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File Parse ga/c2d.js

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            /*"""3D Projective Geometric Algebra.

Written by a generator written by enki.
"""*/

__author__ = 'Enki'

import math


class R310 {
    __init__(value=0, index=0){
        /*"""Initiate a new R310.

        Optional, the component index can be set with value.
        """*/
        this.mvec = [0] * 16
        this._base = ["1", "e1", "e2", "e3", "e4", "e12", "e13", "e14", "e23", "e24", "e34", "e123", "e124", "e134", "e234", "e1234"]
        if (value != 0){
            this.mvec[index] = value
        }
    }

    @classmethod
    fromarray(cls, array){
        /*"""Initiate a new R310 from an array-like object.

        The first axis of the array is assumed to correspond to the elements
        of the algebra, and needs to have the same length. Any other dimensions
        are left unchanged, and should have simple operations such as addition
        and multiplication defined. NumPy arrays are therefore a perfect
        candidate.

        :param array: array-like object whose length is the dimension of the algebra.
        :return: new instance of R310.
        """*/
        this = cls()
        if len(array) != len(this){
            raise TypeError('length of array must be identical to the dimension '
                            'of the algebra.')
        }
        this.mvec = array
        return this
    }

    __str__(){
        if isinstance(this.mvec, list){
            res = ' + '.join(filter(None, [("%.7f" % x).rstrip("0").rstrip(".")+(["",this._base[i]][i>0]) if abs(x) > 0.000001 else None for i,x in enumerate(this)]))
        }else{//  # Assume array-like, redirect str conversion
            res = str(this.mvec)
        }

        if (res == ''){
            return "0"
        }
        return res
    }

    __getitem__(key){
        return this.mvec[key]
    }

    __setitem__(key, value){
        this.mvec[key] = value
    }

    __len__(){
        return len(this.mvec)
    }

    __invert__(a){
        /*"""R310.Reverse

        Reverse the order of the basis blades.
        """*/
        res = a.mvec.copy()
        res[0] = a[0]
        res[1] = a[1]
        res[2] = a[2]
        res[3] = a[3]
        res[4] = a[4]
        res[5] = -a[5]
        res[6] = -a[6]
        res[7] = -a[7]
        res[8] = -a[8]
        res[9] = -a[9]
        res[10] = -a[10]
        res[11] = -a[11]
        res[12] = -a[12]
        res[13] = -a[13]
        res[14] = -a[14]
        res[15] = a[15]
        return R310.fromarray(res)
    }

    Dual(a){
        /*"""R310.Dual

        Poincare duality operator.
        """*/
        res = a.mvec.copy()
        res[0]=-a[15]
        res[1]=-a[14]
        res[2]=a[13]
        res[3]=-a[12]
        res[4]=-a[11]
        res[5]=a[10]
        res[6]=-a[9]
        res[7]=-a[8]
        res[8]=a[7]
        res[9]=a[6]
        res[10]=-a[5]
        res[11]=a[4]
        res[12]=a[3]
        res[13]=-a[2]
        res[14]=a[1]
        res[15]=a[0]
        return R310.fromarray(res)
    }

    Conjugate(a){
        /*"""R310.Conjugate

        Clifford Conjugation
        """*/
        res = a.mvec.copy()
        res[0]=a[0]
        res[1]=-a[1]
        res[2]=-a[2]
        res[3]=-a[3]
        res[4]=-a[4]
        res[5]=-a[5]
        res[6]=-a[6]
        res[7]=-a[7]
        res[8]=-a[8]
        res[9]=-a[9]
        res[10]=-a[10]
        res[11]=a[11]
        res[12]=a[12]
        res[13]=a[13]
        res[14]=a[14]
        res[15]=a[15]
        return R310.fromarray(res)
    }

    Involute(a){
        /*"""R310.Involute

        Main involution
        """*/
        res = a.mvec.copy()
        res[0]=a[0]
        res[1]=-a[1]
        res[2]=-a[2]
        res[3]=-a[3]
        res[4]=-a[4]
        res[5]=a[5]
        res[6]=a[6]
        res[7]=a[7]
        res[8]=a[8]
        res[9]=a[9]
        res[10]=a[10]
        res[11]=-a[11]
        res[12]=-a[12]
        res[13]=-a[13]
        res[14]=-a[14]
        res[15]=a[15]
        return R310.fromarray(res)
    }

