# The LearningOnline Network with CAPA - LON-CAPA
# Parsed tree node
#
# $Id: ENode.pm,v 1.6 2023/03/13 22:31:22 raeburn Exp $
#
# Copyright (C) 2014 Michigan State University Board of Trustees
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##
# Parsed tree node. ENode.toMathML(hcolors) contains the code for the transformation into MathML.
##
package Apache::math_parser::ENode;
use strict;
use warnings;
use utf8;
use Switch 'Perl6';
use aliased 'Apache::math_parser::CalcException';
use aliased 'Apache::math_parser::Operator';
use aliased 'Apache::math_parser::ParseException';
use aliased 'Apache::math_parser::QMatrix';
use aliased 'Apache::math_parser::Quantity';
use aliased 'Apache::math_parser::QVector';
use aliased 'Apache::math_parser::QInterval';
use aliased 'Apache::math_parser::QIntervalUnion';
use aliased 'Apache::math_parser::QSet';
use aliased 'Apache::math_parser::Units';
use enum qw(UNKNOWN NAME NUMBER OPERATOR FUNCTION VECTOR INTERVAL SET SUBSCRIPT);
use enum qw(NOT_AN_INTERVAL OPEN_OPEN OPEN_CLOSED CLOSED_OPEN CLOSED_CLOSED);
##
# @param {integer} type - UNKNOWN | NAME | NUMBER | OPERATOR | FUNCTION | VECTOR | INTERVAL | SET | SUBSCRIPT
# @param {Operator} op - The operator
# @param {string} value - Node value as a string, undef for type VECTOR
# @param {ENode[]} children - The children nodes, only for types OPERATOR, FUNCTION, VECTOR, INTERVAL, SET, SUBSCRIPT
# @param {interval_type} - The interval type, NOT_AN_INTERVAL | OPEN_OPEN | OPEN_CLOSED | CLOSED_OPEN | CLOSED_CLOSED
##
sub new {
my ($class, $type, $op, $value, $children, $interval_type) = @_;
if (!defined $interval_type) {
$interval_type = NOT_AN_INTERVAL;
}
my $self = {
_type => $type,
_op => $op,
_value => $value,
_children => $children,
_interval_type => $interval_type,
};
bless $self, $class;
return $self;
}
# Attribute helpers
##
# Node type
# @returns {int} UNKNOWN | NAME | NUMBER | OPERATOR | FUNCTION | VECTOR | INTERVAL | SET | SUBSCRIPT
##
sub type {
my $self = shift;
return $self->{_type};
}
##
# Operator
# @returns {Operator}
##
sub op {
my $self = shift;
return $self->{_op};
}
##
# Node value as a string, undef for type VECTOR.
# @returns {string}
##
sub value {
my $self = shift;
return $self->{_value};
}
##
# The children nodes, only for types OPERATOR, FUNCTION, VECTOR, INTERVAL, SET, SUBSCRIPT
# @returns {ENode[]}
##
sub children {
my $self = shift;
return $self->{_children};
}
##
# The interval type, NOT_AN_INTERVAL | OPEN_OPEN | OPEN_CLOSED | CLOSED_OPEN | CLOSED_CLOSED
# @returns {int}
##
sub interval_type {
my $self = shift;
return $self->{_interval_type};
}
##
# Returns the node as a string, for debug
# @returns {string}
##
sub toString {
my ( $self ) = @_;
my $s = '(';
given ($self->type) {
when (UNKNOWN) { $s .= "UNKNOWN"; }
when (NAME) { $s .= "NAME"; }
when (NUMBER) { $s .= "NUMBER"; }
when (OPERATOR) { $s .= "OPERATOR"; }
when (FUNCTION) { $s .= "FUNCTION"; }
when (VECTOR) { $s .= "VECTOR"; }
when (INTERVAL) { $s .= "INTERVAL"; }
when (SET) { $s .= "SET"; }
when (SUBSCRIPT) { $s .= "SUBSCRIPT"; }
}
if (defined $self->op) {
$s .= " '" . $self->op->id . "'";
}
if (defined $self->value) {
$s .= " '" . $self->value . "'";
}
if (defined $self->{_children}) {
$s .= ' [';
for (my $i = 0; $i < scalar(@{$self->children}); $i++) {
$s .= $self->children->[$i]->toString();
if ($i != scalar(@{$self->children}) - 1) {
$s .= ',';
}
}
$s .= ']';
}
if (defined $self->interval_type) {
$s .= " " . $self->interval_type;
}
$s.= ')';
return $s;
