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Copy pathfunction.cpp
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1196 lines (1096 loc) · 32.6 KB
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#include "function.h"
#include <stdexcept>
#include <sstream>
#include <algorithm>
#include <iostream>
using namespace std;
bool Expression::CanonicalEqualTo(Expression *other) {
if (this->nodeType() != other->nodeType()) return false;
return this->CanonicalEqualToSameType(other);
}
bool Expression::CanonicalSmallerThan(Expression *other) {
if (this->nodeType() < other->nodeType())
return true;
else if (this->nodeType() > other->nodeType())
return false;
else
return this->CanonicalSmallerThanSameType(other);
}
string Expression::stringPrint() const {
string s;
recursivePrint(s, OperatorPrecedence::None);
return s;
}
Expression *Expression::diffSimplify() const {
Expression *d = this->diff();
bool changed;
Expression *dsim = d->simplify(changed);
if (dsim) {
delete d;
return dsim;
} else {
return d;
}
}
void CommutativeOperators::recursivePrintCommutative(string &output,
OperatorPrecedence::Order order,
OperatorPrecedence::Order selfOrder,
char symbol) const {
bool closeParenthese = false;
OperatorPrecedence::Order nextOrder;
if (order >= selfOrder) {
output.push_back('(');
closeParenthese = true;
}
nextOrder = selfOrder;
auto it = childrenSet.begin();
(*it)->recursivePrint(output, nextOrder);
it++;
for (; it != childrenSet.end(); it++) {
output.push_back(symbol);
(*it)->recursivePrint(output, nextOrder);
}
if (closeParenthese) output.push_back(')');
}
void CommutativeOperators::construct(ExpressionSet children) {
if (children.size() <= 1)
throw invalid_argument("childrenSet should have more than 1 element");
for (auto i = children.begin(); i != children.end(); i++)
if (*i == 0) throw invalid_argument("Null pointers in arguments");
this->childrenSet = children;
}
void CommutativeOperators::construct(Expression *a, Expression *b) {
ExpressionSet two;
two.insert(a);
two.insert(b);
construct(two);
}
bool CommutativeOperators::simplifyChildren() {
bool needContinue = true;
bool changed = false;
while (needContinue) {
needContinue = false;
for (auto i = childrenSet.begin(); i != childrenSet.end(); i++) {
bool childChanged;
Expression *simplified = (*i)->simplify(childChanged);
if (simplified) {
changed = true;
needContinue = true;
delete *i;
i = childrenSet.erase(i);
childrenSet.insert(simplified);
if (i == childrenSet.end())
break;
} else if (childChanged) {
changed = true;
needContinue = true;
Expression *afterChange = *i;
i = childrenSet.erase(i);
childrenSet.insert(afterChange);
if (i == childrenSet.end())
break;
}
}
}
return changed;
}
bool CommutativeOperators::CanonicalEqualToSameType(Expression *other) {
assert(other->nodeType() == TypeAdd || other->nodeType() == TypeMulti);
CommutativeOperators *p = static_cast<CommutativeOperators *>(other);
int n = childrenSet.size();
int m = p->childrenSet.size();
if (n != m) {
return false;
} else {
auto i = childrenSet.begin();
auto j = p->childrenSet.begin();
for (; i != childrenSet.end(); i++, j++) {
if (!(*i)->CanonicalEqualTo(*j))
return false;
}
return true;
}
}
bool CommutativeOperators::CanonicalSmallerThanSameType(Expression *other) {
assert(other->nodeType() == TypeAdd || other->nodeType() == TypeMulti);
CommutativeOperators *p = static_cast<CommutativeOperators *>(other);
int n = childrenSet.size();
