Version 3.3
o New: function calibrate() now accepts method = "TFR" to calibrate
ordinal values using the Totally Fuzzy and Relative method.
o Improved: relation between Include and Exclude switches in the
graphical user interface
o Improved: the functions sop() and factorize() now try harder to
simplify the result, where it can be simplified
(thanks to Macartan Humphreys for the suggestion)
o Fixed: minor bug leading to an error in truthTable() function,
for data with a single truth table configuration
(thanks to Ingo Rohlfing for the report)
o Fixed: error in the GUI, when exporting a dataset
(thanks to Ranajoy Choudhury for the report)
o Changed: argument "tilde" in function factorize() renamed to
"use.tilde", making it uniform accross functions.
o Changed: relaxed the error about the 0.5 values in the fuzzy data
from the truthTable() function, to a warning.
o Updated: the latest versions of the jQuery and jQuery-UI in the
graphical user interface.
Version 3.2
o New: dramatically improved function to solve the prime implicants
chart (using Petrick's method), hundreds of times faster when
searching for all solutions
o New: function pofind(), to calculate quick parameters of fit for
atomic conditions (thanks to Alessia Damonte for the suggestion)
o Improved: the minimization object now prints only the unique
intermediate solutions, adding all combinations of conservative and
parsimonious solutions that produced each unique intermediate one
(thanks to Karina Mross for the suggestion)
o Improved: the function pof() no longer throws an error when the data
object is a tibble instead of a native R data frame
o Improved: function translate() now tries harder to throw an error
message when the expression specifies conditions using both lower and
upper case letters (e.g. "ConD" instead of "cond" or "COND")
o Changed: argument "min.pin" in function minimize() is now inactive
by default
o Fixed: bug in compute() when the expression and the column names in
the data simultaneously contain both lower and upper case letters
o Fixed: bug in compute() when the the data contains character columns
(for instance case names, thanks to Alessia Damonte for the report)
o Fixed: bug in fuzzyand() when the the input is a result of a previous
fuzzyand() function (thanks to Alessia Damonte for the report)
o Fixed: bug in XYplot() that prevented calculating parameters of fit
when the input is a vector of class "fuzzy" generated by fuzzyand()
or fuzzyor() functions (thanks to Alessia Damonte for the report)
o Fixed: bug in modelFit() that incorrectly assigned numbers to models
Version 3.1
o New: spinning wheel in the web R console when calculations take a
long time
o Improved: faster version of getRow() that help speeding up finding the
simplifying assumptions
o Fixed: minor bug in the classical QMC algorithm when the PI chart has
exactly one column, irrelevant PIs were reported as sufficient (thanks
to Michael Baumgartner for reporting)
o Fixed: minimization in the classical QMC with exactly two observed
configurations
o Fixed: error in the truth table production when imposing a frequency
cutoff over 1 (thanks to Verena Patock for reporting)
o Fixed: error in fuzzy calibration, when thresholds are outside of the
data range (thanks to Priscilla Alamos-Concha for the report)
Version 3.0
o New: cutting edge, next generation algorithm for Boolean minimization
o New: function causalChain() to enable coincidence analysis comparable
with the version 2.0 of package cna
o New: function modelFit() to enable theory evaluation
o New: function findmin() to find the minimum number of PIs necessary to
solve a PI chart, replacing the function lp() from package lpSolve
o New: arguments "sol.cons" and "sol.cov" added to function minimize()
o New: arguments "enhance" and "model" added to function XYplot()
o New: reactivated the argument "add" to functions pof() and superSubset(),
to allow for more parameter of fit measures in the output
o Improved: function intersection() now accept entire minimization objects
of class "qca" as input
o Improved: function minimize() gains three new arguments "depth", "min.pin"
and "method"
o Improved: function recode() gains two new arguments "cuts" and "values"
o Improved: function truthTable() gains a new argument "dcc" to identify
deviant cases consistency in kind
o Improved: function calibrate() gains a new argument "method", implementing
the indirect method along the traditional direct method of calibration
o Improved: function XYplot() now accepts complex expressions for both x and y
o Improved: when data is available, functions translate(), compute() and pof()
throw an error if the data is multivalue and the expression is not
o Improved: more negation signs (apart of the tilde) are accepted for all
functions that have a character expression as input(s)
o Improved: when printing the truth table, column "OUT" in now spaced out
