May 2001 - GiNaC-devel

Pattern matching in GiNaC CVS
by Christian Bauer 19 Jun '01

19 Jun '01

Hi! I have committed my first attempt at implementing pattern matching facilities in GiNaC to the CVS now. It consists of two new things: - a wildcard class - a match() member function Wildcards have an unsigned label to allow having multiple different wildcards in one pattern. They are constructed with "wild(label)" and denoted "$0", "$1", "$2" etc. in the output and in ginsh. The match() function checks whether an expression matches a given pattern and if so, fills a list with relations of the form "$0 == foo", "$1 == bar", etc. to show the subexpressions matched by the wildcards. In ginsh, match() returns FAIL if there's no match, and the relation list otherwise. The subs() function has been modified to allow wildcards in the patterns and in the replacement expressions. Likewise, has() also understands wildcards. Some examples in ginsh to show how it works, and to show that it is not really intelligent (it's better than nothing, though): > match(a^b,$1^$2); [$1==a,$2==b] > match(a^b,$1^$1); FAIL > match(a^a,$1^$1); [$1==a] > match(a^a,$1^$2); [$1==a,$2==a] > match((a+b)*(a+c),($1+b)*($1+c)); [$1==a] > match((a+b)*(a+c),(a+$1)*(a+$2)); [$1==c,$2==b] (Unpredictable. The result might also be [$1==c,$2==b].) > match((a+b)*(a+c),($1+b)*($1+d)); FAIL > match((a+b)*(a+c),($1+a)*($1+c)); FAIL > match((a+b)*(a+c),($1+$2)*($1+$3)); FAIL (The result is undefined. Here, "$1+$2" matches "a+b" with $1==b,$2==a and the second factor can no longer be matched. Such thing may or may not work, depending on the sort order.) > match(2*(x+y)+2*z-2,2*$1+$2); [$1==z,$2==-2+2*x+2*y] (This is also ambiguous. Another possibility would be [$1=x+y,$2=2*z-2]. It also shows that it is a syntactic match.) > match(a+b+c,a+$1); [$1==c+b] > match(a+b+c,b+$1); [$1==c+a] > match(a+b+c,c+$1); [$1==a+b] > match(a+b+c,a+c+$1); [$1==b] (A single wildcard in a sum or product gobbles up all remaining unmatched terms.) > match(a+b+c,a+$1+$2); [$2==b,$1==c] (Pure coincidence. It may also have happened that one of the wildcards eats the "a", causing the match to fail. But matching with "a+$1" as above is 100% reliable.) > subs(a^2+b^2+c^2,$1^2==$1^4); b^4+a^4+c^4 > subs(a^3+b^3+c^3,$1^2==$1^4); b^3+c^3+a^3 (It's still not an algebraic substitution...) > match(a*b^2,a*b*$1); FAIL (...let alone an algebraic match.) > match(a*b^2,a^$1*b^$2); FAIL (Likewise. The matching is purely syntactic.) > subs(sin(x+y)^2+cos(x+y)^2, cos($1)^2==1-sin($1)^2); 1 (Straightforward now.) > subs(a+b+c,a+b==e); c+a+b (Once again, we still don't do an algebraic substitution.) > subs(a+b+c,a+b+$1==e+$1); c+e (But this works.) > subs(a+b,$1+a==2*$1); 2*b > subs(a+b,$1+b==2*$1); 2*a > subs(a+b,$1+$2==$1*$1); b^2 (Another random result, a^2 would also be possible.) > subs(a+b,$1+$2==$1*$2); a*b > subs(a+b+c,$1+$2==$1*$2); c*(a+b) (As you probably would have guessed by now, it might also have been any of the two other permutations of a, b and c.) > subs(a+b+c,$1+$2+$3==$1*$2*$3); c*a*b (This works again.) > subs(sin(1+sin(x)),sin($1)==cos($1)); cos(1+cos(x)) (This is the way it works now...) > has(a^2+b^2+c^2,$1^2); 1 > has(a^2+b^2+c^2,$1^3); 0 > has(a^2+b^2+c^2,$1+$2); 1 Indices are currently matched by index value only. This will change. You are encouraged to try this for yourself and find bugs. Any suggestions are welcome as long as they are easy to implement. :^) Bye, Christian -- / Coding on PowerPC and proud of it \/ http://www.uni-mainz.de/~bauec002/