int m = p->childrenSet.size();
if (n < m) {
return true;
} else if (n > m) {
return false;
} else {
auto i = childrenSet.begin();
auto j = p->childrenSet.begin();
for (; i != childrenSet.end(); i++, j++) {
if ((*i)->CanonicalSmallerThan(*j))
return true;
}
return false;
}
}
Expression *CommutativeOperators::clone() const {
ExpressionSet cl;
for (auto i = childrenSet.begin(); i != childrenSet.end(); i++)
cl.insert((*i)->clone());
if (this->nodeType() == TypeAdd)
return new Addition(cl);
else if (this->nodeType() == TypeMulti)
return new Multiplication(cl);
else
assert(false);
}
CommutativeOperators::~CommutativeOperators() {
for (auto i = childrenSet.begin(); i != childrenSet.end(); i++)
delete *i;
}
double Addition::operator()(double x) const {
double sum = 0;
for (auto it = childrenSet.begin(); it != childrenSet.end(); it++)
sum += (**it)(x);
return sum;
}
void Addition::recursivePrint(string &output, OperatorPrecedence::Order order) const {
recursivePrintCommutative(output, order, OperatorPrecedence::AddSub, '+');
}
Expression *Addition::diff() const {
multiset<Expression *, ExpressionComparator> d;
for (auto it = childrenSet.begin(); it != childrenSet.end(); it++)
d.insert((*it)->diff());
return new Addition(d);
}
Expression *Addition::TrySimplifyAdding(Expression *right) {
//must have been treated in Addition::simplify()
return nullptr;
}
Expression *Addition::TrySimplifyMultiplying(Expression *right) {
return nullptr;
}
Expression *Addition::simplify(bool &changed) {
bool needContinue = true;
changed = false;
while (needContinue) {
needContinue = false;
if (this->simplifyChildren()) {
changed = true;
//needContinue = true;
}
for (auto it = childrenSet.begin(); it != childrenSet.end(); it++) {
switch ((*it)->nodeType()) {
case TypeAdd: {
Addition *p = static_cast<Addition *>(*it);
//pointer ownership changed
childrenSet.insert(p->childrenSet.begin(), p->childrenSet.end());
p->childrenSet.clear();
delete *it;
it = childrenSet.erase(it);
changed = true;
needContinue = true;
break;
}
case TypeConstant: {
Constant *p = static_cast<Constant *>(*it);
if (p->value() == 0) {
changed = true;
needContinue = true;
delete *it;
it = childrenSet.erase(it);
}
break;
}
default:
break;
}
if (it == childrenSet.end())
break;
auto next = it;
next++;
if (next == childrenSet.end())
continue;
//simplify two by two
for (; next != childrenSet.end(); next++) {
assert(it != next);
if ((*it)->CanonicalEqualTo(*next)) {
//a+a=2*a
changed = true;
needContinue = true;
Expression *r = new Multiplication(new Constant(2), (*it)->clone());
delete *it;
delete *next;
childrenSet.insert(r);
childrenSet.erase(it);
it = childrenSet.erase(next);
break;
} else {
Expression *p = (*it)->TrySimplifyAdding(*next);
if (p) {
changed = true;
needContinue = true;
delete *it;
delete *next;
childrenSet.insert(p);
childrenSet.erase(it);
it = childrenSet.erase(next);
break;
} else {
Expression *pp = (*next)->TrySimplifyAdding(*it);
if (pp) {
changed = true;
needContinue = true;
delete *it;
delete *next;
childrenSet.insert(pp);
childrenSet.erase(it);
it = childrenSet.erase(next);
break;
}
}
}
}
if (it == childrenSet.end())
break;
}
}
if (childrenSet.size() == 0) {
return new Constant(0);
} else if (childrenSet.size() == 1) {
return (*childrenSet.begin())->clone();
} else {
return NULL;
}
}
double Multiplication::operator()(double x) const {
double prod = 1;
for (auto it = childrenSet.begin(); it != childrenSet.end(); it++)
prod *= (**it)(x);
