2'], $fname)) {
324: if (!defined $children[2]) {
325: die CalcException->new("Missing parameter for function [_1].", $fname);
326: }
327: $q2 = $children[2]->calc($env);
328: if (!$q2->isa(Quantity)) {
329: die CalcException->new("The [_1] function is not implemented for this type.", $fname);
330: }
331: }
332: given ($fname) {
333: when ("matrix") { return $self->createVectorOrMatrix($env); }
334: when ("pow") { return $q1->qpow($q2); }
335: when ("sqrt") { return $q1->qsqrt(); }
336: when ("abs") { return $q1->qabs(); }
337: when ("exp") { return $q1->qexp(); }
338: when ("ln") { return $q1->qln(); }
339: when ("log") { return $q1->qln(); }
340: when ("log10") { return $q1->qlog10(); }
341: when ("factorial") { return $q1->qfact(); }
342: when ("mod") { return $q1->qmod($q2); }
343: when ("sgn") { return $q1->qsgn(); }
344: when ("ceil") { return $q1->qceil(); }
345: when ("floor") { return $q1->qfloor(); }
346: when ("sin") { return $q1->qsin(); }
347: when ("cos") { return $q1->qcos(); }
348: when ("tan") { return $q1->qtan(); }
349: when ("asin") { return $q1->qasin(); }
350: when ("acos") { return $q1->qacos(); }
351: when ("atan") { return $q1->qatan(); }
352: when ("atan2") { return $q1->qatan2($q2); }
353: when ("sinh") { return $q1->qsinh(); }
354: when ("cosh") { return $q1->qcosh(); }
355: when ("tanh") { return $q1->qtanh(); }
356: when ("asinh") { return $q1->qasinh(); }
357: when ("acosh") { return $q1->qacosh(); }
358: when ("atanh") { return $q1->qatanh(); }
359: when (["sum","product"]) {
360: if ($env->unit_mode) {
361: die CalcException->new("[_1] cannot work in unit mode.", $fname);
362: }
363: if (scalar(@children) != 5) {
364: die CalcException->new("[_1] should have four parameters.", $fname);
365: }
366: my $var = "".$children[2]->value;
367: if ($var !~ /^[a-zA-Z_][a-zA-Z_0-9]*$/) {
368: die CalcException->new("[_1]: wrong variable name", $fname);
369: }
370: if ($var eq "i") {
371: die CalcException->new("[_1]: please use another variable name, i is the imaginary number.", $fname);
372: }
373: my $initial = $env->getVariable($var);
374: my $var_value_1 = $children[3]->value;
375: my $var_value_2 = $children[4]->value;
376: if ($var_value_1 !~ /^[0-9]+$/) {
377: die CalcException->new("[_1]: the third parameter should be an integer", $fname);
378: }
379: if ($var_value_2 !~ /^[0-9]+$/) {
380: die CalcException->new("[_1]: the fourth parameter should be an integer", $fname);
381: }
382: if ($var_value_1 > $var_value_2) {
383: die CalcException->new("[_1]: are you trying to make me loop forever?", $fname);
384: }
385: my $result;
386: for (my $var_value=$var_value_1; $var_value <= $var_value_2; $var_value++) {
387: $env->setVariable($var, $var_value);
388: my $nq = $children[1]->calc($env);
389: if (!$nq->isa(Quantity) && !$nq->isa(QVector) && !$nq->isa(QMatrix)) {
390: die CalcException->new("[_1]: wrong type for a calculated value", $fname);
391: }
392: if (!defined $result) {
393: $result = $nq;
394: } elsif ($fname eq "sum") {
395: $result += $nq;
396: } else {
397: $result *= $nq;
398: }
399: }
400: $env->setVariable($var, $initial);
401: return $result;
402: }
403: when ("binomial") {
404: if (scalar(@children) != 3) {
405: die CalcException->new("[_1] should have two parameters.", $fname);
406: }
407: my $n = $children[1]->calc($env);
408: my $p = $children[2]->calc($env);
409: if (!$n->isa(Quantity) || !$p->isa(Quantity)) {
410: die CalcException->new("Wrong parameter type for function [_1]", $fname);
411: }
412: return $n->qfact() / ($p->qfact() * ($n - $p)->qfact());
413: }
414: when (["union","intersection"]) {