    __mul__(a,b){
        /*"""R310.Mul

        The geometric product.
        """*/
        if(type(b) in (int, float)){
            return a.muls(b)
        }
        res = a.mvec.copy()
        res[0]=b[0]*a[0]+b[1]*a[1]+b[2]*a[2]+b[3]*a[3]-b[4]*a[4]-b[5]*a[5]-b[6]*a[6]+b[7]*a[7]-b[8]*a[8]+b[9]*a[9]+b[10]*a[10]-b[11]*a[11]+b[12]*a[12]+b[13]*a[13]+b[14]*a[14]-b[15]*a[15]
        res[1]=b[1]*a[0]+b[0]*a[1]-b[5]*a[2]-b[6]*a[3]+b[7]*a[4]+b[2]*a[5]+b[3]*a[6]-b[4]*a[7]-b[11]*a[8]+b[12]*a[9]+b[13]*a[10]-b[8]*a[11]+b[9]*a[12]+b[10]*a[13]-b[15]*a[14]+b[14]*a[15]
        res[2]=b[2]*a[0]+b[5]*a[1]+b[0]*a[2]-b[8]*a[3]+b[9]*a[4]-b[1]*a[5]+b[11]*a[6]-b[12]*a[7]+b[3]*a[8]-b[4]*a[9]+b[14]*a[10]+b[6]*a[11]-b[7]*a[12]+b[15]*a[13]+b[10]*a[14]-b[13]*a[15]
        res[3]=b[3]*a[0]+b[6]*a[1]+b[8]*a[2]+b[0]*a[3]+b[10]*a[4]-b[11]*a[5]-b[1]*a[6]-b[13]*a[7]-b[2]*a[8]-b[14]*a[9]-b[4]*a[10]-b[5]*a[11]-b[15]*a[12]-b[7]*a[13]-b[9]*a[14]+b[12]*a[15]
        res[4]=b[4]*a[0]+b[7]*a[1]+b[9]*a[2]+b[10]*a[3]+b[0]*a[4]-b[12]*a[5]-b[13]*a[6]-b[1]*a[7]-b[14]*a[8]-b[2]*a[9]-b[3]*a[10]-b[15]*a[11]-b[5]*a[12]-b[6]*a[13]-b[8]*a[14]+b[11]*a[15]
        res[5]=b[5]*a[0]+b[2]*a[1]-b[1]*a[2]+b[11]*a[3]-b[12]*a[4]+b[0]*a[5]-b[8]*a[6]+b[9]*a[7]+b[6]*a[8]-b[7]*a[9]+b[15]*a[10]+b[3]*a[11]-b[4]*a[12]+b[14]*a[13]-b[13]*a[14]+b[10]*a[15]
        res[6]=b[6]*a[0]+b[3]*a[1]-b[11]*a[2]-b[1]*a[3]-b[13]*a[4]+b[8]*a[5]+b[0]*a[6]+b[10]*a[7]-b[5]*a[8]-b[15]*a[9]-b[7]*a[10]-b[2]*a[11]-b[14]*a[12]-b[4]*a[13]+b[12]*a[14]-b[9]*a[15]
        res[7]=b[7]*a[0]+b[4]*a[1]-b[12]*a[2]-b[13]*a[3]-b[1]*a[4]+b[9]*a[5]+b[10]*a[6]+b[0]*a[7]-b[15]*a[8]-b[5]*a[9]-b[6]*a[10]-b[14]*a[11]-b[2]*a[12]-b[3]*a[13]+b[11]*a[14]-b[8]*a[15]
        res[8]=b[8]*a[0]+b[11]*a[1]+b[3]*a[2]-b[2]*a[3]-b[14]*a[4]-b[6]*a[5]+b[5]*a[6]+b[15]*a[7]+b[0]*a[8]+b[10]*a[9]-b[9]*a[10]+b[1]*a[11]+b[13]*a[12]-b[12]*a[13]-b[4]*a[14]+b[7]*a[15]
        res[9]=b[9]*a[0]+b[12]*a[1]+b[4]*a[2]-b[14]*a[3]-b[2]*a[4]-b[7]*a[5]+b[15]*a[6]+b[5]*a[7]+b[10]*a[8]+b[0]*a[9]-b[8]*a[10]+b[13]*a[11]+b[1]*a[12]-b[11]*a[13]-b[3]*a[14]+b[6]*a[15]
        res[10]=b[10]*a[0]+b[13]*a[1]+b[14]*a[2]+b[4]*a[3]-b[3]*a[4]-b[15]*a[5]-b[7]*a[6]+b[6]*a[7]-b[9]*a[8]+b[8]*a[9]+b[0]*a[10]-b[12]*a[11]+b[11]*a[12]+b[1]*a[13]+b[2]*a[14]-b[5]*a[15]
        res[11]=b[11]*a[0]+b[8]*a[1]-b[6]*a[2]+b[5]*a[3]+b[15]*a[4]+b[3]*a[5]-b[2]*a[6]-b[14]*a[7]+b[1]*a[8]+b[13]*a[9]-b[12]*a[10]+b[0]*a[11]+b[10]*a[12]-b[9]*a[13]+b[7]*a[14]-b[4]*a[15]
        res[12]=b[12]*a[0]+b[9]*a[1]-b[7]*a[2]+b[15]*a[3]+b[5]*a[4]+b[4]*a[5]-b[14]*a[6]-b[2]*a[7]+b[13]*a[8]+b[1]*a[9]-b[11]*a[10]+b[10]*a[11]+b[0]*a[12]-b[8]*a[13]+b[6]*a[14]-b[3]*a[15]
        res[13]=b[13]*a[0]+b[10]*a[1]-b[15]*a[2]-b[7]*a[3]+b[6]*a[4]+b[14]*a[5]+b[4]*a[6]-b[3]*a[7]-b[12]*a[8]+b[11]*a[9]+b[1]*a[10]-b[9]*a[11]+b[8]*a[12]+b[0]*a[13]-b[5]*a[14]+b[2]*a[15]
        res[14]=b[14]*a[0]+b[15]*a[1]+b[10]*a[2]-b[9]*a[3]+b[8]*a[4]-b[13]*a[5]+b[12]*a[6]-b[11]*a[7]+b[4]*a[8]-b[3]*a[9]+b[2]*a[10]+b[7]*a[11]-b[6]*a[12]+b[5]*a[13]+b[0]*a[14]-b[1]*a[15]
        res[15]=b[15]*a[0]+b[14]*a[1]-b[13]*a[2]+b[12]*a[3]-b[11]*a[4]+b[10]*a[5]-b[9]*a[6]+b[8]*a[7]+b[7]*a[8]-b[6]*a[9]+b[5]*a[10]+b[4]*a[11]-b[3]*a[12]+b[2]*a[13]-b[1]*a[14]+b[0]*a[15]
        return R310.fromarray(res)
    }