}
##
# Evaluates the node, returning a quantity or an object from a more complex class using quantities as base components.
# Can throw a CalcException if a result cannot be calculated.
# @param {CalcEnv} env - Calculation environment.
# @returns {Quantity|QVector|QMatrix|QSet|QInterval|QIntervalUnion}
##
sub calc {
my ( $self, $env ) = @_;
given ($self->type) {
when (UNKNOWN) {
die CalcException->new("Unknown node type: [_1].", $self->value);
}
when (NAME) {
my $name = $self->value;
if ($name =~ /^inf$/i) {
return Quantity->new(9**9**9);
} elsif ($name =~ /^nan$/i) {
return Quantity->new(-sin(9**9**9));
}
if ($env->unit_mode) {
my $cst = $env->getConstant($name);
if (defined $cst) {
return $cst;
}
return $env->convertToSI($name);
} else {
my $q = $env->getVariable($name);
if (!defined $q) {
my $cst = $env->getConstant($name);
if (defined $cst) {
return $cst;
}
die CalcException->new("Variable has undefined value: [_1].", $name);
}
return $q;
}
}
when (NUMBER) {
return Quantity->new($self->value);
}
when (OPERATOR) {
my @children = @{$self->children};
my ($q1, $q2);
if (defined $children[0]) {
$q1 = $children[0]->calc($env);
}
if (defined $children[1]) {
$q2 = $children[1]->calc($env);
}
given ($self->value) {
when ("+") {
if (!overload::Method($q1, '+')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 + $q2);
}
when ("-") {
if (!defined $q2) {
if (!$q1->can('qneg')) {
die CalcException->new("Negation is not implemented for this type.");
}
return($q1->qneg());
} else {
if (!overload::Method($q1, '-')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 - $q2);
}
}
when ("*") {
if (!overload::Method($q1, '*')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 * $q2);
}
when ("/") {
if (!overload::Method($q1, '/')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 / $q2);
}
when ("^") {
if (!overload::Method($q1, '^')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 ^ $q2);
}
when ("!") {
if (!$q1->can('qfact')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return $q1->qfact();
}
when ("%") {
if (!$q1->isa(Quantity) || !$q2->isa(Quantity)) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return(($q1 / Quantity->new(100)) * $q2);
}
when (".") {
# scalar product for vectors, multiplication for matrices
if (!$q1->can('qdot')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1->qdot($children[1]->calc($env)));
}
when ("`") {
if (!overload::Method($q1, '*')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 * $q2);
}
when ("=") {
if (!$q1->can('qeq')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1->qeq($q2, $env->tolerance));
}
when ("<") {
if (!overload::Method($q1, '<')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 < $q2);
}
when ("<=") {
if (!overload::Method($q1, '<=')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 <= $q2);
}
when (">") {
if (!overload::Method($q1, '>')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 > $q2);
}
when (">=") {
if (!overload::Method($q1, '>=')) {
die CalcException->new("The [_1] operator is not implemented for this type.", $self->value);
}
return($q1 >= $q2);
}
default {
die CalcException->new("Unknown operator: [_1].", $self->value);
}
}
}
when (FUNCTION) {
my @children = @{$self->children};
my $fname = $children[0]->value;
if (!defined $children[1]) {
