- GiNaC-devel - ginac.de

CLN compiling issue on Mac OS X 1.3
by Fausto Saporito 10 Apr '05

10 Apr '05

Hello, I have a problem generating configure under Mac OS X 1.3 with Fink. When I run autoconf I don't receive any errors, but when I run configure script I have after a while, checking whether make sets $(MAKE)... yes checking for gcc... gcc checking for C compiler default output file name... a.out checking whether the C compiler works... yes checking whether we are cross compiling... no checking for suffix of executables... checking for suffix of object files... o checking whether we are using the GNU C compiler... yes checking whether gcc accepts -g... yes checking for gcc option to accept ANSI C... none needed checking how to run the C preprocessor... gcc -E checking for g++... g++ checking whether we are using the GNU C++ compiler... yes checking whether g++ accepts -g... yes checking how to run the C++ preprocessor... g++ -E ./configure: line 3318: CL_AS_UNDERSCORE: command not found checking for ranlib... ranlib checking for a BSD-compatible install... /usr/bin/install -c ./configure: line 3478: syntax error near unexpected token `autoconf' ./configure: line 3478: ` CL_CANONICAL_HOST(autoconf)' I'm using autoconf 2.59 is it the right version? What is the exact procedure to generate a configure? I didn't find any autogen.sh script, so I tried to use the autogen.sh present in GiNaC cvs tree. When I run autogen.sh I have some warnings: + Running aclocal: /sw/share/aclocal/pth.m4:43: warning: underquoted definition of _AC_PTH_ERROR run info '(automake)Extending aclocal' or see http://sources.redhat.com/automake/automake.html#Extending-aclocal /sw/share/aclocal/pth.m4:55: warning: underquoted definition of _AC_PTH_VERBOSE /sw/share/aclocal/pth.m4:61: warning: underquoted definition of AC_CHECK_PTH /sw/share/aclocal/pkg.m4:5: warning: underquoted definition of PKG_CHECK_MODULES /sw/share/aclocal/libgcrypt.m4:23: warning: underquoted definition of AM_PATH_LIBGCRYPT /sw/share/aclocal/gtk.m4:7: warning: underquoted definition of AM_PATH_GTK /sw/share/aclocal/glib.m4:8: warning: underquoted definition of AM_PATH_GLIB done. + Running libtoolize: done. + Running autoheader: autoheader: warning: missing template: CL_USE_GMP autoheader: Use AC_DEFINE([CL_USE_GMP], [], [Description]) autoheader: warning: missing template: CL_VERSION autoheader: warning: missing template: CL_VERSION_MAJOR autoheader: warning: missing template: CL_VERSION_MINOR autoheader: warning: missing template: CL_VERSION_PATCHLEVEL done. + Running automake: configure.ac: no proper invocation of AM_INIT_AUTOMAKE was found. configure.ac: You should verify that configure.ac invokes AM_INIT_AUTOMAKE, configure.ac: that aclocal.m4 is present in the top-level directory, configure.ac: and that aclocal.m4 was recently regenerated (using aclocal). configure.ac: installing `autoconf/missing' automake: no `Makefile.am' found for any configure output done. + Running autoconf: done. Any idea? thanks a lot, Fausto

2 1

clifford patch
by Jens Vollinga 01 Apr '05

01 Apr '05

Hi Vladimir, I applied your and C.Dams' patch now. But I also applied a forgotten patch from you from December that changes ex clifford::get_metric(const ex & i, const ex & j) const from return indexed(metric, symmetric2(), i, j); to return indexed(metric, i, j); With this December patch the exams for clifford fail with ----------clifford objects: 2*ONE*[[-1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,-1]]~nu~mu-2*[[-1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,-1]]~mu~nu*ONE erroneously return ed 2*ONE*[[-1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,-1]]~nu~mu-2*[[-1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,-1]]~mu~nu*ONE instead of 0 [[-1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,-1]]~mu~nu*e~lambda-[[-1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,-1]]~nu~mu*e~lambda-0 erroneousl y returned [[-1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,-1]]~mu~nu*e~lambda-[[-1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,-1]]~nu~mu*e~lambda i nstead of 0 Without it, it produces no error. The December patch makes sense to me, because the tutorial promises that one can use non-symmetric metrics. Am I wrong here? So, what should I do about it? Regards, Jens

