Clifford symbolic calculator - (Cl1 to Cl5 with arbitrary signature)
 
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 ...
more at Leibnitz' dream.
or at natural representation of three-space.
 
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  
                                                                  >>   b=3e1-5e3
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(...))
for(k,1,n, do(...))
sum(k,1,n,do(...))
product(k,1,n,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  .
 
Installing  EVA:
 
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 :  
   
Translations :
 
Submitted translations of EVA pages :
French  |  English
                             
                                           Euclidian
                                          Vector
Algebra                            
 

   EVAlgebra