#include <iostream>
#include <stdexcept>
+#ifdef DO_GINAC_ASSERT
+# include <typeinfo>
+#endif
#include "basic.h"
#include "ex.h"
#include "symbol.h"
#include "lst.h"
#include "ncmul.h"
+#include "relational.h"
#include "print.h"
#include "archive.h"
#include "utils.h"
this->print(print_tree(std::cerr));
}
+/** Return relative operator precedence (for parenthizing output). */
+unsigned basic::precedence(void) const
+{
+ return 70;
+}
+
/** Create a new copy of this on the heap. One can think of this as simulating
* a virtual copy constructor which is needed for instance by the refcounted
* construction of an ex from a basic. */
return op(i);
}
-/** Search ocurrences. An object 'has' an expression if it is the expression
+/** Search ocurrences. An object 'has' an expression if it is the expression
* itself or one of the children 'has' it. As a consequence (according to
* the definition of children) given e=x+y+z, e.has(x) is true but e.has(x+y)
- * is false. */
+ * is false. The expression can also contain wildcards. */
bool basic::has(const ex & other) const
{
GINAC_ASSERT(other.bp!=0);
- if (is_equal(*other.bp)) return true;
+ lst repl_lst;
+ if (match(*other.bp, repl_lst)) return true;
if (nops()>0) {
for (unsigned i=0; i<nops(); i++)
if (op(i).has(other))
return false;
}
-/** Return degree of highest power in symbol s. */
+/** Return degree of highest power in object s. */
int basic::degree(const ex & s) const
{
return 0;
}
-/** Return degree of lowest power in symbol s. */
+/** Return degree of lowest power in object s. */
int basic::ldegree(const ex & s) const
{
return 0;
}
-/** Return coefficient of degree n in symbol s. */
+/** Return coefficient of degree n in object s. */
ex basic::coeff(const ex & s, int n) const
{
return n==0 ? *this : _ex0();
}
-/** Sort expression in terms of powers of some symbol.
- * @param s symbol to sort in. */
-ex basic::collect(const ex & s) const
+/** Sort expression in terms of powers of some object(s).
+ * @param s object(s) to sort in
+ * @param distributed recursive or distributed form (only used when s is a list) */
+ex basic::collect(const ex & s, bool distributed) const
{
ex x;
- for (int n=this->ldegree(s); n<=this->degree(s); n++)
- x += this->coeff(s,n)*power(s,n);
+ if (is_ex_of_type(s, lst)) {
+
+ // List of objects specified
+ if (s.nops() == 1)
+ return collect(s.op(0));
+
+ else if (distributed) {
+
+ // Get lower/upper degree of all symbols in list
+ int num = s.nops();
+ struct sym_info {
+ ex sym;
+ int ldeg, deg;
+ int cnt; // current degree, 'counter'
+ ex coeff; // coefficient for degree 'cnt'
+ };
+ sym_info *si = new sym_info[num];
+ ex c = *this;
+ for (int i=0; i<num; i++) {
+ si[i].sym = s.op(i);
+ si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
+ si[i].deg = this->degree(si[i].sym);
+ c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
+ }
+
+ while (true) {
+
+ // Calculate coeff*x1^c1*...*xn^cn
+ ex y = _ex1();
+ for (int i=0; i<num; i++) {
+ int cnt = si[i].cnt;
+ y *= power(si[i].sym, cnt);
+ }
+ x += y * si[num - 1].coeff;
+
+ // Increment counters
+ int n = num - 1;
+ while (true) {
+ si[n].cnt++;
+ if (si[n].cnt <= si[n].deg) {
+ // Update coefficients
+ ex c;
+ if (n == 0)
+ c = *this;
+ else
+ c = si[n - 1].coeff;
+ for (int i=n; i<num; i++)
+ c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
+ break;
+ }
+ if (n == 0)
+ goto done;
+ si[n].cnt = si[n].ldeg;
+ n--;
+ }
+ }
+
+done: delete[] si;
+
+ } else {
+
+ // Recursive form
+ x = *this;
+ for (int n=s.nops()-1; n>=0; n--)
+ x = x.collect(s[n]);
+ }
+
+ } else {
+
+ // Only one object specified
+ for (int n=this->ldegree(s); n<=this->degree(s); ++n)
+ x += this->coeff(s,n)*power(s,n);
+ }
- return x;
+ // correct for lost fractional arguments and return
+ return x + (*this - x).expand();
}
/** Perform automatic non-interruptive symbolic evaluation on expression. */
return false;
}
+/** Check whether the expression matches a given pattern. For every wildcard
+ * object in the pattern, an expression of the form "wildcard == matching_expression"
+ * is added to repl_lst. */
+bool basic::match(const ex & pattern, lst & repl_lst) const
+{
+/*
+ Sweet sweet shapes, sweet sweet shapes,
+ Thats the key thing, right right.