1 0

(no subject)
by Vladimir Kisil 31 Mar '05

31 Mar '05

Dear All, Apologies for flooding this list, but 1. I found one more bug in clifford_prime(): it did not map itself on the usual (commutative) products "mul". 2. I also changed the behaviour of remove_dirac_ONE() slightly: it is now aware of representation_label for Clifford numbers. API and default behaviour remain the same (but not a binary compatibility). So here is the cumulative patch to my previous post on Tue Mar 29 13:34:13. Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ Index: doc/tutorial/ginac.texi =================================================================== RCS file: /home/cvs/GiNaC/doc/tutorial/ginac.texi,v retrieving revision 1.162 diff -r1.162 ginac.texi 3178,3181c3178,3190 < generators @samp{e~k} satisfying the identities < @samp{e~i e~j + e~j e~i = B(i, j)} for some matrix (@code{metric}) < @math{B(i, j)}, which may be non-symmetric. Such generators are created < by the function --- > generators > @tex $e_k$ > @end tex > satisfying the identities > @tex > $e_i e_j + e_j e_i = M(i, j) $ > @end tex > @ifnottex > e~i e~j + e~j e~i = M(i, j) > @end ifnottex > for some matrix (@code{metric}) > @math{M(i, j)}, which may be non-symmetric and containing symbolic > entries. Such generators are created by the function 3188c3197 < generators, @code{metr} defines the metric @math{B(i, j)} and can be --- > generators, @code{metr} defines the metric @math{M(i, j)} and can be 3196c3205 < If the matrix @math{B(i, j)} is in fact symmetric you may prefer to create --- > If the matrix @math{M(i, j)} is in fact symmetric you may prefer to create 3200c3209 < ex e = clifford_unit(mu, indexed(B, sy_symm(), i, j)); --- > ex e = clifford_unit(mu, indexed(M, sy_symm(), i, j)); 3211,3214c3220,3222 < varidx nu(symbol("nu"), 3); < matrix M(3, 3) = 1, 0, 0, < 0,-1, 0, < 0, 0, 0; --- > varidx nu(symbol("nu"), 4); > realsymbol s("s"); > ex M = diag_matrix(lst(1, -1, 0, s)); 3218a3227 > ex e3 = e.subs(nu == 3); 3223,3224c3232,3238 < will produce three generators of a Clifford algebra with properties < @code{pow(e0, 2) = 1}, @code{pow(e1, 2) = -1} and @code{pow(e2, 2) = 0}. --- > will produce four anti-commuting generators of a Clifford algebra with properties > @tex > $e_0^2=1 $, $e_1^2=-1$, $e_2^2=0$ and $e_3^2=s$. > @end tex > @ifnottex > @code{pow(e0, 2) = 1}, @code{pow(e1, 2) = -1}, @code{pow(e2, 2) = 0} and @code{pow(e3, 2) = s}. > @end ifnottex 3231a3246 > ex lst_to_clifford(const ex & v, const ex & e); 3234,3237c3249,3268 < which converts a list or vector @samp{v = (v~0, v~1, ..., v~n)} into < the Clifford number @samp{v~0 e.0 + v~1 e.1 + ... + v~n e.n} with @samp{e.k} < being created by @code{clifford_unit(mu, metr, rl)}. The previous code < may be rewritten with the help of @code{lst_to_clifford()} as follows --- > which converts a list or vector > @tex > $v = (v^0, v^1, ..., v^n)$ > @end tex > @ifnottex > @samp{v = (v~0, v~1, ..., v~n)} > @end ifnottex > into the > Clifford number > @tex > $v^0 e_0 + v^1 e_1 + ... + v^n e_n$ > @end tex > @ifnottex > @samp{v~0 e.0 + v~1 e.1 + ... + v~n e.n} > @end ifnottex > with @samp{e.k} > directly supplied in the second form of the procedure. In the first form > the Clifford unit @samp{e.k} is generated by the call of > @code{clifford_unit(mu, metr, rl)}. The previous code may be rewritten > with the help of @code{lst_to_clifford()} as follows 3242,3248c3273,3279 < varidx nu(symbol("nu"), 3); < matrix M(3, 3) = 1, 0, 0, < 0,-1, 0, < 0, 0, 0; < ex e0 = lst_to_clifford(lst(1, 0, 0), nu, M); < ex e1 = lst_to_clifford(lst(0, 1, 0), nu, M); < ex e2 = lst_to_clifford(lst(0, 0, 1), nu, M); --- > varidx nu(symbol("nu"), 4); > realsymbol s("s"); > ex M = diag_matrix(lst(1, -1, 0, s)); > ex e0 = lst_to_clifford(lst(1, 0, 0, 0), nu, M); > ex e1 = lst_to_clifford(lst(0, 1, 0, 0), nu, M); > ex e2 = lst_to_clifford(lst(0, 0, 1, 0), nu, M); > ex e3 = lst_to_clifford(lst(0, 0, 0, 1), nu, M); 3261,3262c3292,3305 < @samp{v = (v~0, v~1, ..., v~n)} such that @samp{e = v~0 c.0 + v~1 c.1 + ... < + v~n c.n} with respect to the given Clifford units @code{c} and none of --- > @tex > $v = (v^0, v^1, ..., v^n)$ > @end tex > @ifnottex > @samp{v = (v~0, v~1, ..., v~n)} > @end ifnottex > such that > @tex > $e = v^0 c_0 + v^1 c_1 + ... + v^n c_n$ > @end tex > @ifnottex > @samp{e = v~0 c.0 + v~1 c.1 + ... + v~n c.n} > @end ifnottex > with respect to the given Clifford units @code{c} and none of 3266c3309,3315 < @samp{(e c.k + c.k e)/pow(c.k, 2)}. If @samp{pow(c.k, 2) = 0} for some @samp{k} --- > @tex > $(e c_k + c_k e)/c_k^2$. If $c_k^2$ > @end tex > @ifnottex > @samp{(e c.k + c.k e)/pow(c.k, 2)}. If @samp{pow(c.k, 2)} > @end ifnottex > is zero or is not a @code{numeric} for some @samp{k} 3292a3342,3344 > @ifnottex > e* > @end ifnottex 3296a3349,3351 > @ifnottex > @code{\bar@{e@}} > @end ifnottex 3309c3364 < $||e||^2 = e\overline{e}$ --- > $||e||^2 = e\overline{e}$. 3311,3312c3366,3369 < . The inverse of a Clifford expression is returned < by the function --- > @ifnottex > @code{||e||^2 = e \bar@{e@}} > @end ifnottex > The inverse of a Clifford expression is returned by the function 3320c3377 < $e^{-1} = e/||e||^2$ --- > $e^{-1} = \overline{e}/||e||^2$. 3322c3379,3382 < . If --- > @ifnottex > @math{e^@{-1@} = \bar@{e@}/||e||^2} > @end ifnottex > If 3325a3386,3388 > @ifnottex > @math{||e||=0} > @end ifnottex 3350,3354c3413,3418 < It takes a list or vector @code{v} and makes the Moebius < (conformal or linear-fractional) transformation @samp{v -> < (av+b)/(cv+d)} defined by the matrix @samp{M = [[a, b], [c, d]]}. The < parameter @code{G} defines the metric of the surrounding < (pseudo-)Euclidean space. The returned value of this function is a list --- > It takes a list or vector @code{v} and makes the Moebius (conformal or > linear-fractional) transformation @samp{v -> (av+b)/(cv+d)} defined by > the matrix @samp{M = [[a, b], [c, d]]}. The parameter @code{G} defines > the metric of the surrounding (pseudo-)Euclidean space. This can be a > matrix or a Clifford unit, in the later case the parameter @code{rl} is > ignored even if supplied. The returned value of this function is a list 3356a3421,3453 > LaTeX output for Clifford units looks like @code{\clifford[1]@{e@}^@{@{\nu@}@}}, > where @code{1} is the @code{representation_label} and @code{\nu} is the > index of the corresponding unit. This provides a flexible typesetting > with a suitable defintion of the @code{\clifford} command. For example, the > definition > @example > \newcommand@{\clifford@}[1][]@{@} > @end example > typesets all Clifford units identically, while the alternative definition > @example > \newcommand@{\clifford@}[2][]@{\ifcase #1 #2\or \tilde@{#2@} \or \breve@{#2@} \fi@} > @end example > prints units with @code{representation_label=0} as > @tex > $e$, > @end tex > @ifnottex > @code{e}, > @end ifnottex > with @code{representation_label=1} as > @tex > $\tilde{e}$ > @end tex > @ifnottex > @code{\tilde@{e@}} > @end ifnottex > and with @code{representation_label=2} as > @tex > $\breve{e}$. > @end tex > @ifnottex > @code{\breve@{e@}}. > @end ifnottex Index: ginac/clifford.h =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.h,v retrieving revision 1.55 diff -r1.55 clifford.h 278,279c278,284 < /** Replaces all dirac_ONE's in e with 1 (effectively removing them). */ < ex remove_dirac_ONE(const ex & e); --- > /** Replaces dirac_ONE's (with a representation_label no less than rl) in e with 1. > * For the default value rl = 0 remove all of them. Aborts if e contains any > * clifford_unit with representation_label to be removed. > * > * @param e Expression to be processed > * @param rl Value of representation label */ > ex remove_dirac_ONE(const ex & e, unsigned char rl = 0); 292a298 > * @param e Clifford unit object 294a301 > ex lst_to_clifford(const ex & v, const ex & e); 304c311,312 < * @param algebraic Use algebraic or symbolic algorithm for extractions */ --- > * @param algebraic Use algebraic or symbolic algorithm for extractions > * @return List of components of a Clifford vector*/ 318,319c326,328 < * @param G Metric of the surrounding space < * @param rl Representation label */ --- > * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored > * @param rl Representation label > * @return List of components of the transformed vector*/ 327,328c336,338 < * @param G Metric of the surrounding space < * @param rl Representation label */ --- > * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored > * @param rl Representation label > * @return List of components of the transformed vector*/ Index: ginac/clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.cpp,v retrieving revision 1.84 diff -r1.84 clifford.cpp 216c216,217 < } else --- > } else { > c.s << "\\clifford[" << int(representation_label) << "]"; 217a219 > } 227c229 < DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}") --- > DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbf{1}") 940c942 < ex canonicalize_clifford(const ex & e) --- > ex canonicalize_clifford(const ex & e_) 944,946c946,948 < if (is_a<matrix>(e) // || is_a<pseries>(e) || is_a<integral>(e) < || is_a<lst>(e)) { < return e.map(fcn); --- > if (is_a<matrix>(e_) // || is_a<pseries>(e) || is_a<integral>(e) > || is_a<lst>(e_)) { > return e_.map(fcn); 947a950 > ex e=simplify_indexed(e_); 1007,1008c1010,1011 < } else if (is_a<add>(e) || is_a<ncmul>(e) // || is_a<pseries>(e) || is_a<integral>(e) < || is_a<matrix>(e) || is_a<lst>(e)) { --- > } else if (is_a<add>(e) || is_a<ncmul>(e) || is_a<mul>(e) //|| is_a<pseries>(e) || is_a<integral>(e) > || is_a<matrix>(e) || is_a<lst>(e)) { 1016c1019 < ex remove_dirac_ONE(const ex & e) --- > ex remove_dirac_ONE(const ex & e, unsigned char rl) 1018,1020c1021,1026 < pointer_to_map_function fcn(remove_dirac_ONE); < if (is_a<clifford>(e) && is_a<diracone>(e.op(0))) { < return 1; --- > pointer_to_map_function_1arg<unsigned char> fcn(remove_dirac_ONE, rl); > if (is_a<clifford>(e) && ex_to<clifford>(e).get_representation_label() >= rl) { > if (is_a<diracone>(e.op(0))) > return 1; > else > throw(std::invalid_argument("Expression is a non-scalar Clifford number!")); 1022c1028 < || is_a<matrix>(e) || is_a<lst>(e)) { --- > || is_a<matrix>(e) || is_a<lst>(e)) { 1046d1051 < unsigned min, max; 1049,1050c1054,1056 < unsigned dim = (ex_to<numeric>(ex_to<idx>(mu).get_dim())).to_int(); < ex c = clifford_unit(mu, metr, rl); --- > ex e = clifford_unit(mu, metr, rl); > return lst_to_clifford(v, e); > } 1052,1063c1058,1075 < if (is_a<matrix>(v)) { < if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) { < min = ex_to<matrix>(v).rows(); < max = ex_to<matrix>(v).cols(); < } else { < min = ex_to<matrix>(v).cols(); < max = ex_to<matrix>(v).rows(); < } < if (min == 1) { < if (dim == max) < if (is_a<varidx>(mu)) // need to swap variance < return indexed(v, ex_to<varidx>(mu).toggle_variance()) * c; --- > ex lst_to_clifford(const ex & v, const ex & e) { > unsigned min, max; > > if (is_a<clifford>(e)) { > varidx mu = ex_to<varidx>(e.op(1)); > unsigned dim = (ex_to<numeric>(mu.get_dim())).to_int(); > > if (is_a<matrix>(v)) { > if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) { > min = ex_to<matrix>(v).rows(); > max = ex_to<matrix>(v).cols(); > } else { > min = ex_to<matrix>(v).cols(); > max = ex_to<matrix>(v).rows(); > } > if (min == 1) { > if (dim == max) > return indexed(v, ex_to<varidx>(mu).toggle_variance()) * e; 1065c1077,1082 < return indexed(v, mu) * c; --- > throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch")); > } else > throw(std::invalid_argument("First argument should be a vector vector")); > } else if (is_a<lst>(v)) { > if (dim == ex_to<lst>(v).nops()) > return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * e; 1067c1084 < throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch")); --- > throw(std::invalid_argument("List length and dimension of clifford unit mismatch")); 1069,1074c1086 < throw(std::invalid_argument("First argument should be a vector vector")); < } else if (is_a<lst>(v)) { < if (dim == ex_to<lst>(v).nops()) < return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * c; < else < throw(std::invalid_argument("List length and dimension of clifford unit mismatch")); --- > throw(std::invalid_argument("Cannot construct from anything but list or vector")); 1076c1088 < throw(std::invalid_argument("Cannot construct from anything but list or vector")); --- > throw(std::invalid_argument("The second argument should be a Clifford unit")); 1146c1158,1159 < if (pow(c.subs(mu == i), 2) == 0) --- > if (pow(c.subs(mu == i), 2).is_zero() > or (not is_a<numeric>(pow(c.subs(mu == i), 2)))) 1165,1171c1178 < ex x, D; < if (is_a<indexed>(G)) < D = ex_to<varidx>(G.op(1)).get_dim(); < else if (is_a<matrix>(G)) < D = ex_to<matrix>(G).rows(); < else < throw(std::invalid_argument("metric should be an indexed object or matrix")); --- > ex x, D, cu; 1173,1174d1179 < varidx mu((new symbol)->setflag(status_flags::dynallocated), D); < 1176a1182,1194 > > if (is_a<clifford>(G)) { > cu = G; > } else { > if (is_a<indexed>(G)) > D = ex_to<varidx>(G.op(1)).get_dim(); > else if (is_a<matrix>(G)) > D = ex_to<matrix>(G).rows(); > else throw(std::invalid_argument("metric should be an indexed object, matrix, or a Clifford unit")); > > varidx mu((new symbol)->setflag(status_flags::dynallocated), D); > cu = clifford_unit(mu, G, rl); > } 1178c1196 < x = lst_to_clifford(v, mu, G, rl); --- > x = lst_to_clifford(v, cu); 1180d1197 < ex cu = clifford_unit(mu, G); Index: check/exam_clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/check/exam_clifford.cpp,v retrieving revision 1.23 diff -r1.23 exam_clifford.cpp 344c344,345 < e = lst_to_clifford(lst(t, x, y, z), mu, G) * lst_to_clifford(lst(1, 2, 3, 4), nu, G); --- > ex c = clifford_unit(nu, G, 1); > e = lst_to_clifford(lst(t, x, y, z), mu, G, 1) * lst_to_clifford(lst(1, 2, 3, 4), c); 346c347 < result += check_equal((e*e1).simplify_indexed().normal(), dirac_ONE()); --- > result += check_equal((e*e1).simplify_indexed().normal(), dirac_ONE(1));

