- eta(x,y) was broken all along since ages: eta(I,I) for instance ought
authorRichard Kreckel <Richard.Kreckel@uni-mainz.de>
Wed, 27 Jun 2001 23:07:30 +0000 (23:07 +0000)
committerRichard Kreckel <Richard.Kreckel@uni-mainz.de>
Wed, 27 Jun 2001 23:07:30 +0000 (23:07 +0000)
  to return 0 but... that formula that reduces eta(x,y) to theta functions
  is basically to naive.

check/exam_inifcns.cpp
ginac/inifcns.cpp

index 47cc10404c43f45217890a0a0f694a8e91826440..96ea9cc7cd4a3feb8e3750d45eba145b062ea6a5 100644 (file)
@@ -90,6 +90,27 @@ static unsigned inifcns_consist_trans(void)
                ++result;
        }
        
+       // check consistency of log and eta phases:
+       for (int r1=-1; r1<=1; ++r1) {
+               for (int i1=-1; i1<=1; ++i1) {
+                       ex x1 = r1+I*i1;
+                       if (x1.is_zero())
+                               continue;
+                       for (int r2=-1; r2<=1; ++r2) {
+                               for (int i2=-1; i2<=1; ++i2) {
+                                       ex x2 = r2+I*i2;
+                                       if (x2.is_zero())
+                                               continue;
+                                       if (abs(evalf(eta(x1,x2)-log(x1*x2)+log(x1)+log(x2)))>.1e-12) {
+                                               clog << "either eta(x,y), log(x), log(y) or log(x*y) is wrong"
+                                                    << " at x==" << x1 << ", y==" << x2 << endl;
+                                               ++result;
+                                       }
+                               }
+                       }
+               }
+       }
+               
        return result;
 }
 
@@ -100,7 +121,7 @@ static unsigned inifcns_consist_gamma(void)
        unsigned result = 0;
        ex e;
        
-       e = tgamma(ex(1));
+       e = tgamma(1);
        for (int i=2; i<8; ++i)
                e += tgamma(ex(i));
        if (e != numeric(874)) {
@@ -109,7 +130,7 @@ static unsigned inifcns_consist_gamma(void)
                ++result;
        }
        
-       e = tgamma(ex(1));
+       e = tgamma(1);
        for (int i=2; i<8; ++i)
                e *= tgamma(ex(i));     
        if (e != numeric(24883200)) {
index f64597e5c3cb50031b57e577b7c221f060d4d999..316eea6c26e621779b23ffc9d64bf15d45987e84 100644 (file)
@@ -126,57 +126,78 @@ REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
 
 
 //////////
-// Eta function: log(x*y) == log(x) + log(y) + eta(x,y).
+// Eta function: eta(x,y) == log(x*y) - log(x) - log(y).
 //////////
 
-static ex eta_evalf(const ex & x, const ex & y)
+static ex eta_evalf(const ex &x, const ex &y)
 {
-       BEGIN_TYPECHECK
-               TYPECHECK(x,numeric)
-               TYPECHECK(y,numeric)
-       END_TYPECHECK(eta(x,y))
-               
-       numeric xim = imag(ex_to<numeric>(x));
-       numeric yim = imag(ex_to<numeric>(y));
-       numeric xyim = imag(ex_to<numeric>(x*y));
-       return evalf(I/4*Pi)*((csgn(-xim)+1)*(csgn(-yim)+1)*(csgn(xyim)+1)-(csgn(xim)+1)*(csgn(yim)+1)*(csgn(-xyim)+1));
+       // It seems like we basically have to replicate the eval function here,
+       // since the expression might not be fully evaluated yet.
+       if (x.info(info_flags::positive) || y.info(info_flags::positive))
+               return _ex0();
+
+       if (x.info(info_flags::numeric) &&      y.info(info_flags::numeric)) {
+               const numeric nx = ex_to<numeric>(x);
+               const numeric ny = ex_to<numeric>(y);
+               const numeric nxy = ex_to<numeric>(x*y);
+               int cut = 0;
+               if (nx.is_real() && nx.is_negative())
+                       cut -= 4;
+               if (ny.is_real() && ny.is_negative())
+                       cut -= 4;
+               if (nxy.is_real() && nxy.is_negative())
+                       cut += 4;
+               return evalf(I/4*Pi)*((csgn(-imag(nx))+1)*(csgn(-imag(ny))+1)*(csgn(imag(nxy))+1)-
+                                     (csgn(imag(nx))+1)*(csgn(imag(ny))+1)*(csgn(-imag(nxy))+1)+cut);
+       }
+
+       return eta(x,y).hold();
 }
 