+ Feed feed face, feed feed shapes,
+ But who is the king tonight?
+ Who is the king tonight?
+ Pattern is the thing, the key thing-a-ling,
+ But who is the king of pattern?
+ But who is the king, the king thing-a-ling,
+ Who is the king of Pattern?
+ Bog is the king, the king thing-a-ling,
+ Bog is the king of Pattern.
+ Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
+ Bog is the king of Pattern.
+*/
+
+ if (is_ex_exactly_of_type(pattern, wildcard)) {
+
+ // Wildcard matches anything, but check whether we already have found
+ // a match for that wildcard first (if so, it the earlier match must
+ // be the same expression)
+ for (unsigned i=0; i<repl_lst.nops(); i++) {
+ if (repl_lst.op(i).op(0).is_equal(pattern))
+ return is_equal(*repl_lst.op(i).op(1).bp);
+ }
+ repl_lst.append(pattern == *this);
+ return true;
+
+ } else {
+
+ // Expression must be of the same type as the pattern
+ if (tinfo() != pattern.bp->tinfo())
+ return false;
+
+ // Number of subexpressions must match
+ if (nops() != pattern.nops())
+ return false;
+
+ // No subexpressions? Then just compare the objects (there can't be
+ // wildcards in the pattern)
+ if (nops() == 0)
+ return is_equal(*pattern.bp);
+
+ // Otherwise the subexpressions must match one-to-one
+ for (unsigned i=0; i<nops(); i++)
+ if (!op(i).match(pattern.op(i), repl_lst))
+ return false;
+
+ // Looks similar enough, match found
+ return true;
+ }
+}
+
/** Substitute a set of objects by arbitrary expressions. The ex returned
* will already be evaluated. */
-ex basic::subs(const lst & ls, const lst & lr) const
+ex basic::subs(const lst & ls, const lst & lr, bool no_pattern) const
{
GINAC_ASSERT(ls.nops() == lr.nops());
- for (unsigned i=0; i<ls.nops(); i++) {
- if (is_equal(*ls.op(i).bp))
- return lr.op(i);
+ if (no_pattern) {
+ for (unsigned i=0; i<ls.nops(); i++) {
+ if (is_equal(*ls.op(i).bp))
+ return lr.op(i);
+ }
+ } else {
+ for (unsigned i=0; i<ls.nops(); i++) {
+ lst repl_lst;
+ if (match(*ls.op(i).bp, repl_lst))
+ return lr.op(i).bp->subs(repl_lst, true); // avoid infinite recursion when re-substituting the wildcards
+ }
}
return *this;
* replacement arguments: 1) a relational like object==ex and 2) a list of
* relationals lst(object1==ex1,object2==ex2,...), which is converted to
* subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
-ex basic::subs(const ex & e) const
+ex basic::subs(const ex & e, bool no_pattern) const
{
if (e.info(info_flags::relation_equal)) {
- return subs(lst(e));
+ return subs(lst(e), no_pattern);
}
if (!e.info(info_flags::list)) {
throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
for (unsigned i=0; i<e.nops(); i++) {
ex r = e.op(i);
if (!r.info(info_flags::relation_equal)) {
- throw(std::invalid_argument("basic::subs(ex): argument must be a list or equations"));
+ throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
}
ls.append(r.op(0));
lr.append(r.op(1));
}
- return subs(ls, lr);
+ return subs(ls, lr, no_pattern);
}
/** Compare objects to establish canonical ordering.
throw(std::runtime_error("cannot modify multiply referenced object"));
}
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned basic::precedence = 70;
-
//////////
// global variables
//////////
git://www.ginac.de / ginac.git / blobdiff