return prod;
}
void Multiplication::recursivePrint(string &output, OperatorPrecedence::Order order) const {
recursivePrintCommutative(output, order, OperatorPrecedence::MultiDivide,
'*');
}
Expression *Multiplication::diff() const {
ExpressionSet term;
ExpressionSet sum;
for (auto k = childrenSet.begin(); k != childrenSet.end(); k++) {
for (auto i = childrenSet.begin(); i != childrenSet.end(); i++) {
if (i == k)
term.insert((*i)->diff());
else
term.insert((*i)->clone());
}
sum.insert(new Multiplication(term));
term.clear();
}
return new Addition(sum);
}
Expression *Multiplication::TrySimplifyAdding(Expression *right) {
// a*b*c+a*b*d = a*b*(c+d)
// a*b*c*d + b*d = (a*c+1)*(b*d)
// find common elements in this->childrenSet and right->childrenSet
// this: a *c*d*e *g
// right: b*c *e*f*g
// common: c *e *g
// A: a *d // if NULL, A=1
// B: b *f // if NULL, B=1
// simplify: (A+B)*common = (a*d+b*f)*c*e*g
// !!! A,B,commonElements don't have ownership of their elements
ExpressionSet A, B, commonElements;
A = this->childrenSet;
if (right->nodeType() == TypeMulti) {
Multiplication *p = static_cast<Multiplication *>(right);
B = p->childrenSet;
} else {
// case of: a*b*c + c
B.insert(right);
}
auto i = A.begin();
auto j = B.begin();
while (i != A.end() && j != B.end()) {
if ((*i)->CanonicalSmallerThan(*j)) {
i++;
} else if ((*i)->CanonicalEqualTo(*j)) {
commonElements.insert(*i);
i = A.erase(i);
j = B.erase(j);
} else {
j++;
}
}
// case of a*b + c
if (commonElements.empty())
return NULL;
// case of this==right should be already treated in Addition: a+a=2*a
assert(!(A.empty() && B.empty()));
// now, Aown,Bown,commonElementsOwn have the ownership of their elements
ExpressionSet Aown, Bown, commonElementsOwn;
for (auto item : A) {
Aown.insert(item->clone());
}
for (auto item : B) {
Bown.insert(item->clone());
}
for (auto item : commonElements) {
commonElementsOwn.insert(item->clone());
}
Expression *multiA;
Expression *multiB;
if (Aown.empty()) {
multiA = new Constant(1);
multiB = (Bown.size() == 1) ? *(Bown.begin()) : new Multiplication(Bown);
} else if (B.empty()) {
multiB = new Constant(1);
multiA = (Aown.size() == 1) ? *(Aown.begin()) : new Multiplication(Aown);
} else {
multiA = (Aown.size() == 1) ? *(Aown.begin()) : new Multiplication(Aown);
multiB = (Bown.size() == 1) ? *(Bown.begin()) : new Multiplication(Bown);
}
Expression *AplusB = new Addition(multiA, multiB);
commonElementsOwn.insert(AplusB);
Expression *final = new Multiplication(commonElementsOwn);
bool changed;
Expression *finalSimplified = final->simplify(changed);
if (finalSimplified) {
delete final;
return finalSimplified;
}
else
return final;
}
Expression *Multiplication::TrySimplifyMultiplying(Expression *right) {
//must have been treated in Multiplication::simplify()
return nullptr;
}
Expression *Multiplication::simplify(bool &changed) {
bool needContinue = true;
changed = false;
while (needContinue) {
needContinue = false;
if (this->simplifyChildren()) {
changed = true;
//needContinue = true;
}
for (auto it = childrenSet.begin(); it != childrenSet.end(); it++) {
switch ((*it)->nodeType()) {
case TypeMulti: {
Multiplication *p = static_cast<Multiplication *>(*it);
it = childrenSet.erase(it);
childrenSet.insert(p->childrenSet.begin(), p->childrenSet.end());
p->childrenSet.clear();
delete p;
changed = true;
needContinue = true;
break;
}
case TypeConstant: {
Constant *p = static_cast<Constant *>(*it);