3 8

problem with print_csrc and mul
by Hugo LECLERC 24 May '01

24 May '01

Dear GiNaC developpers, with GiNaC V0.8.2 and V0.8.3, there is a problem when one wants to print a formula with print_csrc_context and a mul into: #include <iostream.h> #include <ginac/ginac.h> using namespace GiNaC; int main(int argc, char *argv[]) { symbol x("x"),y("y"); ex expr=x*y; expr.print(print_csrc_double(cout)); return EXIT_SUCCESS; } gives : (y*x ( and not y*x ) It becomes better when in mul.cpp, line 139, we had if (precedence <= level) before c.s << "("; That's all. Best regards and many thanks for your work! PS: I'm actually looking for how to convert GiNaC list of expressions in optimized C code (like "convert to C" in mathlab). I've already begun and my question is : is there anything done in this domain? - Hugo LECLERC L.M.A.R.C. Laboratory of Applied Mechanics R. Chaléat UMR CNRS 6604, UFR Sciences et Techniques 24, chemin de l'Epitaphe 25000 BESANCON - FRANCE Tel : +33 (0)3 81 66 60 11 ou +33 (0)3 81 66 67 21 Fax : +33 (0)3 81 66 67 00

2 1

Small bug in power::print_latex
by Stefan Weinzierl 24 May '01

24 May '01

Hi, if I do symbol x("x"); ex f=pow(x,10); f.print(print_latex(cout)); I get x^10 which latex prints out roughly as 1 x 0 Putting some curly braces around the exponent should fix the problem, e.g. if one replaces line 200 in power.cpp (GiNaC 0.8.3) exponent.print(x,precedence) by something like if (is_of_type(c,print_latex)) c.s<<"{"; exponent.print(x,precedence) if (is_of_type(c,print_latex)) c.s<<"}"; Best wishes, Stefan

1 0

polynomial arithmetic over ginac
by Parisse Bernard 23 May '01

23 May '01

I have now a little bit improved the package of my polynomial and rational fractions utilities over GiNaC (0.6.4) It provides now gcd normalization, factor (square-free and rational roots), partfrac & integrate (assuming factor works on the denominator), for example: integrate '1/(x^4-1)^5' returns -1155/8192*log(1+x)-1155/4096*atan(x)+1155/8192*log(-1+x)+1/2048*(-893*x-1375*x^9+1755*x^5+385*x^13)*(-1+x^4)^(-4) # Time for (integrate)0.04 You can retrieve and test it at ftp://fourier.ujf-grenoble.fr/pub/hp48/giac.tgz Bye, Bernard Parisse

4 9

Wildcards for subs()
by Christian Bauer 23 May '01

23 May '01

Hi! It has been suggested to me that it would be a desirable feature for subs() to be able to specify wildcards for indices and function arguments so you could, for example - in "sin(x-1)+sin(2*y)", substitute sin(?) by cos(?)/2 to get "cos(x-1)/2+cos(2*y)/2" - in "atan2(x+y,z^2)", substitute atan2(?1,?2) by ?2/?1 to get "z^2/(x+y)" - in "F.mu*g.nu.rho+F.nu*g.mu.rho", substitute F.? by a.?+b.? to get "(a.mu+b.mu)*g.nu.rho+(a.nu+b.nu)*g.mu.rho" This should be relatively easy to implement by extending indexed::subs() and function::subs() and adding a new "wildcard/wild" class that has an integer member to distinguish multiple wildcards. Function substitution would then go something like e.subs(atan2(wild(1), wild(2)) == wild(2)/wild(1)); and substitution of base expressions of indexed objects is similar: e.subs(indexed(wild(), mu) == indexed(wild(), mu)/2+indexed(A, mu)); Wildcards for indices are a little more involved because indices must be of class idx, so one would have to write e.subs(indexed(F, varidx(wild(), 4)) == indexed(a, varidx(wild(), 4)) + indexed(b, varidx(wild(), 4))); which is a little clumsy but has the advantage of taking index dimensions and variance into account (this can also be a disadvantage because it could only substitute F~mu, not F.mu). Any comments/suggestions? Bye, Christian -- / Coding on PowerPC and proud of it \/ http://www.uni-mainz.de/~bauec002/