415: if (!defined $children[2]) {
416: die CalcException->new("Missing parameter for function [_1].", $fname);
417: }
418: my $p1 = $children[1]->calc($env);
419: my $p2 = $children[2]->calc($env);
420: if (!$p1->isa(QSet) && !$p1->isa(QInterval) && !$p1->isa(QIntervalUnion)) {
421: die CalcException->new("Wrong type for function [_1] (should be a set or interval).", $fname);
422: }
423: if ($fname eq "union") {
424: return $p1->union($p2);
425: } else {
426: return $p1->intersection($p2);
427: }
428: }
429: default { die CalcException->new("Unknown function: [_1].",$fname); }
430: }
431: }
432: when (VECTOR) {
433: return $self->createVectorOrMatrix($env);
434: }
435: when (INTERVAL) {
436: my @children = @{$self->children};
437: if (scalar(@children) != 2) {
438: die CalcException->new("Interval should have two parameters.");
439: }
440: my $qmin = $children[0]->calc($env);
441: my $qmax = $children[1]->calc($env);
442: my ($qminopen, $qmaxopen);
443: given ($self->interval_type) {
444: when (OPEN_OPEN) { $qminopen = 1; $qmaxopen = 1; }
445: when (OPEN_CLOSED) { $qminopen = 1; $qmaxopen = 0; }
446: when (CLOSED_OPEN) { $qminopen = 0; $qmaxopen = 1; }
447: when (CLOSED_CLOSED) { $qminopen = 0; $qmaxopen = 0; }
448: }
449: return QInterval->new($qmin, $qmax, $qminopen, $qmaxopen);
450: }
451: when (SET) {
452: my @t = ();
453: foreach my $child (@{$self->children}) {
454: push(@t, $child->calc($env));
455: }
456: return QSet->new(\@t);
457: }
458: when (SUBSCRIPT) {
459: die CalcException->new("Subscript cannot be evaluated: [_1].", $self->value);
460: }
461: }
462: }
463:
464: ##
465: # Returns the equation as a string with the Maxima syntax.
466: # @returns {string}
467: ##
468: sub toMaxima {
469: my ( $self, $env ) = @_;
470:
471: given ($self->type) {
472: when (UNKNOWN) {
473: die CalcException->new("Unknown node type: [_1].", $self->value);
474: }
475: when (NAME) {
476: my $name = $self->value;
477: my $cst = $env->getConstant($name);
478: if (defined $cst) {
479: return $cst;
480: }
481: return($name);
482: }
483: when (NUMBER) {
484: if ($self->value eq "i") {
485: return "%i";
486: } else {
487: return $self->value;
488: }
489: }
490: when (OPERATOR) {
491: my @children = @{$self->children};
492: given ($self->value) {
493: when ("+") {
494: if ($children[0]->type == SET && $children[1]->type == SET) {
495: return("union(".$children[0]->toMaxima().", ".$children[1]->toMaxima().")");
496: } else {
497: return("(".$children[0]->toMaxima()."+".$children[1]->toMaxima().")");
498: }
499: }
500: when ("-") {
501: if (!defined $children[1]) {
502: return("(-".$children[0]->toMaxima().")");
503: } else {
504: return("(".$children[0]->toMaxima()."-".$children[1]->toMaxima().")");
505: }
506: }
507: when ("*") {
508: return("(".$children[0]->toMaxima()."*".$children[1]->toMaxima().")");
509: }
510: when ("/") {
511: return("(".$children[0]->toMaxima()."/".$children[1]->toMaxima().")");
512: }
513: when ("^") {
514: return("(".$children[0]->toMaxima()."^".$children[1]->toMaxima().")");
515: }
516: when ("!") {
517: return("factorial(".$children[0]->toMaxima().")");
518: }
519: when ("%") {
520: return("((".$children[0]->toMaxima()."/100)*".$children[1]->toMaxima().")");
521: }
522: when (".") {
523: # scalar product for vectors, multiplication for matrices
524: return("(".$children[0]->toMaxima().".".$children[1]->toMaxima().")");
525: }
526: when ("`") {
527: return("(".$children[0]->toMaxima()."`".$children[1]->toMaxima().")");
528: }
529: when ("=") {
530: # NOTE: should we use is(...) to evaluate the expression ?