    __rmul__=__mul__

    __xor__(a,b){
        res = a.mvec.copy()
        res[0]=b[0]*a[0]
        res[1]=b[1]*a[0]+b[0]*a[1]
        res[2]=b[2]*a[0]+b[0]*a[2]
        res[3]=b[3]*a[0]+b[0]*a[3]
        res[4]=b[4]*a[0]+b[0]*a[4]
        res[5]=b[5]*a[0]+b[2]*a[1]-b[1]*a[2]+b[0]*a[5]
        res[6]=b[6]*a[0]+b[3]*a[1]-b[1]*a[3]+b[0]*a[6]
        res[7]=b[7]*a[0]+b[4]*a[1]-b[1]*a[4]+b[0]*a[7]
        res[8]=b[8]*a[0]+b[3]*a[2]-b[2]*a[3]+b[0]*a[8]
        res[9]=b[9]*a[0]+b[4]*a[2]-b[2]*a[4]+b[0]*a[9]
        res[10]=b[10]*a[0]+b[4]*a[3]-b[3]*a[4]+b[0]*a[10]
        res[11]=b[11]*a[0]+b[8]*a[1]-b[6]*a[2]+b[5]*a[3]+b[3]*a[5]-b[2]*a[6]+b[1]*a[8]+b[0]*a[11]
        res[12]=b[12]*a[0]+b[9]*a[1]-b[7]*a[2]+b[5]*a[4]+b[4]*a[5]-b[2]*a[7]+b[1]*a[9]+b[0]*a[12]
        res[13]=b[13]*a[0]+b[10]*a[1]-b[7]*a[3]+b[6]*a[4]+b[4]*a[6]-b[3]*a[7]+b[1]*a[10]+b[0]*a[13]
        res[14]=b[14]*a[0]+b[10]*a[2]-b[9]*a[3]+b[8]*a[4]+b[4]*a[8]-b[3]*a[9]+b[2]*a[10]+b[0]*a[14]
        res[15]=b[15]*a[0]+b[14]*a[1]-b[13]*a[2]+b[12]*a[3]-b[11]*a[4]+b[10]*a[5]-b[9]*a[6]+b[8]*a[7]+b[7]*a[8]-b[6]*a[9]+b[5]*a[10]+b[4]*a[11]-b[3]*a[12]+b[2]*a[13]-b[1]*a[14]+b[0]*a[15]
        return R310.fromarray(res)
    }