1 0

Patches for clifford (cumulative)
by Vladimir Kisil 29 Mar '05

29 Mar '05

Dear All, Here is a cumulative patch for clifford.cpp and related files. New features: 1. clifford_to_lst() now checks that all e_j^2 are non zero and numeric in order to allow the algebraic method. For symbolic (non-numeric) values of e_j^2 later substitutions may produce a division by zero for algebraic answer. 2. Further documentation improvement. This patch includes my previous patch from Feb 23 12:19:32 and Chris Dams patch from Mar 21 14:46:17. However I slightly altered Chris' addition by pushing the simplify_indexed() down after canonicalize_clifford() maps itself into all lists or matrices (since simplify_indexed() does not do it itself). Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ Index: doc/tutorial/ginac.texi =================================================================== RCS file: /home/cvs/GiNaC/doc/tutorial/ginac.texi,v retrieving revision 1.162 diff -r1.162 ginac.texi 3178,3181c3178,3190 < generators @samp{e~k} satisfying the identities < @samp{e~i e~j + e~j e~i = B(i, j)} for some matrix (@code{metric}) < @math{B(i, j)}, which may be non-symmetric. Such generators are created < by the function --- > generators > @tex $e_k$ > @end tex > satisfying the identities > @tex > $e_i e_j + e_j e_i = M(i, j) $ > @end tex > @ifnottex > e~i e~j + e~j e~i = M(i, j) > @end ifnottex > for some matrix (@code{metric}) > @math{M(i, j)}, which may be non-symmetric and containing symbolic > entries. Such generators are created by the function 3188c3197 < generators, @code{metr} defines the metric @math{B(i, j)} and can be --- > generators, @code{metr} defines the metric @math{M(i, j)} and can be 3196c3205 < If the matrix @math{B(i, j)} is in fact symmetric you may prefer to create --- > If the matrix @math{M(i, j)} is in fact symmetric you may prefer to create 3200c3209 < ex e = clifford_unit(mu, indexed(B, sy_symm(), i, j)); --- > ex e = clifford_unit(mu, indexed(M, sy_symm(), i, j)); 3211,3214c3220,3225 < varidx nu(symbol("nu"), 3); < matrix M(3, 3) = 1, 0, 0, < 0,-1, 0, < 0, 0, 0; --- > varidx nu(symbol("nu"), 4); > realsymbol s("s"); > matrix M(4, 4) = 1, 0, 0, 0, > 0,-1, 0, 0, > 0, 0, 0, 0, > 0, 0, 0, s; 3218a3230 > ex e3 = e.subs(nu == 3); 3223,3224c3235,3241 < will produce three generators of a Clifford algebra with properties < @code{pow(e0, 2) = 1}, @code{pow(e1, 2) = -1} and @code{pow(e2, 2) = 0}. --- > will produce four generators of a Clifford algebra with properties > @tex > $e_0^2=1 $, $e_1^2=-1$, $e_2^2=0$ and $e_3^2=s$. > @end tex > @ifnottex > @code{pow(e0, 2) = 1}, @code{pow(e1, 2) = -1}, @code{pow(e2, 2) = 0} and @code{pow(e3, 2) = s}. > @end ifnottex 3231a3249 > ex lst_to_clifford(const ex & v, const ex & e); 3234,3237c3252,3271 < which converts a list or vector @samp{v = (v~0, v~1, ..., v~n)} into < the Clifford number @samp{v~0 e.0 + v~1 e.1 + ... + v~n e.n} with @samp{e.k} < being created by @code{clifford_unit(mu, metr, rl)}. The previous code < may be rewritten with the help of @code{lst_to_clifford()} as follows --- > which converts a list or vector > @tex > $v = (v^0, v^1, ..., v^n)$ > @end tex > @ifnottex > @samp{v = (v~0, v~1, ..., v~n)} > @end ifnottex > into the > Clifford number > @tex > $v^0 e_0 + v^1 e_1 + ... + v^n e_n$ > @end tex > @ifnottex > @samp{v~0 e.0 + v~1 e.1 + ... + v~n e.n} > @end ifnottex > with @samp{e.k} > directly supplied in the second form of the procedure. In the first form > the Clifford unit @samp{e.k} is generated by the call of > @code{clifford_unit(mu, metr, rl)}. The previous code may be rewritten > with the help of @code{lst_to_clifford()} as follows 3242,3248c3276,3285 < varidx nu(symbol("nu"), 3); < matrix M(3, 3) = 1, 0, 0, < 0,-1, 0, < 0, 0, 0; < ex e0 = lst_to_clifford(lst(1, 0, 0), nu, M); < ex e1 = lst_to_clifford(lst(0, 1, 0), nu, M); < ex e2 = lst_to_clifford(lst(0, 0, 1), nu, M); --- > varidx nu(symbol("nu"), 4); > realsymbol s("s"); > matrix M(4, 4) = 1, 0, 0, 0, > 0,-1, 0, 0, > 0, 0, 0, 0, > 0, 0, 0, s; > ex e0 = lst_to_clifford(lst(1, 0, 0, 0), nu, M); > ex e1 = lst_to_clifford(lst(0, 1, 0, 0), nu, M); > ex e2 = lst_to_clifford(lst(0, 0, 1, 0), nu, M); > ex e3 = lst_to_clifford(lst(0, 0, 0, 1), nu, M); 3261,3262c3298,3311 < @samp{v = (v~0, v~1, ..., v~n)} such that @samp{e = v~0 c.0 + v~1 c.1 + ... < + v~n c.n} with respect to the given Clifford units @code{c} and none of --- > @tex > $v = (v^0, v^1, ..., v^n)$ > @end tex > @ifnottex > @samp{v = (v~0, v~1, ..., v~n)} > @end ifnottex > such that > @tex > $e = v^0 c_0 + v^1 c_1 + ... + v^n c_n$ > @end tex > @ifnottex > @samp{e = v~0 c.0 + v~1 c.1 + ... + v~n c.n} > @end ifnottex > with respect to the given Clifford units @code{c} and none of 3266c3315,3321 < @samp{(e c.k + c.k e)/pow(c.k, 2)}. If @samp{pow(c.k, 2) = 0} for some @samp{k} --- > @tex > $(e c_k + c_k e)/c_k^2$. If $c_k^2$ > @end tex > @ifnottex > @samp{(e c.k + c.k e)/pow(c.k, 2)}. If @samp{pow(c.k, 2)} > @end ifnottex > is zero or is not a @code{numeric} for some @samp{k} 3292a3348,3350 > @ifnottex > e* > @end ifnottex 3296a3355,3357 > @ifnottex > @code{\bar@{e@}} > @end ifnottex 3309c3370 < $||e||^2 = e\overline{e}$ --- > $||e||^2 = e\overline{e}$. 3311,3312c3372,3375 < . The inverse of a Clifford expression is returned < by the function --- > @ifnottex > @code{||e||^2 = e \bar@{e@}} > @end ifnottex > The inverse of a Clifford expression is returned by the function 3320c3383 < $e^{-1} = e/||e||^2$ --- > $e^{-1} = \overline{e}/||e||^2$. 