die CalcException->new("Missing parameter for function [_1].", $fname);
}
my ($q1, $q2);
if (string_in_array(['pow', 'sqrt', 'abs', 'exp', 'ln', 'log', 'log10', 'factorial',
'mod', 'sgn', 'ceil', 'floor', 'sin', 'cos', 'tan', 'asin', 'acos', 'atan',
'atan2', 'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh'], $fname)) {
$q1 = $children[1]->calc($env);
if (!$q1->isa(Quantity)) {
die CalcException->new("The [_1] function is not implemented for this type.", $fname);
}
}
if (string_in_array(['pow', 'mod', 'atan2'], $fname)) {
if (!defined $children[2]) {
die CalcException->new("Missing parameter for function [_1].", $fname);
}
$q2 = $children[2]->calc($env);
if (!$q2->isa(Quantity)) {
die CalcException->new("The [_1] function is not implemented for this type.", $fname);
}
}
given ($fname) {
when ("matrix") { return $self->createVectorOrMatrix($env); }
when ("pow") { return $q1->qpow($q2); }
when ("sqrt") { return $q1->qsqrt(); }
when ("abs") { return $q1->qabs(); }
when ("exp") { return $q1->qexp(); }
when ("ln") { return $q1->qln(); }
when ("log") { return $q1->qln(); }
when ("log10") { return $q1->qlog10(); }
when ("factorial") { return $q1->qfact(); }
when ("mod") { return $q1->qmod($q2); }
when ("sgn") { return $q1->qsgn(); }
when ("ceil") { return $q1->qceil(); }
when ("floor") { return $q1->qfloor(); }
when ("sin") { return $q1->qsin(); }
when ("cos") { return $q1->qcos(); }
when ("tan") { return $q1->qtan(); }
when ("asin") { return $q1->qasin(); }
when ("acos") { return $q1->qacos(); }
when ("atan") { return $q1->qatan(); }
when ("atan2") { return $q1->qatan2($q2); }
when ("sinh") { return $q1->qsinh(); }
when ("cosh") { return $q1->qcosh(); }
when ("tanh") { return $q1->qtanh(); }
when ("asinh") { return $q1->qasinh(); }
when ("acosh") { return $q1->qacosh(); }
when ("atanh") { return $q1->qatanh(); }
when (["sum","product"]) {
if ($env->unit_mode) {
die CalcException->new("[_1] cannot work in unit mode.", $fname);
}
if (scalar(@children) != 5) {
die CalcException->new("[_1] should have four parameters.", $fname);
}
my $var = "".$children[2]->value;
if ($var !~ /^[a-zA-Z_][a-zA-Z_0-9]*$/) {
die CalcException->new("[_1]: wrong variable name", $fname);
}
if ($var eq "i") {
die CalcException->new("[_1]: please use another variable name, i is the imaginary number.", $fname);
}
my $initial = $env->getVariable($var);
my $var_value_1 = $children[3]->value;
my $var_value_2 = $children[4]->value;
if ($var_value_1 !~ /^[0-9]+$/) {
die CalcException->new("[_1]: the third parameter should be an integer", $fname);
}
if ($var_value_2 !~ /^[0-9]+$/) {
die CalcException->new("[_1]: the fourth parameter should be an integer", $fname);
}
if ($var_value_1 > $var_value_2) {
die CalcException->new("[_1]: are you trying to make me loop forever?", $fname);
}
my $result;
for (my $var_value=$var_value_1; $var_value <= $var_value_2; $var_value++) {
$env->setVariable($var, $var_value);
my $nq = $children[1]->calc($env);
if (!$nq->isa(Quantity) && !$nq->isa(QVector) && !$nq->isa(QMatrix)) {
die CalcException->new("[_1]: wrong type for a calculated value", $fname);
}
if (!defined $result) {
$result = $nq;
} elsif ($fname eq "sum") {
$result += $nq;
} else {
$result *= $nq;
}
}
$env->setVariable($var, $initial);
return $result;
}
when ("binomial") {
if (scalar(@children) != 3) {
