DEF IsRealVect2 = IsSeqOf:IsReal;
IsRealVect2:<1.2,1.0,3.0,0.0>;
IsRealVect2:<<1,2>,1.0>;

DEF IsFunVect2  = IsSeqOf:IsFun;
DEF IsVect2     = OR ~ [IsRealVect,IsFunVect];

DEF v1=<1.0,0.0,2.0>;
DEF v2=<2.0,1.0,0.0>;
v1;
v2;
<v1,v2>;
TRANS:<v1,v2>;

AA:+:(TRANS:<v1,v2>);

DEF vectSum2        = AA:+ ~ TRANS;
vectSum2:<v1,v2>;

DEF VectNeg2 = AA:-;
VectNeg2:v1;

DEF vectDiff2       = AA:- ~ TRANS;
vectDiff2:<v1,v2>;

DEF Sqr            = ID * ID;
DEF VectNorm       = SQRT ~ + ~ AA:Sqr;
SQRT:(+:(AA:Sqr:v1));

DEF scalVectProd   = AA:* ~ DISTL;
v1;
DISTL:<2,v1>;
AA:*:(DISTL:<2,v1>);



DEF InnerProd      = + ~ AA:* ~ TRANS;
v1;
v2;
TRANS:<v1,v2>;
+:(AA:*:(TRANS:<v1,v2>));


DEF UnitVect (v::IsVect) = ScalVectProd:<1 / VectNorm:v, v>;


DEF VectProd (u,v::IsVect) = <w1, w2, w3>
    WHERE
      w1 = (u2 * v3) - (u3 * v2),
      w2 = (u3 * v1) - (u1 * v3),
      w3 = (u1 * v2) - (u2 * v1),
      u1 = s1:u,   u2 = s2:u,   u3 = s3:u, 
      v1 = s1:v,   v2 = s2:v,   v3 = s3:v
    END; 


<1,2,3> vectSum <10,20,30>;
<1,2,3> vectDiff <10,20,30>;
<1,0,0> VectProd <1,1,0>;
2 scalVectProd <11,22,33>;
UnitVect:<10,20,30>;
(VectNorm ~ UnitVect):<10,20,30>;

DEF u = mkvector:<0,0.5,0>:<0.5,0,0>
DEF v = mkvector:<0.5,0,0>:<1,1,0>
DEF w = mkvector:<1,1,0>:<1,1.5,0.5>
DEF somma = mkvector:<0,0.5,0>:<
out=STRUCT:< u,v,w,somma, mkframe >

% 3 vettori e la somma ultimi 2 %
def v0=<0,0.5,0>;
def v1=<0.5,-0.5,0>;
def v2=< 0.5 , 1 , 0 >;
def vsomma=VectSum:<v1,v2>;
<v0,v1,v2,vsomma>;

% dei punti ottenuti come azione affine dell'origine e vetttori %
% (0,v0)->p0 %
def p0=VectSum:<<0,0,0>,v0>;
% (p0,v1)->p1 %
def p1=VectSum:<p0,v1>;
% (p1,v2)->p2 %
def p2=VectSum:<p1,v2>;
% (p0,v2)->p1b %
def p1b=VectSum:<p0,v2>;
% (p1b,v1)->p2b %
def p2b=VectSum:<p1b,v1>;
% (p0,vsomma)-> psomma %
def psomma=VectSum:<p0,vsomma>;
<p0,p1,p2,p1b,p2b,psomma>;

% disegno %
DEF p0p1 = mkvector:p0:p1 color cyan;
DEF p1p2 = mkvector:p1:p2 color magenta;
DEF p0p1b = mkvector:p0:p1b color cyan;
DEF p1bp2b = mkvector:p1b:p2b color magenta;
DEF p0psomma = mkvector:p0:psomma color yellow;
DEF OUT=STRUCT:< mkframe, p0p1,p1p2,p0p1b,p1bp2b,p0psomma >;
OUT;