    __and__(a,b){
        res = a.mvec.copy()
        res[15]=1*(a[15]*b[15])
        res[14]=-1*(a[14]*-1*b[15]+a[15]*b[14]*-1)
        res[13]=1*(a[13]*b[15]+a[15]*b[13])
        res[12]=-1*(a[12]*-1*b[15]+a[15]*b[12]*-1)
        res[11]=1*(a[11]*b[15]+a[15]*b[11])
        res[10]=1*(a[10]*b[15]+a[13]*b[14]*-1-a[14]*-1*b[13]+a[15]*b[10])
        res[9]=-1*(a[9]*-1*b[15]+a[12]*-1*b[14]*-1-a[14]*-1*b[12]*-1+a[15]*b[9]*-1)
        res[8]=1*(a[8]*b[15]+a[11]*b[14]*-1-a[14]*-1*b[11]+a[15]*b[8])
        res[7]=1*(a[7]*b[15]+a[12]*-1*b[13]-a[13]*b[12]*-1+a[15]*b[7])
        res[6]=-1*(a[6]*-1*b[15]+a[11]*b[13]-a[13]*b[11]+a[15]*b[6]*-1)
        res[5]=1*(a[5]*b[15]+a[11]*b[12]*-1-a[12]*-1*b[11]+a[15]*b[5])
        res[4]=-1*(a[4]*-1*b[15]+a[7]*b[14]*-1-a[9]*-1*b[13]+a[10]*b[12]*-1+a[12]*-1*b[10]-a[13]*b[9]*-1+a[14]*-1*b[7]+a[15]*b[4]*-1)
        res[3]=1*(a[3]*b[15]+a[6]*-1*b[14]*-1-a[8]*b[13]+a[10]*b[11]+a[11]*b[10]-a[13]*b[8]+a[14]*-1*b[6]*-1+a[15]*b[3])
        res[2]=-1*(a[2]*-1*b[15]+a[5]*b[14]*-1-a[8]*b[12]*-1+a[9]*-1*b[11]+a[11]*b[9]*-1-a[12]*-1*b[8]+a[14]*-1*b[5]+a[15]*b[2]*-1)
        res[1]=1*(a[1]*b[15]+a[5]*b[13]-a[6]*-1*b[12]*-1+a[7]*b[11]+a[11]*b[7]-a[12]*-1*b[6]*-1+a[13]*b[5]+a[15]*b[1])
        res[0]=1*(a[0]*b[15]+a[1]*b[14]*-1-a[2]*-1*b[13]+a[3]*b[12]*-1-a[4]*-1*b[11]+a[5]*b[10]-a[6]*-1*b[9]*-1+a[7]*b[8]+a[8]*b[7]-a[9]*-1*b[6]*-1+a[10]*b[5]+a[11]*b[4]*-1-a[12]*-1*b[3]+a[13]*b[2]*-1-a[14]*-1*b[1]+a[15]*b[0])
        return R310.fromarray(res)
    }