if (p->value() == 1) {
changed = true;
needContinue = true;
delete *it;
it = childrenSet.erase(it);
} else if (p->value() == 0) {
for (auto item : childrenSet)
delete item;
childrenSet.clear();
changed = true;
return new Constant(0);
}
break;
}
}
if (it == childrenSet.end())
break;
auto next = it;
next++;
if (next == childrenSet.end())
continue;
//simplify two by two
for (; next != childrenSet.end(); next++) {
Expression *p = (*it)->TrySimplifyMultiplying(*next);
if (p) {
changed = true;
needContinue = true;
delete *it;
delete *next;
childrenSet.insert(p);
childrenSet.erase(it);
it = childrenSet.erase(next);
break;
} else {
Expression *pp = (*next)->TrySimplifyMultiplying(*it);
if (pp) {
changed = true;
needContinue = true;
delete *it;
delete *next;
childrenSet.insert(pp);
childrenSet.erase(it);
it = childrenSet.erase(next);
break;
}
}
}
}
}
if (childrenSet.size() == 0) {
return new Constant(0);
} else if (childrenSet.size() == 1) {
return (*childrenSet.begin())->clone();
} else {
return NULL;
}
}
bool Division::simplifyChildren() {
bool childChanged;
bool changed = false;
Expression *nume = numerator->simplify(childChanged);
if (nume) {
changed = true;
delete numerator;
numerator = nume;
} else {
changed = childChanged || changed;
}
Expression *deno = denominator->simplify(childChanged);
if (deno) {
changed = true;
delete denominator;
denominator = deno;
} else {
changed = childChanged || changed;
}
return changed;
}
Division::Division(Expression *numerator, Expression *denominator) :
Expression(TypeDivide) {
this->numerator = numerator;
this->denominator = denominator;
if (!numerator || !denominator)
throw invalid_argument("null argument in Division");
}
bool Division::CanonicalEqualToSameType(Expression *other) {
assert(other->nodeType() == TypeDivide);
Division *p = static_cast<Division *>(other);
return this->denominator->CanonicalEqualTo(p->denominator)
&& this->numerator->CanonicalEqualTo(p->numerator);
}
bool Division::CanonicalSmallerThanSameType(Expression *other) {
assert(other->nodeType() == TypeDivide);
Division *p = static_cast<Division *>(other);
if (this->denominator->CanonicalSmallerThan(p->denominator))
return true;
else if (this->numerator->CanonicalSmallerThan(p->denominator))
return true;
else
return false;
}
double Division::operator()(double x) const {
return (*numerator)(x) / (*denominator)(x);
}
void Division::recursivePrint(string &output, OperatorPrecedence::Order order) const {
bool closeParenthese = false;
OperatorPrecedence::Order nextOrder;
if (order >= OperatorPrecedence::MultiDivide) {
output.push_back('(');
closeParenthese = true;
}
nextOrder = OperatorPrecedence::MultiDivide;
numerator->recursivePrint(output, nextOrder);
output.push_back('/');
denominator->recursivePrint(output, nextOrder);
if (closeParenthese) output.push_back(')');
}
Expression *Division::diff() const {
Expression *df_g = new Multiplication(numerator->diff(),
denominator->clone());
Expression *f_dg = new Multiplication(numerator->clone(),
denominator->diff());
Expression *g2 = new Multiplication(denominator->clone(),
denominator->clone());
Expression *dfg_fdg = new Addition(df_g,
new Multiplication(new Constant(-1), f_dg));
return new Division(dfg_fdg, g2);
}
Expression *Division::clone() const {
return new Division(numerator->clone(), denominator->clone());
}
Division::~Division() {
delete numerator;
delete denominator;
}
Expression *Division::TrySimplifyAdding(Expression *right) {
