src/algebra/clifford.spad

690         exteriorProdTerm(op1mult : K, op1type : SINT, op2mult : K, op2type : SINT) : % ==
692           And(op1type, op2type) ~= 0 => resul -- if common terms return without adding
694           bz := Or(op1type, op2type)-- combine terms from both operands
695           for i in 0..n-1 | bit?(op1type, i) repeat
698             for j in i+1..n-1 | bit?(op1type, j) repeat k := k+1
706         regressiveProdTerm(op1mult : K, op1type : SINT, op2mult : K, op2type : SINT) : % ==
707           op1 := New; op1.op1type := 1$K
731         lcProdTerm(op1mult : K, op1type : SINT, op2mult : K, op2type : SINT) : % ==
733           grade1 := gradeTerm(op1type) -- grade of first operand
740 … resul.(0$NNI) := resul.(0$NNI) + op1mult * op2mult * bilinear(op1type, op2type) -- add scalar term
746             left : % := _/_\(lcProdTerm(op1mult, op1type, op2mult, uType), inner2)
748             resul := resul + left + _/_\(inner4, lcProdTerm(-op1mult, op1type, op2mult, vType))
752           uType : SINT := leftMostBase(op1type) -- highest ^factor
753           vType : SINT := xor(op1type, uType) -- remaining ^factors
761         rcProdTerm(op1mult : K, op1type : SINT, op2mult : K, op2type : SINT) : % ==
763           grade1 := gradeTerm(op1type) -- grade of first operand
766             resul.op1type := resul.op1type + op1mult*op2mult
770 … resul.(0$NNI) := resul.(0$NNI) + op1mult * op2mult * bilinear(op1type, op2type) -- add scalar term
773             uType : SINT := rightMostBase(op1type) -- lowest ^factor
774             vType : SINT := xor(op1type, uType) -- remaining ^factors
780               s1 := concat[toStringTerm(op1mult,op1type),"L",toStringTerm(op2mult,op2type)]
792           resul := resul+ rc(rcProdTerm(op1mult, op1type, op2mult, vType), inner2)
794             s1 := concat[toStringTerm(op1mult,op1type),"L",toStringTerm(op2mult,op2type)]
795             s2 := concat["= (",toStringTerm(op1mult,op1type),"L",toStringTerm(op2mult,vType)]
819         cliffordProdTerm(op1mult : K, op1type : SINT, op2mult : K, op2type : SINT) : % ==
821           grade1 := gradeTerm(op1type) -- grade of first operand
827             resul.op1type := resul.op1type + op1mult*op2mult
830 … resul.(0$NNI) := resul.(0$NNI) + op1mult * op2mult * bilinear(op1type, op2type) -- add scalar term
831 …         resul := resul + exteriorProdTerm(op1mult, op1type, op2mult, op2type) -- add exterior term
838             xt : % := New; xt.op1type := 1$K
842               +  _/_\(lcProdTerm(1$K, op1type, 1$K, uType), vt)_
843 …+  _/_\(gradeInvolutionTerm(1$K, uType), lcProdTerm(1$K, op1type, 1$K, vType)) -- gradeinvolution(…
849             uType : SINT := rightMostBase(op1type) -- lowest ^factor
850             vType : SINT := xor(op1type, uType) -- remaining ^factors
861           xType : SINT := rightMostBase(op1type) -- highest ^factor
862           uType : SINT := xor(op1type, xType) -- remaining ^factors
873             s1 := concat[toStringTerm(op1mult,op1type),"*",toStringTerm(op2mult,op2type)]
889         cliffordDiagonalTerm(op1mult : K, op1type : SINT, op2mult : K, op2type : SINT) : % ==
892             for i in 0..n-1 | bit?(op1type, i) repeat
895                 for j in i+1..n-1 | bit?(op1type, j) repeat k := k+1