more evidently, to differentiate it from the other columns and create a natural
separation between the configurations and the parameters of fit
o Improved: better documentation, including the HTML version from the GUI
o Improved: functions fuzzyand() and fuzzyor() gain two new arguments called
"na.rm" (indicating to remove missing values) and "use.tilde", to signal
negations when constructing attribute expressions
o Improved: function findRows() now accepts a matrix in addition to a truth table,
for demonstration purposes
o Improved: function findRows() gains a new argument called "type", to find
contradictory simplifying assumptions and simultaneous subset relations
o Changed: objects of class "fctr" now have class "factorize"
o Changed: objects of class "deMorgan" are now proper character vectors instead of
lists containing these vectors
o Changed: objects of class "pic" (prime implicants chart) and "translate" are now
proper matrices instead of lists containing matrices
o Changed: function makeChart() gained three new arguments: "mv", "use.tilde"
and "collapse" for a complete flexibility, and its output gained the class "pic"
o Changed: the argument "data" in function minimize() is renamed to "input"
(but still backwards compatible)
o Changed: argument "omit" from function minimize() renamed to "exclude"
o Changed: simplified function minimize(), the following arguments are dropped
but still backwards compatible: outcome, conditions, incl.cut, show.cases,
n.cut, use.letters, inf.test as they were duplicating the same arguments from
function truthTable(), to which they are sent anyways; in addition, arguments
relation and explain did not have any real use
o Changed: crisp calibration now include the thresholds values in the upper
groups, to maintain backwards compatibility and be consistent with the
default function findInterval() which now crisp calibration employs. Users
who actually want to _exclude_ the thresholds from the upper groups, should
simply set them to an upper value (thanks to Yan Turgeon for the report).
o Changed: function deMorgan() renamed to negate()
o Changed: function eqmcc() renamed to minimize()
o Fixed: minor bug in the web GUI, the data editor did not display the
correct cell value on double click, when scrolling horizontally
o Fixed: bug in function minimize(), with all directional expectations as
don't cares it should return the complex solution
(thanks to Eva Thomann for the report)
Version 2.6
o Improved: function superSubset() is now many orders of magnitude faster
o New: argument "depth" added to functions superSubset() and allExpressions()
o New: functions createMatrix() and allExpressions() are now able to produce
all possible combinations up to certain length of conjunctions via "depth"
o Fixed a couple of minor bugs in the web interface
o New: arguments "ron.cut" and "pri.cut" added to function superSubset()
(thanks to Carsten Schneider for the suggestion)
o New: component "minmat" to the truth table object
(thanks to Markus Siewert for the suggestion)
o Changed: function plot1() renamed to Xplot()
o Fixed: a couple of minor bugs in the user interface behavior
o Fixed: a couple of minor bugs in functions translate() and deMorgan()
when feeding multivalue conditions with multiple levels
Version 2.5
o Packages QCA and QCAGUI merged back into a single package QCA.
o New in GUI: redesigned dialog for the calibrate menu, which now contains
a thresholds setter area for both crisp and fuzzy calibrations.
o New: function sop() to transform any expression into a simpler (minimal)
equivalent sum of products
o New: the truth table object now contains an additional component with the
matrix between cases and truth table rows
o New: function plot1() to examine the distribution of values for a single
causal condition (typically for calibration purposes)
o Improved: SOP expressions now allow the negation of multivalue conditions,
as well as unions of multiple levels for the same causal condition.
o Improved: deMorgan() now allows negating multivalue expression, providing
a new argument called "noflevels"
o Improved: treatment of commands in the GUI console
o Improved: for boolean expressions only (not multivalue), the function
translate() now allows duplicated set names in the same product
o Removed: argument "include" from function calibrate(): it only applied to
the crisp calibration, and did not have any practical advantage, users could
simply move the threshold one more (lower or upper) value.
o Removed: argument "add" from function pof(), both PRI and RoN are now
formally included in the output.
o Removed: arguments "prod.split" and "complete" from function deMorgan().
o Changed: argument "dep" in function retention(), to "dependent".
o Changed: argument "row.no" in function findSubsets(), to "input".
o Changed: argument "maximum" in function findSubsets(), to "stop".
o Changed: argument "input.combs" in function findSupersets(), to "input".
