Mv.inv is very slow about galgebra HOT 17 CLOSED

The following is not slow for me -
'
from galgebra.ga import Ga
from sympy import Symbol
from galgebra.printer import Format, xtex
Format()
GA, e_0, e_1, e_2, e_3 = Ga.build("e*0|1|2|3", g='-1 0 0 0, 0 1 0 0, 0 0 1 0, 0 0 0 1')

e_0_inv = e_0.inv()

print('e_0^{-1} =', e_0_inv)

p = GA.mv((1, Symbol('p1'), Symbol('p2'), Symbol('p3')), 'vector')
q = GA.mv((0, Symbol('q1'), Symbol('q2'), Symbol('q3')), 'vector')
r = GA.mv((0, Symbol('r1'), Symbol('r2'), Symbol('r3')), 'vector')
print('p =',p)
print('q =',q)
print('r =',r)

A = q ^ r
X = (p ^ A) # A plane

print(r'q\W r = A =',A)
print(r'p\W A = X =',X)

D = e_0_inv<X

print(r'e_0^{-1}\lfloor X = D =', e_0_inv<X)
#Dinv = D.rev()/(DD.rev()).scalar()
Dinv = D.inv()
print('D^{-1} =', Dinv.Fmt(3))
print('DD^{-1} =', DDinv)
N = e_0_inv < (e_0 ^ X)
print(r'e_0^{-1}\lfloor (e_0\W X) = N', N)

d = (e_0_inv < (e_0 ^ X)) * Dinv # Support vector from plane

print(r'(e_0^{-1}\lfloor (e_0\W X)) D^{-1} =',d.Fmt(3))

print('N/D =',N/D)
xtex()

'
Output is attached -
newslow.pdf

from galgebra.

It seems you don't compute d.inv() only d, but maybe I can compute d.inv() without calling this method.

from galgebra.

Here is the code for multivector division. The limitation in the code is that it only works if A.inv() can be computed which for my code can only be computed if A*A.rev() is a scalar. For you case there should be no problem since in 3d the inverse of any bivector can be computed.

def __div__(self, A):
    if isinstance(A,Mv):
        return self * A.inv()
    else:
        return self * (S(1)/A)

from galgebra.

Here is the whole thing method test11_6. This test checks a few formulas about duality with projective geometry. I don't restrain myself to P4 because I want to check various sign issues.

from galgebra.

Remind me how to run your code. It has been a long time since I used unittest.

from galgebra.

If you use pycharm, the IDE is able to run tests.

If you don't, you can add at the end of the file.

if __name__ == '__main__':
    unittest.main()

If you run the script, it will run all the tests. You can just delete other tests. If it complains about path. You can add them at the top with

import sys
sys.path.append("a-path-to-galgebra")

from galgebra.

Is it supposed to pass all the tests?

from galgebra.

do you have a write up for what test11_12_2_2 is testing for? Symbolically (LaTeX) what is being tested? A reference or a link would be good if possible.

from galgebra.

One problem I found was that subs for a multivector expression was not substituting correctly.

from galgebra.

All tests available in test_chapter11.py pass. You can ignore all test but test11_6 for this issue. test11_12_2_2 is an attempt at solving an exercise in Leo Dorst book. L and x_t describe the same line, t_x just retrieve t from x if x is a point of L.

from galgebra.

One problem I found was that subs for a multivector expression was not substituting correctly.

Which one ?

from galgebra.

test11_12_2_2 could have a problem with subs. If I comment that test out all the others run successfully in 5 sec.

from galgebra.

Sorry, I disabled the slow expressions before committing my work. You need to remove several #.

from galgebra.

To get an idea of what is happening I ran a python notebook -
chap11slow.zip
I think the output shows why everthing slows down.
I also ordered a copy of Dorst's book so I know what you are talking about. I should get the book Wednesday so if you could tell me which equations you are programming that would help.

from galgebra.

I don't know if this has any relevance to your issues but I included some conformal model tests in my examples. Three of the examples in this file are for the conformal model -
latex_check.pdf

from galgebra.

I read the book and learn how to use galbegra. When I read something interesting, I write a test named after the chapter or the exercise. If a test is named test11_6, you can open the book at the chapter 11 section 6 and you will find the equations. I will probably add a few tests about the conformal model later, thanks.

d becomes a very large expression.

from galgebra.

We can close this issue. galgebra isn't designed to make geometric proof but calculus. If I want to achieve some kind of proofs, I need to reduce the expression lenght myself by fixing things, ignoring norms if useless, using the right basis... :)

from galgebra.