die CalcException->new("[_1] should have two parameters.", $fname);
}
my $n = $children[1]->calc($env);
my $p = $children[2]->calc($env);
if (!$n->isa(Quantity) || !$p->isa(Quantity)) {
die CalcException->new("Wrong parameter type for function [_1]", $fname);
}
return $n->qfact() / ($p->qfact() * ($n - $p)->qfact());
}
when (["union","intersection"]) {
if (!defined $children[2]) {
die CalcException->new("Missing parameter for function [_1].", $fname);
}
my $p1 = $children[1]->calc($env);
my $p2 = $children[2]->calc($env);
if (!$p1->isa(QSet) && !$p1->isa(QInterval) && !$p1->isa(QIntervalUnion)) {
die CalcException->new("Wrong type for function [_1] (should be a set or interval).", $fname);
}
if ($fname eq "union") {
return $p1->union($p2);
} else {
return $p1->intersection($p2);
}
}
default { die CalcException->new("Unknown function: [_1].",$fname); }
}
}
when (VECTOR) {
return $self->createVectorOrMatrix($env);
}
when (INTERVAL) {
my @children = @{$self->children};
if (scalar(@children) != 2) {
die CalcException->new("Interval should have two parameters.");
}
my $qmin = $children[0]->calc($env);
my $qmax = $children[1]->calc($env);
my ($qminopen, $qmaxopen);
given ($self->interval_type) {
when (OPEN_OPEN) { $qminopen = 1; $qmaxopen = 1; }
when (OPEN_CLOSED) { $qminopen = 1; $qmaxopen = 0; }
when (CLOSED_OPEN) { $qminopen = 0; $qmaxopen = 1; }
when (CLOSED_CLOSED) { $qminopen = 0; $qmaxopen = 0; }
}
return QInterval->new($qmin, $qmax, $qminopen, $qmaxopen);
}
when (SET) {
my @t = ();
foreach my $child (@{$self->children}) {
push(@t, $child->calc($env));
}
return QSet->new(\@t);
}
when (SUBSCRIPT) {
die CalcException->new("Subscript cannot be evaluated: [_1].", $self->value);
}
}
}
##
# Returns the equation as a string with the Maxima syntax.
# @returns {string}
##
sub toMaxima {
my ( $self, $env ) = @_;
given ($self->type) {
when (UNKNOWN) {
die CalcException->new("Unknown node type: [_1].", $self->value);
}
when (NAME) {
my $name = $self->value;
my $cst = $env->getConstant($name);
if (defined $cst) {
return $cst;
}
return($name);
}
when (NUMBER) {
if ($self->value eq "i") {
return "%i";
} else {
return $self->value;
}
}
when (OPERATOR) {
my @children = @{$self->children};
given ($self->value) {
when ("+") {
if ($children[0]->type == SET && $children[1]->type == SET) {
return("union(".$children[0]->toMaxima().", ".$children[1]->toMaxima().")");
} else {
return("(".$children[0]->toMaxima()."+".$children[1]->toMaxima().")");
}
}
when ("-") {
if (!defined $children[1]) {
return("(-".$children[0]->toMaxima().")");
} else {
return("(".$children[0]->toMaxima()."-".$children[1]->toMaxima().")");
}
}
when ("*") {
return("(".$children[0]->toMaxima()."*".$children[1]->toMaxima().")");
}
when ("/") {
return("(".$children[0]->toMaxima()."/".$children[1]->toMaxima().")");
}
when ("^") {
return("(".$children[0]->toMaxima()."^".$children[1]->toMaxima().")");
}
when ("!") {
return("factorial(".$children[0]->toMaxima().")");
}
when ("%") {
return("((".$children[0]->toMaxima()."/100)*".$children[1]->toMaxima().")");
}
when (".") {
# scalar product for vectors, multiplication for matrices
return("(".$children[0]->toMaxima().".".$children[1]->toMaxima().")");
}
when ("`") {
return("(".$children[0]->toMaxima()."`".$children[1]->toMaxima().")");