531: return("(".$children[0]->toMaxima()."=".$children[1]->toMaxima().")");
532: }
533: when ("<") {
534: return("(".$children[0]->toMaxima()."<".$children[1]->toMaxima().")");
535: }
536: when (">") {
537: return("(".$children[0]->toMaxima().">".$children[1]->toMaxima().")");
538: }
539: when ("<=") {
540: return("(".$children[0]->toMaxima()."<=".$children[1]->toMaxima().")");
541: }
542: when (">=") {
543: return("(".$children[0]->toMaxima().">=".$children[1]->toMaxima().")");
544: }
545: default {
546: die CalcException->new("Unknown operator: [_1].", $self->value);
547: }
548: }
549: }
550: when (FUNCTION) {
551: my @children = @{$self->children};
552: my $fname = $children[0]->value;
553:
554: given ($fname) {
555: when ("log10") { return "log(".$children[1]->toMaxima().")/log(10)"; }
556: when ("sgn") { return "signum(".$children[1]->toMaxima().")"; }
557: when ("ceil") { return "ceiling(".$children[1]->toMaxima().")"; }
558: default {
559: my $s = $fname."(";
560: for (my $i=1; $i<scalar(@children); $i++) {
561: if ($i != 1) {
562: $s .= ", ";
563: }
564: $s .= $children[$i]->toMaxima();
565: }
566: $s .= ")";
567: return($s);
568: }
569: }
570: }
571: when (VECTOR) {
572: my @children = @{$self->children};
573: my $s;
574: if ($children[0]->type == VECTOR) {
575: $s = "matrix(";
576: } else {
577: $s = "[";
578: }
579: for (my $i=0; $i<scalar(@children); $i++) {
580: if ($i != 0) {
581: $s .= ", ";
582: }
583: $s .= $children[$i]->toMaxima();
584: }
585: if ($children[0]->type == VECTOR) {
586: $s .= ")";
587: } else {
588: $s .= "]";
589: }
590: return($s);
591: }
592: when (INTERVAL) {
593: die CalcException->new("Maxima syntax: intervals are not implemented.");
594: # see http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=5959544
595: # "New Package in Maxima for Single-Valued Interval Computation on Real Numbers"
596: }
597: when (SET) {
598: my @children = @{$self->children};
599: my $s = "{";
600: for (my $i=0; $i<scalar(@children); $i++) {
601: if ($i != 0) {
602: $s .= ", ";
603: }
604: $s .= $children[$i]->toMaxima();
605: }
606: $s .= "}";
607: return($s);
608: }
609: when (SUBSCRIPT) {
610: my @children = @{$self->children};
611: return("(".$children[0]->toMaxima()."_".$children[1]->toMaxima().")");
612: }
613: }
614: }
615:
616: ##
617: # Returns the equation as a string with the TeX syntax.