// a/c + b/c = (a+b)/c
if (right->nodeType() == TypeDivide) {
Division *p = static_cast<Division *>(right);
if (denominator->CanonicalEqualTo(p->denominator)) {
Expression *a_plus_b = new Addition(numerator->clone(), p->numerator->clone());
Expression *c = p->denominator->clone();
Expression *abc = new Division(a_plus_b, c);
bool changed;
Expression *simplify = abc->simplify(changed);
if (simplify) {
delete abc;
return simplify;
} else {
return abc;
}
}
}
return NULL;
}
Expression *Division::TrySimplifyMultiplying(Expression *right) {
if (right->nodeType() == TypeDivide) {
// (a/b)*(c/d)=(a*c)/(b*d)
Division *p = static_cast<Division *>(right);
Expression *ac = new Multiplication(numerator->clone(), p->denominator->clone());
Expression *bd = new Multiplication(denominator->clone(), p->numerator->clone());
Expression *acbd = new Division(ac, bd);
bool changed;
Expression *simplify = acbd->simplify(changed);
if (simplify) {
delete acbd;
return simplify;
} else {
return acbd;
}
} else {
// (a/b)*c = a*c / b
Expression *ac = new Multiplication(numerator->clone(), right->clone());
Expression *acb = new Division(ac, denominator->clone());
bool changed;
Expression *simplify = acb->simplify(changed);
if (simplify) {
delete acb;
return simplify;
} else {
return acb;
}
}
return NULL;
}
Expression *Division::simplify(bool &changed) {
changed = false;
changed = simplifyChildren() || changed;
// 0/a = 0
if (numerator->nodeType() == TypeConstant) {
Constant *p = static_cast<Constant *>(numerator);
if (p->value() == 0) {
return new Constant(0);
}
}
// a/1 = a
if (denominator->nodeType() == TypeConstant) {
Constant *p = static_cast<Constant *>(denominator);
if (p->value() == 1) {
return numerator->clone();
}
}
// (a/b)/(c/d) = ad/bc
{
bool numeDivision = numerator->nodeType() == TypeDivide;
bool denoDivision = denominator->nodeType() == TypeDivide;
Expression *a = 0, *b = 0, *c = 0, *d = 0;
if (numeDivision) {
changed = true;
Division *p = static_cast<Division *>(numerator);
//change ownership
a = p->numerator;
b = p->denominator;
p->numerator = NULL;
p->denominator = NULL;
delete p;
numerator = a;
}
if (denoDivision) {
changed = true;
Division *p = static_cast<Division *>(denominator);
//change ownership
c = p->numerator;
d = p->denominator;
p->numerator = NULL;
p->denominator = NULL;
delete p;
denominator = c;
}
if (b)
denominator = new Multiplication(denominator, b);
if (d)
numerator = new Multiplication(numerator, d);
}
changed = simplifyChildren() || changed;
return NULL;
}
Composition::Composition(Expression *left, Expression *right) :
Expression(TypeCompo), left(left), right(right) {
if (!left || !right) throw invalid_argument("null pointer in Composition");
}
bool Composition::CanonicalEqualToSameType(Expression *other) {
assert(other->nodeType() == TypeCompo);
Composition *p = static_cast<Composition *>(other);
return this->left->CanonicalEqualTo(p->left)
&& this->right->CanonicalEqualTo(p->right);
}
bool Composition::CanonicalSmallerThanSameType(Expression *other) {
assert(other->nodeType() == TypeCompo);
Composition *p = static_cast<Composition *>(other);
if (this->left->CanonicalSmallerThan(p->left))
return true;
else if (this->right->CanonicalSmallerThan(p->right))
return true;
else
return false;
}
void Composition::recursivePrint(string &output, OperatorPrecedence::Order order) const {
bool closeParentheses = false;
OperatorPrecedence::Order nextOrder;
