i i,j,l; i mu,nu,mup,nup,a1,a2,a3,a4,al,alp,bep,als,bes; v pp,pm,qp,qm,Qp,Qm,Q,q,k; s intQ,intq,Q2,q2,s,t,u,[s+Q2+q2],aux,n,betvQ,betvq; s ae,be; s aeC,beC; s aQ,bQ,aQC,bQC,aq,bq,aqC,bqC,mQ,mq,Md,Mc,MdC,McC,tau,ups,upsp,betQ,betq; s abe,abeC; s abQp,abQm,abQ,abQC,abqp,abqm,abq,abqC; s abep,abem,abep,abem,Ped,Pec; s zero,xq,xQ,[1-xQ-xq]; s xq,xqs,xscs,xcss,xscc,xcsc,xcmb1,xcmb2,xcmb3,xcmb4; s abcqp,abcqpm,abcqmp,abcqm,abecqp,rabe,rabQ,rabq; s int,taui,rltau,taus,upsi,rlups,upss,one; s xQs,xQc,xqs,xqc; s rvQ,raQ,rvq,raq; s qq,alq,alsq; s aQs,bQs,aqs,bqs; s sel,selQ,selq,selp,selm,sel0; s betQs,betqs; s me,mes,xQ,xq,s,sp,t,tp,u,up,kp,km,zp,zm,x1,x2,y,tau; s tM,tpM,uM,upM,kpM,kmM,aux1,aux2; s tm,tpm,um,upm,kpm,kmm; cf eps,epsC; f Bremd,Bremc,BremdC,BremcC; f Prp,Prm,Prip,Prim,Pripc,Primc; s Y,one,[x2-1]; s taup,kpr,upr; s betvQq,aQq,bQq,aQbq,aqbQ,betQqs,sep,sem,app; s sevv,seva,seav,seaa; f vbs,us,gd,gd5; f rTQdd,rTqdd,rTQcc,rTqcc,rTQdc,rTQcd,rTqdc,rTqcd; s [tau+x1-x2+y],[y+x1-x2],[tau+1+y-xQ-xq],[y+1-xQ-xq],[x1-xQ-xq],[y+1-x1], [y-x2+xQ+xq],[tau+x1-xQ-xq],[1-xQ-xq-x1+x2],[y+1-x2] s AC,BC,eg,eq,eQ,etQ,bq,be,ct,st,cp,sp,mue; s intt,inty; cf R1,R3,OR3,R1y,R3y,R1y_Q,R3y_Q,Ln,Lny,R1y_app,R3y_app,R5; s [1-x1+x2-xQ-xq],[1-x1],[x1-xQ-xq],[1+x2-2*x1],[x2-x1]; s [x2+1-2*xQ-2*xq],[x2-xQ-xq],[x1-x2-1+xQ+xq],[x1-x2],[1-xQ-xq]; cf IQ,Iq,IQ_0,IQ_1,Iq_0,Iq_1; s [xQ+xq-1],[x1-1]; s [xQ+xq],[y-1],[y+1],[y-1+xQ+xq],[xQ+xq-2]; s xp,xm,[xp-1]; s sel2,sel1,sel0; s Ry,Rz,z,[y-z],sRz,ay,by,cy,Ay,By,[ay*cy-by^2],ray; s [1-x2],[tau+1-xQ-xq]; cf R,R0; cf sr1,sr3,AY,BY; s coll,Q1,Q2,Q3,Q4; s [x2*[x1-1]-[x2-1]*[x2-xq]],[xQ*[x2-1]-[x1-1]],[[x2-1]*[1-xq]-[x1-1]], [x2*[x1-1]-xQ*[x2-1]]; s [[x1-1]-[1-1/x2]*[x2-xq]],[[x1-1]-xQ*[1-1/x2]], [[x1-1]-xQ*[x2-1]],[[x1-1]-[x2-1]*[1-xq]]; s [1-1/x2],[1-xq],[x2-xq],[1-xQ],[xQ-1],[xQ+xq-1-[x2-1]*[1-xq]]; s [xQ+xq-1-xQ*[1-1/x2]],[xQ+xq-1-[1-1/x2]*[x2-xq]]; s [xq-1],[[x2-1]-thq],[[1-1/x2]*xq-thq],[thQ-[1-1/x2]*[x2-xq]]; s [[1-1/x2]*[x2-xQ]-thq],[thQ-xQ*[1-1/x2]]); s [[x2-1]*[1-xQ]-thq],[thQ-xQ*[x2-1]]; s sxQ,sxq; s thq,thQ,[thQ-[x2-1]]; s La,Lb,[xq-2],two,[x2-xQ],[xQ-x2]; s [[2*x2-xq]-x2/[x2-1]*thq],[[x2-1]-thQ]; s SL1,SL2,SL3,SL4,SL5,SL6,SL7; s [1/thQ^2-1/thq^2],[1/thQ+1/thq]; s [1/[[1-1/x2]*xq-thq]^2-1/[thQ-[1-1/x2]*[x2-xq]]^2], [1/[[1-1/x2]*xq-thq]-1/[thQ-[1-1/x2]*[x2-xq]]], [1/[[x2-1]*[1-xQ]-thq]^2-1/[thQ-xQ*[x2-1]]^2], [1/[[x2-1]*[1-xQ]-thq]-1/[thQ-xQ*[x2-1]]]; s [1/[[1-1/x2]*[x2-xQ]-thq]-1/[thQ-xQ*[1-1/x2]]], [1/[thQ-[x2-1]]+1/thq], [1/[[x2-1]-thq]-1/thQ]; s [1/[thQ-[1-1/x2]*[x2-xq]]^2+1/thq^2], [1/[thQ-[1-1/x2]*[x2-xq]]+1/thq]; s [thQ+thq]; s div,fin; s canc,rest; s [2*x1-x2-1]; cf H1,K1,H2,J0,L0,L1; s [R1([y+1-xQ-xq])-R1([x1-xQ-xq])],[R1([y+1-xQ-xq])+R1(0)]; s [R3([y+x1-x2])+R3([y+1-xQ-xq])],[R3(0)+R3([x1-xQ-xq])]; s [x2+xq/(xQ-1)],[x2+xQ/(xq-1)],[x2-xQ]; s [[x2-1]-Q1/xq]; s [[x2-1]-Q1/xq],[[x2-1]+Q4/xQ]; s struct; s [[x2-1]+Q2/xQ],[x2+(xq+Q2)/(xQ-1)],[xQ+xq-1+Q2]; s [xQ+xq-1+Q2/xQ],[xQ+xq-1+Q2/xQ]; s [[x2-1]*([x2-1]+Q2/xQ)],[(xQ+xq-1)*(xQ+xq-1+Q2)]; s [(xQ+xq-1)*(xQ+xq-1+Q2/xQ)]; s [(x2+(xq+Q2)/(xQ-1))*(x2+xq/(xQ-1))]; s [[x2-1]^2*([x2-1]+Q2/xQ)]; s [Q2+xQ*[x2-1]],[Q2+xQ*(xQ+xq-1)],[Q2+xq+(xQ-1)*x2],[Q2+xQ+xq-1]; s [x2+(xQ-Q3)/(xq-1)],[[x2-1]+Q3],[xQ+xq-1-Q3]; s [[x2-1]*([x2-1]+Q3)],[(x2+xQ/(xq-1))*(x2+(xQ-Q3)/(xq-1))]; s [(xQ+xq-1-Q3)*(xQ+xq-1)],[xQ+xq-1+Q3],[xQ+xq-1-Q3/xq]; s [(xQ+xq-1-Q3)*(xQ+xq-1)],[(xQ+xq-1+Q3)*(xQ+xq-1)],[(xQ+xq-1-Q3/xq)*(xQ+xq-1)]; s [Q3+[x2-1]],[Q3+(1-xq)*x2-xQ],[Q3+1-xQ-xq],[Q3+1-xQ-xq],[Q3-1+xQ+xq]; s sa,sb,sc,disc; s aQ1; s [[x2-1]+Q2/(xQ-1)],[x2+(xq+Q1)/(xQ-1)]; s [([x2-1]+Q2/(xQ-1))*[x2-1]]; s [([x2-1]-Q1/xq)*[x2-1]]; s [(x2+(xq+Q1)/(xQ-1))*(x2+xq/(xQ-1))]; s [1-xQ-xq+Q1/xq],[(xQ+xq-1)*(1-xQ-xq+Q1/xq)]; * .global * *------------------------------------------------------------------- * #procedure testu(dummy) * g wi_Q= vbs(pp)*(Bremd(al)+Bremc(al))*us(pm)*Q(mu)*kp*km*tp*t*up*u; * id Bremd(al?)= gd(i,al)*Prp*gd(i,mu)*(ae+be*gd5(i))*Prim* gd(i,nu)*(ae+be*gd5(i))+ gd(i,mu)*(ae+be*gd5(i))*Prip*gd(i,al)*Prim*gd(i,nu)* (ae+be*gd5(i))+ gd(i,mu)*(ae+be*gd5(i))*Prip*gd(i,nu)*(ae+be*gd5(i))* Prm*gd(i,al); id Bremc(al?)= gd(i,al)*Prp*gd(i,nu)*(ae+be*gd5(i))*Primc* gd(i,mu)*(ae+be*gd5(i))+ gd(i,nu)*(ae+be*gd5(i))*Pripc*gd(i,al)*Primc*gd(i,mu)* (ae+be*gd5(i))+ gd(i,nu)*(ae+be*gd5(i))*Pripc*gd(i,mu)*(ae+be*gd5(i))* Prm*gd(i,al); * id Prp= (i_*(gd(i,pp)-gd(i,k)))/(-kp); al Prm= (-i_*(gd(i,pm)-gd(i,k)))/(-km); al Prip= (i_*(gd(i,pp)-gd(i,Q)))/(-tp); al Prim= (-i_*(gd(i,pm)-gd(i,q)))/(-t); al Pripc= (i_*(gd(i,pp)-gd(i,q)))/(-up); al Primc= (-i_*(gd(i,pm)-gd(i,Q)))/(-u); * repeat; id gd(i,mu?)*gd5(i)= -gd5(i)*gd(i,mu); endrepeat; id gd5(i)*gd5(i)= 1; * id gd(i,Q)*gd(i,Q)= Q2; * repeat; id ae^2= 1/2*(abep+abem); id be^2= 1/2*(abep-abem); endrepeat; id ae*be= abe; * repeat; id gd(i,pm)*gd(i,mu?)= -gd(i,mu)*gd(i,pm)+2*pm(mu); endrepeat; id gd(i,pm)*us(pm)= 0; * repeat; id gd(i,mu?)*gd(i,pp)= -gd(i,pp)*gd(i,mu)+2*pp(mu); endrepeat; * repeat; id gd5(i)*gd(i,pp)= -gd(i,pp)*gd5(i); endrepeat; id vbs(pp)*gd(i,pp)= 0; * id gd(i,q)= gd(i,pp)+gd(i,pm)-gd(i,Q)-gd(i,k); id gd(i,Q)*gd(i,Q)= Q2; * repeat; id gd(i,pm)*gd(i,mu?)= -gd(i,mu)*gd(i,pm)+2*pm(mu); endrepeat; id gd(i,pm)*us(pm)= 0; * repeat; id gd(i,mu?)*gd(i,pp)= -gd(i,pp)*gd(i,mu)+2*pp(mu); endrepeat; * repeat; id gd5(i)*gd(i,pp)= -gd(i,pp)*gd5(i); endrepeat; id vbs(pp)*gd(i,pp)= 0; * id gd(i,Q)*gd(i,k)= -gd(i,k)*gd(i,Q)+2*Q.k; id gd(i,k)*gd(i,k)= 0; * id pp.pm= -1/2*s; al q.Q= -1/2*(sp+q2+Q2); al pm.q= 1/2*(t+q2); al pp.Q= 1/2*(tp+Q2); al pm.Q= 1/2*(u+Q2); al pp.q= 1/2*(up+q2); al pp.k= 1/2*kp; al pm.k= 1/2*km; al Q.k= 1/2*(-zp-Q2); al q.k= 1/2*(-zm-q2); * id Q2= -xQ*s; al q2= -xq*s; * id sp= x2*s; al t= tau*s; al t^-1= 1/tau/s; al km= y*s; al km^-1= 1/y/s; al zm= s*(-x2+x1+xq); al tp= s*(x1-x2+y+tau); al u= s*(-1-y-tau+xQ+xq); al up= s*(-x1-tau+xQ+xq); al kp= s*(-1+x2-y); al zp= s*(1-x1+xQ); * b i_,vbs,us,abep,abem,abe,kp,km,tp,t,up,u,pp,pm; print; * .store * #endprocedure * #procedure testl(dummy) * g wi_q= vbs(pp)*(Bremd(al)+Bremc(al))*us(pm)*q(nu)*kp*km*tp*t*up*u; * id Bremd(al?)