o Changed: argument "type" in function calibrate() is now "fuzzy" by default
o Fixed: a situation when all directional expectations are "don't cares", and
the intermediate solutions should be identical to the parsimonious solutions
(thanks to Carsten Schneider for reporting)
o Fixed: a bug giving an error for a non-calibrated original dataset, when the
minimized object was already produced by truthTable()
(thanks to Nena Oana and Carsten Schneider for the report)
Version 2.4
o Improved: major rewrite of the GUI code to allow working with multiple
datasets / objects in the same time
o New: minimization in the user interface now allow input from both data and
truth table objects
o Changed: removed argument size from function XYplot()
(due to compatibility with the web user interface)
o Fixed: examples sections to allow building the sources for Mavericks
o Fixed: server code to avoid duplicating commands in the GUI console
o Fixed: plot window in the GUI did not reopen after close
o Fixed: minor bug in the recode() function, affecting numeric conditions when
using a range from lowest to a number, below the actual minimum
Version 2.3
o New: the user interface gained the possibility to plot graphics from the
command line
o New: plots produced in the command line can be saved in various formats
o New: the menu dialogs and the command line in the interface work with the
same objects in the workspace
o New: function findRows(), to find patterns of rows in a truth table, usually
to be served as the "omit" argument in the function eqmcc()
(thanks to Eva Thomann for the suggestion)
o New: argument "clabels" to function XYplot() to add case labels to the plot
o Changed: function compute() now returns the scores for the entire expression
while for individual paths it has gained an argument called "separate"
o Changed: deprecated functions is.tt(x), is.qca(x), is.sS(x), is.deMorgan(x)
and is.pof(x), in favor of the more consistent, for example, is(x, "tt")
o Changed: reverted value of argument "hclustm" to "complete", and default
value of argument "distm" to "euclidean", in the function findTh()
o Improved: for argument sort.by in function truthTable(), it is now possible
to use "+" and "-" to signal "increasing" or "decreasing"
o Improved: splitting strings now possible using "+" and "-" to signal
"increasing" or "decreasing", when using sort.by in function truthTable()
o Fixed: an outstanding bug assigning cases from truth table rows to solution,
when subsetting based on the frequency threshold (thanks to Nena Oana and
Carsten Schneider for the report)
o Fixed: diagonal and middle guides in XYplot were drawing outside of the plot
region when using multiple plots in the same graphics device
o Fixed: bug in the GUI version of calibrate(), when switching from fuzzy to
crisp it preserved the names of the thresholds and triggered an error
o Fixed: bug in assigning rownames to a matrix, when selecting rows from the
truth table based on the frequency cut-off (thanks to Ben Gibson for the report)
Version 2.2
o New: first attempt of an R console in the web GUI
o New: function XYplot()
o New: functions fuzzyand() and fuzzyor() at user level
o Changed: entire documentation of the package is now rewritten and more clear
o Changed: all core, inner functions moved to package QCA
o Changed: function demoChart() renamed to makeChart()
o Changed: arguments "incl.cut1" and "incl.cut0" replaced by "incl.cut"
(but still backwards compatible), for eqmcc(), pof() and truthTable()
o Changed: binomial inference testing requires a significantly greater value for
both thresholds "incl.cut1" and "incl.cut0" to code the outcome as "1" or "C",
in function truthTable()
o Changed: binomial inference testing for function pof(), both one-tailed tests
now have the alternative hypothesis "greater".
o Changed: default value of argument "hclustm" to "ward.D2", and default
value of argument "distm" to "canberra", in the function findTh()
o Changed: argument "groups" with argument "n" for the function findTh()
o Changed: arguments "p" and "q" to "below" and "above" in function calibrate()
o Removed: argument "logical" from the function createMatrix()
o Improved: the user interface for the calibrate() function
o Improved: function pof() is now even more flexible, see examples
o Improved: function truthTable() now faster for very large data
o Fixed: correct treatment of the "PRI" column, if one of the causal conditions
is also named "PRI" (for example the Porter data)
Version 2.1
o New: function translate() for an DNF expression
o New: function compute() for an DNF expression, using translate()
(thanks to Jirka Lewandowski for suggesting both functions)
o New: function retention() for calculating the retention probability of a csQCA
solution, in different perturbation scenarios
o New: the GUI is now able to draw Venn diagrams up to 7 sets
o New: better shapes of the Venn diagrams for 4 and 5 sets (especially for
small intersections)
o Fixed: minor bugs at the web interface
o Fixed: minor bugs at the printing functions
o Changed: function intersection() now uses translate(), which makes the