3322c3385,3388 < . If --- > @ifnottex > @math{e^@{-1@} = \bar@{e@}/||e||^2} > @end ifnottex > If 3325a3392,3394 > @ifnottex > @math{||e||=0} > @end ifnottex 3350,3354c3419,3424 < It takes a list or vector @code{v} and makes the Moebius < (conformal or linear-fractional) transformation @samp{v -> < (av+b)/(cv+d)} defined by the matrix @samp{M = [[a, b], [c, d]]}. The < parameter @code{G} defines the metric of the surrounding < (pseudo-)Euclidean space. The returned value of this function is a list --- > It takes a list or vector @code{v} and makes the Moebius (conformal or > linear-fractional) transformation @samp{v -> (av+b)/(cv+d)} defined by > the matrix @samp{M = [[a, b], [c, d]]}. The parameter @code{G} defines > the metric of the surrounding (pseudo-)Euclidean space. This can be a > matrix or a Clifford unit, in the later case the parameter @code{rl} is > ignored even if supplied. The returned value of this function is a list 3356a3427,3459 > LaTeX output for Clifford units looks like @code{\clifford[1]@{e@}^@{@{\nu@}@}}, > where @code{1} is the @code{representation_label} and @code{\nu} is the > index of the corresponding unit. This provides a flexible typesetting > with a suitable defintion of the @code{\clifford} command. For example, the > definition > @example > \newcommand@{\clifford@}[1][]@{@} > @end example > typesets all Clifford units identically, while the alternative definition > @example > \newcommand@{\clifford@}[2][]@{\ifcase #1 #2\or \tilde@{#2@} \or \breve@{#2@} \fi@} > @end example > prints units with @code{representation_label=0} as > @tex > $e$, > @end tex > @ifnottex > @code{e}, > @end ifnottex > with @code{representation_label=1} as > @tex > $\tilde{e}$ > @end tex > @ifnottex > @code{\tilde@{e@}} > @end ifnottex > and with @code{representation_label=2} as > @tex > $\breve{e}$. > @end tex > @ifnottex > @code{\breve@{e@}}. > @end ifnottex Index: ginac/clifford.h =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.h,v retrieving revision 1.55 diff -r1.55 clifford.h 292a293 > * @param e Clifford unit object 294a296 > ex lst_to_clifford(const ex & v, const ex & e); 304c306,307 < * @param algebraic Use algebraic or symbolic algorithm for extractions */ --- > * @param algebraic Use algebraic or symbolic algorithm for extractions > * @return List of components of a Clifford vector*/ 318,319c321,323 < * @param G Metric of the surrounding space < * @param rl Representation label */ --- > * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored > * @param rl Representation label > * @return List of components of the transformed vector*/ 327,328c331,333 < * @param G Metric of the surrounding space < * @param rl Representation label */ --- > * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored > * @param rl Representation label > * @return List of components of the transformed vector*/ Index: ginac/clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.cpp,v retrieving revision 1.84 diff -r1.84 clifford.cpp 216c216,217 < } else --- > } else { > c.s << "\\clifford[" << int(representation_label) << "]"; 217a219 > } 227c229 < DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}") --- > DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbf{1}") 940c942 < ex canonicalize_clifford(const ex & e) --- > ex canonicalize_clifford(const ex & e_) 944,946c946,948 < if (is_a<matrix>(e) // || is_a<pseries>(e) || is_a<integral>(e) < || is_a<lst>(e)) { < return e.map(fcn); --- > if (is_a<matrix>(e_) // || is_a<pseries>(e) || is_a<integral>(e) > || is_a<lst>(e_)) { > return e_.map(fcn); 947a950 > ex e=simplify_indexed(e_); 1046d1048 < unsigned min, max; 1049,1050c1051,1053 < unsigned dim = (ex_to<numeric>(ex_to<idx>(mu).get_dim())).to_int(); < ex c = clifford_unit(mu, metr, rl); --- > ex e = clifford_unit(mu, metr, rl); > return lst_to_clifford(v, e); > } 1052,1063c1055,1072 < if (is_a<matrix>(v)) { < if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) { < min = ex_to<matrix>(v).rows(); < max = ex_to<matrix>(v).cols(); < } else { < min = ex_to<matrix>(v).cols(); < max = ex_to<matrix>(v).rows(); < } < if (min == 1) { < if (dim == max) < if (is_a<varidx>(mu)) // need to swap variance < return indexed(v, ex_to<varidx>(mu).toggle_variance()) * c; --- > ex lst_to_clifford(const ex & v, const ex & e) { > unsigned min, max; > > if (is_a<clifford>(e)) { > varidx mu = ex_to<varidx>(e.op(1)); > unsigned dim = (ex_to<numeric>(mu.get_dim())).to_int(); > > if (is_a<matrix>(v)) { > if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) { > min = ex_to<matrix>(v).rows(); > max = ex_to<matrix>(v).cols(); > } else { > min = ex_to<matrix>(v).cols(); > max = ex_to<matrix>(v).rows(); > } > if (min == 1) { > if (dim == max) > return indexed(v, ex_to<varidx>(mu).toggle_variance()) * e; 1065c1074,1079 < return indexed(v, mu) * c; --- > throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch")); > } else > throw(std::invalid_argument("First argument should be a vector vector")); > } else if (is_a<lst>(v)) { > if (dim == ex_to<lst>(v).nops()) > return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * e; 1067c1081 < throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch")); --- > throw(std::invalid_argument("List length and dimension of clifford unit mismatch")); 1069,1074c1083 < throw(std::invalid_argument("First argument should be a vector vector")); < } else if (is_a<lst>(v)) { < if (dim == ex_to<lst>(v).nops()) < return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * c; < else < throw(std::invalid_argument("List length and dimension of clifford unit mismatch")); --- > throw(std::invalid_argument("Cannot construct from anything but list or vector")); 1076c1085 < throw(std::invalid_argument("Cannot construct from anything but list or vector")); --- > throw(std::invalid_argument("The second argument should be a Clifford unit")); 1146c1155,1156 < if (pow(c.subs(mu == i), 2) == 0) --- > if (pow(c.subs(mu == i), 2).is_zero() > or (not is_a<numeric>(pow(c.subs(mu == i), 2)))) 1165,1171c1175 < ex x, D; < if (is_a<indexed>(G)) < D = ex_to<varidx>(G.op(1)).get_dim(); < else if (is_a<matrix>(G)) < D = ex_to<matrix>(G).rows(); < else < throw(std::invalid_argument("metric should be an indexed object or matrix")); --- > ex x, D, cu; 1173,1174d1176 < varidx mu((new symbol)->setflag(status_flags::dynallocated), D); < 1176a1179,1191 > > if (is_a<clifford>(G)) { > cu = G; > } else { > if (is_a<indexed>(G)) > D = ex_to<varidx>(G.op(1)).get_dim(); > else if (is_a<matrix>(G)) > D = ex_to<matrix>(G).rows(); > else throw(std::invalid_argument("metric should be an indexed object, matrix, or a Clifford unit")); > > varidx mu((new symbol)->setflag(status_flags::dynallocated), D); > cu = clifford_unit(mu, G, rl); > } 1178c1193 < x = lst_to_clifford(v, mu, G, rl); --- > x = lst_to_clifford(v, cu); 1180d1194 < ex cu = clifford_unit(mu, G); Index: check/exam_clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/check/exam_clifford.cpp,v retrieving revision 1.23 diff -r1.23 exam_clifford.cpp 344c344,345 < e = lst_to_clifford(lst(t, x, y, z), mu, G) * lst_to_clifford(lst(1, 2, 3, 4), nu, G); --- > ex c = clifford_unit(nu, G, 1); > e = lst_to_clifford(lst(t, x, y, z), mu, G, 1) * lst_to_clifford(lst(1, 2, 3, 4), c); 346c347 < result += check_equal((e*e1).simplify_indexed().normal(), dirac_ONE()); --- > result += check_equal((e*e1).simplify_indexed().normal(), dirac_ONE(1));

