A small library implementing linear combinations of "stuff". Such a linear combination is stored as a map, mapping "stuff" to its coefficient. That is {"a" 5, "b" 17} stands for the linear combination 5 * "a" + 17 * "b":
import linear_combination.linear_combination as lc
lc1 = lc.LinearCombination( {"x":7,"y":8} )
lc2 = lc.LinearCombination( {"x":2.1, "z":3} )
print( lc1 + lc2 )
# => "+9.10 x +8 y +3 z"The main application is to Hopf Algebras.
The package comes with two sample implementations of Hopf algebrase; the concatenation Hop algebra and, its dual, the shuffle algebras (Reutenauer - Free Lie algebras). Much of its code is borrowed from free-lie-algebra-py, by Jeremy Reizenstein.
Example usage:
import linear_combination.linear_combination as lc
import linear_combination.words as words
print( lc.lift( words.ShuffleWord( (1,2 ) ) ) * lc.lift( words.ShuffleWord( (3,4 ) ) ) )
# => 1234 + 1324 + 1342 + 3124 + 3142 + 3412
print( words.parse_s('12') * words.parse_s('34') )
# => 1234 + 1324 + 1342 + 3124 + 3142 + 3412
print( words.parse_c('12') * words.parse_c('34') )
# => 1234
import linear_combination.linear_combination as lc
import linear_combination.words as words
import sympy
a1, a2 = sympy.var('a1,a2')
print( a1 * words.parse_s('12') + (a2 * words.parse_s('34'))**2 )
# => +(a1) 12 +(2*a2**2) 3434 +(4*a2**2) 3344
a10,a01,a20,a11,a02 = sympy.var('a10,a01,a20,a11,a02')
b10,b01,b20,b11,b02 = sympy.var('b10,b01,b20,b11,b02')
x1 = words.parse_s('1')
x2 = words.parse_s('2')
xtilde1 = a10 * x1 + a01 * x2 + a20 * x1**2 + a11 * x1*x2 + a02 * x2**2
xtilde2 = b10 * x1 + b01 * x2 + b20 * x1**2 + b11 * x1*x2 + b02 * x2**2
print( words.hs( xtilde1, xtilde2 ) )Install with:
pip install git+https://github.com/diehlj/linear-combination-pyCopyright © 2018 Joscha Diehl
Distributed under the Eclipse Public License.