- expairseq.cpp: moved expairseq::to_rational to...
[ginac.git] / ginac / inifcns.cpp
index f9b797ee6eeb7d2297355538a5337cfecf5136a1..f7d2864ef9ae64035eae269d140b6c36b6d41169 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's initially known functions. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
  *
  *  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
 #include "numeric.h"
 #include "power.h"
 #include "relational.h"
-#include "series.h"
+#include "pseries.h"
 #include "symbol.h"
+#include "utils.h"
+
+#ifndef NO_NAMESPACE_GINAC
+namespace GiNaC {
+#endif // ndef NO_NAMESPACE_GINAC
+
+//////////
+// absolute value
+//////////
+
+static ex abs_evalf(const ex & x)
+{
+    BEGIN_TYPECHECK
+        TYPECHECK(x,numeric)
+    END_TYPECHECK(abs(x))
+    
+    return abs(ex_to_numeric(x));
+}
+
+static ex abs_eval(const ex & x)
+{
+    if (is_ex_exactly_of_type(x, numeric))
+        return abs(ex_to_numeric(x));
+    else
+        return abs(x).hold();
+}
+
+REGISTER_FUNCTION(abs, eval_func(abs_eval).
+                       evalf_func(abs_evalf));
+
+
+//////////
+// Complex sign
+//////////
+
+static ex csgn_evalf(const ex & x)
+{
+    BEGIN_TYPECHECK
+        TYPECHECK(x,numeric)
+    END_TYPECHECK(csgn(x))
+    
+    return csgn(ex_to_numeric(x));
+}
+
+static ex csgn_eval(const ex & x)
+{
+    if (is_ex_exactly_of_type(x, numeric))
+        return csgn(ex_to_numeric(x));
+    
+    if (is_ex_exactly_of_type(x, mul)) {
+        numeric oc = ex_to_numeric(x.op(x.nops()-1));
+        if (oc.is_real()) {
+            if (oc > 0)
+                // csgn(42*x) -> csgn(x)
+                return csgn(x/oc).hold();
+            else
+                // csgn(-42*x) -> -csgn(x)
+                return -csgn(x/oc).hold();
+        }
+        if (oc.real().is_zero()) {
+            if (oc.imag() > 0)
+                // csgn(42*I*x) -> csgn(I*x)
+                return csgn(I*x/oc).hold();
+            else
+                // csgn(-42*I*x) -> -csgn(I*x)
+                return -csgn(I*x/oc).hold();
+        }
+    }
+    
+    return csgn(x).hold();
+}
+
+static ex csgn_series(const ex & x, const relational & rel, int order)
+{
+    const ex x_pt = x.subs(rel);
+    if (x_pt.info(info_flags::numeric)) {
+        if (ex_to_numeric(x_pt).real().is_zero())
+            throw (std::domain_error("csgn_series(): on imaginary axis"));
+        epvector seq;
+        seq.push_back(expair(csgn(x_pt), _ex0()));
+        return pseries(rel,seq);
+    }
+    epvector seq;
+    seq.push_back(expair(csgn(x_pt), _ex0()));
+    return pseries(rel,seq);
+}
+
+REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
+                        evalf_func(csgn_evalf).
+                        series_func(csgn_series));
 
 //////////
 // dilogarithm
 //////////
 
-ex Li2_eval(ex const & x)
+static ex Li2_eval(const ex & x)
 {
     if (x.is_zero())
         return x;
-    if (x.is_equal(exONE()))
-        return power(Pi, 2) / 6;
-    if (x.is_equal(exMINUSONE()))
-        return -power(Pi, 2) / 12;
+    if (x.is_equal(_ex1()))
+        return power(Pi, _ex2()) / _ex6();
+    if (x.is_equal(_ex_1()))
+        return -power(Pi, _ex2()) / _ex12();
     return Li2(x).hold();
 }
 
-REGISTER_FUNCTION(Li2, Li2_eval, NULL, NULL, NULL);
+REGISTER_FUNCTION(Li2, eval_func(Li2_eval));
 
 //////////
 // trilogarithm
 //////////
 
-ex Li3_eval(ex const & x)
+static ex Li3_eval(const ex & x)
 {
     if (x.is_zero())
         return x;
     return Li3(x).hold();
 }
 