1 0

patch for canonicalize_clifford
by Chris Dams 21 Mar '05

21 Mar '05

Dear developers, I found out that the result of ex f=dirac_gamma(varidx(nu,dim)) *dirac_slash(k,dim) *dirac_gamma(varidx(mu,dim)) *indexed(n,varidx(nu,dim,true)) *indexed(k,varidx(mu,dim,true)); cout << "before canon_cl: " << f << endl; f=canonicalize_clifford(f); cout << "after canon_cl: " << f << endl; is before canon_cl: n.nu*(gamma~nu*k\*gamma~mu)*k.mu after canon_cl: 2*n\*k.mu*k~mu-2*n~mu*k.mu*k\+k\*n\*k\ I think it is strange that canonicalize_clifford can return something that contains k\*n\*k\ because this looks particularly uncanonicalized. I suggest the patch Index: ginac/clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.cpp,v retrieving revision 1.84 diff -r1.84 clifford.cpp 940c940 < ex canonicalize_clifford(const ex & e) --- > ex canonicalize_clifford(const ex & e_) 941a942 > ex e=simplify_indexed(e_); With this patch the test program gives before canon_cl: n.nu*(gamma~nu*k\*gamma~mu)*k.mu after canon_cl: n\*k.symbol8*k~symbol8 Best wishes, Chris