}
when ("=") {
# NOTE: should we use is(...) to evaluate the expression ?
return("(".$children[0]->toMaxima()."=".$children[1]->toMaxima().")");
}
when ("<") {
return("(".$children[0]->toMaxima()."<".$children[1]->toMaxima().")");
}
when (">") {
return("(".$children[0]->toMaxima().">".$children[1]->toMaxima().")");
}
when ("<=") {
return("(".$children[0]->toMaxima()."<=".$children[1]->toMaxima().")");
}
when (">=") {
return("(".$children[0]->toMaxima().">=".$children[1]->toMaxima().")");
}
default {
die CalcException->new("Unknown operator: [_1].", $self->value);
}
}
}
when (FUNCTION) {
my @children = @{$self->children};
my $fname = $children[0]->value;
given ($fname) {
when ("log10") { return "log(".$children[1]->toMaxima().")/log(10)"; }
when ("sgn") { return "signum(".$children[1]->toMaxima().")"; }
when ("ceil") { return "ceiling(".$children[1]->toMaxima().")"; }
default {
my $s = $fname."(";
for (my $i=1; $i<scalar(@children); $i++) {
if ($i != 1) {
$s .= ", ";
}
$s .= $children[$i]->toMaxima();
}
$s .= ")";
return($s);
}
}
}
when (VECTOR) {
my @children = @{$self->children};
my $s;
if ($children[0]->type == VECTOR) {
$s = "matrix(";
} else {
$s = "[";
}
for (my $i=0; $i<scalar(@children); $i++) {
if ($i != 0) {
$s .= ", ";
}
$s .= $children[$i]->toMaxima();
}
if ($children[0]->type == VECTOR) {
$s .= ")";
} else {
$s .= "]";
}
return($s);
}
when (INTERVAL) {
die CalcException->new("Maxima syntax: intervals are not implemented.");
# see http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=5959544
# "New Package in Maxima for Single-Valued Interval Computation on Real Numbers"
}
when (SET) {
my @children = @{$self->children};
my $s = "{";
for (my $i=0; $i<scalar(@children); $i++) {
if ($i != 0) {
$s .= ", ";
}
$s .= $children[$i]->toMaxima();
}
$s .= "}";
return($s);
}
when (SUBSCRIPT) {
my @children = @{$self->children};
return("(".$children[0]->toMaxima()."_".$children[1]->toMaxima().")");
}
}
}
##
# Returns the equation as a string with the TeX syntax.
# @returns {string}
##
sub toTeX {
my ( $self ) = @_;
given ($self->type) {
when (UNKNOWN) {
die CalcException->new("Unknown node type: [_1].", $self->value);
}
when (NAME) {
my $name = $self->value;
if ($name =~ /^([a-zA-Z]+)([0-9]+)$/) {
return($1."_{".$2."}");
}
my @greek = (
"alpha", "beta", "gamma", "delta", "epsilon", "zeta",
"eta", "theta", "iota", "kappa", "lambda", "mu",
"nu", "xi", "omicron", "pi", "rho", "sigma",
"tau", "upsilon", "phi", "chi", "psi", "omega",
"Alpha", "Beta", "Gamma", "Delta", "Epsilon", "Zeta",
"Eta", "Theta", "Iota", "Kappa", "Lambda", "Mu",
"Nu", "Xi", "Omicron", "Pi", "Rho", "Sigma",
"Tau", "Upsilon", "Phi", "Chi", "Psi", "Omega",
);
if (string_in_array(\@greek, $name)) {
return('\\'.$name);
} elsif ($name eq "hbar") {
return("\\hbar");
} elsif ($name eq "inf") {
return("\\infty");
} elsif ($name eq "minf") {
return("-\\infty");
} else {
return($name);
}
}
when (NUMBER) {
return $self->value;
}
when (OPERATOR) {
my @children = @{$self->children};
my $c0 = $children[0];
my $c1 = $children[1];
given ($self->value) {
when ("+") {
# should we add parenthesis ? We need to check if there is a '-' to the left of c1
my $par = 0;
my $first = $c1;
while ($first->type == OPERATOR) {
if ($first->value eq "-" && scalar(@{$first->children}) == 1) {
$par = 1;
last;
} elsif ($first->value eq "+" || $first->value eq "-" || $first->value eq "*") {
$first = $first->children->[0];