= gd(i,al)*Prp*gd(i,mu)*(ae+be*gd5(i))*Prim* gd(i,nu)*(ae+be*gd5(i))+ gd(i,mu)*(ae+be*gd5(i))*Prip*gd(i,al)*Prim*gd(i,nu)* (ae+be*gd5(i))+ gd(i,mu)*(ae+be*gd5(i))*Prip*gd(i,nu)*(ae+be*gd5(i))* Prm*gd(i,al); id Bremc(al?)= gd(i,al)*Prp*gd(i,nu)*(ae+be*gd5(i))*Primc* gd(i,mu)*(ae+be*gd5(i))+ gd(i,nu)*(ae+be*gd5(i))*Pripc*gd(i,al)*Primc*gd(i,mu)* (ae+be*gd5(i))+ gd(i,nu)*(ae+be*gd5(i))*Pripc*gd(i,mu)*(ae+be*gd5(i))* Prm*gd(i,al); * id Prp= (i_*(gd(i,pp)-gd(i,k)))/(-kp); al Prm= (-i_*(gd(i,pm)-gd(i,k)))/(-km); al Prip= (i_*(gd(i,pp)-gd(i,Q)))/(-tp); al Prim= (-i_*(gd(i,pm)-gd(i,q)))/(-t); al Pripc= (i_*(gd(i,pp)-gd(i,q)))/(-up); al Primc= (-i_*(gd(i,pm)-gd(i,Q)))/(-u); * repeat; id gd(i,mu?)*gd5(i)= -gd5(i)*gd(i,mu); endrepeat; id gd5(i)*gd5(i)= 1; * id gd(i,q)*gd(i,q)= q2; * repeat; id ae^2= 1/2*(abep+abem); id be^2= 1/2*(abep-abem); endrepeat; id ae*be= abe; * repeat; id gd(i,pm)*gd(i,mu?)= -gd(i,mu)*gd(i,pm)+2*pm(mu); endrepeat; id gd(i,pm)*us(pm)= 0; * repeat; id gd(i,mu?)*gd(i,pp)= -gd(i,pp)*gd(i,mu)+2*pp(mu); endrepeat; * repeat; id gd5(i)*gd(i,pp)= -gd(i,pp)*gd5(i); endrepeat; id vbs(pp)*gd(i,pp)= 0; * id gd(i,Q)= gd(i,pp)+gd(i,pm)-gd(i,q)-gd(i,k); id gd(i,q)*gd(i,q)= q2; * repeat; id gd(i,pm)*gd(i,mu?)= -gd(i,mu)*gd(i,pm)+2*pm(mu); endrepeat; id gd(i,pm)*us(pm)= 0; * repeat; id gd(i,mu?)*gd(i,pp)= -gd(i,pp)*gd(i,mu)+2*pp(mu); endrepeat; * repeat; id gd5(i)*gd(i,pp)= -gd(i,pp)*gd5(i); endrepeat; id vbs(pp)*gd(i,pp)= 0; * id gd(i,q)*gd(i,k)= -gd(i,k)*gd(i,q)+2*q.k; id gd(i,k)*gd(i,k)= 0; * id pp.pm= -1/2*s; al q.Q= -1/2*(sp+q2+Q2); al pm.q= 1/2*(t+q2); al pp.Q= 1/2*(tp+Q2); al pm.Q= 1/2*(u+Q2); al pp.q= 1/2*(up+q2); al pp.k= 1/2*kp; al pm.k= 1/2*km; al Q.k= 1/2*(-zp-Q2); al q.k= 1/2*(-zm-q2); * id Q2= -xQ*s; al q2= -xq*s; * id sp= x2*s; al t= tau*s; al t^-1= 1/tau/s; al km= y*s; al km^-1= 1/y/s; al zm= s*(-x2+x1+xq); al tp= s*(x1-x2+y+tau); al u= s*(-1-y-tau+xQ+xq); al up= s*(-x1-tau+xQ+xq); al kp= s*(-1+x2-y); al zp= s*(1-x1+xQ); * b i_,vbs,us,abep,abem,abe,kp,km,tp,t,up,u,pp,pm; print; * #endprocedure * #procedure finalstate(dummy) * g TQdd= g_(j,mup)*(aQC*gi_(j)+bQC*g5_(j))*(-i_*g_(j,Qm)+mQ*gi_(j))* g_(j,mu)*(aQ*gi_(j)+bQ*g5_(j))*(-i_*g_(j,Qp)-mQ*gi_(j))*intQ; g Tqdd= g_(l,nup)*(aqC*gi_(l)+bqC*g5_(l))*(-i_*g_(l,qm)+mq*gi_(l))* g_(l,nu)*(aq*gi_(l)+bq*g5_(l))*(-i_*g_(l,qp)-mq*gi_(l))*intq; g TQcc= g_(j,nup)*(aQC*gi_(j)+bQC*g5_(j))*(-i_*g_(j,Qm)+mQ*gi_(j))* g_(j,nu)*(aQ*gi_(j)+bQ*g5_(j))*(-i_*g_(j,Qp)-mQ*gi_(j))*intQ; g Tqcc= g_(l,mup)*(aqC*gi_(l)+bqC*g5_(l))*(-i_*g_(l,qm)+mq*gi_(l))* g_(l,mu)*(aq*gi_(l)+bq*g5_(l))*(-i_*g_(l,qp)-mq*gi_(l))*intq; g TQdc= g_(j,mup)*(aQC*gi_(j)+bQC*g5_(j))*(-i_*g_(j,Qm)+mQ*gi_(j))* g_(j,nu)*(aQ*gi_(j)+bQ*g5_(j))*(-i_*g_(j,Qp)-mQ*gi_(j))*intQ; g TQcd= g_(j,nup)*(aQC*gi_(j)+bQC*g5_(j))*(-i_*g_(j,Qm)+mQ*gi_(j))* g_(j,mu)*(aQ*gi_(j)+bQ*g5_(j))*(-i_*g_(j,Qp)-mQ*gi_(j))*intQ; g Tqdc= g_(l,nup)*(aqC*gi_(l)+bqC*g5_(l))*(-i_*g_(l,qm)+mq*gi_(l))* g_(l,mu)*(aq*gi_(l)+bq*g5_(l))*(-i_*g_(l,qp)-mq*gi_(l))*intq; g Tqcd= g_(l,mup)*(aqC*gi_(l)+bqC*g5_(l))*(-i_*g_(l,qm)+mq*gi_(l))* g_(l,nu)*(aq*gi_(l)+bq*g5_(l))*(-i_*g_(l,qp)-mq*gi_(l))*intq; * nwrite statistics; * trace4,j; trace4,l; contract; * al Qp.Qp= -mQ^2; al Qm.Qm= -mQ^2; al qp.qp= -mq^2; al qm.qm= -mq^2; al Q.Q= Q2; al q.q= q2; * id aQ*aQC= aQs; id bQ*bQC= bQs; id aQ*bQC= abQ; id aQC*bQ= abQC; id abQ= -abQC+2*rabQ; * id aq*aqC= aqs; id bq*bqC= bqs; id aq*bqC= abq; id aqC*bq= abqC; id abq= -abqC+2*rabq; * id Qp(a1?)*Qm(a2?)*intQ= IQ_0*d_(a1,a2)+IQ_1*Q(a1)*Q(a2); id e_(Qp,Qm,mu?,nu?)*intQ= e_(a1,a2,mu,nu)*(IQ_0*d_(a1,a2)+IQ_1*Q(a1)*Q(a2)); id e_(qp,qm,mu?,nu?)*intq= e_(a3,a4,mu,nu)*(Iq_0*d_(a3,a4)+Iq_1*q(a3)*q(a4)); id qp(a1?)*qm(a2?)*intq= Iq_0*d_(a1,a2)+Iq_1*q(a1)*q(a2); id intQ= IQ; id intq= Iq; * id Qp.Qm= mQ^2+1/2*Q2; id qp.qm= mq^2+1/2*q2; * id IQ_0= Q2*betQ^2/12*IQ; al IQ_1= 1/12*betvQ*IQ; id Iq_0= q2*betq^2/12*Iq; al Iq_1= 1/12*betvq*Iq; id mQ^2= -1/4*(1-betQ^2)*Q2; id mq^2= -1/4*(1-betq^2)*q2; * id IQ= betQ/2; al Iq= betq/2; * id betQ^2= betQs; id betq^2= betqs; * id aQs*betQs= (-2*betvQ+3)*aQs; id aqs*betqs= (-2*betvq+3)*aqs; * b betvQ,betvq,betQ,betq,betQs,betqs,aQs,aqs,bQs,bqs,Q2,q2,d_,Q,q,e_; print; * #endprocedure * #procedure initialstate(dummy) * g Tedd= -BremdC(als)*(-i_*g_(i,pp))*Bremd(alp)* (-i_*g_(i,pm))*epsC(als)*eps(alp); g Tecc= -BremcC(als)*(-i_*g_(i,pp))*Bremc(alp)* (-i_*g_(i,pm))*epsC(als)*eps(alp); g Tedc= -BremdC(als)*(-i_*g_(i,pp))*Bremc(alp)* (-i_*g_(i,pm))*epsC(als)*eps(alp); g Tecd= -BremcC(als)*(-i_*g_(i,pp))*Bremd(alp)* (-i_*g_(i,pm))*epsC(als)*eps(alp); * nwrite statistics; * id Bremd(al?)= g_(i,al)*Prp*g_(i,mu)*(ae+be*g5_(i))*Prim* g_(i,nu)*(ae+be*g5_(i))+ g_(i,mu)*(ae+be*g5_(i))*Prip*g_(i,al)*Prim*g_(i,nu)* (ae+be*g5_(i))+ g_(i,mu)*(ae+be*g5_(i))*Prip*g_(i,nu)*(ae+be*g5_(i))* Prm*g_(i,al); id Bremc(al?)= g_(i,al)*Prp*g_(i,nu)*(ae+be*g5_(i))*Primc* g_(i,mu)*(ae+be*g5_(i))+ g_(i,nu)*(ae+be*g5_(i))*Pripc*g_(i,al)*Primc*g_(i,mu)* (ae+be*g5_(i))+ g_(i,nu)*(ae+be*g5_(i))*Pripc*g_(i,mu)*(ae+be*g5_(i))* Prm*g_(i,al); * id BremdC(al?)= g_(i,nup)*(ae+be*g5_(i))*Prim*g_(i,mup)* (ae+be*g5_(i))*Prp*g_(i,al)+ g_(i,nup)*(ae+be*g5_(i))*Prim*g_(i,al)*Prip* g_(i,mup)*(ae+be*g5_(i))+ g_(i,al)*Prm*g_(i,nup)*(ae+be*g5_(i))*Prip* g_(i,mup)*(ae+be*g5_(i)); id BremcC(al?)= g_(i,mup)*(ae+be*g5_(i))*Primc*g_(i,nup)* (ae+be*g5_(i))*Prp*g_(i,al)+ g_(i,mup)*(ae+be*g5_(i))*Primc*g_(i,al)*Pripc* g_(i,nup)*(ae+be*g5_(i))+ g_(i,al)*Prm*g_(i,mup)*(ae+be*g5_(i))*Pripc* g_(i,nup)*(ae+be*g5_(i)); * id Prp= (i_*(g_(i,pp)-g_(i,k)))/(-kp); al Prm= (-i_*(g_(i,pm)-g_(i,k)))/(-km); al Prip= (i_*(g_(i,pp)-g_(i,Q)))/(-tp); al Pripc= (i_*(g_(i,pp)-g_(i,q)))/(-up); al Prim= (-i_*(g_(i,pm)-g_(i,q)))/(-t); al Primc= (-i_*(g_(i,pm)-g_(i,Q)))/(-u); * id epsC(a1?)