1 0

clifford patch
by Vladimir Kisil 23 Feb '05

23 Feb '05

Dear All, I propose some further patches related to Clifford numbers. They are 1. LaTeX printing of Clifford object includes the command \clifford[rl] which make a use of the representation labels for separation of different algebras. 2. Alternative forms for functions lst_to_clifford() and clifford_moebius_map() which may got the structure of Clifford algebra out of a sample Clifford unit. The changes are reflected in documentation (which also slightly polished) and in the exam_clifford.cpp. All the best, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ Index: doc/tutorial/ginac.texi =================================================================== RCS file: /home/cvs/GiNaC/doc/tutorial/ginac.texi,v retrieving revision 1.161 diff -r1.161 ginac.texi 3178,3179c3178,3188 < generators @samp{e~k} satisfying the identities < @samp{e~i e~j + e~j e~i = B(i, j)} for some matrix (@code{metric}) --- > generators > @tex $e_k$ > @end tex > satisfying the identities > @tex > $e_i e_j + e_j e_i = B(i, j) $ > @end tex > @ifnottex > e~i e~j + e~j e~i = B(i, j) > @end ifnottex > for some matrix (@code{metric}) 3223a3233,3236 > @tex > $e_0^2=1 $, $e_1^2=-1$ and $e_2^2=0$. > @end tex > @ifnottex 3224a3238 > @end ifnottex 3231a3246 > ex lst_to_clifford(const ex & v, const ex & e); 3234,3237c3249,3268 < which converts a list or vector @samp{v = (v~0, v~1, ..., v~n)} into < the Clifford number @samp{v~0 e.0 + v~1 e.1 + ... + v~n e.n} with @samp{e.k} < being created by @code{clifford_unit(mu, metr, rl)}. The previous code < may be rewritten with the help of @code{lst_to_clifford()} as follows --- > which converts a list or vector > @tex > $v = (v^0, v^1, ..., v^n)$ > @end tex > @ifnottex > @samp{v = (v~0, v~1, ..., v~n)} > @end ifnottex > into the > Clifford number > @tex > $v^0 e_0 + v^1 e_1 + ... + v^n e_n$ > @end tex > @ifnottex > @samp{v~0 e.0 + v~1 e.1 + ... + v~n e.n} > @end ifnottex > with @samp{e.k} > directly supplied in the second form of the procedure. In the first form > the Clifford unit @samp{e.k} is generated by the call of > @code{clifford_unit(mu, metr, rl)}. The previous code may be rewritten > with the help of @code{lst_to_clifford()} as follows 3261,3262c3292,3305 < @samp{v = (v~0, v~1, ..., v~n)} such that @samp{e = v~0 c.0 + v~1 c.1 + ... < + v~n c.n} with respect to the given Clifford units @code{c} and none of --- > @tex > $v = (v^0, v^1, ..., v^n)$ > @end tex > @ifnottex > @samp{v = (v~0, v~1, ..., v~n)} > @end ifnottex > such that > @tex > $e = v^0 c_0 + v^1 c_1 + ... + v^n c_n$ > @end tex > @ifnottex > @samp{e = v~0 c.0 + v~1 c.1 + ... + v~n c.n} > @end ifnottex > with respect to the given Clifford units @code{c} and none of 3266c3309,3315 < @samp{(e c.k + c.k e)/pow(c.k, 2)}. If @samp{pow(c.k, 2) = 0} for some @samp{k} --- > @tex > $(e c_k + c_k e)/c_k^2$. If $c_k^2=0$ > @end tex > @ifnottex > @samp{(e c.k + c.k e)/pow(c.k, 2)}. If @samp{pow(c.k, 2) = 0} > @end ifnottex > for some @samp{k} 3292a3342,3344 > @ifnottex > e* > @end ifnottex 3296a3349,3351 > @ifnottex > @code{\bar@{e@}} > @end ifnottex 3309c3364 < $||e||^2 = e\overline{e}$ --- > $||e||^2 = e\overline{e}$. 3311,3312c3366,3369 < . The inverse of a Clifford expression is returned < by the function --- > @ifnottex > @code{||e||^2 = e \bar@{e@}} > @end ifnottex > The inverse of a Clifford expression is returned by the function 3320c3377 < $e^{-1} = e/||e||^2$ --- > $e^{-1} = \overline{e}/||e||^2$. 3322c3379,3382 < . If --- > @ifnottex > @math{e^@{-1@} = \bar@{e@}/||e||^2} > @end ifnottex > If 3325a3386,3388 > @ifnottex > @math{||e||=0} > @end ifnottex 3350,3354c3413,3418 < It takes a list or vector @code{v} and makes the Moebius < (conformal or linear-fractional) transformation @samp{v -> < (av+b)/(cv+d)} defined by the matrix @samp{M = [[a, b], [c, d]]}. The < parameter @code{G} defines the metric of the surrounding < (pseudo-)Euclidean space. The returned value of this function is a list --- > It takes a list or vector @code{v} and makes the Moebius (conformal or > linear-fractional) transformation @samp{v -> (av+b)/(cv+d)} defined by > the matrix @samp{M = [[a, b], [c, d]]}. The parameter @code{G} defines > the metric of the surrounding (pseudo-)Euclidean space. This can be a > matrix or a Clifford unit, in the later case the parameter @code{rl} is > ignored even if supplied. The returned value of this function is a list 3356a3421,3453 > LaTeX output for Clifford units looks like @code{\clifford[1]@{e@}^@{@{\nu@}@}}, > where @code{1} is the @code{representation_label} and @code{\nu} is the > index of the corresponding unit. This provides a flexible typesetting > with a suitable defintion of the @code{\clifford} command. For example, the > definition > @example > \newcommand@{\clifford@}[1][]@{@} > @end example > typesets all Clifford units identically, while the alternative definition > @example > \newcommand@{\clifford@}[2][]@{\ifcase #1 #2\or \tilde@{#2@} \or \breve@{#2@} \fi@} > @end example > prints units with @code{representation_label=0} as > @tex > $e$, > @end tex > @ifnottex > @code{e}, > @end ifnottex > with @code{representation_label=1} as > @tex > $\tilde{e}$ > @end tex > @ifnottex > @code{\tilde@{e@}} > @end ifnottex > and with @code{representation_label=2} as > @tex > $\breve{e}$. > @end tex > @ifnottex > @code{\breve@{e@}}. > @end ifnottex Index: ginac/clifford.h =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.h,v retrieving revision 1.55 diff -r1.55 clifford.h 292a293 > * @param e Clifford unit object 294a296 > ex lst_to_clifford(const ex & v, const ex & e); 304c306,307 < * @param algebraic Use algebraic or symbolic algorithm for extractions */ --- > * @param algebraic Use algebraic or symbolic algorithm for extractions > * @return List of components of a Clifford vector*/ 318,319c321,323 < * @param G Metric of the surrounding space < * @param rl Representation label */ --- > * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored > * @param rl Representation label > * @return List of components of the transformed vector*/ 327,328c331,333 < * @param G Metric of the surrounding space < * @param rl Representation label */ --- > * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored > * @param rl Representation label > * @return List of components of the transformed vector*/ Index: ginac/clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.cpp,v retrieving revision 1.84 diff -r1.84 clifford.cpp 216c216,217 < } else --- > } else { > c.s << "\\clifford[" << int(representation_label) << "]"; 217a219 > } 227c229 < DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}") --- > DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbf{1}") 1046d1047 < unsigned min, max; 1049,1050c1050,1052 < unsigned dim = (ex_to<numeric>(ex_to<idx>(mu).get_dim())).to_int(); < ex c = clifford_unit(mu, metr, rl); --- > ex e = clifford_unit(mu, metr, rl); > return lst_to_clifford(v, e); > } 1052,1063c1054,1071 < if (is_a<matrix>(v)) { < if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) { < min = ex_to<matrix>(v).rows(); < max = ex_to<matrix>(v).cols(); < } else { < min = ex_to<matrix>(v).cols(); < max = ex_to<matrix>(v).rows(); < } < if (min == 1) { < if (dim == max) < if (is_a<varidx>(mu)) // need to swap variance < return indexed(v, ex_to<varidx>(mu).toggle_variance()) * c; --- > ex lst_to_clifford(const ex & v, const ex & e) { > unsigned min, max; > > if (is_a<clifford>(e)) { > varidx mu = ex_to<varidx>(e.op(1)); > unsigned dim = (ex_to<numeric>(mu.get_dim())).to_int(); > > if (is_a<matrix>(v)) { > if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) { > min = ex_to<matrix>(v).rows(); > max = ex_to<matrix>(v).cols(); > } else { > min = ex_to<matrix>(v).cols(); > max = ex_to<matrix>(v).rows(); > } > if (min == 1) { > if (dim == max) > return indexed(v, ex_to<varidx>(mu).toggle_variance()) * e; 1065c1073,1078 < return indexed(v, mu) * c; --- > throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch")); > } else > throw(std::invalid_argument("First argument should be a vector vector")); > } else if (is_a<lst>(v)) { > if (dim == ex_to<lst>(v).nops()) > return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * e; 1067c1080 < throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch")); --- > throw(std::invalid_argument("List length and dimension of clifford unit mismatch")); 1069,1074c1082 < throw(std::invalid_argument("First argument should be a vector vector")); < } else if (is_a<lst>(v)) { < if (dim == ex_to<lst>(v).nops()) < return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * c; < else < throw(std::invalid_argument("List length and dimension of clifford unit mismatch")); --- > throw(std::invalid_argument("Cannot construct from anything but list or vector")); 1076c1084 < throw(std::invalid_argument("Cannot construct from anything but list or vector")); --- > throw(std::invalid_argument("The second argument should be a Clifford unit")); 1165,1171c1173 < ex x, D; < if (is_a<indexed>(G)) < D = ex_to<varidx>(G.op(1)).get_dim(); < else if (is_a<matrix>(G)) < D = ex_to<matrix>(G).rows(); < else < throw(std::invalid_argument("metric should be an indexed object or matrix")); --- > ex x, D, cu; 1173,1174d1174 < varidx mu((new symbol)->setflag(status_flags::dynallocated), D); < 1176a1177,1189 > > if (is_a<clifford>(G)) { > cu = G; > } else { > if (is_a<indexed>(G)) > D = ex_to<varidx>(G.op(1)).get_dim(); > else if (is_a<matrix>(G)) > D = ex_to<matrix>(G).rows(); > else throw(std::invalid_argument("metric should be an indexed object, matrix, or a Clifford unit")); > > varidx mu((new symbol)->setflag(status_flags::dynallocated), D); > cu = clifford_unit(mu, G, rl); > } 1178c1191 < x = lst_to_clifford(v, mu, G, rl); --- > x = lst_to_clifford(v, cu); 1180d1192 < ex cu = clifford_unit(mu, G); Index: check/exam_clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/check/exam_clifford.cpp,v retrieving revision 1.23 diff -r1.23 exam_clifford.cpp 344c344,345 < e = lst_to_clifford(lst(t, x, y, z), mu, G) * lst_to_clifford(lst(1, 2, 3, 4), nu, G); --- > ex c = clifford_unit(nu, G, 1); > e = lst_to_clifford(lst(t, x, y, z), mu, G, 1) * lst_to_clifford(lst(1, 2, 3, 4), c); 346c347 < result += check_equal((e*e1).simplify_indexed().normal(), dirac_ONE()); --- > result += check_equal((e*e1).simplify_indexed().normal(), dirac_ONE(1));