3 4

bug: get_precedence() is not working
by Pearu Peterson 20 May '01

20 May '01

Hi again, The output of, for example #include <ginac/ginac.h> using namespace GiNaC; main() { symbol x("x"), y("y"); std::cout << ex_to_add(x+y).get_precedence() << std::endl; } should be 40 but I am getting 70 It seems to me that one has to define for each class, that redefines basic::precedence, also the get_precedence() function. Clearly it is not C++ way, but may be it is due to that basic::precedence is defined static. Sorry, but right now I don't have any idea how to fix it... Pearu

3 6

mul::print bug
by Pearu Peterson 16 May '01

16 May '01

Hi! It appears that in the print_csrc context of mul::print function a line if (precedence <= level) is missing just before of the line #139 in mul.cpp c.s << "("; which is causing the following incorrect result: >>> ((x+y)**(x*y)).to_csrc() pow(y+x,(y*x) for instance. Regards, Pearu

2 1

Version 0.8.3 is on the wire.
by Richard B. Kreckel 11 May '01

11 May '01

This is from the NEWS file: - color and clifford classes are functional and documented. - New "spinidx" class for dotted/undotted indices. - Predefined spinor metric tensor (created by spinor_metric()). - Symbols can have a LaTeX name, e.g. symbol s("s", "\\sigma"); - LaTeX output of indexed objects is much nicer. - Fix some build-problems (with recent libreadline). (*) - Semantics of arithmetic operators now follows the C++ rules more strictly. (*) Hi Julian! ;-) Enjoy -richy. -- Richard Kreckel <Richard.Kreckel(a)Uni-Mainz.DE> <http://wwwthep.physik.uni-mainz.de/~kreckel/>

1 0

Wishlist (relational, pseries, matrix)
by Pearu Peterson 07 May '01

07 May '01

Hi! I have been working with GiNaC's interface to Python for some time now and I have collected the following notes that I have found important in this kind of applications: 1) Having relational::get_operator() would be useful (read: necessary) for extensions that can perform symbolic operations like (a < b) && (b > a) -> a < b 2) If a,b are compatible pseries then ex(a) * ex(b) would automatically produce ex(a.mul_series(b)) The same for operations +,-,scalar_mul,scalar_div. If a,b are incompatible, then apply current behaviour (that is, do nothing). I have implemented this behaviour in the GiNaC->Python interface but it does not cover cases where multiplication is carried out inside GiNaC functions. I am thinking of applications where, for example, a matrix consists of compatible pseries and the task is to find its inverse. 3) If a,b are compatible matrices (for a given operation) then ex(a) * ex(b) -> ex(a.mul(b)) The same for operations +,-,scalar_mul,scalar_div. That's all for now. Regards, Pearu

2 2

gTybalt 0.0.4
by Stefan Weinzierl 03 May '01

03 May '01

Dear all, for those who are interested, I put a new version of gTybalt on the web. (http://www.fis.unipr.it/~stefanw/gtybalt.html) gTybalt is a small program build on top of some other packages (GiNaC, TeXmacs, Root, ...) and provides basically TeX-type fonts output for GiNaC and some basic plotting routines. The installation of the new version has become a little bit more user-friendlier, no modifications or adjustment of TeXmacs or GiNaC are needed any more. Enjoy it, Stefan

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