Artifact 4d7a12221a97dc1836201385dec92b8a50cd375b349334ce4d5a55f3412a6f1b:
- Executable file
r36/xlog/DECOMPOS.LOG
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[f2fda60abd]
at
2011-09-02 18:13:33
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— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 9706) [annotate] [blame] [check-ins using] [more...]
REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ... % Test for the univariate and multivariate polynomial decomposition. % Herbert Melenk, ZIB Berlin, 1990. procedure testdecompose u; begin scalar r,p,val,nextvar; write "decomposition of ",u; r := decompose u; if length r = 1 then rederr "decomposition failed"; write " leads to ",r; % test if the result is algebraically correct. r := reverse r; nextvar := lhs first r; val := rhs first r; r := rest r; while not(r={}) do << p := first r; r := rest r; if 'equal = part(p,0) then <<val := sub(nextvar=val,rhs p); nextvar := lhs p>> else val := sub(nextvar=val,p); >>; if val = u then write " O.K. " else <<write "**** reconstructed polynomial: "; write val; rederr "reconstruction leads to different polynomial"; >>; end; testdecompose % univariate decompositions testdecompose(x**4+x**2+1); 4 2 decomposition of x + x + 1 2 2 leads to {u + u + 1,u=x } O.K. testdecompose(x**6+9x**5+52x**4+177x**3+435x**2+630x+593); 6 5 4 3 2 decomposition of x + 9*x + 52*x + 177*x + 435*x + 630*x + 593 3 2 2 leads to {u + 25*u + 210*u + 593,u=x + 3*x} O.K. testdecompose(x**6+6x**4+x**3+9x**2+3x-5); 6 4 3 2 decomposition of x + 6*x + x + 9*x + 3*x - 5 2 3 leads to {u + u - 5,u=x + 3*x} O.K. testdecompose(x**8-88*x**7+2924*x**6-43912*x**5+263431*x**4-218900*x**3+ 65690*x**2-7700*x+234); 8 7 6 5 4 3 decomposition of x - 88*x + 2924*x - 43912*x + 263431*x - 218900*x 2 + 65690*x - 7700*x + 234 2 leads to {u + 35*u + 234, 2 u=v + 10*v, 2 v=x - 22*x} O.K. % multivariate cases testdecompose(u**2+v**2+2u*v+1); 2 2 decomposition of u + 2*u*v + v + 1 2 leads to {w + 1,w=u + v} O.K. testdecompose(x**4+2x**3*y + 3x**2*y**2 + 2x*y**3 + y**4 + 2x**2*y +2x*y**2 + 2y**3 + 5 x**2 + 5*x*y + 6*y**2 + 5y + 9); 4 3 2 2 2 2 3 2 decomposition of x + 2*x *y + 3*x *y + 2*x *y + 5*x + 2*x*y + 2*x*y + 5*x*y 4 3 2 + y + 2*y + 6*y + 5*y + 9 2 2 2 leads to {u + 5*u + 9,u=x + x*y + y + y} O.K. testdecompose sub(u=(2 x**2 + 17 x+y + y**3),u**2+2 u + 1); 4 3 2 3 2 2 3 decomposition of 4*x + 68*x + 4*x *y + 4*x *y + 293*x + 34*x*y + 34*x*y 6 4 3 2 + 34*x + y + 2*y + 2*y + y + 2*y + 1 2 2 3 leads to {u + 2*u + 1,u=2*x + 17*x + y + y} O.K. testdecompose sub(u=(2 x**2 *y + 17 x+y + y**3),u**2+2 u + 1); 4 2 3 2 4 2 2 2 2 decomposition of 4*x *y + 68*x *y + 4*x *y + 4*x *y + 4*x *y + 289*x 3 6 4 3 2 + 34*x*y + 34*x*y + 34*x + y + 2*y + 2*y + y + 2*y + 1 2 2 3 leads to {u + 2*u + 1,u=2*x *y + 17*x + y + y} O.K. % some cases which require a special (internal) mapping testdecompose ( (x + y)**2); 2 2 decomposition of x + 2*x*y + y 2 leads to {u ,u=x + y} O.K. testdecompose ((x + y**2)**2); 2 2 4 decomposition of x + 2*x*y + y 2 2 leads to {u ,u=x + y } O.K. testdecompose ( (x**2 + y)**2); 4 2 2 decomposition of x + 2*x *y + y 2 2 leads to {u ,u=x + y} O.K. testdecompose ( (u + v)**2 +10 ); 2 2 decomposition of u + 2*u*v + v + 10 2 leads to {w + 10,w=u + v} O.K. % the decomposition is not unique and might generate quite % different images: testdecompose ( (u + v + 10)**2 -100 ); 2 2 decomposition of u + 2*u*v + 20*u + v + 20*v leads to {w*(w + 20),w=u + v} O.K. % some special (difficult) cases testdecompose (X**4 + 88*X**3*Y + 2904*X**2*Y**2 - 10*X**2 + 42592*X*Y**3 - 440*X*Y + 234256*Y**4 - 4840*Y**2); 4 3 2 2 2 3 decomposition of x + 88*x *y + 2904*x *y - 10*x + 42592*x*y - 440*x*y 4 2 + 234256*y - 4840*y 2 leads to {u*(u - 10),u=v ,v=x + 22*y} O.K. % a polynomial with complex coefficients on complex; testdecompose(X**4 + (88*I)*X**3*Y - 2904*X**2*Y**2 - 10*X**2 - (42592*I)*X*Y**3 - (440*I)*X*Y + 234256*Y**4 + 4840*Y**2); 4 3 2 2 2 3 decomposition of x + 88*i*x *y - 2904*x *y - 10*x - 42592*i*x*y - 440*i*x*y 4 2 + 234256*y + 4840*y 2 leads to {u*(u - 10),u=v ,v=x + 22*i*y} O.K. off complex; % Examples given by J. Gutierrez and J.M. Olazabal. f1:=x**6-2x**5+x**4-3x**3+3x**2+5$ testdecompose(f1); 6 5 4 3 2 decomposition of x - 2*x + x - 3*x + 3*x + 5 2 3 2 leads to {u - 3*u + 5,u=x - x } O.K. f2:=x**32-1$ testdecompose(f2); 32 decomposition of x - 1 2 2 2 2 2 leads to {u - 1,u=v ,v=w ,w=a ,a=x } O.K. f3:=x**4-(2/3)*x**3-(26/9)*x**2+x+3$ testdecompose(f3); 4 3 2 9*x - 6*x - 26*x + 9*x + 27 decomposition of -------------------------------- 9 2 u - 9*u + 27 2 leads to {---------------,u=3*x - x} 9 O.K. f4:=sub(x=x**4-x**3-2x+1,x**3-x**2-1)$ testdecompose(f4); 12 11 10 9 8 7 6 5 decomposition of x - 3*x + 3*x - 7*x + 14*x - 10*x + 14*x - 20*x 4 3 2 + 9*x - 9*x + 8*x - 2*x - 1 3 2 4 3 leads to {u + 2*u + u - 1,u=x - x - 2*x} O.K. f5:=sub(x=f4,x**5-5)$ testdecompose(f5); 60 59 58 57 56 55 decomposition of x - 15*x + 105*x - 485*x + 1795*x - 5873*x 54 53 52 51 50 + 17255*x - 45845*x + 112950*x - 261300*x + 567203*x 49 48 47 46 - 1164475*x + 2280835*x - 4259830*x + 7604415*x 45 44 43 42 - 13053437*x + 21545220*x - 34200855*x + 52436150*x 41 40 39 38 - 77668230*x + 111050794*x - 153746645*x + 206190770*x 37 36 35 - 267484170*x + 336413145*x - 410387890*x 34 33 32 + 484672110*x - 555048350*x + 616671710*x 31 30 29 - 663135380*x + 690884384*x - 697721320*x 28 27 26 + 681039235*x - 642661265*x + 586604975*x 25 24 23 - 516016275*x + 437051535*x - 356628245*x 22 21 20 + 278991765*x - 208571965*x + 149093999*x 19 18 17 16 - 101204325*x + 64656350*x - 38848040*x + 21710870*x 15 14 13 12 - 10971599*x + 4928210*x - 1904450*x + 519730*x 11 10 9 8 7 - 15845*x - 71947*x + 52015*x - 26740*x + 5510*x 6 5 4 3 + 3380*x - 1972*x - 75*x + 195*x - 10*x - 6 5 4 3 2 leads to {u - 5*u + 10*u - 10*u + 5*u - 6, 3 2 u=v + 2*v + v, 4 3 v=x - x - 2*x} O.K. clear f1,f2,f3,f4,f5; end; (TIME: decompos 2550 2810)