618: # @returns {string}
619: ##
620: sub toTeX {
621: my ( $self ) = @_;
622:
623: given ($self->type) {
624: when (UNKNOWN) {
625: die CalcException->new("Unknown node type: [_1].", $self->value);
626: }
627: when (NAME) {
628: my $name = $self->value;
629: if ($name =~ /^([a-zA-Z]+)([0-9]+)$/) {
630: return($1."_{".$2."}");
631: }
632: my @greek = (
633: "alpha", "beta", "gamma", "delta", "epsilon", "zeta",
634: "eta", "theta", "iota", "kappa", "lambda", "mu",
635: "nu", "xi", "omicron", "pi", "rho", "sigma",
636: "tau", "upsilon", "phi", "chi", "psi", "omega",
637: "Alpha", "Beta", "Gamma", "Delta", "Epsilon", "Zeta",
638: "Eta", "Theta", "Iota", "Kappa", "Lambda", "Mu",
639: "Nu", "Xi", "Omicron", "Pi", "Rho", "Sigma",
640: "Tau", "Upsilon", "Phi", "Chi", "Psi", "Omega",
641: );
642: if (string_in_array(\@greek, $name)) {
643: return('\\'.$name);
644: } elsif ($name eq "hbar") {
645: return("\\hbar");
646: } elsif ($name eq "inf") {
647: return("\\infty");
648: } elsif ($name eq "minf") {
649: return("-\\infty");
650: } else {
651: return($name);
652: }
653: }
654: when (NUMBER) {
655: return $self->value;
656: }
657: when (OPERATOR) {
658: my @children = @{$self->children};
659: my $c0 = $children[0];
660: my $c1 = $children[1];
661: given ($self->value) {
662: when ("+") {
663: # should we add parenthesis ? We need to check if there is a '-' to the left of c1
664: my $par = 0;
665: my $first = $c1;
666: while ($first->type == OPERATOR) {
667: if ($first->value eq "-" && scalar(@{$first->children}) == 1) {
668: $par = 1;
669: last;
670: } elsif ($first->value eq "+" || $first->value eq "-" || $first->value eq "*") {
671: $first = $first->children->[0];
672: } else {
673: last;
674: }
675: }
676: my $s = $c0->toTeX()." + ".$c1->toTeX();
677: if ($par) {
678: $s = "(".$s.")";
679: }
680: return $s;
681: }
682: when ("-") {
683: if (!defined $c1) {
684: return("-".$c0->toTeX());
685: } else {
686: my $s = $c0->toTeX()." - ";
687: my $par = ($c1->type == OPERATOR &&
688: ($c1->value eq "+" || $c1->value eq "-"));
689: if ($par) {
690: $s .= "(".$c1->toTeX().")";
691: } else {
692: $s .= $c1->toTeX();
693: }
694: return $s;
695: }
696: }
697: when ("*") {
698: my $par = ($c0->type == OPERATOR && ($c0->value eq "+" || $c0->value eq "-"));
699: my $s = $c0->toTeX();
700: if ($par) {
701: $s = "(".$s.")";
702: }
703: # should the x operator be visible ? We need to check if there is a number to the left of c1
704: my $firstinc1 = $c1;
705: while ($firstinc1->type == OPERATOR) {
706: $firstinc1 = $firstinc1->children->[0];
707: }
708: # ... and if it's an operation between vectors/matrices, the * operator should be displayed
709: # (it is ambiguous otherwise)
710: # note: this will not work if the matrix is calculated, for instance with 2[1;2]*[3;4]
711: if ($c0->type == VECTOR && $c1->type == VECTOR) {
712: $s .= " * ";
713: } elsif ($firstinc1->type == NUMBER) {
714: $s .= " \\times ";
715: } else {
716: $s .= " ";
717: }
718: $par = ($c1->type == OPERATOR && ($c1->value eq "+" || $c1->value eq "-"));
719: if ($par) {
720: $s .= "(".$c1->toTeX().")";
721: } else {
