// Script #1 (main types)
var s1=new series([1,3],[3,5],2,1); // args=p,q,nu,tau
var s2=mmgd("d4+g2.d7+(g4.d10).[g2.d3]*"); // s2 
var m1=new smatrix([[s1,s1,s1],[s2,s2,s2]]);
m1.set(0,1,seps());
output.value='s1='+s1+'\n';  //default string format
output.value+='s1='+s1.etvo()+'\n'; // etvo compatible format 
output.value+='s2='+s2.etvo()+'\n'; // etvo compatible format 
output.value+=m1+'\n';
output.value+=m1.etvo()+'\n';
output.value+='m1(0,2)='+m1.get(0,2).etvo()+'\n';

//Script #2
// shortcut functions
var eps=seps();  //new series([],[],0,0)
var e=sgd(0,0); // series g0.d0
var m1=sgd(2,5); // series g2.d5
var p1=spoly([0,1,2,5,3,6]); // series g0.d1+g2.d5+g3.d6
var s1=sseries([0,3],[2,5,3,6],3,4); // series g0.d3+(g2.d5+g3.d6).[g3.d4]*
// it is also possible to parse rational expressions
var p2=mmgd("g0.d1+g2.d5+g3.d6");
var s2=mmgd("g0.d3+(g2.d5+g3.d6).[g3.d4]*");
output.value=m1.etvo()+'\n';
output.value+=p1.etvo()+'\n';
output.value+=s1.etvo()+'\n';
output.value+=p2+'\n';
output.value+=s2+'\n';


//Script #3 (main operations)
s1=mmgd("d1+(g1.d2+g2.d3).[g2.d2]*"); //series([0,1],[1,2,2,3],2,2);
s2=mmgd("d4.[g3.d3]*"); // series([],[0,4],3,3);
s3=mmgd("d3.[g4.d5]*"); // series([],[0,3],4,5);
s0=mmgd("g3.d4+g5.d6"); // poly([3,4,5,6]);
output.value = s1.etvo()+'\n';
var s4=s2.oplus(s3);
output.value += s4.etvo()+'\n';
output.value+='s4.p='+s4.p+'\n';
output.value+='s4.q='+s4.q+'\n';
s4=s2.otimes(s3);
output.value+= s4.etvo()+'\n';
s4=s0.star();
output.value += s4.etvo()+'\n';

//Script #4 (neutral feedback control)
H=mmgd("(d4+g2.d7).[g3.d4]*"); //sseries([],[0,4,2,7],3,4);
F=H.frac(H).frac(H);
output.value += F.etvo()+'\n';
Fcaus=F.prcaus();
output.value += Fcaus.etvo()+'\n';
//check neutrality
G=H.otimes(Fcaus.otimes(H).star());
output.value += 'open loop=' + H.etvo()+'\n';
output.value += 'closed loop=' + G.etvo()+'\n';

//Script #5 
var eps=seps();
A=ssmatrix([[eps,eps,eps,sgd(2,0)],
[sgd(0,2),eps,eps,eps],
[eps,sgd(0,0),eps,eps],
[eps,eps,sgd(0,3),eps]])
B= new smatrix([[sgd(0,0)],[eps],[eps],[eps]]);
C= new smatrix([[eps,sgd(0,0),eps,sgd(1,0)]]);
output.value=A.etvo()+'\n';
output.value+=B.etvo()+'\n';
output.value+=C.etvo()+'\n';
H=C.otimes(A.star()).otimes(B)
output.value+='H='+H.etvo()+'\n';

//Script #6 (Automatica 2001) 
var eps=seps();
A=ssmatrix([[sgd(1,2),eps,eps],
[eps,sgd(1,3),eps],
[sgd(1,3),sgd(0,8),sgd(1,2)]]);
B=ssmatrix([[sgd(0,0),eps],[eps,sgd(0,0)],[eps,eps]]);
C=ssmatrix([[eps,eps,sgd(0,2)]]);
CAs=C.otimes(A.star());
output.value='CAs='+CAs.etvo()+'\n';
H=CAs.otimes(B);
output.value+='H='+H.etvo()+'\n';
var s=sseries([],[0,0],1,3);
Gref=ssmatrix([[H.get(0,0).otimes(s),H.get(0,1).otimes(s)]]);
output.value+='Gref='+Gref.etvo()+'\n';
Sr=Gref.lfrac(CAs).rfrac(H);
output.value+='Sr='+Sr.etvo()+'\n';
Srp=Sr.prcaus();
output.value+='Sr+='+Srp.etvo()+'\n';
//Gcl=((CA*Sr)*)H
Gcl=(CAs.otimes(Srp)).star().otimes(H);
output.value+='Gcl='+Gcl.etvo()+'\n';


//script #7
var s=mmgd("g3.d4+g5.d7+g8.d11+g9.d13"); //spoly([3,4,5,7,8,11,9,13])
var s= s.star();
output.value='s='+s+'\n';  // default string output
output.value+='s='+s.etvo()+'\n'; // etvo compatible
output.value+='s.p=' + s.p +'\n'; 
output.value+='s.q=' + s.q + '\n'; 
var i;
for(i=0;i<s.p.length;i++){ output.value+=s.p[i]+',';}
for(i=0;i<s.q.length;i++){ output.value+=s.q[i]+',';}