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Clifford patch (cumulative)
by Vladimir Kisil 10 Feb '05

10 Feb '05

Hi, I discovered that clifford_moebius_map() function was ignorant of representative labels for Clifford numbers, which generates misbehaviour. I include the cumulative patch which this issue along with the previous one. Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ Index: doc/tutorial/ginac.texi =================================================================== RCS file: /home/cvs/GiNaC/doc/tutorial/ginac.texi,v retrieving revision 1.159 diff -r1.159 ginac.texi 3179,3180c3179,3181 < @samp{e~i e~j + e~j e~i = B(i, j)} for some symmetric matrix (@code{metric}) < @math{B(i, j)}. Such generators are created by the function --- > @samp{e~i e~j + e~j e~i = B(i, j)} for some matrix (@code{metric}) > @math{B(i, j)}, which may be non-symmetric. Such generators are created > by the function 3194a3196,3204 > If the matrix @math{B(i, j)} is in fact symmetric you may prefer to create > the Clifford algebra units with a call like that > > @example > ex e = clifford_unit(mu, indexed(B, sy_symm(), i, j)); > @end example > > since this may yield some further automatic simplifications. > 3336c3346,3347 < const ex & d, const ex & v, const ex & G); --- > const ex & d, const ex & v, const ex & G, unsigned char rl = 0); > ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl = 0); 3341c3352 < (av+b)/(cv+d)} defined by the matrix @samp{[[a, b], [c, d]]}. The last --- > (av+b)/(cv+d)} defined by the matrix @samp{M = [[a, b], [c, d]]}. The Index: ginac/clifford.h =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.h,v retrieving revision 1.53 diff -r1.53 clifford.h 318,319c318,320 < * @param G Metric of the surrounding space */ < ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G); --- > * @param G Metric of the surrounding space > * @param rl Representation label*/ > ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G, unsigned char rl = 0); 326,327c327,329 < * @param G Metric of the surrounding space */ < ex clifford_moebius_map(const ex & M, const ex & v, const ex & G); --- > * @param G Metric of the surrounding space > * @param rl Representation label*/ > ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl = 0); Index: ginac/clifford.cpp =================================================================== RCS file: /home/cvs/GiNaC/ginac/clifford.cpp,v retrieving revision 1.82 diff -r1.82 clifford.cpp 1163c1163 < ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G) --- > ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G, unsigned char rl) 1178c1178 < x = lst_to_clifford(v, mu, G); --- > x = lst_to_clifford(v, mu, G, rl); 1184c1184 < ex clifford_moebius_map(const ex & M, const ex & v, const ex & G) --- > ex clifford_moebius_map(const ex & M, const ex & v, const ex & G,unsigned char rl) 1188c1188 < ex_to<matrix>(M)(1,0), ex_to<matrix>(M)(1,1), v, G); --- > ex_to<matrix>(M)(1,0), ex_to<matrix>(M)(1,1), v, G, rl);

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patch for integral::series.
by Chris Dams 06 Feb '05

06 Feb '05

Dear developers, We, of course, do not want zero as a coefficient in a power series. However, my integral::series can give such a result. Here is a patch. Best wishes, Chris

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A patch to Clifford
by Vladimir Kisil 04 Feb '05

04 Feb '05

Hi, I am wondering is my patch submitted here on (Thu Dec 2 16:22:03 2004) was lost or rejected.... Best, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/

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Re: [GiNaC-devel] Crash during startup
by Richard B. Kreckel 01 Feb '05

01 Feb '05

Dear Chris, On Thu, 20 Jan 2005, Chris Dams wrote: [...] > Okay, I can reproduce it now. The placement news that occured in my last > patch appears to solve something, but not everything. Another problem are > the refences _num_25 and so on. When are these going to be initialized? > By the linker, I suppose. Hmmm, good question. > At least that would explain the point at which I > am seeing segfaults now. Are you saying your patch still segfaults? > But how is the linker supposed to know where > memory is going to be allocated? Here's a patch that also throws the > references out of the library. Could you please explain what you're doing in plain English? I'm sure we'll all get some better understanding of the issues this way. Anyways, you got me slabbing my forehead really hard with your way of cheerfully writing (_num0_p = new numeric(0))->setflag(status_flags::dynallocated); instead of the more convoluted _num0_p = static_cast<const numeric*>(&((new numeric(0))->setflag(status_flags::dynallocated))); This looks good. Regards -richy. -- Richard B. Kreckel <http://www.ginac.de/~kreckel/>

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