-static ex eta_eval(const ex & x, const ex & y)
+static ex eta_eval(const ex &x, const ex &y)
 {
-       if (is_ex_exactly_of_type(x, numeric) &&
-               is_ex_exactly_of_type(y, numeric)) {
+       // trivial:  eta(x,c) -> 0  if c is real and positive
+       if (x.info(info_flags::positive) || y.info(info_flags::positive))
+               return _ex0();
+
+       if (x.info(info_flags::numeric) &&      y.info(info_flags::numeric)) {
                // don't call eta_evalf here because it would call Pi.evalf()!
-               numeric xim = imag(ex_to<numeric>(x));
-               numeric yim = imag(ex_to<numeric>(y));
-               numeric xyim = imag(ex_to<numeric>(x*y));
-               return (I/4)*Pi*((csgn(-xim)+1)*(csgn(-yim)+1)*(csgn(xyim)+1)-(csgn(xim)+1)*(csgn(yim)+1)*(csgn(-xyim)+1));
+               const numeric nx = ex_to<numeric>(x);
+               const numeric ny = ex_to<numeric>(y);
+               const numeric nxy = ex_to<numeric>(x*y);
+               int cut = 0;
+               if (nx.is_real() && nx.is_negative())
+                       cut -= 4;
+               if (ny.is_real() && ny.is_negative())
+                       cut -= 4;
+               if (nxy.is_real() && nxy.is_negative())
+                       cut += 4;
+               return (I/4)*Pi*((csgn(-imag(nx))+1)*(csgn(-imag(ny))+1)*(csgn(imag(nxy))+1)-
+                                (csgn(imag(nx))+1)*(csgn(imag(ny))+1)*(csgn(-imag(nxy))+1)+cut);
        }
        
        return eta(x,y).hold();
 }
 
-static ex eta_series(const ex & arg1,
-                     const ex & arg2,
+static ex eta_series(const ex & x, const ex & y,
                      const relational & rel,
                      int order,
                      unsigned options)
 {
-       const ex arg1_pt = arg1.subs(rel);
-       const ex arg2_pt = arg2.subs(rel);
-       if (ex_to<numeric>(arg1_pt).imag().is_zero() ||
-               ex_to<numeric>(arg2_pt).imag().is_zero() ||
-               ex_to<numeric>(arg1_pt*arg2_pt).imag().is_zero()) {
-               throw (std::domain_error("eta_series(): on discontinuity"));
-       }
+       const ex x_pt = x.subs(rel);
+       const ex y_pt = y.subs(rel);
+       if ((x_pt.info(info_flags::numeric) && x_pt.info(info_flags::negative)) ||
+           (y_pt.info(info_flags::numeric) && y_pt.info(info_flags::negative)) ||
+           ((x_pt*y_pt).info(info_flags::numeric) && (x_pt*y_pt).info(info_flags::negative)))
+                       throw (std::domain_error("eta_series(): on discontinuity"));
        epvector seq;
-       seq.push_back(expair(eta(arg1_pt,arg2_pt), _ex0()));
+       seq.push_back(expair(eta(x_pt,y_pt), _ex0()));
        return pseries(rel,seq);
 }
 
 REGISTER_FUNCTION(eta, eval_func(eta_eval).
                        evalf_func(eta_evalf).
-                       series_func(eta_series).
+                                      series_func(eta_series).
                        latex_name("\\eta"));
 
 
@@ -419,7 +440,7 @@ ex lsolve(const ex &eqns, const ex &symbols)
        if (eqns.info(info_flags::relation_equal)) {
                if (!symbols.info(info_flags::symbol))
                        throw(std::invalid_argument("lsolve(): 2nd argument must be a symbol"));
-               ex sol=lsolve(lst(eqns),lst(symbols));
+               const ex sol = lsolve(lst(eqns),lst(symbols));
                
                GINAC_ASSERT(sol.nops()==1);
                GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
@@ -451,10 +472,10 @@ ex lsolve(const ex &eqns, const ex &symbols)
        matrix vars(symbols.nops(),1);
        
        for (unsigned r=0; r<eqns.nops(); r++) {
-               ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
+               const 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);
+                       const ex co = eq.coeff(ex_to<symbol>(symbols.op(c)),1);
                        linpart -= co*symbols.op(c);
                        sys(r,c) = co;
                }