    __or__(a,b){
        res = a.mvec.copy()
        res[0]=b[0]*a[0]+b[1]*a[1]+b[2]*a[2]+b[3]*a[3]-b[4]*a[4]-b[5]*a[5]-b[6]*a[6]+b[7]*a[7]-b[8]*a[8]+b[9]*a[9]+b[10]*a[10]-b[11]*a[11]+b[12]*a[12]+b[13]*a[13]+b[14]*a[14]-b[15]*a[15]
        res[1]=b[1]*a[0]+b[0]*a[1]-b[5]*a[2]-b[6]*a[3]+b[7]*a[4]+b[2]*a[5]+b[3]*a[6]-b[4]*a[7]-b[11]*a[8]+b[12]*a[9]+b[13]*a[10]-b[8]*a[11]+b[9]*a[12]+b[10]*a[13]-b[15]*a[14]+b[14]*a[15]
        res[2]=b[2]*a[0]+b[5]*a[1]+b[0]*a[2]-b[8]*a[3]+b[9]*a[4]-b[1]*a[5]+b[11]*a[6]-b[12]*a[7]+b[3]*a[8]-b[4]*a[9]+b[14]*a[10]+b[6]*a[11]-b[7]*a[12]+b[15]*a[13]+b[10]*a[14]-b[13]*a[15]
        res[3]=b[3]*a[0]+b[6]*a[1]+b[8]*a[2]+b[0]*a[3]+b[10]*a[4]-b[11]*a[5]-b[1]*a[6]-b[13]*a[7]-b[2]*a[8]-b[14]*a[9]-b[4]*a[10]-b[5]*a[11]-b[15]*a[12]-b[7]*a[13]-b[9]*a[14]+b[12]*a[15]
        res[4]=b[4]*a[0]+b[7]*a[1]+b[9]*a[2]+b[10]*a[3]+b[0]*a[4]-b[12]*a[5]-b[13]*a[6]-b[1]*a[7]-b[14]*a[8]-b[2]*a[9]-b[3]*a[10]-b[15]*a[11]-b[5]*a[12]-b[6]*a[13]-b[8]*a[14]+b[11]*a[15]
        res[5]=b[5]*a[0]+b[11]*a[3]-b[12]*a[4]+b[0]*a[5]+b[15]*a[10]+b[3]*a[11]-b[4]*a[12]+b[10]*a[15]
        res[6]=b[6]*a[0]-b[11]*a[2]-b[13]*a[4]+b[0]*a[6]-b[15]*a[9]-b[2]*a[11]-b[4]*a[13]-b[9]*a[15]
        res[7]=b[7]*a[0]-b[12]*a[2]-b[13]*a[3]+b[0]*a[7]-b[15]*a[8]-b[2]*a[12]-b[3]*a[13]-b[8]*a[15]
        res[8]=b[8]*a[0]+b[11]*a[1]-b[14]*a[4]+b[15]*a[7]+b[0]*a[8]+b[1]*a[11]-b[4]*a[14]+b[7]*a[15]
        res[9]=b[9]*a[0]+b[12]*a[1]-b[14]*a[3]+b[15]*a[6]+b[0]*a[9]+b[1]*a[12]-b[3]*a[14]+b[6]*a[15]
        res[10]=b[10]*a[0]+b[13]*a[1]+b[14]*a[2]-b[15]*a[5]+b[0]*a[10]+b[1]*a[13]+b[2]*a[14]-b[5]*a[15]
        res[11]=b[11]*a[0]+b[15]*a[4]+b[0]*a[11]-b[4]*a[15]
        res[12]=b[12]*a[0]+b[15]*a[3]+b[0]*a[12]-b[3]*a[15]
        res[13]=b[13]*a[0]-b[15]*a[2]+b[0]*a[13]+b[2]*a[15]
        res[14]=b[14]*a[0]+b[15]*a[1]+b[0]*a[14]-b[1]*a[15]
        res[15]=b[15]*a[0]+b[0]*a[15]
        return R310.fromarray(res)
    }


    __add__(a,b){
        /*"""R310.Add

        Multivector addition
        """*/
        if(type(b) in (int, float)){
            return a.adds(b)
        }
        res = a.mvec.copy()
        res[0] = a[0]+b[0]
        res[1] = a[1]+b[1]
        res[2] = a[2]+b[2]
        res[3] = a[3]+b[3]
        res[4] = a[4]+b[4]
        res[5] = a[5]+b[5]
        res[6] = a[6]+b[6]
        res[7] = a[7]+b[7]
        res[8] = a[8]+b[8]
        res[9] = a[9]+b[9]
        res[10] = a[10]+b[10]
        res[11] = a[11]+b[11]
        res[12] = a[12]+b[12]
        res[13] = a[13]+b[13]
        res[14] = a[14]+b[14]
        res[15] = a[15]+b[15]
        return R310.fromarray(res)
    }
    __radd__=__add__

    __sub__(a,b){
        /*"""R310.Sub

        Multivector subtraction
        """*/
        if(type(b) in (int, float)){
            return a.subs(b)
        }
        res = a.mvec.copy()
        res[0] = a[0]-b[0]
        res[1] = a[1]-b[1]
        res[2] = a[2]-b[2]
        res[3] = a[3]-b[3]
        res[4] = a[4]-b[4]
        res[5] = a[5]-b[5]
        res[6] = a[6]-b[6]
        res[7] = a[7]-b[7]
        res[8] = a[8]-b[8]
        res[9] = a[9]-b[9]
        res[10] = a[10]-b[10]
        res[11] = a[11]-b[11]
        res[12] = a[12]-b[12]
        res[13] = a[13]-b[13]
        res[14] = a[14]-b[14]
        res[15] = a[15]-b[15]
        return R310.fromarray(res)
    }

