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Complex\(\mathbb R_{0,1} \cong \mathbb C\)

Dual\(\mathbb R_{0,0,1} \cong \mathbb D\)

Quaternion\(\mathbb R_{0,2} \cong \mathbb H\)

Timespace\(\mathbb R_{1,3} \cong \mathbb M\)

3D GA\(\mathbb R_{3}\)

2D PGA\(\mathbb R_{2,0,1}\)

3D PGA\(\mathbb R_{3,0,1}\)

2D CGA\(\mathbb R_{3,1}\)

3D CGA\(\mathbb R_{4,1}\)

3D Mother Algebra\(\mathbb R_{4,4}\)

2D CSGA\(\mathbb R_{5,3}\)

3D CCGA\(\mathbb R_{6,3}\)

3D QCGA\(\mathbb R_{9,6}\)

Cubic 2D GA\(\mathbb R_{9,7}\)

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#	Grade	Name	Value

Basis and Metric

Ganja.js supports operator overloading and algebraic literals.

Operator	Javascript	Name
\(a*b\)	a*b	Geometric Product
\(a\cdot b\)	a\|b	Inner Product
\(a\wedge b\)	a^b	Outer Product
\(a\vee b\)	a&b	Regressive Product
\(a\rfloor b\)	a<<b	Left Contraction
\(ab\tilde a\)	a>>>b	Sandwich Product
\(\tilde a\)	~a	Conjugate
\(\bar a\)	!a	Dual
\(\bar{\bar a}\)	a.Reverse	Reverse
\(a^{-1}\)	a**-1	Inverse
\(e^a\)	Math.E**a	Exponentiation
\(a_{\langle b \rangle}\)	a.Grade(b)	Grade Extraction
\(a+b\) or \(a-b\)	a+b or a-b	Multivector Addition/Subtraction
\(4.2e_{12}\)	4.2e12	Blade Literals

Ganja.js supports vectors and matrices with multivector elements.

Operator	Javascript	Name
\(\bold v = \begin{bmatrix} e_1 & 0 \end{bmatrix} \)	v = [1e1,0];	Vector
\(\bold A = \begin{bmatrix} 1 & 0 \\ 0 & e_{12} \end{bmatrix} \)	A = [[1,0],[0,1e12]];	Matrix
\(\bold v \cdot \bold w\)	v*w	Vector-Vector dot product.
\(A \bold v\)	A*v	Matrix-Vector product.
\(AB\)	A*B	Matrix-Matrix product.
\(A^{HT}\)	~A	Conjugate-Transpose Matrix

Ganja.js can graph 2D and 3D PGA and CGA elements.

Element	Description
multivector	point, pair, line, circle, sphere, plane
number	Sets color. (e.g. #80FF0000 - transparent red)
string	Label for the last drawn item
[point,point]	Line segment between two points
[point,point,...,point]	(convex) polygon

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