EVA is a symbolic calculator working with Clifford numbers.
The Clifford algebra is generated by vectors of real space Rn together with an associative, bilinear, vector product wich satisfies the basic axiom that the square of a vector is a scalar :
a a = |a|²
This allows the theory and properties of the algebra to be built up in an intuitive, geometric way.
Clifford algebra is usefull in physics problems. It provides a more compact and intuitive description of classical and quantum mechanics, electromagnetic theory and relativity. Also usefull for computer vision, robotics, etc ...
The main objective of this project is providing to students a simple tool to make easy calculations in Clifford algebra as with Clical (P. Lounesto). Difference is the access to source, possibility to change, add, improve functions, write new scripts.
Some EVA command examples :
define basis e0,e1,e2,e3,e12,e13,e23,e123 >> Cl(3)
define vectors a=(3,2,-1), b=(3,0,-5) >> a=3e1+2e2-e3
geometric product a b >> gp(a,b)
inner product a.b >> inp(a,b)
outer product a^b >> outp(a,b)
define multivector B=(3,1,-5,0,1,1,0,0) : >> B=3e0+e1-5e2+e12+2e13
grade projection : scalar >> grade(B,0) : 3e0
vector >> grade(B,1) : e1-5e2
bivector >> grade(B,2) : e12+2e13
pseudoscalar >> grade(B,3) : 0
involutions : reversal >> rev(B) : 3e0+e1-5e2-e12-2e13
grade involution >> invol(B) : 3e0-e1+5e2+e12+2e13
clifford conjugation >> cj(B) : 3e0-e1+5e2+e12+2e13
inverse 1/B >> inverse(B)
dual B >> dual(B)
magnitude |B| >> magnitude(B)
normalize B/|B| >> normalize(B)
math functions :
exp1, log1, sqrt1, pow1, sin1, cos1, tan1, sinh1, cosh1, tanh1
asin1, acos1, atan1, asinh1, acosh1, atanh1
Mastering EVA syntaxis need only few days practice.
EVA is based on Eigenmath script language, making easy to modify the original EVA functions, implement new functions, adapt to your own needs.
script control instructions :
do( expression1, expression2,..., last_expression) return last_expression
test( predicate1, do(...), predicate2, do(...),..., do(...))
if only one expression, do(...) not necessary.
A tutorial on Eigenmath is here.
If you are interested on quantum computig, you may find an introduction here and there.
EVA version 2.0 suppport Cl(p,q) with p+q number of basis vectors, p positive squares and q negative squares .
1. download EVAlgebra.exe and EVA.txt at source forge and copy to Desktop.
2. start EVAlgebra.exe
3. function use examples at help/Clifford
Some tutorials :
Submitted translations of EVA pages :
French | English