argument "prod.split" obsolete, and argument "conditions" renamed to "snames"
o Changed: argument "neg.out" in pof() and eqmcc() is now deprecated, but still
backwards compatible. Negation of the outcome is detected by a "~" sign
in front of the outcome name
o Changed: complete rewrite of the factorize() function, now orders of magnitude
faster for very complex inputs and producing more accurate results; it also
automatically detects the product split, if a "*"
o Improved: deMorgan() can also return products of sums
o Improved: pof() function now accepts a DNF expression, in addition to current
functionality
Version 2.0
o Temporary split of the code between packages QCA and QCAGUI
o New: first attempt of a Javascript based, graphical user interface
o New: introduced function intersection()
o New: introduced function recode()
o New: introduced function export(), to create a column for the row names
o Improved: a couple of relevant error messages, especially useful for the web
context
o Improved: the truthTable() function always returns a complete truth table
but printed on the screen only if complete = TRUE
o Improved: similarly, the truth table object always contains the cases, which
are printed on the screen only if show.cases = TRUE
o Improved: decreasing argument in the truthTable() function can be a vector,
to allow for complete flexibility when sorting by multiple arguments
o Improved: argument thresholds in the calibrate() function now has names
o Improved: functions pof() and superSubset() now accept additional measures,
a first one being "ron" (for relevance of necessity), using the argument "add"
o Improved: function pof() now recognizes "1 - " to automatically negate the input
o Changed: component "opts" from the output of eqmcc() is now called "options"
o Changed: argument "logistic" in the calibrate() function is now TRUE by default,
for compatibility with fsQCA
o Changed: removed formal argument "decreasing" in the truthTable() function
(it is still recognised as an unformal argument, for backwards compatibility)
o Changed: arguments from truthTable() and eqmcc() which needed vectors of
values now accept a single character containing those values, separated
by commas
o Fixed: deMorgan() now able to negate disjunctions of single conditions
(e.g. "A + B")
o Fixed: intermediate solutions now properly identified in some particular, rare
circumstances (thanks to Maarten Vink)
Version 1.1-3
o New: number of PIs processable by solveChart() now limited (maximum integer
number that can be treated by the machine)
o New: three data sets added (d.AS, d.HMN, d.Kil)
o Improved: documentation for various functions
o Changed: argument "all.sol" in function eqmcc() renamed to "min.dis"
o Changed: argument "inf.test" in eqmcc() placed before "use.tilde"
o Renamed: in output from various functions prefix "S" (solution) renamed to
"M" (model)
o Fixed: argument "neg.out" with curly bracket notation in argument "outcome"
to function eqmcc() not operative
o Fixed: matrix dimensions dropped in function getSolution()
o Fixed: case names assigned to incorrect PIs in function
demoChart() under some conditions (thanks to M. Vink)
o Fixed: very large pof() objects did not generate an error on print
o Fixed: more informative error message when the truth table did not contain any
explained values (thanks to M. Zulianello)
Version 1.1-2
o Fixed: missing data triggered an error message in function truthTable()
o Fixed: calibration of negative end-point concepts with logistic function
produced incorrect set membership scores (thanks to C. Schneider)
Version 1.1-1
o Improved: speed for resolution of PI chart
o Fixed: an error message was generated when fuzzy sets were not normalized
o Fixed: prime implicants were joined together for single-column PI charts
by function solveChart() instead of being identified as alternative solutions
o Fixed: PRI column did not print in truth tables when argument PRI = TRUE
Version 1.1-0
o New: functionality for analyzing path models with function eqmcc()
o New: function deMorgan() computes negations of set expressions
o New: functionality for multivalent outcome sets
o New: inference-statistical tests for truth table configurations
(currently only csQCA and mvQCA)
o New: additional values "sufnec" and "necsuf" to argument "relation" in function
superSubset()
o New: argument "row.dom" in function solveChart()
o Improved: documentation for function eqmcc()
o Improved: output structure of eqmcc() with respect to intermediate solutions
o Changed: default value to argument "row.dom" of function eqmcc() from TRUE
to FALSE
o Changed: argument "row.dom" works independently of argument "all.sol" in
function eqmcc()
o Renamed: arguments "rowdom" and "direxp" in function eqmcc() to "row.dom"
and "dir.exp"
o Renamed: values "necessity" (now "nec") and "sufficiency" (now "suf") to
argument "relation" in function superSubset()
o Dropped: function readTosmana()
o Fixed: when number of solutions was large, printing was not optimal
o Fixed: printing of column names (thanks to A. Sevilla)
o Fixed: when providing directional expectations, empty "SA" components caused
error