*eps(a2?)= d_(a1,a2); *id epsC(a1?)*eps(a2?)= k(a1)*k(a2); * .store * g lod= Tedd*rTQdd*rTqdd; g loc= Tecc*rTQcc*rTqcc; g loi= Tedc*rTQdc*rTqdc+Tecd*rTQcd*rTqcd; * nwrite statistics; * id rTQdd= d_(mu,mup)*Q2*betvQ*betQ*aQs * ( 2/3 ) + d_(mu,mup)*Q2*betQ*bQs*betQs * ( 2/3 ); al rTqdd= d_(nu,nup)*q2*betvq*betq*aqs * ( 2/3 ) + d_(nu,nup)*q2*betq*bqs*betqs * ( 2/3 ); al rTQcc= d_(nu,nup)*Q2*betvQ*betQ*aQs * ( 2/3 ) + d_(nu,nup)*Q2*betQ*bQs*betQs * ( 2/3 ); al rTqcc= d_(mu,mup)*q2*betvq*betq*aqs * ( 2/3 ) + d_(mu,mup)*q2*betq*bqs*betqs * ( 2/3 ); al rTQdc= d_(nu,mup)*Q2*betvQ*betQ*aQs * ( 2/3 ) + d_(nu,mup)*Q2*betQ*bQs*betQs * ( 2/3 ); al rTQcd= d_(mu,nup)*Q2*betvQ*betQ*aQs * ( 2/3 ) + d_(mu,nup)*Q2*betQ*bQs*betQs * ( 2/3 ); al rTqdc= d_(mu,nup)*q2*betvq*betq*aqs * ( 2/3 ) + d_(mu,nup)*q2*betq*bqs*betqs * ( 2/3 ); al rTqcd= d_(nu,mup)*q2*betvq*betq*aqs * ( 2/3 ) + d_(nu,mup)*q2*betq*bqs*betqs * ( 2/3 ); * .store * #endprocedure * #procedure trace(dummy) * g nlod= lod/betQ/betq; g nloc= loc/betQ/betq; g nloi= loi/betQ/betq; * nwrite statistics; * trace4,symmetrize,i; contract; * id k.k= 0; al pp.pp= 0; al pm.pm= 0; al Q.Q= Q2; al q.q= q2; id e_(a1?,a2?,a3?,k)= e_(a1,a2,a3,pp)+e_(a1,a2,a3,pm)-e_(a1,a2,a3,Q)- e_(a1,a2,a3,q); * repeat; id ae^2= 1/2*(abep+abem); id be^2= 1/2*(abep-abem); endrepeat; id ae*be= abe; * id pp.pm= -1/2*s; al q.Q= -1/2*(sp+q2+Q2); al pm.q= 1/2*(t+q2); al pp.Q= 1/2*(tp+Q2); al pm.Q= 1/2*(u+Q2); al pp.q= 1/2*(up+q2); al pp.k= 1/2*kp; al pm.k= 1/2*km; al Q.k= 1/2*(-zp-Q2); al q.k= 1/2*(-zm-q2); * id Q2= -xQ*s; al q2= -xq*s; * .store * #endprocedure * #procedure integration(dummy) * *g totp= (nlod+nloc+nloi)*sep*sevv*intt*[2*x1-x2-1]*[x1-x2-1+xQ+xq]*[x1-xQ-xq]; g totp= (nlod+nloc+nloi)*sep*sevv; * id betvQ*betvq= betvQq; al betQs*betqs= betQqs; al aQs*aqs= aQq; al bQs*bqs= bQq; al aQs*bqs= aQbq; al aqs*bQs= aqbQ; * id abep^2*sep= 1; id sep= 0; * id betvQq*aQq*sevv= 1; id sevv= 0; * id sp= x2*s; al t= tau*s; al t^-1= 1/tau/s; al km= y*s; al km^-1= 1/y/s; al zm= s*(-x2+x1+xq); al tp= s*(x1-x2+y+tau); al u= s*(-1-y-tau+xQ+xq); al up= s*(-x1-tau+xQ+xq); al kp= s*(-1+x2-y); al zp= s*(1-x1+xQ); * id tp^-1= 1/taup/s; al kp^-1= -1/[y+1-x2]/s; al u^-1= 1/ups/s; al up^-1= 1/upsp/s; * id Q2= -xQ*s; al q2= -xq*s; * id taup^-1= 1/[tau+x1-x2+y]; id ups^-1= -1/[tau+1+y-xQ-xq]; id upsp^-1= -1/[tau+x1-xQ-xq]; * ratio,tau,[tau+x1-x2+y],[y+x1-x2]; ratio,tau,[tau+1+y-xQ-xq],[y+1-xQ-xq]; ratio,tau,[tau+x1-xQ-xq],[x1-xQ-xq]; ratio,[tau+x1-xQ-xq],[tau+1+y-xQ-xq],[y+1-x1]; ratio,[tau+x1-x2+y],[tau+1+y-xQ-xq],[1-xQ-xq-x1+x2]; ratio,[tau+x1-xQ-xq],[tau+x1-x2+y],[y-x2+xQ+xq]; * id [tau+x1-x2+y]^-1= 1/taup; id [tau+1+y-xQ-xq]^-1= -1/ups; id [tau+x1-xQ-xq]^-1= -1/upsp; * ratio,[y+x1-x2],[y+1-xQ-xq],[1-x1+x2-xQ-xq]; ratio,[y+x1-x2],[y+1-x2],[1-x1]; ratio,[y-x2+xQ+xq],[y+x1-x2],[x1-xQ-xq]; ratio,[y+x1-x2],[y+1-x1],[1+x2-2*x1]; ratio,[y+1-x1],[y+1-xQ-xq],[x1-xQ-xq]; ratio,[y-x2+xQ+xq],[y+1-xQ-xq],[x2+1-2*xQ-2*xq]; ratio,[y+1-x2],[y+1-xQ-xq],[x2-xQ-xq]; ratio,[y+1-x1],[y-x2+xQ+xq],[x1-x2-1+xQ+xq]; ratio,[y+1-x1],[y+1-x2],[x1-x2]; ratio,[y-x2+xQ+xq],[y+1-x2],[1-xQ-xq]; ratio,y,[y+x1-x2],[x1-x2]; ratio,y,[y+1-xQ-xq],[1-xQ-xq]; ratio,y,[y+1-x1],[1-x1]; ratio,[y-x2+xQ+xq],y,[x2-xQ-xq]; ratio,[y+1-x2],y,[x2-1]; ratio,y,[y+1-x2],aux; id aux= -[x2-1]; al aux^-1= -1/[x2-1]; * id [1+x2-2*x1]= 1+x2-2*x1; al [x1-xQ-xq]= x1-xQ-xq; al [x2-xQ-xq]= x2-xQ-xq; al [1-xQ-xq]= 1-xQ-xq; * id [x1-1]= x1-1; al [1-x1]= 1-x1; al [x2-1]= x2-1; al [1-x1]^-1= -1/[x1-1]; id [x1-x2]= x1-x2; * ratio,[x1-1],x1,one; ratio,[x2-1],x2,one; id one= 1; al one= -1; * ratio [x1-x2],x1,x2; id [1-x1]^-1= -1/[x1-1]; ratio,[x1-1],x1,one; ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; id [x1-x2]^-1= -1/[x2-x1]; ratio,[x2-x1],x2,x1; id [x2-x1]^-1= -1/[x1-x2]; * ratio,[x1-xQ-xq],x1,aux; ratio,[x2-xQ-xq],x2,aux; id aux= xQ+xq; * id [1-x1+x2-xQ-xq]^-1= -1/[x1-x2-1+xQ+xq]; id [1-xQ-xq-x1+x2]^-1= -1/[x1-x2-1+xQ+xq]; * ratio,[x1-1],x1,one; id one= 1; al one^-1= 1; ratio,[x1-x2-1+xQ+xq],x1,aux; id aux= x2+1-xQ-xq; ratio,[x1-x2],[x1-xQ-xq],[x2-xQ-xq]; ratio,[x2-xQ-xq],x2,aux; id aux= xQ+xq; ratio,[x1-x2-1+xQ+xq],[x1-1],[x2-xQ-xq]; ratio,[x2-xQ-xq],x2,aux; id aux= xQ+xq; * ratio,[x1-x2],[x1-1],[x2-1]; id [1+x2-2*x1]^-1= -1/[2*x1-x2-1]; ratio,[x1-xQ-xq],[2*x1-x2-1],[x1-x2-1+xQ+xq]; * b s,tau,taup,ups,upsp,y,[y+1-x2],[y+x1-x2],[y+1-xQ-xq],[y+1-x1],[y-x2+xQ+xq]; print; * .store * g totpt= totp*intt; * id intt*tau^-2= -OR3(0); id intt*taup^-2= -OR3([y+x1-x2]); id intt*ups^-2= OR3([y+1-xQ-xq]); id intt*upsp^-2= OR3([x1-xQ-xq]); * id [y+x1-x2]= y+x1-x2; * id OR3([y+1-xQ-xq])= ( y * ( - xQ*[x2-1] + xq*[x2-1] + [x1-1]*[x2-1] + 2*[x1-1] - [x2-1] - [x2-1]^2 ) + xQ*[x2-1]^2 - [x1-1]*[x2-1])*R3([y+1-xQ-xq]); id OR3(0)= ( y * ( - xQ*[x2-1] + xq*[x2-1] + [x1-1]*[x2-1] + 2*[x1-1] - [x2-1] ) - xq*[x2-1]^2 - [x1-1]*[x2-1] + [x2-1]^2)*R3(0); id OR3([y+x1-x2])= ( y * ( - xQ*[x2-1] + xq*[x2-1] + [x1-1]*[x2-1] + 2*[x1-1] - [x2-1] - [x2-1]^2 ) - xq*[x2-1]^2 - [x1-1]*[x2-1] - [x1-1]*[x2-1]^2 + [x2-1]^2 + [x2-1]^3)*R3([y+x1-x2]); id OR3([x1-xQ-xq])= ( y * ( - xQ*[x2-1] + xq*[x2-1] + [x1-1]*[x2-1] + 2*[x1-1] - [x2-1] ) + xQ*[x2-1]^2 - [x1-1]*[x2-1] - [x1-1]*[x2-1]^2)*R3([x1-xQ-xq]); * id intt*tau^-1= R1(0); id intt*taup^-1= R1([y+x1-x2]); id intt*ups^-1= R1([y+1-xQ-xq]); id intt*upsp^-1= R1([x1-xQ-xq]); * id intt= -1/[x2-1]; * ratio,[y+x1-x2],[y+1-xQ-xq],[1-x1+x2-xQ-xq]; ratio,[y+x1-x2],[y+1-x2],[1-x1]; ratio,[y-x2+xQ+xq],[y+x1-x2],[x1-xQ-xq]; ratio,[y+x1-x2],[y+1-x1],[1+x2-2*x1]; ratio,[y+1-x1],[y+1-xQ-xq],[x1-xQ-xq]; ratio,[y-x2+xQ+xq],[y+1-xQ-xq],[x2+1-2*xQ-2*xq]; ratio,[y+1-x2],[y+1-xQ-xq],[x2-xQ-xq]; ratio,[y+1-x1],[y-x2+xQ+xq],[x1-x2-1+xQ+xq]; ratio,[y+1-x1],[y+1-x2],[x1-x2]; ratio,[y-x2+xQ+xq],[y+1-x2],[1-xQ-xq]; ratio,y,[y+x1-x2],[x1-x2]; ratio,y,[y+1-xQ-xq],[1-xQ-xq]; ratio,y,[y+1-x1],[1-x1]; ratio,[y-x2+xQ+xq],y,[x2-xQ-xq]; ratio,[y+1-x2],y,[x2-1]; ratio,y,[y+1-x2],aux; id