-REGISTER_FUNCTION(Li3, Li3_eval, NULL, NULL, NULL);
+REGISTER_FUNCTION(Li3, eval_func(Li3_eval));
 
 //////////
 // factorial
 //////////
 
-ex factorial_evalf(ex const & x)
+static ex factorial_evalf(const ex & x)
 {
     return factorial(x).hold();
 }
 
-ex factorial_eval(ex const & x)
+static ex factorial_eval(const ex & x)
 {
     if (is_ex_exactly_of_type(x, numeric))
         return factorial(ex_to_numeric(x));
@@ -83,18 +173,19 @@ ex factorial_eval(ex const & x)
         return factorial(x).hold();
 }
 
-REGISTER_FUNCTION(factorial, factorial_eval, factorial_evalf, NULL, NULL);
+REGISTER_FUNCTION(factorial, eval_func(factorial_eval).
+                             evalf_func(factorial_evalf));
 
 //////////
 // binomial
 //////////
 
-ex binomial_evalf(ex const & x, ex const & y)
+static ex binomial_evalf(const ex & x, const ex & y)
 {
     return binomial(x, y).hold();
 }
 
-ex binomial_eval(ex const & x, ex const &y)
+static ex binomial_eval(const ex & x, const ex &y)
 {
     if (is_ex_exactly_of_type(x, numeric) && is_ex_exactly_of_type(y, numeric))
         return binomial(ex_to_numeric(x), ex_to_numeric(y));
@@ -102,18 +193,19 @@ ex binomial_eval(ex const & x, ex const &y)
         return binomial(x, y).hold();
 }
 
-REGISTER_FUNCTION(binomial, binomial_eval, binomial_evalf, NULL, NULL);
+REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
+                            evalf_func(binomial_evalf));
 
 //////////
 // Order term function (for truncated power series)
 //////////
 
-ex Order_eval(ex const & x)
+static ex Order_eval(const ex & x)
 {
        if (is_ex_exactly_of_type(x, numeric)) {
 
                // O(c)=O(1)
-               return Order(exONE()).hold();
+               return Order(_ex1()).hold();
 
        } else if (is_ex_exactly_of_type(x, mul)) {
 
@@ -127,18 +219,43 @@ ex Order_eval(ex const & x)
        return Order(x).hold();
 }
 
-ex Order_series(ex const & x, symbol const & s, ex const & point, int order)
+static ex Order_series(const ex & x, const relational & r, int order)
 {
-       // Just wrap the function into a series object
+       // Just wrap the function into a pseries object
        epvector new_seq;
-       new_seq.push_back(expair(Order(exONE()), numeric(min(x.ldegree(s), order))));
-       return series(s, point, new_seq);
+    GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
+    const symbol *s = static_cast<symbol *>(r.lhs().bp);
+       new_seq.push_back(expair(Order(_ex1()), numeric(min(x.ldegree(*s), order))));
+       return pseries(r, new_seq);
 }
 
-REGISTER_FUNCTION(Order, Order_eval, NULL, NULL, Order_series);
+// Differentiation is handled in function::derivative because of its special requirements
+
+REGISTER_FUNCTION(Order, eval_func(Order_eval).
+                         series_func(Order_series));
 
-/** linear solve. */
-ex lsolve(ex const &eqns, ex const &symbols)
+//////////
+// Inert partial differentiation operator
+//////////
+
+static ex Derivative_eval(const ex & f, const ex & l)
+{
+       if (!is_ex_exactly_of_type(f, function)) {
+        throw(std::invalid_argument("Derivative(): 1st argument must be a function"));
+       }
+    if (!is_ex_exactly_of_type(l, lst)) {
+        throw(std::invalid_argument("Derivative(): 2nd argument must be a list"));
+    }
+       return Derivative(f, l).hold();
+}
+
+REGISTER_FUNCTION(Derivative, eval_func(Derivative_eval));
+
+//////////
+// Solve linear system
+//////////
+
+ex lsolve(const ex &eqns, const ex &symbols)
 {
     // solve a system of linear equations
     if (eqns.info(info_flags::relation_equal)) {
@@ -147,8 +264,8 @@ ex lsolve(ex const &eqns, ex const &symbols)
         }
         ex sol=lsolve(lst(eqns),lst(symbols));
         
