1% Test only multipliation: 2easy1 := (x1+1*x2)*(x1-1*x2); 3easy2 := (a()*partial(x1)+b())*(c()*partial(x1)+d()); 4 5% Domain for the next factorizations: 6lpdoset lpdoweyl(1,x1,x2); 7 8% Not really binomial but caused problems at some point: 9b3 := (a-partial(x1))*(a+partial(x1)); 10lpdofactorize b3; 11 12% Differential binomial formulas: 13bin1 := (a()+partial(x1))*(a()+partial(x1)); 14lpdofactorize bin1; 15bin2 := (a()-partial(x1))*(a()-partial(x1)); 16lpdofactorize bin2; 17bin3 := (a()-partial(x1))*(a()+partial(x1)); 18lpdofactorize bin3; 19 20% Beals-Kartashova 2005, Section 5.3, special case 21bkf := (partial(x1)+partial(x2)+(a10-a01)/2) * 22 (partial(x1)-partial(x2)+(a10+a01)/2); 23lpdofactorize bkf; 24 25% Ad hoc example: 26sth := (partial(x1)+partial(x2)+(a10+a01)) * 27 (partial(x1)-partial(x2)+(a10+a01)); 28lpdofactorize sth; 29 30% Blumberg 1912: 31p := partial(x1)+x1*partial(x2); 32q := partial(x1)+1; 33r := partial(x1)^2+x1*partial(x1)*partial(x2)+partial(x1)+ 34 (2+x1)*partial(x2); 35d := partial(x1)^3+x1*partial(x1)^2*partial(x2)+2*partial(x1)^2+ 36 2*(x1+1)*partial(x1)*partial(x2)+(x1+2)*partial(x2)+partial(x1); 37d - q*q*p; 38d - r*q; 39lpdofactorize(d,a()*partial(x1)+b()); 40 41% Approximate factorisations: 42 43% Blumberg 1912: 44lpdofactorizex(r,-1<x1<1 and -1<x2<1,q,p); 45 46sol1 := lpdofactorizex(r,-1<x1<1 and -1<x2<1,q,partial(x1)+a()*partial(x2),1); 47r - first second first sol1 * second second first sol1; 48 49sol2 := lpdofactorizex(r,-2<x1<2 and -2<x2<2,q,partial(x1)+a()*partial(x2),1); 50r - first second first sol2 * second second first sol2; 51 52end; 53