aux= -[x2-1]; al aux^-1= -1/[x2-1]; * id [1+x2-2*x1]= 1+x2-2*x1; al [x1-xQ-xq]= x1-xQ-xq; al [x2-xQ-xq]= x2-xQ-xq; al [1-xQ-xq]= 1-xQ-xq; * id [x1-1]= x1-1; al [1-x1]= 1-x1; al [x2-1]= x2-1; al [1-x1]^-1= -1/[x1-1]; id [x1-x2]= x1-x2; * ratio,[x1-1],x1,one; ratio,[x2-1],x2,one; id one= 1; al one= -1; * ratio [x1-x2],x1,x2; id [1-x1]^-1= -1/[x1-1]; ratio,[x1-1],x1,one; ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; id [x1-x2]^-1= -1/[x2-x1]; ratio,[x2-x1],x2,x1; id [x2-x1]^-1= -1/[x1-x2]; * ratio,[x1-xQ-xq],x1,aux; ratio,[x2-xQ-xq],x2,aux; id aux= xQ+xq; * id [1-x1+x2-xQ-xq]^-1= -1/[x1-x2-1+xQ+xq]; id [1-xQ-xq-x1+x2]^-1= -1/[x1-x2-1+xQ+xq]; * ratio,[x1-1],x1,one; id one= 1; al one^-1= 1; ratio,[x1-x2-1+xQ+xq],x1,aux; id aux= x2+1-xQ-xq; ratio,[x1-x2],[x1-xQ-xq],[x2-xQ-xq]; ratio,[x2-xQ-xq],x2,aux; id aux= xQ+xq; ratio,[x1-x2-1+xQ+xq],[x1-1],[x2-xQ-xq]; ratio,[x2-xQ-xq],x2,aux; id aux= xQ+xq; * ratio,[x1-x2],[x1-1],[x2-1]; id [1+x2-2*x1]^-1= -1/[2*x1-x2-1]; ratio,[x1-xQ-xq],[2*x1-x2-1],[x1-x2-1+xQ+xq]; * *-------------------------------------------------------- * * Transformation properties y -> -y+x2-1 * * y+x1-x2 --> -y+x1-1 = -(y+1-x1) * y+1-xQ-xq -y+x2-xQ-xq= -(y-x2+xQ+xq) * y+1-x2 -y * * * Root(y+x1-x2) Root(y+1-xQ-xq) * Root(x1-xQ-xq) Root(0) * *-------------------------------------------------------- * id R1([y+x1-x2])*[y+x1-x2]^-2= R1([y+1-xQ-xq])*[y+1-x1]^-2; id R1([y+x1-x2])*[y+x1-x2]^-1= -R1([y+1-xQ-xq])*[y+1-x1]^-1; id R1(0)*[y+x1-x2]^-2= R1([x1-xQ-xq])*[y+1-x1]^-2; id R1(0)*[y+x1-x2]^-1= -R1([x1-xQ-xq])*[y+1-x1]^-1; id R1([y+x1-x2])*[y-x2+xQ+xq]^-1= -R1([y+1-xQ-xq])*[y+1-xQ-xq]^-1; id R1([x1-xQ-xq])*[y-x2+xQ+xq]^-1= -R1(0)*[y+1-xQ-xq]^-1; id R1([y+x1-x2])*[y+1-x2]^-1= -R1([y+1-xQ-xq])*y^-1; id R1([y+1-xQ-xq])*[y+1-x2]^-1= -R1([y+x1-x2])*y^-1; id R1([x1-xQ-xq])*[y+1-x2]^-1= -R1(0)*y^-1; id R1(0)*[y+1-x2]^-1= -R1([x1-xQ-xq])*y^-1; * id R3([y+x1-x2])*[y+x1-x2]^-2= R3([y+1-xQ-xq])*[y+1-x1]^-2; id R3([y+x1-x2])*[y+x1-x2]^-1= -R3([y+1-xQ-xq])*[y+1-x1]^-1; id R3(0)*[y+x1-x2]^-2= R3([x1-xQ-xq])*[y+1-x1]^-2; id R3(0)*[y+x1-x2]^-1= -R3([x1-xQ-xq])*[y+1-x1]^-1; id R3([y+x1-x2])*[y-x2+xQ+xq]^-1= -R3([y+1-xQ-xq])*[y+1-xQ-xq]^-1; id R3([x1-xQ-xq])*[y-x2+xQ+xq]^-1= -R3(0)*[y+1-xQ-xq]^-1; id R3([y+x1-x2])*[y+1-x2]^-1= -R3([y+1-xQ-xq])*y^-1; id R3([y+1-xQ-xq])*[y+1-x2]^-1= -R3([y+x1-x2])*y^-1; id R3([x1-xQ-xq])*[y+1-x2]^-1= -R3(0)*y^-1; id R3(0)*[y+1-x2]^-1= -R3([x1-xQ-xq])*y^-1; * id R1([y+1-xQ-xq])*[y+1-x1]^-2= (R1([x1-xQ-xq])+ [R1([y+1-xQ-xq])-R1([x1-xQ-xq])])*[y+1-x1]^-2; id R1([y+1-xQ-xq])*[y+1-x1]^-1= (R1([x1-xQ-xq])+ [R1([y+1-xQ-xq])-R1([x1-xQ-xq])])*[y+1-x1]^-1; id R1([y+1-xQ-xq])*[y+1-xQ-xq]^-1= (-R1(0)+ [R1([y+1-xQ-xq])+R1(0)])*[y+1-xQ-xq]^-1; * * *---------------------------------------------------- * * for the WI * *id R1([x1-xQ-xq])*[y+x1-x2]^-1= -R1(0)*[y+1-x1]^-1; *id [y+1-xQ-xq]= y+1-xQ-xq; ** *id [2*x1-x2-1]= 2*x1-x2-1; *id [2*x1-x2-1]= 2*x1-x2-1; *al [x1-x2-1+xQ+xq]= x1-x2-1+xQ+xq; *al [x1-xQ-xq]= x1-xQ-xq; * *---------------------------------------------------- * ratio,[x1-x2],x1,x2; ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; * id x1= [x1-1]+1; al x2= [x2-1]+1; * b s,y,[y+1-x2],[y+x1-x2],[y+1-xQ-xq],[y+1-x1],[y-x2+xQ+xq], [R1([y+1-xQ-xq])-R1([x1-xQ-xq])],[R1([y+1-xQ-xq])+R1(0)], [R3([y+x1-x2])+R3([y+1-xQ-xq])],[R3(0)+R3([x1-xQ-xq])], R1,R3; print; * *----------------------------------------------------------------- * .store * #endprocedure * #procedure testint(dummy) * g totpt1= totpt*canc; * id R1([y+1-xQ-xq])*y^-1*canc= 1; id canc= 0; * id [x1-1]= xQ*[x2-1]; al [x1-1]^-1= xQ^-1*[x2-1]^-1; al [x1-x2-1+xQ+xq]^-1= [xQ-1]^-1*[x2+xq/(xQ-1)]^-1; ratio,[x2-1],[x2-xQ-xq],[1-xQ-xq]; ratio,[x2-1],[x2+xq/(xQ-1)],aux; id aux= (xQ+xq-1)/[xQ-1]; al aux^-1= (1-xQ)/[1-xQ-xq]; ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * ratio,[x2-xQ-xq],[x2+xq/(xQ-1)],aux; id aux= xQ/[xQ-1]*(xQ+xq-1); al aux^-1= -(xQ-1)/xQ/[1-xQ-xq]; ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * id [1-xQ-xq]^-1= -1/[xQ+xq-1]; ratio,xQ,[xQ+xq-1],aux; id aux= xq-1; * b s,y,[y+1-x2],[y+x1-x2],[y+1-xQ-xq],[y+1-x1],[y-x2+xQ+xq], [R1([y+1-xQ-xq])-R1([x1-xQ-xq])],[R1([y+1-xQ-xq])+R1(0)], [R3([y+x1-x2])+R3([y+1-xQ-xq])],[R3(0)+R3([x1-xQ-xq])], R1,R3,[x2-1],[x2-xQ-xq],[x2+xQ/(xq-1)],[x2+xq/(xQ-1)],x2; print; * *------------------------------------------------------------------ * .store * g totpt2= totpt*canc*struct; * id R1([y+x1-x2])*y^-1*canc= 1; id canc= 0; id [x1-1]= [x2-1]/x2*(x2-xq); al [x1-1]^-1= ([x2-1]+1)/[x2-1]/[x2-xq]; al [x1-x2]^-1= -([x2-1]+1)/xq/[x2-1]; al [x1-x2-1+xQ+xq]^-1= ([x2-1]+1)/[xQ-1]/[x2+xq/(xQ-1)]; * ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; * ratio,[x2-1],[x2-xQ-xq],[1-xQ-xq]; id [1-xQ-xq]= 1-xQ-xq; ratio,[x2-1],[x2+xq/(xQ-1)],aux; id aux= (xQ+xq-1)/[xQ-1]; al aux^-1= (1-xQ)/[1-xQ-xq]; ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * ratio,[x2-xQ-xq],[x2+xq/(xQ-1)],aux; id aux= xQ/[xQ-1]*(xQ+xq-1); al aux^-1= -(xQ-1)/xQ/[1-xQ-xq]; ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * id [1-xQ-xq]^-1= -1/[xQ+xq-1]; ratio,xQ,[xQ+xq-1],aux; id aux= xq-1; * ratio,[x2-xQ-xq],x2,[xQ+xq]; ratio,xQ,[xQ+xq],xq; * id [xQ+xq]= xQ+xq; id [x2-1]= x2-1; ratio,xQ,[xQ+xq-1],aux; id aux= xq-1; * id struct*x2^-1= [xQ+xq]/x2*rest; id [xQ+xq]= xQ+xq; id rest= 1/[xQ+xq]; * id struct*[x2-1]^-1= [xQ+xq-1]/[x2-1]*rest; id [xQ+xq-1]= xQ+xq-1; id rest= 1/[xQ+xq-1]; * id struct*[x2-xQ-xq]^-1= [xQ+xq]*[xQ+xq-1]/[x2-xQ-xq]*rest; id [xQ+xq]= xQ+xq; al [xQ+xq-1]= xQ+xq-1; id rest= 1/[xQ+xq]/[xQ+xq-1]; * id struct= 1; * id xq^4*xQ^2= xq^2*xQ^2*(1+[xQ+xq])^2-( xq^2*xQ^2 + xq^2*xQ^4 +2*xq^3*xQ^3); ratio,[xQ+xq-1],[xQ+xq],one; id one= 1; al one^-1= 1; * b s,y,[y+1-x2],[y+x1-x2],[y+1-xQ-xq],[y+1-x1],[y-x2+xQ+xq], [R1([y+1-xQ-xq])-R1([x1-xQ-xq])],[R1([y+1-xQ-xq])+R1(0)], [R3([y+x1-x2])+R3([y+1-xQ-xq])],[R3(0)+R3([x1-xQ-xq])], R1,R3,[x2-1],[x2-xQ-xq],[x2+xQ/(xq-1)],[x2+xq/(xQ-1)],x2,[xQ+xq], [xQ+xq-1]; print; * *------------------------------------------------------------------ * .store * g totpt3= totpt*canc*struct; * id R1([x1-xQ-xq])*y^-1*canc= 1; id canc= 0; * id [x1-1]= xQ*[x2-1]/x2; al [x1-1]^-1= ([x2-1]+1)/[x2-1]/xQ; al [x1-x2]^-1= -([x2-1]+1)/[x2-1]/[x2-xQ]; al [x1-xQ-xq]^-1= -([x2-1]+1)/[xq-1]/[x2+xQ/(xq-1)]; * ratio,[xq-1],xq,one; id one= 1; al one^-1= 1; id [xq-1]= xq-1; * ratio,[x2-1],[x2-xQ-xq],[1-xQ-xq]; id [1-xQ-xq]= 1-xQ-xq; ratio,[x2-1],[x2+xQ/(xq-1)],aux; id aux= (xQ+xq-1)/[xq-1]; al aux^-1= (xq-1)/[xQ+xq-1]; * ratio,[x2-xQ-xq],[x2+xQ/(xq-1)],aux; id aux= xq/[xq-1]*(xQ+xq-1); al aux^-1= (xq-1)/xq/[xQ+xq-1]; * ratio,[x2-xQ-xq],x2,[xQ+xq]; ratio,xQ,[xQ+xq],xq; ratio,[xq-1],xq,one; id one= 1; al one^-1= 1; * id [1-xQ-xq]^-1= -1/[xQ+xq-1]; ratio,xq,[xQ+xq-1],aux; id aux= xQ-1; * ratio,[xq-1],[xQ+xq-1],xQ; * id [xQ+xq]= xQ+xq; id [x2-1]= x2-1; ratio,xQ,[xQ+xq-1],aux; id aux= xq-1; * id struct*x2^-1= [xQ+xq]/x2*rest; id [xQ+xq]= xQ+xq; id rest= 1/[xQ+xq]; * id struct*[x2-1]^-1= [xQ+xq-1]/[x2-1]*rest; id [xQ+xq-1]= xQ+xq-1; id rest= 1/[xQ+xq-1]; * id struct*[x2-xQ-xq]^-1= [xQ+xq]*[xQ+xq-1]/[x2-xQ-xq]*rest; id [xQ+xq]= xQ+xq; al [xQ+xq-1]= xQ+xq-1; id rest= 1/[xQ+xq]/[xQ+xq-1]; * id struct= 1; * id xq^4*xQ^2= xq^2*xQ^2*(1+[xQ+xq])^2-( xq^2*xQ^2 + xq^2*xQ^4 +2*xq^3*xQ^3); ratio,[xQ+xq-1],[xQ+xq],one; id one= 1; al one^-1= 1; * b s,y,[y+1-x2],[y+x1-x2],[y+1-xQ-xq],[y+1-x1],[y-x2+xQ+xq], [R1([y+1-xQ-xq])-R1([x1-xQ-xq])],[R1([y+1-xQ-xq])+R1(0)], [R3([y+x1-x2])+R3([y+1-xQ-xq])],[R3(0)+R3([x1-xQ-xq])], R1,R3,[x2-1],[x2-xQ-xq],[x2+xQ/(xq-1)],[x2+xq/(xQ-1)],x2, [xQ+xq],[xQ+xq-1]; print; * *------------------------------------------------------- * .store * g totpt4= totpt*canc; * id R1(0)*y^-1*canc= 1; id canc= 0; id [x1-1]= [x2-1]*(1-xq); al [x1-1]^-1= -1/[xq-1]/[x2-1]; al [x1-x2]^-1= -1/xq/[x2-1]; al [x1-xQ-xq]^-1= -1/[xq-1]/[x2+xQ/(xq-1)]; * ratio,[xq-1],xq,one; id one= 1; al one^-1= 1; id [xq-1]= xq-1; * ratio,[x2-1],[x2-xQ-xq],[1-xQ-xq]; id [1-xQ-xq]= 1-xQ-xq; ratio,[x2-1],[x2+xQ/(xq-1)],aux; id aux= (xQ+xq-1)/[xq-1]; al aux^-1= (xq-1)/[xQ+xq-1]; * ratio,[x2-xQ-xq],[x2+xQ/(xq-1)],aux; id aux= xq/[xq-1]*(xQ+xq-1); al aux^-1= (xq-1)/xq/[xQ+xq-1]; * ratio,xQ,[xQ+xq],xq; ratio,[xq-1],xq,one; id one= 1; al one^-1= 1; * id [1-xQ-xq]^-1= -1/[xQ+xq-1]; ratio,xq,[xQ+xq-1],aux; id aux= xQ-1; * ratio,[xq-1],[xQ+xq-1],xQ; * b s,y,[y+1-x2],[y+x1-x2],[y+1-xQ-xq],[y+1-x1],[y-x2+xQ+xq], [R1([y+1-xQ-xq])-R1([x1-xQ-xq])],[R1([y+1-xQ-xq])+R1(0)], [R3([y+x1-x2])+R3([y+1-xQ-xq])],[R3(0)+R3([x1-xQ-xq])], R1,R3,[x2-1],[x2-xQ-xq],[x2+xQ/(xq-1)],[x2+xq/(xQ-1)],x2; print; * *------------------------------------------------------- * .store * g totpt5= totpt*canc; * id R3([y+x1-x2])*y^-1*canc= 1; id canc= 0; id [x1-1]= ([x2-1]*([x2-1]+1-xq)+Q1)/x2; al [x1-x2]^-1= -([x2-1]+1)/xq/[[x2-1]-Q1/xq]; * ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; ratio,[[x2-1]-Q1/xq],[x2-1],aux; id aux= Q1/xq; al aux^-1= xq/Q1; id [x2-1]= x2-1; * b s,y,[y+1-x2],[y+x1-x2],[y+1-xQ-xq],[y+1-x1],[y-x2+xQ+xq], [R1([y+1-xQ-xq])-R1([x1-xQ-xq])],[R1([y+1-xQ-xq])+R1(0)], [R3([y+x1-x2])+R3([y+1-xQ-xq])],[R3(0)+R3([x1-xQ-xq])], R1,R3,[x2-1],[[x2-1]-Q1/xq],x2; print; * *------------------------------------------------------------------ * .store * g totpt6= totpt*canc; * id R3([x1-xQ-xq])*y^-1*canc= 1; id canc= 0; * id [x1-1]= (xQ*[x2-1]+Q4)/x2; al [x1-1]^-1= ([x2-1]+1)/xQ/[[x2-1]+Q4/xQ]; * ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; ratio,[x2-1],[[x2-1]+Q4/xQ],aux; id aux= Q4/xQ; al aux^-1= xQ/Q4; * id [x2-1]= x2-1; * b s,y,[y+1-x2],[y+x1-x2],[y+1-xQ-xq],[y+1-x1],[y-x2+xQ+xq], [R1([y+1-xQ-xq])-R1([x1-xQ-xq])],[R1([y+1-xQ-xq])+R1(0)], [R3([y+x1-x2])+R3([y+1-xQ-xq])],[R3(0)+R3([x1-xQ-xq])], R1,R3,x2,[[x2-1]+Q4/xQ]; print; * *------------------------------------------------------------------- * .store * g totpt_Q2= totpt*canc; * id R1([y+1-xQ-xq])*y^-1*canc= 1; id canc= 0; * id [x1-1]= xQ*[x2-1]+Q2; al [x1-1]^-1= 1/xQ/[[x2-1]+Q2/xQ]; al [x1-x2-1+xQ+xq]^-1= [xQ-1]^-1*[x2+(xq+Q2)/(xQ-1)]^-1; * ratio,[x2-1],[[x2-1]+Q2/xQ],aux; id aux= Q2/xQ; al aux^-1= xQ/Q2; * ratio,[x2-1],[x2+(xq+Q2)/(xQ-1)],aux; id aux= [xQ+xq-1+Q2]/[xQ-1]; al aux^-1= [xQ+xq-1+Q2]^-1*(xQ-1); * ratio,[x2-xQ-xq],[[x2-1]+Q2/xQ],[xQ+xq-1+Q2/xQ]; * ratio,[x2-xQ-xq],[x2+(xq+Q2)/(xQ-1)],aux; id aux= xQ/[xQ-1]*[xQ+xq-1+Q2/xQ]; al aux^-1= (xQ-1)/xQ/[xQ+xq-1+Q2/xQ]; * id [[x2-1]+Q2/xQ]^-1= 1/[x2-1]-Q2/xQ/[[x2-1]*([x2-1]+Q2/xQ)]; id [xQ+xq-1+Q2]^-1= 1/[xQ+xq-1]-Q2/[(xQ+xq-1)*(xQ+xq-1+Q2)]; id [xQ+xq-1+Q2/xQ]^-1= 1/[xQ+xq-1]-Q2/xQ/[(xQ+xq-1)*(xQ+xq-1+Q2/xQ)]; id [x2+(xq+Q2)/(xQ-1)]^-1= 1/[x2+xq/(xQ-1)]-Q2/[xQ-1]/ [(x2+(xq+Q2)/(xQ-1))*(x2+xq/(xQ-1))]; * ratio,[x2-xQ-xq],[x2+xq/(xQ-1)],aux; id aux= xQ/[xQ-1]*(xQ+xq-1); al aux^-1= (xQ-1)/xQ/[xQ+xq-1]; * id [xQ+xq-1+Q2]= xQ+xq-1+Q2; * ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * ratio,xQ,[xQ+xq-1],aux; id aux= xq-1; * id [x2-1]^-1*[[x2-1]*([x2-1]+Q2/xQ)]^-1= [[x2-1]^2*([x2-1]+Q2/xQ)]^-1; id [x2-1]^-2= [[x2-1]*([x2-1]+Q2/xQ)]^-1+Q2/xQ/[[x2-1]^2*([x2-1]+Q2/xQ)]; * id [[x2-1]*([x2-1]+Q2/xQ)]^-1= 1/[x2-1]/[[x2-1]+Q2/xQ]; al [(xQ+xq-1)*(xQ+xq-1+Q2)]^-1= 1/[xQ+xq-1]/[xQ+xq-1+Q2]; al [(xQ+xq-1)*(xQ+xq-1+Q2/xQ)]^-1= 1/[xQ+xq-1]/[xQ+xq-1+Q2/xQ]; al [(x2+(xq+Q2)/(xQ-1))*(x2+xq/(xQ-1))]^-1= 1/[x2+(xq+Q2)/(xQ-1)]/[x2+xq/(xQ-1)]; al [[x2-1]^2*([x2-1]+Q2/xQ)]^-1= 1/[x2-1]^2/[[x2-1]+Q2/xQ]; * id [[x2-1]+Q2/xQ]^-1= 1/xQ/[Q2+xQ*[x2-1]]; al [xQ+xq-1+Q2/xQ]^-1= 1/xQ/[Q2+xQ*(xQ+xq-1)]; al [x2+(xq+Q2)/(xQ-1)]^-1= (xQ-1)/[Q2+xq+(xQ-1)*x2]; al [xQ+xq-1+Q2]^-1= 