} else {
last;
}
}
my $s = $c0->toTeX()." + ".$c1->toTeX();
if ($par) {
$s = "(".$s.")";
}
return $s;
}
when ("-") {
if (!defined $c1) {
return("-".$c0->toTeX());
} else {
my $s = $c0->toTeX()." - ";
my $par = ($c1->type == OPERATOR &&
($c1->value eq "+" || $c1->value eq "-"));
if ($par) {
$s .= "(".$c1->toTeX().")";
} else {
$s .= $c1->toTeX();
}
return $s;
}
}
when ("*") {
my $par = ($c0->type == OPERATOR && ($c0->value eq "+" || $c0->value eq "-"));
my $s = $c0->toTeX();
if ($par) {
$s = "(".$s.")";
}
# should the x operator be visible ? We need to check if there is a number to the left of c1
my $firstinc1 = $c1;
while ($firstinc1->type == OPERATOR) {
$firstinc1 = $firstinc1->children->[0];
}
# ... and if it's an operation between vectors/matrices, the * operator should be displayed
# (it is ambiguous otherwise)
# note: this will not work if the matrix is calculated, for instance with 2[1;2]*[3;4]
if ($c0->type == VECTOR && $c1->type == VECTOR) {
$s .= " * ";
} elsif ($firstinc1->type == NUMBER) {
$s .= " \\times ";
} else {
$s .= " ";
}
$par = ($c1->type == OPERATOR && ($c1->value eq "+" || $c1->value eq "-"));
if ($par) {
$s .= "(".$c1->toTeX().")";
} else {
$s .= $c1->toTeX();
}
return $s;
}
when ("/") {
# NOTE: cfrac would be better but tth does not handle it
return("\\frac{".$c0->toTeX()."}{".$c1->toTeX()."}");
}
when ("^") {
my $par;
if ($c0->type == FUNCTION) {
if ($c0->value eq "sqrt" || $c0->value eq "abs" || $c0->value eq "matrix" ||
$c0->value eq "diff") {
$par = 0;
} else {
$par = 1;
}
} elsif ($c0->type == OPERATOR) {
$par = 1;
} else {
$par = 0;
}
if ($par) {
return("(".$c0->toTeX().")^{".$c1->toTeX()."}");
} else {
return($c0->toTeX()."^{".$c1->toTeX()."}");
}
}
when ("!") {
my $s = $c0->toTeX();
if ($c0->type == OPERATOR) {
$s = "(".$s.")";
}
$s .= " !";
return $s;
}
when ("%") {
return($c0->toTeX()." \\% ".$c1->toTeX());
}
when (".") {
# scalar product for vectors, multiplication for matrices
my $par = ($c0->type == OPERATOR && ($c0->value eq "+" || $c0->value eq "-"));
my $s = $c0->toTeX();
if ($par) {
$s = "(".$s.")";
}
$s .= " \\cdot ";
$par = ($c1->type == OPERATOR && ($c1->value eq "+" || $c1->value eq "-"));
if ($par) {
$s .= "(".$c1->toTeX().")";
} else {
$s .= $c1->toTeX();
}
return $s;
}
when ("`") {
return($c0->toTeX()." \\mathrm{".$c1->toTeX()."}");
}
when ("=") {
return($c0->toTeX()." = ".$c1->toTeX());
}
when ("#") {
return($c0->toTeX()." \\not ".$c1->toTeX());
}
when ("<") {
return($c0->toTeX()." < ".$c1->toTeX());
}
when (">") {
return($c0->toTeX()." > ".$c1->toTeX());
}
when ("<=") {
return($c0->toTeX()." \\leq ".$c1->toTeX());
}
when (">=") {
return($c0->toTeX()." \\geq ".$c1->toTeX());
}
default {
die CalcException->new("Unknown operator: [_1].", $self->value);
}
}
}
when (FUNCTION) {
my @children = @{$self->children};
my $fname = $children[0]->value;
my $c1 = $children[1];
my $c2 = $children[2];
my $c3 = $children[3];
my $c4 = $children[4];
given ($fname) {
when ("sqrt") { return "\\sqrt{".$c1->toTeX()."}"; }
when ("abs") { return "|".$c1->toTeX()."|"; }
when ("exp") { return "\\mathrm{e}^{".$c1->toTeX()."}"; }
when ("factorial") {
my $s = $c1->toTeX();
if ($c1->type == OPERATOR) {
$s = "(".$s.")";
}
$s .= " !";
return $s;
}
when ("diff") {
if (scalar(@children) == 3) {
return "\\frac{d}{d".$c2->toTeX()."} ".$c1->toTeX();
} else {
return "\\frac{d^{".$c3->toTeX()."}}{d ".$c2->toTeX().