722: $s .= $c1->toTeX();
723: }
724: return $s;
725: }
726: when ("/") {
727: # NOTE: cfrac would be better but tth does not handle it
728: return("\\frac{".$c0->toTeX()."}{".$c1->toTeX()."}");
729: }
730: when ("^") {
731: my $par;
732: if ($c0->type == FUNCTION) {
733: if ($c0->value eq "sqrt" || $c0->value eq "abs" || $c0->value eq "matrix" ||
734: $c0->value eq "diff") {
735: $par = 0;
736: } else {
737: $par = 1;
738: }
739: } elsif ($c0->type == OPERATOR) {
740: $par = 1;
741: } else {
742: $par = 0;
743: }
744: if ($par) {
745: return("(".$c0->toTeX().")^{".$c1->toTeX()."}");
746: } else {
747: return($c0->toTeX()."^{".$c1->toTeX()."}");
748: }
749: }
750: when ("!") {
751: my $s = $c0->toTeX();
752: if ($c0->type == OPERATOR) {
753: $s = "(".$s.")";
754: }
755: $s .= " !";
756: return $s;
757: }
758: when ("%") {
759: return($c0->toTeX()." \\% ".$c1->toTeX());
760: }
761: when (".") {
762: # scalar product for vectors, multiplication for matrices
763: my $par = ($c0->type == OPERATOR && ($c0->value eq "+" || $c0->value eq "-"));
764: my $s = $c0->toTeX();
765: if ($par) {
766: $s = "(".$s.")";
767: }
768: $s .= " \\cdot ";
769: $par = ($c1->type == OPERATOR && ($c1->value eq "+" || $c1->value eq "-"));
770: if ($par) {
771: $s .= "(".$c1->toTeX().")";
772: } else {
773: $s .= $c1->toTeX();
774: }
775: return $s;
776: }
777: when ("`") {
778: return($c0->toTeX()." \\mathrm{".$c1->toTeX()."}");
779: }
780: when ("=") {
781: return($c0->toTeX()." = ".$c1->toTeX());
782: }
783: when ("#") {
784: return($c0->toTeX()." \\not ".$c1->toTeX());
785: }
786: when ("<") {
787: return($c0->toTeX()." < ".$c1->toTeX());
788: }
789: when (">") {
790: return($c0->toTeX()." > ".$c1->toTeX());
791: }
792: when ("<=") {
793: return($c0->toTeX()." \\leq ".$c1->toTeX());
794: }
795: when (">=") {
796: return($c0->toTeX()." \\geq ".$c1->toTeX());
797: }
798: default {
799: die CalcException->new("Unknown operator: [_1].", $self->value);
800: }
801: }
802: }
803: when (FUNCTION) {
804: my @children = @{$self->children};
805: my $fname = $children[0]->value;
806: my $c1 = $children[1];
807: my $c2 = $children[2];
808: my $c3 = $children[3];
809: my $c4 = $children[4];
810:
811: given ($fname) {
812: when ("sqrt") { return "\\sqrt{".$c1->toTeX()."}"; }
813: when ("abs") { return "|".$c1->toTeX()."|"; }
814: when ("exp") { return "\\mathrm{e}^{".$c1->toTeX()."}"; }
815: when ("factorial") {
816: my $s = $c1->toTeX();
817: if ($c1->type == OPERATOR) {
818: $s = "(".$s.")";
819: }
820: $s .= " !";
821: return $s;
822: }
823: when ("diff") {
824: if (scalar(@children) == 3) {
825: return "\\frac{d}{d".$c2->toTeX()."} ".$c1->toTeX();
826: } else {
827: return "\\frac{d^{".$c3->toTeX()."}}{d ".$c2->toTeX().
828: "^{".$c3->toTeX()."}} ".$c1->toTeX();
829: }
830: }
831: when ("integrate") {
832: if (scalar(@children) == 3) {
833: return "\\int ".$c1->toTeX()." \\ d ".$c2->toTeX();
834: } else {
835: return "\\int_{".$c3->toTeX()."}^{".$c4->toTeX()."} ".
836: $c1->toTeX()." \\ d ".$c2->toTeX();
837: }
838: }
839: when ("sum") {
840: return "\\sum_{".$c2->toTeX()."=".$c3->toTeX().
