From e31f4ca5848e18328d5263cea5a5a640d27a247d Mon Sep 17 00:00:00 2001 From: Jens Vollinga Date: Wed, 10 Mar 2004 16:19:50 +0000 Subject: [PATCH] Modifications for improved series expansion. --- check/exam_pseries.cpp | 40 +++++++++++++++++++++++++--------------- check/time_antipode.cpp | 2 +- 2 files changed, 26 insertions(+), 16 deletions(-) diff --git a/check/exam_pseries.cpp b/check/exam_pseries.cpp index a0cea2bc..8ecbe7ac 100644 --- a/check/exam_pseries.cpp +++ b/check/exam_pseries.cpp @@ -28,7 +28,7 @@ static unsigned check_series(const ex &e, const ex &point, const ex &d, int orde { ex es = e.series(x==point, order); ex ep = ex_to(es).convert_to_poly(); - if (!(ep - d).is_zero()) { + if (!(ep - d).expand().is_zero()) { clog << "series expansion of " << e << " at " << point << " erroneously returned " << ep << " (instead of " << d << ")" << endl; @@ -71,15 +71,15 @@ static unsigned exam_series1() result += check_series(e, 1, d); e = pow(x + pow(x, 3), -1); - d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + Order(pow(x, 7)); + d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + pow(x, 7) + Order(pow(x, 8)); result += check_series(e, 0, d); e = pow(pow(x, 2) + pow(x, 4), -1); - d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + Order(pow(x, 6)); + d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + pow(x, 6) + Order(pow(x, 8)); result += check_series(e, 0, d); e = pow(sin(x), -2); - d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + Order(pow(x, 5)); + d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + pow(x, 6) / 675 + Order(pow(x, 8)); result += check_series(e, 0, d); e = sin(x) / cos(x); @@ -87,7 +87,7 @@ static unsigned exam_series1() result += check_series(e, 0, d); e = cos(x) / sin(x); - d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 + Order(pow(x, 6)); + d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 - pow(x, 7) / 4725 + Order(pow(x, 8)); result += check_series(e, 0, d); e = pow(numeric(2), x); @@ -105,6 +105,16 @@ static unsigned exam_series1() result += check_series(e, 0, d, 1); result += check_series(e, 0, d, 2); + e = pow(x, 8) * pow(pow(x,3)+ pow(x + pow(x,3), 2), -2); + d = pow(x, 4) - 2*pow(x, 5) + Order(pow(x, 6)); + result += check_series(e, 0, d, 6); + + e = cos(x) * pow(sin(x)*(pow(x, 5) + 4 * pow(x, 2)), -3); + d = pow(x, -9) / 64 - 3 * pow(x, -6) / 256 - pow(x, -5) / 960 + 535 * pow(x, -3) / 96768 + + pow(x, -2) / 1280 - pow(x, -1) / 14400 - numeric(283, 129024) - 2143 * x / 5322240 + + Order(pow(x, 2)); + result += check_series(e, 0, d, 2); + return result; } @@ -115,7 +125,7 @@ static unsigned exam_series2() ex e, d; e = pow(sin(x), -1).series(x==0, 8) + pow(sin(-x), -1).series(x==0, 12); - d = Order(pow(x, 6)); + d = Order(pow(x, 8)); result += check_series(e, 0, d); return result; @@ -144,8 +154,9 @@ static unsigned exam_series4() d = 4 - 4*pow(x, 2) + 4*pow(x, 4)/3 + Order(pow(x, 5)); result += check_series(e, 0, d); - e = pow(tgamma(x), 2).series(x==0, 3); - d = pow(x,-2) - 2*Euler/x + (pow(Pi,2)/6+2*pow(Euler,2)) + Order(x); + e = pow(tgamma(x), 2).series(x==0, 2); + d = pow(x,-2) - 2*Euler/x + (pow(Pi,2)/6+2*pow(Euler,2)) + + x*(-4*pow(Euler, 3)/3 -pow(Pi,2)*Euler/3 - 2*zeta(3)/3) + Order(pow(x, 2)); result += check_series(e, 0, d); return result; @@ -209,17 +220,16 @@ static unsigned exam_series7() ex e = tan(x*Pi/2); ex d = pow(x-1,-1)/Pi*(-2) + pow(x-1,1)*Pi/6 + pow(x-1,3)*pow(Pi,3)/360 +pow(x-1,5)*pow(Pi,5)/15120 + pow(x-1,7)*pow(Pi,7)/604800 - +Order(pow(x-1,8)); - return check_series(e,1,d,8); + +Order(pow(x-1,9)); + return check_series(e,1,d,9); } // Series expansion of log(sin(x==0)) static unsigned exam_series8() { ex e = log(sin(x)); - ex d = log(x) - pow(x,2)/6 - pow(x,4)/180 - pow(x,6)/2835 - +Order(pow(x,8)); - return check_series(e,0,d,8); + ex d = log(x) - pow(x,2)/6 - pow(x,4)/180 - pow(x,6)/2835 - pow(x,8)/37800 + Order(pow(x,9)); + return check_series(e,0,d,9); } // Series expansion of Li2(sin(x==0)) @@ -282,8 +292,8 @@ static unsigned exam_series11() result += check_series(e,0,d,5); e = log((1-x)/x); - d = log(1-x) - (x-1) + pow(x-1,2)/2 - pow(x-1,3)/3 + Order(pow(x-1,4)); - result += check_series(e,1,d,4); + d = log(1-x) - (x-1) + pow(x-1,2)/2 - pow(x-1,3)/3 + pow(x-1,4)/4 + Order(pow(x-1,5)); + result += check_series(e,1,d,5); return result; } diff --git a/check/time_antipode.cpp b/check/time_antipode.cpp index 524aa063..d618fabe 100644 --- a/check/time_antipode.cpp +++ b/check/time_antipode.cpp @@ -455,7 +455,7 @@ static unsigned test_tree(const node tree_generator(unsigned)) // ...the sum, when evaluated and reexpanded, is the antipode... ex result = 0; for (vector::iterator i=counter.begin(); i!=counter.end(); ++i) - result = (result+i->evaluate(x,vertices)).series(x==0,vertices).expand(); + result = (result+i->evaluate(x,vertices-1)).series(x==0,vertices-1).expand(); // ...and has the nice property that in each term all the Eulers cancel: if (result.has(Euler)) { -- 2.39.1