if (order >= OperatorPrecedence::Composition) {
output.push_back('(');
closeParentheses = true;
}
nextOrder = OperatorPrecedence::Composition;
ElementryFunction *f = dynamic_cast<ElementryFunction *>(left);
if (f) {
f->compositionPrint(output, right);
} else {
left->recursivePrint(output, nextOrder);
output.push_back('o');
right->recursivePrint(output, nextOrder);
}
if (closeParentheses) output.push_back(')');
}
Expression *Composition::diff() const {
Expression *dfog = new Composition(left->diff(), right->clone());
Expression *dg = right->diff();
return new Multiplication(dfog, dg);
}
Expression *Composition::clone() const {
return new Composition(left->clone(), right->clone());
}
Expression *Composition::TrySimplifyAdding(Expression *right) {
return nullptr;
}
Expression *Composition::TrySimplifyMultiplying(Expression *right) {
return nullptr;
}
Expression *Composition::simplify(bool &changed) {
if (this->right->nodeType() == TypeVariable) {
changed = true;
return this->left->clone();
}
changed = false;
return nullptr;
}
bool Constant::CanonicalEqualToSameType(Expression *other) {
assert(other->nodeType() == TypeConstant);
const Constant *p = static_cast<const Constant *>(other);
return c == p->c;
}
bool Constant::CanonicalSmallerThanSameType(Expression *other) {
assert(other->nodeType() == TypeConstant);
const Constant *p = static_cast<const Constant *>(other);
return c < p->c;
}
void Constant::recursivePrint(string &output, OperatorPrecedence::Order order) const {
stringstream ss;
ss << this->c;
output += ss.str();
}
Expression *Constant::TrySimplifyAdding(Expression *right) {
switch (right->nodeType()) {
case TypeConstant: {
Constant *p = static_cast<Constant *>(right);
return new Constant(this->c + p->c);
}
case TypeVariable: {
return Polynomial::create(1, this->c);
}
case TypePoly: {
Polynomial *p = static_cast<Polynomial * >(right);
vector<double> para = p->getParameter();
assert(para.size() > 1);
para[0] += this->c;
return Polynomial::create(para);
}
default:
return NULL;
}
}
Expression *Constant::TrySimplifyMultiplying(Expression *right) {
assert(this->c != 0);
switch (right->nodeType()) {
case TypeConstant: {
Constant *p = static_cast<Constant *>(right);
return new Constant(this->c * p->c);
}
case TypeVariable: {
return Polynomial::create(this->c, 0);
}
case TypePoly: {
Polynomial *p = static_cast<Polynomial * >(right);
vector<double> para = p->getParameter();
assert(para.size() > 1);
for (auto it = para.begin(); it != para.end(); it++) {
*it *= this->c;
}
return Polynomial::create(para);
}
default:
return NULL;
}
}
Expression *VariableX::TrySimplifyAdding(Expression *right) {
switch (right->nodeType()) {
case TypeConstant:
assert(false);//should be treated by Constant
case TypeVariable: {
return Polynomial::create(2, 0);
}
case TypePoly: {
Polynomial *p = static_cast<Polynomial * >(right);
vector<double> para = p->getParameter();
assert(para.size() > 1);
para[1] += 1;
return Polynomial::create(para);
}
default:
return NULL;
}
}
Expression *VariableX::TrySimplifyMultiplying(Expression *right) {
switch (right->nodeType()) {
case TypeVariable: {
vector<double> para;
para.push_back(0);
para.push_back(0);
para.push_back(1);
return Polynomial::create(para);
}
case TypePoly: {
Polynomial *p = static_cast<Polynomial * >(right);
vector<double> para = p->getParameter();
assert(para.size() > 1);
para.push_back(0);
for (auto it = para.rbegin(); it != para.rend(); it++) {
*it = *(it + 1);
