- GiNaC-devel - ginac.de

proposed integration algorithm
by Jose Antonio Garcia Peiro 10 Sep '10

10 Sep '10

Hi I am very interested in GiNaC, but I also need symbolic integration, and GiNaC only compute basic integrals. I wrote a simple recursive routine that applies a basic integration rules, matching the input function. It is a good way to implement integration algoritm? Thanks int(c,x) = c*x int(x,x) = x^2/2 int(f+g,x) = int(f,x) + int(g,x) int(c*f,x) = c*int(f,x) int( f^c*1,x) = f^(c+1)/(c+1) or log(f) int( f^c*f',x) = f^(c+1)/(c+1) or log(f) some examples: cout << "int(1+x,x) = " << myinteg( 1 + x, x ) << endl; // 1/2*x^2+x cout << "int(3*x^2+x+6,x) = " << myinteg( 3*pow(x,2)+x+6, x ) << endl; // 1/2*x^2+x^3+6*x cout << "int((3*x+5)^2*3,x) = " << myinteg( pow(3*x+5,2)*3, x ) << endl; // 1/3*(5+3*x)^3 cout << "int((3*x+5)^(-1)*3,x) = " << myinteg( pow(3*x+5,-1)*3, x ) << endl; // log(5+3*x) cout << "int((3*x+5)^b*3,x) = " << myinteg( pow(3*x+5,b)*3, x ) << endl; // (1+b)^(-1)*(5+3*x)^(1+b) the code (with debug messages): ex myinteg( const ex &f, const symbol &x ){ exmap repls; cout << endl << "f(x) = " << f << endl; //int(c,x) c*x if( !has( f, x ) ){ cout << "match int(c,x)" << endl; return f*x; } //int(x,x) x^2/2 if( f.is_equal(x) ){ cout << "match int(x,x)" << endl; return pow(x,2)/2; } //int(f+g,x) int(f,x)+int(g,x) if( f.match( wild(0)+wild(1), repls ) ){ cout << "match int(f+g,x)" << endl; cout << "wild(0)+wild(1) = " << repls << endl; ex f, g; for( exmap::const_iterator i=repls.begin(); i!=repls.end(); ++i){ if(i->first.is_equal(wild(0)) ){ f = i->second; }else if(i->first.is_equal(wild(1))){ g = i->second; } } cout << "f = " << f << endl; cout << "g = " << g << endl; return myinteg( f, x ) + myinteg( g, x ); } //int(c*f,x) c*int(f,x) if( f.match( wild(0)*wild(1), repls ) ){ cout << "match int(c*f,x)" << endl; cout << "wild(0)*wild(1) = " << repls << endl; ex c, f; for( exmap::const_iterator i=repls.begin(); i!=repls.end(); ++i){ if(i->first.is_equal(wild(0)) ){ c = i->second; }else if(i->first.is_equal(wild(1))){ f = i->second; } } if( !has( c, x ) && has( f, x )){ return c*myinteg( f, x ); }if( has( c, x ) && !has( f, x )){ return f*myinteg( c, x ); } } //int( pow( f, c ), x ) pow( f, c+1 ) * pow( c+1, -1 ) if c != -1, or ln( f ) if c == -1 if( f.match( pow(wild(0),wild(1)), repls ) ){ cout << "match int( pow( f, c ), x )" << endl; cout << "pow(wild(0),wild(1)) = " << repls << endl; ex f, c; for( exmap::const_iterator i=repls.begin(); i!=repls.end(); ++i){ if(i->first.is_equal(wild(0)) ){ f = i->second; }else if(i->first.is_equal(wild(1))){ c = i->second; } } cout << "f = " << f << endl; cout << "c = " << c << endl; if( has( f, x ) && !has( c, x ) ){ ex dft = f.diff(x,1); ex df = 1; cout << "df/dft = " << df/dft << endl; if( !has(df/dft,x) ){ cout << "!has(df/dft,x)" << endl; if( c.is_equal(-1) ){ return log( f ) * (df/dft); }else{ cout << "df = " << df << endl; cout << "dft = " << dft << endl; cout << "(df/dft) = " << (df/dft) << endl; cout << "(1/dft) = " << (1/dft) << endl; cout << "pow(dft,-1) = " << pow(dft,-1) << endl; cout << "f = " << f << endl; cout << "c = " << c << endl; cout << "(pow( f, c+1 )/( c+1 )) = " << (pow( f, c+1 )/( c+1 )) << endl; cout << "pow( f, c+1 )*pow( c+1, -1) = " << pow( f, c+1 )*pow( c+1, -1) << endl; cout << "(pow( f, c+1 )/( c+1 ))*(df/dft) = " << (pow( f, c+1 )/( c+1 ))*(df/dft) << endl; cout << "pow( f, c+1 )*pow( c+1, -1) = " << pow( f, c+1 )*pow( c+1, -1)*df*pow( dft, -1) << endl; return (pow( f, c+1 )/( c+1 )) * (df/dft); } } } } //int( pow( f, c ) * f', x ) pow( f, c+1 ) * pow( c+1, -1 ) if c != -1, or ln( f ) if c == -1 if( f.match( wild(0)*pow(wild(1),wild(2)), repls ) ){ cout << "match int( pow( f, c ) * f', x )" << endl; cout << "wild(0)*pow(wild(1),wild(2)) = " << repls << endl; ex df, f, c; for( exmap::const_iterator i=repls.begin(); i!=repls.end(); ++i){ if(i->first.is_equal(wild(0)) ){ df = i->second; }else if(i->first.is_equal(wild(1))){ f = i->second; }else if(i->first.is_equal(wild(2))){ c = i->second; } } cout << "f' = " << df << endl; cout << "f = " << f << endl; cout << "c = " << c << endl; if( has( f, x ) && !has( c, x ) ){ ex dft = f.diff(x,1); cout << "df/dft = " << df/dft << endl; if( !has(df/dft,x) ){ cout << "!has(df/dft,x)" << endl; if( c.is_equal(-1) ){ return log( f ) * (df/dft); }else{ return pow( f, c+1 )*pow( c+1, -1) * (df/dft); } } } } return 0; }