"^{".$c3->toTeX()."}} ".$c1->toTeX();
}
}
when ("integrate") {
if (scalar(@children) == 3) {
return "\\int ".$c1->toTeX()." \\ d ".$c2->toTeX();
} else {
return "\\int_{".$c3->toTeX()."}^{".$c4->toTeX()."} ".
$c1->toTeX()." \\ d ".$c2->toTeX();
}
}
when ("sum") {
return "\\sum_{".$c2->toTeX()."=".$c3->toTeX().
"}^{".$c4->toTeX()."} ".$c1->toTeX();
}
when ("product") {
return "\\prod_{".$c2->toTeX()."=".$c3->toTeX().
"}^{".$c4->toTeX()."} ".$c1->toTeX();
}
when ("limit") {
if (scalar(@children) < 4) {
return "\\lim ".$c1->toTeX();
} elsif (scalar(@children) == 4) {
return "\\lim_{".$c2->toTeX()." \\to ".$c3->toTeX().
"}".$c1->toTeX();
} else {
my $s = "\\lim_{".$c2->toTeX()." \\to ".$c3->toTeX();
if ($c4->value eq "plus") {
$s .= "+";
} elsif ($c4->value eq "minus") {
$s .= "-";
}
$s .= "}".$c1->toTeX();
return $s;
}
}
when ("binomial") {
return "\\binom{".$c1->toTeX()."}{".$c2->toTeX()."}";
}
when (["union","intersection"]) {
if (!defined $children[2]) {
die CalcException->new("Missing parameter for function [_1].", $fname);
}
if ($c1->type != SET && $c1->type != INTERVAL && $c1->type != FUNCTION) {
die CalcException->new("Wrong type for function [_1] (should be a set or interval).", $fname);
}
if ($fname eq "union") {
return $c1->toTeX().' \cup '.$c2->toTeX();
} else {
return $c1->toTeX().' \cap '.$c2->toTeX();
}
}
when ("sin") { return "\\sin ".$c1->toTeX(); }
when ("cos") { return "\\cos ".$c1->toTeX(); }
when ("tan") { return "\\tan ".$c1->toTeX(); }
when ("asin") { return "\\arcsin ".$c1->toTeX(); }
when ("acos") { return "\\arccos ".$c1->toTeX(); }
when ("atan") { return "\\arctan ".$c1->toTeX(); }
when ("sinh") { return "\\sinh ".$c1->toTeX(); }
when ("cosh") { return "\\cosh ".$c1->toTeX(); }
when ("tanh") { return "\\tanh ".$c1->toTeX(); }
default {
my $s = $fname."(";
for (my $i=1; $i<scalar(@children); $i++) {
if ($i != 1) {
$s .= ", ";
}
$s .= $children[$i]->toTeX();
}
$s .= ")";
return($s);
}
}
}
when (VECTOR) {
my @children = @{$self->children};
# my $s = "\\begin{pmatrix}";
# NOTE: pmatrix would be easier, but tth does not recognize it
my $col;
if (scalar(@children) == 0) {
$col = 0;
} elsif ($children[0]->type == VECTOR) {
$col = scalar(@{$children[0]->children});
} else {
$col = 1;
}
my $s = "\\left( \\begin{array}{".('c' x $col)."}";
for (my $i=0; $i<scalar(@children); $i++) {
if ($i != 0) {
$s .= " \\\\ ";
}
if ($children[0]->type == VECTOR) {
# matrix
for (my $j=0; $j<scalar(@{$children[$i]->children}); $j++) {
if ($j != 0) {
