clifford.Cl

clifford.Cl(p=0, q=0, r=0, sig=None, names=None, firstIdx=1, mvClass=<class 'clifford._multivector.MultiVector'>)

Returns a Layout and basis blade MultiVectors for the geometric algebra \(Cl_{p,q,r}\).

The notation \(Cl_{p,q,r}\) means that the algebra is \(p+q+r\)-dimensional, with the first \(p\) vectors with positive signature, the next \(q\) vectors negative, and the final \(r\) vectors with null signature.

Parameters

• p (int) – number of positive signature basis vectors

• q (int) – number of negative signature basis vectors

• r (int) – number of zero signature basis vectors

• sig – See the docs for clifford.Layout. If sig is passed, then p, q, and r are ignored.

• names – See the docs for clifford.Layout. If sig is passed, then p, q, and r are ignored.

• firstIdx – See the docs for clifford.Layout. If sig is passed, then p, q, and r are ignored.

Returns

• layout (Layout) – The resulting layout

• blades (Dict[str, MultiVector]) – The blades of the returned layout, equivalent to layout.blades.