1 0

Patch 4
by Jan Rheinländer 09 Sep '10

09 Sep '10

MSVC unknown functions/symbols Problem: 1. MSVC does not know __func__ 2. MSVC does not like sizeof(void*) 3. MSVC does not have __alignof__ Solution: 1. a) Put AC_CPP_FUNC in acinclude.m4 b) Added check to configure.ac c) Changed parser/debug.h 2. a) Added AC_CHECK_SIZEOF(void*) to configure.ac b) Changed polynomial/primes_factory.h 3. a) Added AC_CHECK_ALIGNOF(void*) to configure.ac b) Changed polynomial/primes_factory.h

3 4

Patch 2
by Jan Rheinländer 09 Sep '10

09 Sep '10

Problem: Return type of function is "ex". MSVC complains that it cannot convert "GiNaC::power*" to "ex" Solution: Changed expression to "GiNaC::power" and removed statusflags::dynallocated

3 2

Patch 3 updated description
by Jan Rheinländer 09 Sep '10

09 Sep '10

symmetry::compare_same_type(): const-correctness fix Problem: The method in question is const, therefore one should use const_iterator to access indices. Some compilers (for instance, MSVC) are very strict about this, and won't accept (invalid) code using non-const iterator. Solution: Changed it to const_iterator

1 0

Patch 5
by Jan Rheinländer 09 Sep '10

09 Sep '10

Problem: MSVC chokes on "struct" Solution: Removed it

1 0

Patch 3
by Jan Rheinländer 09 Sep '10

09 Sep '10

Problem: MSVC wants a const_iterator Solution: Changed it

1 0

Patch
by Jan private 02 Sep '10

02 Sep '10

Hello Alexei, thank you for your patience. Attached the patch Best regards, Jan ---------------------------- 1. Problem: MSVC chokes on "or" and "not" 2. Solution: Replaced with "||" and "!"