}
para[0] = 0;
return Polynomial::create(para);
}
default:
return NULL;
}
}
Polynomial::Polynomial(const vector<double> ¶metre) :
Expression(TypePoly) {
this->para = parametre;
// clear zeros at the end of list
for (int i = para.size() - 1; i >= 0; i--) {
if (para[i] == 0)
para.pop_back();
else
break;
}
bool isConst = true;
if (para.size() <= 1) {
throw invalid_argument(
"Degenerate case not allowed, Polynomial can't be constant");
}
}
Polynomial::Polynomial(double a, double b) :
Expression(TypePoly) {
if (a == 0)
throw invalid_argument(
"Degenerate case not allowed, Polynomial can't be constant");
this->para.push_back(b);
this->para.push_back(a);
}
Expression *Polynomial::create(const vector<double> ¶metre) {
vector<double> para = parametre;
// clear zeros at the end of list
for (int i = para.size() - 1; i >= 0; i--) {
if (para[i] == 0)
para.pop_back();
else
break;
}
if (para.size() == 0) {
return new Constant(0);
} else if (para.size() == 1) {
return new Constant(para[0]);
} else {
return new Polynomial(para);
}
}
Expression *Polynomial::create(double a, double b) {
//ax+b
if (a == 0)
return new Constant(b);
else
return new Polynomial(a, b);
}
bool Polynomial::CanonicalEqualToSameType(Expression *other) {
assert(other->nodeType() == TypePoly);
Polynomial *p = static_cast<Polynomial *>(other);
if (para.size() != p->para.size()) {
return false;
} else {
for (int i = para.size() - 1; i >= 0; i--)
if (para[i] != p->para[i]) return false;
return true;
}
}
bool Polynomial::CanonicalSmallerThanSameType(Expression *other) {
assert(other->nodeType() == TypePoly);
Polynomial *p = static_cast<Polynomial *>(other);
if (para.size() < p->para.size()) {
return true;
} else {
for (int i = para.size() - 1; i >= 0; i--)
if (para[i] < p->para[i]) return true;
return false;
}
}
double Polynomial::operator()(double x) const {
assert(para.size() > 0);
double xPowerK = 1;
double sum = 0;
for (vector<double>::const_iterator it = para.begin(); it != para.end();
it++) {
sum += (*it) * xPowerK;
xPowerK *= x;
}
return sum;
}
void Polynomial::recursivePrint(string &output, OperatorPrecedence::Order order) const {
stringstream ss;
bool firstItem = true;
// special treatment to the first constant
// not "ax^0", but "a"
assert(para.size() >= 2);
if (para[0] != 0) {
ss << para[0];
firstItem = false;
}
// special treatment to the second term
// not "ax^1", but "ax"
if (para[1] != 0) {
char sym;
sym = para[1] > 0 ? '+' : '-';
// -x not -1x
if (sym == '-' || !firstItem)
ss << sym;
if (para[1] != 1 && para[1] != -1)
ss << abs(para[1]);
ss << "x";
firstItem = false;
}
for (int i = 2; i < para.size(); i++) {
if (para[i] == 0) continue;
char sym;
sym = para[i] > 0 ? '+' : '-';
// -x not -1x
if (sym == '-' || !firstItem)
ss << sym;
if (para[i] != 1 && para[i] != -1)
ss << abs(para[i]);
ss << "x^" << i;
firstItem = false;
}
string s("Poly[");
s += ss.str();
s += "]";
output += s;
}
Expression *Polynomial::diff() const {
assert(para.size() >= 2);
vector<double> temp;
vector<double>::const_iterator it = para.begin();
it++;
int k = 1;
for (; it != para.end(); it++) {
temp.push_back(k * (*it)); // d(a*x^k)=a*k*x^(k-1)
k++;
}
return Polynomial::create(temp);
}
Expression *Polynomial::clone() const {
return new Polynomial(*this);
}
Expression *Polynomial::TrySimplifyAdding(Expression *right) {
switch (right->nodeType()) {
case TypeConstant://should be treated by Constant
case TypeVariable:// etc.
assert(false);