version 3.19
This function finds all combinations of common factors in a Boolean expression written in SOP - Sum Of Products form.
factorize(input, snames = "", noflevels, pos = FALSE, ...)
input |
A string containing the SOP expression, or an object of class "qca" . |
|||
snames |
A string containing the sets' names, separated by commas. | |||
noflevels |
Numerical vector containing the number of levels for each set. | |||
pos |
Logical, if possible factorize using product(s) of sums. | |||
... |
Other arguments (mainly for backwards compatibility). |
Factorization is a process of finding common factors in a Boolean expression, written in a SOP - sum of products (or DNF - disjunctive normal form). Whenever possible, the factorization can also be performed in a POS - product of sums form.
Conjunctions should preferably be indicated with a star *
sign,
but this is not necessary when conditions have single letters or when the expression is
expressed in multi-value notation.
The number of levels in noflevels
is needed only when negating
multivalue conditions, and it should complement the snames
argument.
If input
is an object of class "qca"
(the result of the
minimize()
function), a factorization is performed
for each of the minimized solutions.
Ragin, C.C. (1987) The Comparative Method. Moving beyond qualitative and quantitative strategies, Berkeley: University of California Press
# typical example with redundant conditions factorize("a~b~cd + a~bc~d + a~bcd + abc~d")F1: a(~bd + c~d) F2: a~b(c + d) + abc~d F3: a~b~cd + ac(~b + ~d) F4: a~bd + ac~d F5: a(~b~cd + bc~d) + a~bc# results presented in alphabetical order factorize("~one*two*~four + ~one*three + three*~four")F1: ~four*(three + ~one*two) + ~one*three F2: ~four*three + ~one*(three + ~four*two) F3: ~four*~one*two + three*(~four + ~one)# to preserve a certain order of the set names factorize("~one*two*~four + ~one*three + three*~four", snames = "one, two, three, four")F1: ~one*(three + two*~four) + three*~four F2: ~one*two*~four + three*(~one + ~four) F3: ~four*(three + ~one*two) + ~one*three # using pos - products of sums factorize("~a~c + ~ad + ~b~c + ~bd", pos = TRUE)F1: (~a + ~b)(~c + d)# using an object of class "qca" produced with minimize() pCVF <- minimize(CVF, outcome = "PROTEST", incl.cut = 0.8, include = "?", use.letters = TRUE) factorize(pCVF)M1: ~E + ~A*B*D + A*B*C + A*C*D F1: ~E + ~A*B*D + A*C*(B + D) F2: ~E + A*C*D + B*(~A*D + A*C) F3: ~E + A*B*C + D*(~A*B + A*C) M2: ~E + ~A*B*D + A*B*~D + A*C*D F1: ~E + ~A*B*D + A*(B*~D + C*D) F2: ~E + A*C*D + B*(~A*D + A*~D) F3: ~E + A*B*~D + D*(~A*B + A*C) M3: ~E + A*B*C + A*C*D + B*C*D F1: ~E + B*C*D + A*C*(B + D) F2: ~E + A*C*D + B*C*(A + D) F3: ~E + C*(A*B + A*D + B*D) F4: ~E + A*B*C + C*D*(A + B) M4: ~E + A*B*~D + A*C*D + B*C*D F1: ~E + B*C*D + A*(B*~D + C*D) F2: ~E + A*C*D + B*(A*~D + C*D) F3: ~E + A*B*~D + C*D*(A + B)# using an object of class "deMorgan" produced with negate() factorize(negate(pCVF))M1: ~A~BE + ~A~DE + A~CE + ~B~DE F1: E(~A~B + ~A~D + A~C + ~B~D) F2: ~AE(~B + ~D) + E(A~C + ~B~D) F3: ~BE(~A + ~D) + E(~A~D + A~C) F4: ~DE(~A + ~B) + E(~A~B + A~C) M2: ~A~BE + ~A~DE + ~B~DE + A~CDE F1: E(~A~B + ~A~D + ~B~D + A~CD) F2: ~AE(~B + ~D) + E(~B~D + A~CD) F3: ~BE(~A + ~D) + E(~A~D + A~CD) F4: ~DE(~A + ~B) + E(~A~B + A~CD) M3: ~CE + ~A~BE + ~A~DE + ~B~DE F1: E(~C + ~A~B + ~A~D + ~B~D) F2: ~AE(~B + ~D) + E(~C + ~B~D) F3: ~BE(~A + ~D) + E(~C + ~A~D) F4: ~DE(~A + ~B) + E(~C + ~A~B) M4: ~A~BE + ~A~DE + ~B~DE + ~CDE F1: E(~A~B + ~A~D + ~B~D + ~CD) F2: ~AE(~B + ~D) + E(~B~D + ~CD) F3: ~BE(~A + ~D) + E(~A~D + ~CD) F4: ~DE(~A + ~B) + E(~A~B + ~CD)Author
Adrian Dusa