    __rsub__(a,b){
        /*"""R310.Sub

        Multivector subtraction
        """*/
        return b + -1 * a
    }


    smul(a,b){
        res = a.mvec.copy()
        res[0] = a*b[0]
        res[1] = a*b[1]
        res[2] = a*b[2]
        res[3] = a*b[3]
        res[4] = a*b[4]
        res[5] = a*b[5]
        res[6] = a*b[6]
        res[7] = a*b[7]
        res[8] = a*b[8]
        res[9] = a*b[9]
        res[10] = a*b[10]
        res[11] = a*b[11]
        res[12] = a*b[12]
        res[13] = a*b[13]
        res[14] = a*b[14]
        res[15] = a*b[15]
        return R310.fromarray(res)
    }


    muls(a,b){
        res = a.mvec.copy()
        res[0] = a[0]*b
        res[1] = a[1]*b
        res[2] = a[2]*b
        res[3] = a[3]*b
        res[4] = a[4]*b
        res[5] = a[5]*b
        res[6] = a[6]*b
        res[7] = a[7]*b
        res[8] = a[8]*b
        res[9] = a[9]*b
        res[10] = a[10]*b
        res[11] = a[11]*b
        res[12] = a[12]*b
        res[13] = a[13]*b
        res[14] = a[14]*b
        res[15] = a[15]*b
        return R310.fromarray(res)
    }


    sadd(a,b){
        res = a.mvec.copy()
        res[0] = a+b[0]
        res[1] = b[1]
        res[2] = b[2]
        res[3] = b[3]
        res[4] = b[4]
        res[5] = b[5]
        res[6] = b[6]
        res[7] = b[7]
        res[8] = b[8]
        res[9] = b[9]
        res[10] = b[10]
        res[11] = b[11]
        res[12] = b[12]
        res[13] = b[13]
        res[14] = b[14]
        res[15] = b[15]
        return R310.fromarray(res)
    }


    adds(a,b){
        res = a.mvec.copy()
        res[0] = a[0]+b
        res[1] = a[1]
        res[2] = a[2]
        res[3] = a[3]
        res[4] = a[4]
        res[5] = a[5]
        res[6] = a[6]
        res[7] = a[7]
        res[8] = a[8]
        res[9] = a[9]
        res[10] = a[10]
        res[11] = a[11]
        res[12] = a[12]
        res[13] = a[13]
        res[14] = a[14]
        res[15] = a[15]
        return R310.fromarray(res)
    }


    ssub(a,b){
        res = a.mvec.copy()
        res[0] = a-b[0]
        res[1] = -b[1]
        res[2] = -b[2]
        res[3] = -b[3]
        res[4] = -b[4]
        res[5] = -b[5]
        res[6] = -b[6]
        res[7] = -b[7]
        res[8] = -b[8]
        res[9] = -b[9]
        res[10] = -b[10]
        res[11] = -b[11]
        res[12] = -b[12]
        res[13] = -b[13]
        res[14] = -b[14]
        res[15] = -b[15]
        return R310.fromarray(res)
    }


    subs(a,b){
        res = a.mvec.copy()
        res[0] = a[0]-b
        res[1] = a[1]
        res[2] = a[2]
        res[3] = a[3]
        res[4] = a[4]
        res[5] = a[5]
        res[6] = a[6]
        res[7] = a[7]
        res[8] = a[8]
        res[9] = a[9]
        res[10] = a[10]
        res[11] = a[11]
        res[12] = a[12]
        res[13] = a[13]
        res[14] = a[14]
        res[15] = a[15]
        return R310.fromarray(res)
    }


    norm(a){
        return abs((a * a.Conjugate())[0]) ** 0.5
    }

    inorm(a){
        return a.Dual().norm()
    }

    normalized(a){
        return a * (1 / a.norm())
    }
}



e1 = R310(1.0, 1)
e2 = R310(1.0, 2)
e3 = R310(1.0, 3)
e4 = R310(1.0, 4)
e12 = R310(1.0, 5)
e13 = R310(1.0, 6)
e14 = R310(1.0, 7)
e23 = R310(1.0, 8)
e24 = R310(1.0, 9)
e34 = R310(1.0, 10)
e123 = R310(1.0, 11)
e124 = R310(1.0, 12)
e134 = R310(1.0, 13)
e234 = R310(1.0, 14)
e1234 = R310(1.0, 15)


// if __name__ == '__main__':
print("e1*e1         :", str(e1*e1))
print("pss           :", str(e1234))
print("pss*pss       :", str(e1234*e1234))


copy