1/[Q2+xQ+xq-1]; * ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * ratio,[Q2+xQ*[x2-1]],[Q2+xQ*(xQ+xq-1)],aux; id aux= xQ*(xQ+xq-x2); al aux^-1= -1/xQ/[x2-xQ-xq]; * ratio,[Q2+xQ*(xQ+xq-1)],[Q2+xq+(xQ-1)*x2],aux; id aux= (xQ-1)*(x2-xQ-xq); al aux^-1= 1/[xQ-1]/[x2-xQ-xq]; * ratio,[Q2+xq+(xQ-1)*x2],[Q2+xQ+xq-1],aux; id aux= -[x2-1]*(xQ-1); al aux^-1= 1/[xQ-1]/[x2-1]; * b s,Q2,[x1-1],[x2-1],[[x2-1]+Q2/xQ],[x2+(xq+Q2)/(xQ-1)],[x2-xQ-xq], [[x2-1]*([x2-1]+Q2/xQ)],[(xQ+xq-1)*(xQ+xq-1+Q2)], [(xQ+xq-1)*(xQ+xq-1+Q2/xQ)],[(x2+(xq+Q2)/(xQ-1))*(x2+xq/(xQ-1))], [x2+xq/(xQ-1)],[[x2-1]^2*([x2-1]+Q2/xQ)],[xQ+xq-1+Q2],[xQ+xq-1+Q2/xQ], [Q2+xQ*[x2-1]],[Q2+xQ*(xQ+xq-1)],[Q2+xq+(xQ-1)*x2],[Q2+xQ+xq-1]; print; * *------------------------------------------------------------------ * .store * g totpt_Q3= totpt*canc; * id R1(0)*y^-1*canc= 1; id canc= 0; id [x1-1]= [x2-1]*(1-xq)+Q3; al [x1-xQ-xq]^-1= -1/[xq-1]/[x2+(xQ-Q3)/(xq-1)]; al [x1-x2]^-1= -1/xq/[[x2-1]+Q3]; * ratio,[x2-1],[x2+(xQ-Q3)/(xq-1)],aux; id aux= (xQ+xq-1-Q3)/[xq-1]; al aux^-1= (xq-1)/[xQ+xq-1-Q3]; * ratio,[x2-1],[[x2-1]+Q3],Q3; ratio,[x2-xQ-xq],[[x2-1]+Q3],[xQ+xq-1+Q3]; ratio,[x2-xQ-xq],[x2+(xQ-Q3)/(xq-1)],aux; id aux= xq/[xq-1]*(xQ+xq-1-Q3/xq); al aux^-1= (xq-1)/xq/[xQ+xq-1-Q3/xq]; * ratio,[xq-1],xq,one; id one= 1; al one^-1= 1; * id [xQ+xq-1-Q3]^-1= 1/[xQ+xq-1]+Q3/[(xQ+xq-1-Q3)*(xQ+xq-1)]; al [xQ+xq-1+Q3]^-1= 1/[xQ+xq-1]-Q3/[(xQ+xq-1+Q3)*(xQ+xq-1)]; al [xQ+xq-1-Q3/xq]^-1= 1/[xQ+xq-1]+Q3/xq/[(xQ+xq-1-Q3/xq)*(xQ+xq-1)]; * id [[x2-1]+Q3]^-1= 1/[x2-1]-Q3/[[x2-1]*([x2-1]+Q3)]; al [x2+(xQ-Q3)/(xq-1)]^-1= 1/[x2+xQ/(xq-1)]+Q3/[xq-1]/ [(x2+xQ/(xq-1))*(x2+(xQ-Q3)/(xq-1))]; * ratio,xq,[xQ+xq-1],aux; id aux= xQ-1; ratio,[xq-1],[xQ+xq-1],xQ; * id [x2-1]^-2= 1/[[x2-1]*([x2-1]+Q3)]+Q3/[x2-1]^2/[[x2-1]+Q3]; * id [[x2-1]*([x2-1]+Q3)]^-1= 1/[x2-1]/[Q3+[x2-1]]; al [(x2+xQ/(xq-1))*(x2+(xQ-Q3)/(xq-1))]^-1= -1/[x2+xQ/(xq-1)]*(xq-1)/[Q3+(1-xq)*x2-xQ]; al [(xQ+xq-1-Q3/xq)*(xQ+xq-1)]^-1= -1/[xQ+xq-1]*xq/[Q3+1-xQ-xq]; al [(xQ+xq-1-Q3)*(xQ+xq-1)]^-1= -1/[xQ+xq-1]/[Q3+1-xQ-xq]; al [(xQ+xq-1+Q3)*(xQ+xq-1)]^-1= 1/[xQ+xq-1]/[Q3-1+xQ+xq]; * ratio,[Q3-1+xQ+xq],[Q3+[x2-1]],[x2-xQ-xq]; ratio,[Q3+(1-xq)*x2-xQ],[Q3+1-xQ-xq],aux; id aux= (xq-1)*[x2-1]; al aux^-1= 1/[xq-1]/[x2-1]; * ratio,[x2-xQ-xq],[x2-1],[xQ+xq-1]; * ratio,[xq-1],[xQ+xq-1],xQ; ratio,[xq-1],xq,one; id one= 1; al one^-1= 1; * b s,Q3,[x2-1],[x2+(xQ-Q3)/(xq-1)],[[x2-1]+Q3], [[x2-1]*([x2-1]+Q3)],[(x2+xQ/(xq-1))*(x2+(xQ-Q3)/(xq-1))], [x2+xQ/(xq-1)],[x2-xQ-xq],[(xQ+xq-1-Q3/xq)*(xQ+xq-1)], [(xQ+xq-1-Q3)*(xQ+xq-1)],[(xQ+xq-1+Q3)*(xQ+xq-1)], [Q3+[x2-1]],[Q3+(1-xq)*x2-xQ],[Q3+1-xQ-xq],[Q3+1-xQ-xq],[Q3-1+xQ+xq]; print; * *--------------------------------------------------------------- * .store * g totpt_Q34= totpt*canc; * id R3(0)*y*canc= -(sc/Q3-(sb*[x2-1]+sc)/Q4); id R3(0)*canc= sb/Q3-(sa*[x2-1]+sb)/Q4; id canc= 0; * id sa= 1 - 2*xQ*xq - 2*xQ*[x1-1] - 2*xQ + xQ^2 + 2*xq*[x1-1] - 2*xq + xq^2 + 2* [x1-1] + [x1-1]^2; al sb= xQ*xq*[x2-1] - xQ*[x1-1] + xQ*[x2-1] - xq*[x1-1]*[x2-1] - xq*[x1-1] + 2* xq*[x2-1] - xq^2*[x2-1] - [x1-1]*[x2-1] + [x1-1] + [x1-1]^2 - [x2-1]; al sc= 2*xq*[x1-1]*[x2-1] - 2*xq*[x2-1]^2 + xq^2*[x2-1]^2 - 2*[x1-1]*[x2-1] + [x1-1]^2 + [x2-1]^2; * repeat; id [x1-1]*Q3^-1= ([x2-1]*(1-xq)+Q3)/Q3; id [x1-1]*Q4^-1= (xQ*[x2-1]+Q4)/x2/Q4; endrepeat; * ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; * b s,Q3,Q4; print; * *--------------------------------------------------------------- * .store * g totpt_Q12= totpt*canc; * id R3([y+1-xQ-xq])*[y+1-x1]^-1*canc= 0; id R3([y+1-xQ-xq])*y*canc= -(sc/Q2-(sb*[x2-1]+sc)/Q1); id R3([y+1-xQ-xq])*canc= sb/Q2-(sa*[x2-1]+sb)/Q1; id canc= 0; * id sa= 1 - 2*xQ*xq - 2*xQ*[x1-1] + 2*xQ*[x2-1] - 2*xQ + xQ^2 + 2*xq*[x1-1] - 2* xq*[x2-1] - 2*xq + xq^2 - 2*[x1-1]*[x2-1] - 2*[x1-1] + [x1-1]^2 + 2* [x2-1] + [x2-1]^2; al sb= xQ*xq*[x2-1] + xQ*[x1-1]*[x2-1] + xQ*[x1-1] + xQ*[x2-1] - xQ*[x2-1]^2 - xQ^2*[x2-1] + xq*[x1-1] - [x1-1]*[x2-1] - [x1-1] + [x1-1]^2; al sc= - 2*xQ*[x1-1]*[x2-1] + xQ^2*[x2-1]^2 + [x1-1]^2; * repeat; id [x1-1]*Q1^-1= (([x2-1]+1-xq)*[x2-1]+Q1)/x2/Q1; id [x1-1]*Q2^-1= (xQ*[x2-1]+Q2)/Q2; endrepeat; * ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; * b s,Q1,Q2; print; * *--------------------------------------------------------------- * .store * g totpt_Q21= totpt*canc; * id R3([y+x1-x2])*y^-1*canc= 0; id R3([y+x1-x2])*y*canc= -(sc/Q1-(sb*[x2-1]+sc)/Q2); id R3([y+x1-x2])*canc= sb/Q1-(sa*[x2-1]+sb)/Q2; id canc= 0; * id sa= 1 - 2*xQ*xq - 2*xQ*[x1-1] + 2*xQ*[x2-1] - 2*xQ + xQ^2 + 2*xq*[x1-1] - 2* xq*[x2-1] - 2*xq + xq^2 - 2*[x1-1]*[x2-1] - 2*[x1-1] + [x1-1]^2 + 2* [x2-1] + [x2-1]^2; al sb= xQ*xq*[x2-1] + xQ*[x1-1]*[x2-1] - xQ*[x1-1] + xQ*[x2-1] - xQ*[x2-1]^2 - 2*xq*[x1-1]*[x2-1] - xq*[x1-1] + 2*xq*[x2-1] + 2*xq*[x2-1]^2 - xq^2* [x2-1] + 3*[x1-1]*[x2-1] + 2*[x1-1]*[x2-1]^2 + [x1-1] - [x1-1]^2*[x2-1] - [x1-1]^2 - [x2-1] - 2*[x2-1]^2 - [x2-1]^3; al sc= 2*xq*[x1-1]*[x2-1] + 2*xq*[x1-1]*[x2-1]^2 - 2*xq*[x2-1]^2 - 2*xq* [x2-1]^3 + xq^2*[x2-1]^2 - 2*[x1-1]*[x2-1] - 4*[x1-1]*[x2-1]^2 - 2* [x1-1]*[x2-1]^3 + 2*[x1-1]^2*[x2-1] + [x1-1]^2*[x2-1]^2 + [x1-1]^2 + [x2-1]^2 + 2*[x2-1]^3 + [x2-1]^4; * repeat; id [x1-1]*Q1^-1= (([x2-1]+1-xq)*[x2-1]+Q1)/x2/Q1; id [x1-1]*Q2^-1= (xQ*[x2-1]+Q2)/Q2; endrepeat; * ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; * b s,Q1,Q2; print; * *--------------------------------------------------------------- * .store * g totpt_Q43= totpt*canc; * id R3([x1-xQ-xq])*[y+1-x1]^-1*canc= 0; id R3([x1-xQ-xq])*y^-1*canc= 0; id R3([x1-xQ-xq])*y*canc= -(sc/Q4-(sb*[x2-1]+sc)/Q3); id R3([x1-xQ-xq])*canc= sb/Q4-(sa*[x2-1]+sb)/Q3; id canc= 0; * id sa= 1 - 2*xQ*xq - 2*xQ*[x1-1] - 2*xQ + xQ^2 + 2*xq*[x1-1] - 2*xq + xq^2 + 2* [x1-1] + [x1-1]^2; al sb= xQ*xq*[x2-1] + 2*xQ*[x1-1]*[x2-1] + xQ*[x1-1] + xQ*[x2-1] - xQ^2*[x2-1] - xq*[x1-1]*[x2-1] + xq*[x1-1] - [x1-1]*[x2-1] - [x1-1] - [x1-1]^2* [x2-1] - [x1-1]^2; al