841: "}^{".$c4->toTeX()."} ".$c1->toTeX();
842: }
843: when ("product") {
844: return "\\prod_{".$c2->toTeX()."=".$c3->toTeX().
845: "}^{".$c4->toTeX()."} ".$c1->toTeX();
846: }
847: when ("limit") {
848: if (scalar(@children) < 4) {
849: return "\\lim ".$c1->toTeX();
850: } elsif (scalar(@children) == 4) {
851: return "\\lim_{".$c2->toTeX()." \\to ".$c3->toTeX().
852: "}".$c1->toTeX();
853: } else {
854: my $s = "\\lim_{".$c2->toTeX()." \\to ".$c3->toTeX();
855: if ($c4->value eq "plus") {
856: $s .= "+";
857: } elsif ($c4->value eq "minus") {
858: $s .= "-";
859: }
860: $s .= "}".$c1->toTeX();
861: return $s;
862: }
863: }
864: when ("binomial") {
865: return "\\binom{".$c1->toTeX()."}{".$c2->toTeX()."}";
866: }
867: when (["union","intersection"]) {
868: if (!defined $children[2]) {
869: die CalcException->new("Missing parameter for function [_1].", $fname);
870: }
871: if ($c1->type != SET && $c1->type != INTERVAL && $c1->type != FUNCTION) {
872: die CalcException->new("Wrong type for function [_1] (should be a set or interval).", $fname);
873: }
874: if ($fname eq "union") {
875: return $c1->toTeX().' \cup '.$c2->toTeX();
876: } else {
877: return $c1->toTeX().' \cap '.$c2->toTeX();
878: }
879: }
880: when ("sin") { return "\\sin ".$c1->toTeX(); }
881: when ("cos") { return "\\cos ".$c1->toTeX(); }
882: when ("tan") { return "\\tan ".$c1->toTeX(); }
883: when ("asin") { return "\\arcsin ".$c1->toTeX(); }
884: when ("acos") { return "\\arccos ".$c1->toTeX(); }
885: when ("atan") { return "\\arctan ".$c1->toTeX(); }
886: when ("sinh") { return "\\sinh ".$c1->toTeX(); }
887: when ("cosh") { return "\\cosh ".$c1->toTeX(); }
888: when ("tanh") { return "\\tanh ".$c1->toTeX(); }
889: default {
890: my $s = $fname."(";
891: for (my $i=1; $i<scalar(@children); $i++) {
892: if ($i != 1) {
893: $s .= ", ";
894: }
895: $s .= $children[$i]->toTeX();
896: }
897: $s .= ")";
898: return($s);
899: }
900: }
901: }
902: when (VECTOR) {
903: my @children = @{$self->children};
904: # my $s = "\\begin{pmatrix}";
905: # NOTE: pmatrix would be easier, but tth does not recognize it
906: my $col;
907: if (scalar(@children) == 0) {
908: $col = 0;
909: } elsif ($children[0]->type == VECTOR) {
910: $col = scalar(@{$children[0]->children});
911: } else {
912: $col = 1;
913: }
914: my $s = "\\left( \\begin{array}{".('c' x $col)."}";
915: for (my $i=0; $i<scalar(@children); $i++) {
916: if ($i != 0) {
917: $s .= " \\\\ ";
918: }
919: if ($children[0]->type == VECTOR) {
920: # matrix
921: for (my $j=0; $j<scalar(@{$children[$i]->children}); $j++) {
922: if ($j != 0) {
923: $s .= " & ";
924: }
925: $s .= $children[$i]->children->[$j]->toTeX();
926: }
927: } else {
928: # vector
929: $s .= $children[$i]->toTeX();
930: }
931: }
932: # $s .= "\\end{pmatrix}";
933: $s .= "\\end{array} \\right)";
934: return($s);
935: }
936: when (INTERVAL) {
937: my @children = @{$self->children};
938: if (scalar(@children) != 2) {