$s .= " & ";
}
$s .= $children[$i]->children->[$j]->toTeX();
}
} else {
# vector
$s .= $children[$i]->toTeX();
}
}
# $s .= "\\end{pmatrix}";
$s .= "\\end{array} \\right)";
return($s);
}
when (INTERVAL) {
my @children = @{$self->children};
if (scalar(@children) != 2) {
die CalcException->new("Interval should have two parameters.");
}
my ($qminopen, $qmaxopen);
given ($self->interval_type) {
when (OPEN_OPEN) { $qminopen = 1; $qmaxopen = 1; }
when (OPEN_CLOSED) { $qminopen = 1; $qmaxopen = 0; }
when (CLOSED_OPEN) { $qminopen = 0; $qmaxopen = 1; }
when (CLOSED_CLOSED) { $qminopen = 0; $qmaxopen = 0; }
}
my $s = "\\left";
if ($qminopen) {
$s .= "(";
} else {
$s .= "[";
}
$s .= $children[0]->toTeX();
$s .= ", ";
$s .= $children[1]->toTeX();
$s .= "\\right";
if ($qmaxopen) {
$s .= ")";
} else {
$s .= "]";
}
return($s);
}
when (SET) {
my @children = @{$self->children};
my $s = "\\left\\{ {";
for (my $i=0; $i<scalar(@children); $i++) {
if ($i != 0) {
$s .= ", ";
}
$s .= $children[$i]->toTeX();
}
$s .= "}\\right\\}";
return($s);
}
when (SUBSCRIPT) {
my @children = @{$self->children};
return($children[0]->toTeX()."_{".$children[1]->toTeX()."}");
}
}
}
##
# Creates a vector or a matrix with this node
# @param {CalcEnv} env - Calculation environment.
# @returns {QVector|QMatrix}
##
sub createVectorOrMatrix {
my ( $self, $env ) = @_;
my @children = @{$self->children};
my @t = (); # 1d or 2d array of Quantity
my $start;
if ($self->type == FUNCTION) {
$start = 1;
} else {
$start = 0;
}
my $nb1;
for (my $i=0; $i < scalar(@children) - $start; $i++) {
my $qv = $children[$i+$start]->calc($env);
my $nb2;
if ($qv->isa(Quantity)) {
$nb2 = 1;
} else {
$nb2 = scalar(@{$qv->quantities});
}
if (!defined $nb1) {
$nb1 = $nb2;
} elsif ($nb2 != $nb1) {
die CalcException->new("Inconsistent number of elements in a matrix.");
}
if ($qv->isa(Quantity)) {
$t[$i] = $qv;
} else {
$t[$i] = [];
for (my $j=0; $j < scalar(@{$qv->quantities}); $j++) {
$t[$i][$j] = $qv->quantities->[$j];
}
}
}
if (ref($t[0]) eq 'ARRAY') {
return QMatrix->new(\@t);
} else {
return QVector->new(\@t);
}
}
##
# Tests if a string is in an array (using eq) (to avoid using $value ~~ @array)
# @param {Array<string>} array - reference to the array of strings
# @param {string} value - the string to look for
# @returns 1 if found, 0 otherwise
##
sub string_in_array {
my ($array, $value) = @_;
foreach my $v (@{$array}) {
if ($v eq $value) {
return 1;
}
}
return 0;
}
1;
__END__
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