1 0

Patch
by Jan private 02 Sep '10

02 Sep '10

Hello Alexei, here is my first try at a patch (GiNaC 1.5.8.) Please let me know if it is OK this way Jan ---------------------------- 1. Problem: MSVC chokes on "or" and "not" 2. Replaced with "||" and "!" --- clifford.cpp.orig 2010-09-02 07:40:19 +0000 +++ clifford.cpp 2010-09-02 07:42:42 +0000 @@ -1291,11 +1291,11 @@ if (algebraic) // check if algebraic method is applicable for (unsigned int i = 0; i < D; i++) if (pow(c.subs(mu == i, subs_options::no_pattern), 2).is_zero() - or (not is_a<numeric>(pow(c.subs(mu == i, subs_options::no_pattern), 2)))) + || (! is_a<numeric>(pow(c.subs(mu == i, subs_options::no_pattern), 2)))) algebraic = false; lst V; ex v0 = remove_dirac_ONE(canonicalize_clifford(e +clifford_prime(e)).normal())/2; - if (not v0.is_zero()) + if (! v0.is_zero()) V.append(v0); ex e1 = canonicalize_clifford(e - v0 * dirac_ONE(ex_to<clifford>(c).get_representation_label())); if (algebraic) { @@ -1312,7 +1312,7 @@ e1 = canonicalize_clifford(expand_dummy_sum(e, true)); V.remove_all(); v0 = remove_dirac_ONE(canonicalize_clifford(e1 +clifford_prime(e1)).normal())/2; - if (not v0.is_zero()) { + if (! v0.is_zero()) { V.append(v0); e1 = canonicalize_clifford(e1 - v0 * dirac_ONE(ex_to<clifford>(c).get_representation_label())); }

1 0

Re: [GiNaC-devel] Compile with MSVC 98% successful
by Jan private 23 Aug '10

23 Aug '10

Hello Alexei, > I thought you've posted this to ginac-devel to get your changes applied, > so building (new versions of) GiNaC with msvc won't be an adventure any > more. well, my post was more for the off-chance that someone might be interested. If it seems that people are interested, I will try to make patches out of those changes that seem to be OK. I am aware that a lot of them are just bad hacks that happen to work. Also, I suspect that a lot of them are bad hacks because I don't know better. E.g. the problems that MSVC has with extern declarations inside classes (which I solved by putting them all in the global namespace) might be solveable with a compiler option, who knows? I don't. Thank you for the instructions. Jan

1 0

[SCM] GiNaC -- a C++ library for symbolic computations branch, master, updated. release_1-4-0-227-g5f896fa
by git＠ginac.de 23 Aug '10

23 Aug '10

This is an automated email from the git hooks/post-receive script. It was generated because a ref change was pushed to the repository containing the project "GiNaC -- a C++ library for symbolic computations". The branch, master has been updated via 5f896fa7f59bbce727e4bba23df9c4bbdbb55c29 (commit) from beeb0818e9cdb1b5de0ba2754286ad7bb2a9d032 (commit) Those revisions listed above that are new to this repository have not appeared on any other notification email; so we list those revisions in full, below. - Log ----------------------------------------------------------------- commit 5f896fa7f59bbce727e4bba23df9c4bbdbb55c29 Author: Alexei Sheplyakov <alexei.sheplyakov(a)gmail.com> Date: Sun Aug 22 23:09:18 2010 +0300 power::eval(): fix several memory leaks While working on fsolve bug I've noticed the following in valgrind log: ==17455== 136 (56 direct, 80 indirect) bytes in 1 blocks are definitely lost in loss record 16 of 19 ==17455== at 0x4C249C7: operator new(unsigned long) (vg_replace_malloc.c:220) ==17455== by 0x516CA70: GiNaC::power::eval(int) const (power.cpp:540) ==17455== by 0x4FC1E39: GiNaC::ex::construct_from_basic(GiNaC::basic const&) (ex.cpp:310) ==17455== by 0x406FBF: main (ex.h:255) Heap allocated objects definitely need the status_flags::dyncallocated flag. ----------------------------------------------------------------------- Summary of changes: ginac/power.cpp | 2 ++ 1 files changed, 2 insertions(+), 0 deletions(-) hooks/post-receive -- GiNaC -- a C++ library for symbolic computations

1 0