-        ASSERT(sol.nops()==1);
-        ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
+        GINAC_ASSERT(sol.nops()==1);
+        GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
         
         return sol.op(0).op(1); // return rhs of first solution
     }
@@ -157,7 +274,7 @@ ex lsolve(ex const &eqns, ex const &symbols)
     if (!eqns.info(info_flags::list)) {
         throw(std::invalid_argument("lsolve: 1st argument must be a list"));
     }
-    for (int i=0; i<eqns.nops(); i++) {
+    for (unsigned i=0; i<eqns.nops(); i++) {
         if (!eqns.op(i).info(info_flags::relation_equal)) {
             throw(std::invalid_argument("lsolve: 1st argument must be a list of equations"));
         }
@@ -165,7 +282,7 @@ ex lsolve(ex const &eqns, ex const &symbols)
     if (!symbols.info(info_flags::list)) {
         throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
     }
-    for (int i=0; i<symbols.nops(); i++) {
+    for (unsigned i=0; i<symbols.nops(); i++) {
         if (!symbols.op(i).info(info_flags::symbol)) {
             throw(std::invalid_argument("lsolve: 2nd argument must be a list of symbols"));
         }
@@ -175,12 +292,12 @@ ex lsolve(ex const &eqns, ex const &symbols)
     matrix sys(eqns.nops(),symbols.nops());
     matrix rhs(eqns.nops(),1);
     matrix vars(symbols.nops(),1);
-
-    for (int r=0; r<eqns.nops(); r++) {
-        ex eq=eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
-        ex linpart=eq;
-        for (int c=0; c<symbols.nops(); c++) {
-            ex co=eq.coeff(ex_to_symbol(symbols.op(c)),1);
+    
+    for (unsigned r=0; r<eqns.nops(); r++) {
+        ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
+        ex linpart = eq;
+        for (unsigned c=0; c<symbols.nops(); c++) {
+            ex co = eq.coeff(ex_to_symbol(symbols.op(c)),1);
             linpart -= co*symbols.op(c);
             sys.set(r,c,co);
         }
@@ -189,24 +306,22 @@ ex lsolve(ex const &eqns, ex const &symbols)
     }
     
     // test if system is linear and fill vars matrix
-    for (int i=0; i<symbols.nops(); i++) {
+    for (unsigned i=0; i<symbols.nops(); i++) {
         vars.set(i,0,symbols.op(i));
-        if (sys.has(symbols.op(i))) {
+        if (sys.has(symbols.op(i)))
             throw(std::logic_error("lsolve: system is not linear"));
-        }
-        if (rhs.has(symbols.op(i))) {
+        if (rhs.has(symbols.op(i)))
             throw(std::logic_error("lsolve: system is not linear"));
-        }
     }
     
     //matrix solution=sys.solve(rhs);
     matrix solution;
     try {
-        solution=sys.fraction_free_elim(vars,rhs);
-    } catch (runtime_error const & e) {
+        solution = sys.fraction_free_elim(vars,rhs);
+    } catch (const runtime_error & e) {
         // probably singular matrix (or other error)
         // return empty solution list
-        cerr << e.what() << endl;
+        // cerr << e.what() << endl;
         return lst();
     }
     
@@ -222,7 +337,7 @@ ex lsolve(ex const &eqns, ex const &symbols)
     
     // return list of the form lst(var1==sol1,var2==sol2,...)
     lst sollist;
-    for (int i=0; i<symbols.nops(); i++) {
+    for (unsigned i=0; i<symbols.nops(); i++) {
         sollist.append(symbols.op(i)==solution(i,0));
     }
     
@@ -230,10 +345,10 @@ ex lsolve(ex const &eqns, ex const &symbols)
 }
 
 /** non-commutative power. */
-ex ncpower(ex const &basis, unsigned exponent)
+ex ncpower(const ex &basis, unsigned exponent)
 {
     if (exponent==0) {
-        return exONE();
+        return _ex1();
     }
 
     exvector v;
@@ -244,3 +359,12 @@ ex ncpower(ex const &basis, unsigned exponent)
 
     return ncmul(v,1);
 }
+
+/** Force inclusion of functions from initcns_gamma and inifcns_zeta
+ *  for static lib (so ginsh will see them). */
+unsigned force_include_tgamma = function_index_tgamma;
+unsigned force_include_zeta1 = function_index_zeta1;
+
+#ifndef NO_NAMESPACE_GINAC
+} // namespace GiNaC
+#endif // ndef NO_NAMESPACE_GINAC