sc= - 2*xQ*[x1-1]*[x2-1] - 2*xQ*[x1-1]*[x2-1]^2 + xQ^2*[x2-1]^2 + 2* [x1-1]^2*[x2-1] + [x1-1]^2*[x2-1]^2 + [x1-1]^2; * repeat; id [x1-1]*Q3^-1= ([x2-1]*(1-xq)+Q3)/Q3; id [x1-1]*Q4^-1= (xQ*[x2-1]+Q4)/x2/Q4; endrepeat; * ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; * b s,Q3,Q4; print; * *----------------------------------------------------- * .store * * *---------------------------------------------------------------- * .store * g totpt_2a= totpt*canc*selp; g totpt_2b= totpt*canc*selm; * id R1([y+x1-x2])*y^-1*canc= -1/Q1*Ln(Q1,Q2); id R3([y+x1-x2])*y^-1*canc= 1/Q1^2*(1/Q1-1/Q2)-1/Q1^3*Ln(Q1,Q2)- sb/Q1^2/disc*(sb/Q1-(sa*[x2-1]+sb)/Q2); id canc= 0; * id selp*Ln(Q1,Q2)= Ln(Q1,Q2); id selp= 0; id selm*Ln(Q1,Q2)= 0; al selm= disc; * id disc= sa*sc-sb^2; * id sa= 1 - 2*xQ*xq - 2*xQ*[x1-1] + 2*xQ*[x2-1] - 2*xQ + xQ^2 + 2*xq*[x1-1] - 2* xq*[x2-1] - 2*xq + xq^2 - 2*[x1-1]*[x2-1] - 2*[x1-1] + [x1-1]^2 + 2* [x2-1] + [x2-1]^2; al sb= xQ*xq*[x2-1] + xQ*[x1-1]*[x2-1] - xQ*[x1-1] + xQ*[x2-1] - xQ*[x2-1]^2 - 2*xq*[x1-1]*[x2-1] - xq*[x1-1] + 2*xq*[x2-1] + 2*xq*[x2-1]^2 - xq^2* [x2-1] + 3*[x1-1]*[x2-1] + 2*[x1-1]*[x2-1]^2 + [x1-1] - [x1-1]^2*[x2-1] - [x1-1]^2 - [x2-1] - 2*[x2-1]^2 - [x2-1]^3; al sc= 2*xq*[x1-1]*[x2-1] + 2*xq*[x1-1]*[x2-1]^2 - 2*xq*[x2-1]^2 - 2*xq* [x2-1]^3 + xq^2*[x2-1]^2 - 2*[x1-1]*[x2-1] - 4*[x1-1]*[x2-1]^2 - 2* [x1-1]*[x2-1]^3 + 2*[x1-1]^2*[x2-1] + [x1-1]^2*[x2-1]^2 + [x1-1]^2 + [x2-1]^2 + 2*[x2-1]^3 + [x2-1]^4; * id Q1= x2*aQ1; al Q1^-1= 1/x2/aQ1; ratio,aQ1,Q2,aux; id aux= -[x2-1]/x2*(xQ-1)*[x2+xq/(xQ-1)]; al aux^-1= -([x2-1]+1)/[x2-1]/[xQ-1]/[x2+xq/(xQ-1)]; id aQ1= Q1/x2; al aQ1^-1= x2/Q1; * ratio,[x1-x2],[x1-1],[x2-1]; * id [x1-1]^n?*Q1^-3= (([x2-1]+1-xq)*[x2-1]+Q1)^n/x2^n/Q1^3; id [x1-1]^n?*Q1^-2= (([x2-1]+1-xq)*[x2-1]+Q1)^n/x2^n/Q1^2; id [x1-1]^n?*Q1^-1= (([x2-1]+1-xq)*[x2-1]+Q1)^n/x2^n/Q1; id [x1-1]^n?*Q2^-1= (xQ*[x2-1]+Q2)^n/Q2; * id [x1-x2]^-2*Q1^-3= ([x2-1]+1)^2/xq^2/[[x2-1]-Q1/xq]^2/Q1^3; id [x1-x2]^-1*Q1^-3= -([x2-1]+1)/xq/[[x2-1]-Q1/xq]/Q1^3; id [x1-x2]^-2*Q1^-2= ([x2-1]+1)^2/xq^2/[[x2-1]-Q1/xq]^2/Q1^2; id [x1-x2]^-1*Q1^-2= -([x2-1]+1)/xq/[[x2-1]-Q1/xq]/Q1^2; id [x1-x2]^-2*Q1^-1= ([x2-1]+1)^2/xq^2/[[x2-1]-Q1/xq]^2/Q1; id [x1-x2]^-1*Q1^-1= -([x2-1]+1)/xq/[[x2-1]-Q1/xq]/Q1; id [x1-x2]^-1*Q2^-1= 1/[xQ-1]/[[x2-1]+Q2/(xQ-1)]/Q2; * id [x1-x2-1+xQ+xq]^-1*Q1^-3= ([x2-1]+1)/[xQ-1]/[x2+(xq+Q1)/(xQ-1)]/Q1^3; id [x1-x2-1+xQ+xq]^-1*Q1^-2= ([x2-1]+1)/[xQ-1]/[x2+(xq+Q1)/(xQ-1)]/Q1^2; id [x1-x2-1+xQ+xq]^-1*Q1^-1= ([x2-1]+1)/[xQ-1]/[x2+(xq+Q1)/(xQ-1)]/Q1; id [x1-x2-1+xQ+xq]^-1*Q2^-1= 1/[xQ-1]/[x2+(xq+Q2)/(xQ-1)]/Q2; * ratio,[x2-1],x2,one; id one= 1; al one^-1= 1; * .store * g totpt_2aa= totpt_2a*canc; g totpt_2bb= totpt_2b*canc; * id [[x2-1]-Q1/xq]^-1= 1/[x2-1]+Q1/xq/[([x2-1]-Q1/xq)*[x2-1]]; id [x2+(xq+Q1)/(xQ-1)]^-1= 1/[x2+xq/(xQ-1)]-Q1/[xQ-1]/ [(x2+(xq+Q1)/(xQ-1))*(x2+xq/(xQ-1))]; * id [[x2-1]+Q2/(xQ-1)]^-1= 1/[x2-1]-Q2/[xQ-1]/[([x2-1]+Q2/(xQ-1))*[x2-1]]; id [x2+(xq+Q2)/(xQ-1)]^-1= 1/[x2+xq/(xQ-1)]-Q2/[xQ-1]/ [(x2+(xq+Q2)/(xQ-1))*(x2+xq/(xQ-1))]; * id [([x2-1]-Q1/xq)*[x2-1]]^-1= 1/[x2-1]/[[x2-1]-Q1/xq]; al [(x2+(xq+Q1)/(xQ-1))*(x2+xq/(xQ-1))]^-1= 1/[x2+(xq+Q1)/(xQ-1)]/ [x2+xq/(xQ-1)]; * id [([x2-1]+Q2/(xQ-1))*[x2-1]]^-1= 1/[x2-1]/[[x2-1]+Q2/(xQ-1)]; al [(x2+(xq+Q2)/(xQ-1))*(x2+xq/(xQ-1))]^-1= 1/[x2+(xq+Q2)/(xQ-1)]/ [x2+xq/(xQ-1)]; * ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * id [x2-1]^n?*Q1^-2*[[x2-1]-Q1/xq]^-1= [x2-1]^(n-1)*Q1^-2+[x2-1]^(n-1)/Q1/xq/[[x2-1]-Q1/xq]; id [x2-1]^n?*Q1^-1*[[x2-1]-Q1/xq]^-1= [x2-1]^(n-1)*Q1^-1+[x2-1]^(n-1)/xq/[[x2-1]-Q1/xq]; * ratio,x2,[x2+xq/(xQ-1)],aux; id aux= xq/[xQ-1]; al aux^-1= (xQ-1)/xq; ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * ratio,[[x2-1]-Q1/xq],[x2-1],aux; id aux= Q1/xq; al aux^-1= xq/Q1; * id Q1^-2*[[x2-1]-Q1/xq]^-1= Q1^-2/[x2-1]+1/Q1/xq/[x2-1]/[[x2-1]-Q1/xq]; * id Q1^-2*canc= 1/Q1^2; al Q1^-1*canc= 1/Q1; id Q2^-2*canc= 1/Q2^2; al Q2^-1*canc= 1/Q2; id canc= 0; * b s,Q1,Q2,Ln,[x2-1], [[x2-1]-Q1/xq],[[x2-1]+Q2/(xQ-1)],[x2+(xq+Q1)/(xQ-1)],[x2+(xq+Q2)/(xQ-1)], [x2+xq/(xQ-1)]; print; * *----------------------------------------------------- * .store * g acb2= sa*sc-sb^2; * id sa= 1 - 2*xQ*xq - 2*xQ*[x1-1] + 2*xQ*[x2-1] - 2*xQ + xQ^2 + 2*xq*[x1-1] - 2* xq*[x2-1] - 2*xq + xq^2 - 2*[x1-1]*[x2-1] - 2*[x1-1] + [x1-1]^2 + 2* [x2-1] + [x2-1]^2; al sb= xQ*xq*[x2-1] + xQ*[x1-1]*[x2-1] - xQ*[x1-1] + xQ*[x2-1] - xQ*[x2-1]^2 - 2*xq*[x1-1]*[x2-1] - xq*[x1-1] + 2*xq*[x2-1] + 2*xq*[x2-1]^2 - xq^2* [x2-1] + 3*[x1-1]*[x2-1] + 2*[x1-1]*[x2-1]^2 + [x1-1] - [x1-1]^2*[x2-1] - [x1-1]^2 - [x2-1] - 2*[x2-1]^2 - [x2-1]^3; al sc= 2*xq*[x1-1]*[x2-1] + 2*xq*[x1-1]*[x2-1]^2 - 2*xq*[x2-1]^2 - 2*xq* [x2-1]^3 + xq^2*[x2-1]^2 - 2*[x1-1]*[x2-1] - 4*[x1-1]*[x2-1]^2 - 2* [x1-1]*[x2-1]^3 + 2*[x1-1]^2*[x2-1] + [x1-1]^2*[x2-1]^2 + [x1-1]^2 + [x2-1]^2 + 2*[x2-1]^3 + [x2-1]^4; id [x1-1]^n?= (xQ*[x2-1]+Q2)^n; * b Q2; print; * *------------------------------------------------------------------ * .store * g tc= [x1-x2]*( + s*[y+1-x1]^-2*(R1([y+1-xQ-xq])-R1([x1-xQ-xq])) * ( 256/9*xq*xQ^2* [x2-1] - 256/9*xq*xQ^2*[x1-1] - 256/9*xq^2*xQ*[x1-1] - 512/9*xq^2* xQ^3*[x1-1]^-1 - 512/9*xq^3*xQ^2*[x1-x2]^-1 ) + R3([y+1-xQ-xq])*s*[y+1-x1]^-1 * ( - 1024/9*xq*xQ^2*[x2-1]*[x1-1]^2 + 256/9*xq*xQ^2*[x2-1]*[x1-1]^3 + 512/9*xq*xQ^2*[x2-1]^2*[x1-1] - 512/9*xq*xQ^2*[x2-1]^2*[x1-1]^2 + 256/9*xq*xQ^2*[x2-1]^3*[x1-1] + 512/ 9*xq*xQ^2*[x1-1]^3 - 256/9*xq*xQ^3*[x2-1]*[x1-1]^2 + 512/9*xq*xQ^3* [x2-1]^2*[x1-1] - 256/9*xq*xQ^3*[x2-1]^3 - 1024/9*xq^2*xQ^2*[x2-1]* [x1-1] + 256/3*xq^2*xQ^2*[x2-1]*[x1-1]^2 - 256/3*xq^2*xQ^2*[x2-1]^2* [x1-1] + 1024/9*xq^2*xQ^2*[x1-1]^2 - 512/9*xq^2*xQ^3*[x2-1]*[x1-1] + 512/9*xq^2*xQ^3*[x2-1]^2 + 1024/9*xq^3*xQ^2*[x2-1]*[x1-1] + 1024/9* xq^3*xQ^2*[x1-1] - 512/9*xq^3*xQ^3*[x2-1] + 512/9*xq^4*xQ^2*[x2-1] + 512/9*xq^4*xQ^2*[x2-1]^2*[x1-x2]^-1 ) + R3([x1-xQ-xq])*s*[y+1-x1]^-1 * ( - 