EVA version :  1.24
enter Cl(p) or Cl(p,q) :  p+q number basis vectors up to 5  , p positive squares, q negative squares
Cl(4)
oriented volume :
j = e1234
signature :
(1,1,1,1)
 
a4=x0*e0+x1*e1+x2*e2+x3*e3+x4*e4+x12*e12+x13*e13+x14*e14+x23*e23+x24*e24+x34*e34+x123*e123+x124*e124+x134*e134+x234*e234+x1234*e234
 
B=unit(Cldim)
 
for(i,1,Cldim,print(outp(a4,B[i])))
(1 x0,1 x1,1 x2,1 x3,1 x4,1 x12,1 x13,1 x14,1 x23,1 x24,1 x34,1 x123,1 x124,1 x134,1 x234,1 x1234)
(0,1 x0,0,0,0,-x2,-x3,-x4,0,0,0,1 x23,1 x24,1 x34,0,-x234)
(0,0,1 x0,0,0,1 x1,0,0,-x3,-x4,0,-x13,-x14,0,1 x34,1 x134)
(0,0,0,1 x0,0,0,1 x1,0,1 x2,0,-x4,1 x12,0,-x14,-x24,-x124)
(0,0,0,0,1 x0,0,0,1 x1,0,1 x2,1 x3,0,1 x12,1 x13,1 x23,1 x123)
(0,0,0,0,0,1 x0,0,0,0,0,0,1 x3,1 x4,0,0,1 x34)
(0,0,0,0,0,0,1 x0,0,0,0,0,-x2,0,1 x4,0,-x24)
(0,0,0,0,0,0,0,1 x0,0,0,0,0,-x2,-x3,0,1 x23)
(0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,0,0,1 x4,1 x14)
(0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,0,-x3,-x13)
(0,0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,1 x2,1 x12)
(0,0,0,0,0,0,0,0,0,0,0,1 x0,0,0,0,-x4)
(0,0,0,0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x3)
(0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0,0,-x2)
(0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0,1 x1)
(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0)
 
for(i,1,Cldim,print(outp(B[i]),a4))
(1 x0,1 x1,1 x2,1 x3,1 x4,1 x12,1 x13,1 x14,1 x23,1 x24,1 x34,1 x123,1 x124,1 x134,1 x234,1 x1234)
(0,1 x0,0,0,0,1 x2,1 x3,1 x4,0,0,0,1 x23,1 x24,1 x34,0,1 x234)
(0,0,1 x0,0,0,-x1,0,0,1 x3,1 x4,0,-x13,-x14,0,1 x34,-x134)
(0,0,0,1 x0,0,0,-x1,0,-x2,0,1 x4,1 x12,0,-x14,-x24,1 x124)
(0,0,0,0,1 x0,0,0,-x1,0,-x2,-x3,0,1 x12,1 x13,1 x23,-x123)
(0,0,0,0,0,1 x0,0,0,0,0,0,1 x3,1 x4,0,0,1 x34)
(0,0,0,0,0,0,1 x0,0,0,0,0,-x2,0,1 x4,0,-x24)
(0,0,0,0,0,0,0,1 x0,0,0,0,0,-x2,-x3,0,1 x23)
(0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,0,0,1 x4,1 x14)
(0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,0,-x3,-x13)
(0,0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,1 x2,1 x12)
(0,0,0,0,0,0,0,0,0,0,0,1 x0,0,0,0,1 x4)
(0,0,0,0,0,0,0,0,0,0,0,0,1 x0,0,0,-x3)
(0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0,0,1 x2)
(0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0,-x1)
(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0)
oriented volume :
j = e1234
signature :
(1,1,1,1)
(1 x0,1 x1,1 x2,1 x3,1 x4,1 x12,1 x13,1 x14,1 x23,1 x24,1 x34,1 x123,1 x124,1 x134,1 x234,1 x1234)
(0,1 x0,0,0,0,-x2,-x3,-x4,0,0,0,1 x23,1 x24,1 x34,0,-x234)
(0,0,1 x0,0,0,1 x1,0,0,-x3,-x4,0,-x13,-x14,0,1 x34,1 x134)
(0,0,0,1 x0,0,0,1 x1,0,1 x2,0,-x4,1 x12,0,-x14,-x24,-x124)
(0,0,0,0,1 x0,0,0,1 x1,0,1 x2,1 x3,0,1 x12,1 x13,1 x23,1 x123)
(0,0,0,0,0,1 x0,0,0,0,0,0,1 x3,1 x4,0,0,1 x34)
(0,0,0,0,0,0,1 x0,0,0,0,0,-x2,0,1 x4,0,-x24)
(0,0,0,0,0,0,0,1 x0,0,0,0,0,-x2,-x3,0,1 x23)
(0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,0,0,1 x4,1 x14)
(0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,0,-x3,-x13)
(0,0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,1 x2,1 x12)
(0,0,0,0,0,0,0,0,0,0,0,1 x0,0,0,0,-x4)
(0,0,0,0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x3)
(0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0,0,-x2)
(0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0,1 x1)
(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0)
(1 x0,1 x1,1 x2,1 x3,1 x4,1 x12,1 x13,1 x14,1 x23,1 x24,1 x34,1 x123,1 x124,1 x134,1 x234,1 x1234)
(0,1 x0,0,0,0,1 x2,1 x3,1 x4,0,0,0,1 x23,1 x24,1 x34,0,1 x234)
(0,0,1 x0,0,0,-x1,0,0,1 x3,1 x4,0,-x13,-x14,0,1 x34,-x134)
(0,0,0,1 x0,0,0,-x1,0,-x2,0,1 x4,1 x12,0,-x14,-x24,1 x124)
(0,0,0,0,1 x0,0,0,-x1,0,-x2,-x3,0,1 x12,1 x13,1 x23,-x123)
(0,0,0,0,0,1 x0,0,0,0,0,0,1 x3,1 x4,0,0,1 x34)
(0,0,0,0,0,0,1 x0,0,0,0,0,-x2,0,1 x4,0,-x24)
(0,0,0,0,0,0,0,1 x0,0,0,0,0,-x2,-x3,0,1 x23)
(0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,0,0,1 x4,1 x14)
(0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,0,-x3,-x13)
(0,0,0,0,0,0,0,0,0,0,1 x0,0,0,1 x1,1 x2,1 x12)
(0,0,0,0,0,0,0,0,0,0,0,1 x0,0,0,0,1 x4)
(0,0,0,0,0,0,0,0,0,0,0,0,1 x0,0,0,-x3)
(0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0,0,1 x2)
(0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0,-x1)
(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 x0)
>
    test outer product