939: die CalcException->new("Interval should have two parameters.");
940: }
941: my ($qminopen, $qmaxopen);
942: given ($self->interval_type) {
943: when (OPEN_OPEN) { $qminopen = 1; $qmaxopen = 1; }
944: when (OPEN_CLOSED) { $qminopen = 1; $qmaxopen = 0; }
945: when (CLOSED_OPEN) { $qminopen = 0; $qmaxopen = 1; }
946: when (CLOSED_CLOSED) { $qminopen = 0; $qmaxopen = 0; }
947: }
948: my $s = "\\left";
949: if ($qminopen) {
950: $s .= "(";
951: } else {
952: $s .= "[";
953: }
954: $s .= $children[0]->toTeX();
955: $s .= ", ";
956: $s .= $children[1]->toTeX();
957: $s .= "\\right";
958: if ($qmaxopen) {
959: $s .= ")";
960: } else {
961: $s .= "]";
962: }
963: return($s);
964: }
965: when (SET) {
966: my @children = @{$self->children};
967: my $s = "\\left\\{ {";
968: for (my $i=0; $i<scalar(@children); $i++) {
969: if ($i != 0) {
970: $s .= ", ";
971: }
972: $s .= $children[$i]->toTeX();
973: }
974: $s .= "}\\right\\}";
975: return($s);
976: }
977: when (SUBSCRIPT) {
978: my @children = @{$self->children};
979: return($children[0]->toTeX()."_{".$children[1]->toTeX()."}");
980: }
981: }
982: }
983: ##
984: # Creates a vector or a matrix with this node
985: # @param {CalcEnv} env - Calculation environment.
986: # @returns {QVector|QMatrix}
987: ##
988: sub createVectorOrMatrix {
989: my ( $self, $env ) = @_;
990: my @children = @{$self->children};
991: my @t = (); # 1d or 2d array of Quantity
992: my $start;
993: if ($self->type == FUNCTION) {
994: $start = 1;
995: } else {
996: $start = 0;
997: }
998: my $nb1;
999: for (my $i=0; $i < scalar(@children) - $start; $i++) {
1000: my $qv = $children[$i+$start]->calc($env);
1001: my $nb2;
1002: if ($qv->isa(Quantity)) {
1003: $nb2 = 1;
1004: } else {
1005: $nb2 = scalar(@{$qv->quantities});
1006: }
1007: if (!defined $nb1) {
1008: $nb1 = $nb2;
1009: } elsif ($nb2 != $nb1) {
1010: die CalcException->new("Inconsistent number of elements in a matrix.");
1011: }
1012: if ($qv->isa(Quantity)) {
1013: $t[$i] = $qv;
1014: } else {
1015: $t[$i] = [];
1016: for (my $j=0; $j < scalar(@{$qv->quantities}); $j++) {
1017: $t[$i][$j] = $qv->quantities->[$j];
1018: }
1019: }
1020: }
1021: if (ref($t[0]) eq 'ARRAY') {
1022: return QMatrix->new(\@t);
1023: } else {
1024: return QVector->new(\@t);
1025: }
1026: }
1027:
1028: ##
1029: # Tests if a string is in an array (using eq) (to avoid using $value ~~ @array)
1030: # @param {Array<string>} array - reference to the array of strings
1031: # @param {string} value - the string to look for
1032: # @returns 1 if found, 0 otherwise
1033: ##
1034: sub string_in_array {
1035: my ($array, $value) = @_;
1036: foreach my $v (@{$array}) {
1037: if ($v eq $value) {
1038: return 1;
1039: }
1040: }
1041: return 0;
1042: }
1043:
1044: 1;
1045: __END__
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/back.gif){kind=icon}
Return to ENode.pm CVS log ![[TXT]](/icons/text.gif){kind=icon}
![[DIR]](/icons/dir.gif){kind=icon}
Up to [LON-CAPA] / loncom / homework / math_parser