512/9*xq^2*xQ*[x2-1]*[x1-1]^2 + 256/9*xq^2*xQ*[x2-1]*[x1-1]^3 - 256/9*xq^2*xQ*[x2-1]^2*[x1-1]^2 + 512/ 9*xq^2*xQ*[x1-1]^3 + 1024/9*xq^2*xQ^2*[x2-1]*[x1-1] - 256/3*xq^2*xQ^2 *[x2-1]*[x1-1]^2 + 256/3*xq^2*xQ^2*[x2-1]^2*[x1-1] - 1024/9*xq^2*xQ^2 *[x1-1]^2 + 1024/9*xq^2*xQ^3*[x2-1]*[x1-1] - 1024/9*xq^2*xQ^3*[x2-1] - 1024/9*xq^2*xQ^3*[x2-1]^2 + 1024/9*xq^2*xQ^3*[x1-1] - 512/9*xq^2* xQ^4*[x2-1] + 512/9*xq^2*xQ^4*[x2-1]^2*[x1-1]^-1 + 256/9*xq^3*xQ* [x2-1]*[x1-1]^2 - 512/9*xq^3*xQ^2*[x2-1]*[x1-1] + 512/9*xq^3*xQ^3* [x2-1] )); * id R1([y+1-xQ-xq])= 1/Q1-1/2/Q1^3*( 6*x1*x2*xQ - 4*x1*x2*xq + 6*x1*x2 + 2*x1*x2^2 - 4*x1*xQ*xq + 2*x1*xQ^2 - 6*x1*xq + 2*x1*xq^2 + 2*x1 - 4*x1^2*x2 - 4*x1^2*xQ + 4*x1^2*xq - 4* x1^2 + 2*x1^3 + 2*x2*xQ*xq - 2*x2*xQ^2 + 4*x2*xq - 2*x2 - 2*x2^2*xQ - 2* x2^2 + 2*xQ*xq + 2*xq - 2*xq^2)*[y+1-x1]; id R1([x1-xQ-xq])= 1/Q1-1/2/Q1^3*( 4*x1*x2*xQ - 2*x1*x2*xq + 2*x1*x2 - 4*x1*xQ*xq + 2*x1*xQ + 2*x1*xQ^2 - 8 *x1*xq + 2*x1*xq^2 - 2*x1^2*x2 - 4*x1^2*xQ + 4*x1^2*xq - 2*x1^2 + 2*x1^3 + 2*x2*xQ*xq - 2*x2*xQ - 2*x2*xQ^2 + 2*x2*xq + 2*xQ*xq + 4*xq - 2*xq^2)*[y+1-x1]; id R3([y+1-xQ-xq])= 1/Q1^3; id R3([x1-xQ-xq])= 1/Q1^3; * id x1= [x1-1]+1; al x2= [x2-1]+1; * id [x1-x2]= [x1-1]-[x2-1]; * b s,[y+1-x1],Q1; print; * .store * #endprocedure * #procedure yint(dummy) * *--------------------------------------------------------------- * * Q1= x2*[x1-1]-[x2-1]*[x2-xq] * Q2= [x1-1]-xQ*[x2-1] * Q3= [x1-1]-[x2-1]*[1-xq] * Q4= x2*[x1-1]-xQ*[x2-1] * Q5= [x1-1]^2+(1-x2+xq-xQ)*[x1-1]+xQ*[x2-1] * * [y+1-xQ-xq]^-1*R1(0) * beta= |Q5|, R|_y= x2-1 is |Q4|, R|_y=0 is |Q3| * integral is -1/|Q5|*Lna * * [y+1-xQ-xq]^-1*R1([y+1-xQ-xq]) * beta= |Q5|, R_y=x2-1 is |Q1|, R_y=0 is |Q2| * integral is -1/|Q5|*Lnb * * [y+1-x1]^-2*R1([y+1-xQ-xq]) * beta= |Q5|, R_y=x2-1 is |Q1|, R_y=0 is |Q2| * * [y+1-x1]^-2*R1([x1-xQ-xq]) * beta= |Q5|, R_y=x2-1 is |Q3|, R_y=0 is |Q4| * * [y+1-x1]^-1*R1([y+1-xQ-xq]) * beta= |Q5|, R_y=x2-1 is |Q1|, R_y=0 is |Q2| * * [y+1-x1]^-1*R1([x1-xQ-xq]) * beta= |Q5|, R_y=x2-1 is |Q3|, R_y=0 is |Q4| * * R1([y+x1-x2])*y^-1 * beta= |Q1|, R_y=x2-1 is |Q2|, R_y=0 is |Q1| * * R1([y+x1-x2]) * R_y=x2-1 is |Q2|, R_y=0 is |Q1| * * R1([y+1-xQ-xq])*y^-1 * beta= |Q2|, R_y=x2-1 is |Q1|, R_y=0 is |Q2| * * R1([y+1-xQ-xq]) * R_y=x2-1 is |Q1|, R_y=0 is |Q2| * * R1([x1-xQ-xq])*y^-1 * beta= |Q4|, R_y=x2-1 is |Q3|, R_y=0 is |Q4| * * R1([x1-xQ-xq]) * R_y=x2-1 is |Q3|, R_y=0 is |Q4| * * R1(0)*y^-1 * beta= |Q3|, R_y=x2-1 is |Q4|, R_y=0 is |Q3| * * R1(0) * R_y=x2-1 is |Q4|, R_y=0 is |Q3| * * R3([y+x1-x2])y^-1 * beta= |Q1|, R_y=x2-1 is |Q2|, R_y=0 is |Q1| * * R3([y+x1-x2])*(1;y) * R_y=x2-1 is |Q2|, R_y=0 is |Q1| * * R3([y+1-xQ-xq])*(1;y) * R_y=x2-1 is |Q1|, R_y=0 is |Q2| * * R3([y+1-xQ-xq])*[y+1-x1]^-1 * beta= |Q5|, R_y=x2-1 is |Q1|, R_y=0 is |Q2| * * R3([y+1-xQ-xq]) * R_y=x2-1 is |Q1|, R_y=0 is |Q2| * * R3([x1-xQ-xq])*y^-1 * beta= |Q4|, R_y=x2-1 is |Q3|, R_y=0 is |Q4| * * R3([x1-xQ-xq])*(1;y) * R_y=x2-1 is |Q3|, R_y=0 is |Q4| * * R3([x1-xQ-xq])*[y+1-x1]^-1 * beta= |Q5|, R_y=x2-1 is |Q3|, R_y=0 is |Q4| * * R3([x1-xQ-xq]) * R_y=x2-1 is |Q3|, R_y=0 is |Q4| * * R3(0)*(1;y) * R_y=x2-1 is |Q4|, R_y=0 is |Q3| * * Beginning of y-integration * *------------------------------------------------ * Integral type-I *------------------------------------------------ * g inty_1= totpt*canc; * id R1([y+1-xQ-xq])*y^-1*canc= 1; id canc= 0; * id [x1-1]= xQ*[x2-1]+Q2; al [x1-1]^-1= 1/xQ/[[x2-1]+Q2/xQ]; al [x1-x2-1+xQ+xq]^-1= [xQ-1]^-1*[x2+(xq+Q2)/(xQ-1)]^-1; * ratio,[x2-1],[[x2-1]+Q2/xQ],aux; id aux= Q2/xQ; al aux^-1= xQ/Q2; * id [[x2-1]+Q2/xQ]^-1= 1/[x2-1]-Q2/xQ/[[x2-1]*([x2-1]+Q2/xQ)]; id [x2+(xq+Q2)/(xQ-1)]^-1= 1/[x2+xq/(xQ-1)]-Q2/[xQ-1]/ [(x2+(xq+Q2)/(xQ-1))*(x2+xq/(xQ-1))]; * id [[x2-1]*([x2-1]+Q2/xQ)]^-1= 1/[x2-1]/[[x2-1]+Q2/xQ]; al [(x2+(xq+Q2)/(xQ-1))*(x2+xq/(xQ-1))]^-1= 1/[x2+(xq+Q2)/(xQ-1)]/[x2+xq/(xQ-1)]; * id [x2-1]^-1*[[x2-1]*([x2-1]+Q2/xQ)]^-1= [[x2-1]^2*([x2-1]+Q2/xQ)]^-1; id [x2-1]^-2= [[x2-1]*([x2-1]+Q2/xQ)]^-1+Q2/xQ/[[x2-1]^2*([x2-1]+Q2/xQ)]; * id [[x2-1]*([x2-1]+Q2/xQ)]^-1= 1/[x2-1]/[[x2-1]+Q2/xQ]; al [[x2-1]^2*([x2-1]+Q2/xQ)]^-1= 1/[x2-1]^2/[[x2-1]+Q2/xQ]; * ratio,[x2-xQ-xq],[x2+xq/(xQ-1)],aux; id aux= xQ/[xQ-1]*(xQ+xq-1); al aux^-1= (xQ-1)/xQ/[xQ+xq-1]; * ratio,[x2-xQ-xq],[x2-1],[xQ+xq-1]; * ratio,[x2-1],[x2+xq/(xQ-1)],aux; id aux= (xQ+xq-1)/[xQ-1]; al aux^-1= -(1-xQ)/[xQ+xq-1]; * ratio,[xQ-1],xQ,one; id one= 1; al one^-1= 1; * ratio,xQ,[xQ+xq-1],aux; id aux= xq-1; * b s,Q2,[[x2-1]+Q2/xQ],[x2+(xq+Q2)/(xQ-1)]; print; * .store * *------------------------------------------------ * Integral type-II *------------------------------------------------ * g inty_2= totpt*canc; * id R1(0)*y^-1*canc= 1; id canc= 0; id [x1-1]= [x2-1]*(1-xq)+Q3; al [x1-xQ-xq]^-1= -1/[xq-1]/[x2+(xQ-Q3)/(xq-1)]; al [x1-x2]^-1= -1/xq/[[x2-1]+Q3]; * ratio,[x2-1],[[x2-1]+Q3],Q3; * id [[x2-1]+Q3]^-1= 1/[x2-1]-Q3/[[x2-1]*([x2-1]+Q3)]; al [x2+(xQ-Q3)/(xq-1)]^-1= 1/[x2+xQ/(xq-1)]+Q3/[xq-1]/ [(x2+xQ/(xq-1))*(x2+(xQ-Q3)/(xq-1))]; * id [x2-1]^-2= 1/[[x2-1]*([x2-1]+Q3)]+Q3/[x2-1]^2/[[x2-1]+Q3]; * id [[x2-1]*([x2-1]+Q3)]^-1= 1/[x2-1]/[[x2-1]+Q3]; al [(x2+xQ/(xq-1))*(x2+(xQ-Q3)/(xq-1))]^-1= 1/[x2+xQ/(xq-1)]/ [x2+(xQ-Q3)/(xq-1)]; * ratio,[x2-xQ-xq],[x2-1],[xQ+xq-1]; * ratio,[x2-1],[x2+xQ/(xq-1)],aux; id aux= (xQ+xq-1)/[xq-1]; al aux^-1= (xq-1)/[xQ+xq-1]; * ratio,[x2-xQ-xq],[x2+xQ/(xq-1)],aux; id aux= xq/[xq-1]*(xQ+xq-1); al aux^-1= (xq-1)/xq/[xQ+xq-1]; * ratio,[xq-1],xq,one; id one= 1; al one^-1= 1; * ratio,xQ,[xQ+xq-1],aux; id aux= xq-1; * b s,Q3,[[x2-1]+Q3],[x2+(xQ-Q3)/(xq-1)]; print; * .store * #endprocedure * *//////////////////////////////////////////////////////////////////////// * *#call testu{dummy} *#call testl{dummy} * *------------------------------------------ * #call finalstate{dummy} #call initialstate{dummy} #call trace{dummy} #call integration{dummy} *#call testint{dummy} #call yint{dummy} * .end