o Fixed: sometimes redundant solutions were produced when "all.sol = TRUE"
Version 1.0-5
o Improved: version of C code for removing redundant PIs
o Improved: function pof() now also accepts outcome vector as well as a
name of the outcome set
o Improved: multiple solutions from function factorize() now numbered
o Improved: C code in view of upcoming R 3.0.0 version
o Changed: functions superSubset() and pof() now accept "suf" (along with
"sufficiency") and "nec" ("necessity")
Version 1.0-4
o New: argument "all.sol" for functions eqmcc() and solveChart()
(thanks to Michael Baumgartner for the suggestion)
o Improved: speed for functions superSubset() and truthTable()
o Improved: function truthTable() now also calculates number of cases in
remainder configurations
o Renamed: arguments in function factorize()
o Fixed: in function eqmcc() condition names in uppercase letters were not
treated correctly (thanks to Michael Baumgartner for the report)
o Fixed: in function truthTable() case names were not assigned correctly
under some circumstances (thanks to M. Gasser)
Version 1.0-3
o Fixed: various printing issues
Version 1.0-2
o New: argument "neg.out" in functions truthTable() and eqmcc()
o Fixed: PRI scores for arguments "relation = "necessity"" and "neg.out = TRUE"
in function superSubset()
Version 1.0-1
o Fixed: printing of solutions with only one term was prevented
Version 1.0-0
o New: functions eqmcc() and truthTable() now able to process fuzzy sets
o New: function pof() computes parameters of fit for variety of input options
o New: function findTh() finds thresholds for crisp sets calibrations
o New: function calibrate() recodes base variables into crisp and fuzzy sets
o New: function superSubset() for analysing necessity and sufficiency relations
o New: logical argument "rowdom" in function eqmcc() controls application of
row dominance principle
o New: inclusion ("incl") and proportional reduction in inconsistency scores
("PRI")
o New: truth tables can now be sorted using argument "sort.by"
o New: function truthTable() now returns raw truth table with numerical columns
o New: printing methods for PI charts (objects of class "pic"), parameters of fit
(class "pof"), results from function superSubset() (class "ss"), results from
function allExpressions() (class "aE") and results from factorization (class
"fctr")
o Improved: function eqmcc() automatically determines conditions and outcome
when truth table object passed (object of class "tt")
o Changed: functions prettyTable() and createString() now internalized
o Renamed: function findPrimes() to findSubsets()
o Dropped: function qmcc() (fully replaced by function eqmcc())
o Dropped: truth table columns "freq0" and "freq1"
Version 0.6-5
o Improved: functions qmcc() and eqmcc() now also return (invisibly) PI chart
and initial configurations
Version 0.6-4
o Improved: functions qmcc() and eqmcc() now return invisible list with
following components: minimized PIs, number of k PIs necessary to cover
all initial causal combinations in PI chart, final solution(s)
o Changed: redundant code from function verify.data() removed
o Changed: error message on failure to solve PI chart (thanks to J. Jarvi)
Version 0.6-3
o Fixed: in function factorize(); matrix dropped dimensions
Version 0.6-2
o Improved: documentation and citations
o Improved: function findPrimes(); empty prime implicants eliminated (first
line in implicant matrix)
o Changed: function factorize(); argument "use.letters" replaced by "splitmethod"
o Fixed: in function findSubsets(); incorrect calculations for the case of
multi-value data
Version 0.6-1
o Improved: functions findPrimes() and findSubsets(); argument "noflevels"
must now be specified
o Changed: argument "uplow" in function eqmcc() now TRUE by default
o Fixed: incorrect multi-value minimization in function eqmcc() when remainders
excluded (thanks to D. Bol)
Version 0.6-0
o New: function eqmcc() now accepts multivalent data
o New: argument "uplow" in function eqmcc() for printing solutions in
upper/lower case letters
o New: artifical dataset "MV" to test multivalent data
o Improved: function findPrimes() to accommodate multivalent data
o Improved: function createString() to accommodate multivalent data
o Improved: function writePrimeimp() to accommodate multivalent data
o Improved: function prettyString() using native function strwrap()
o Improved: functions qmcc() and eqmcc() using new function prettyString()
o Changed: function demoChart(); argument "use.letters" replaced by
"splitmethod"
o Changed: function prettyString() now internalized
Version 0.5-4
o Dropped: error message when there is only one configuration to explain
(thanks to B. Monroe)
Version 0.5-3
o New: Function truthTable() now allows multivalent data in conditions
o Fixed: in function truthTable(); columns incorrectly arranged with respect
to outcome values
Version 0.5-2
o Fixed: function createMatrix() regarding multivalent data
o Fixed: function solveChart(); error when PI chart was too large
Version 0.5-1
o Improved: function descriptions
o Changed: functions is.tt() and print.tt() now accessible to user
o Fixed: function rowDominance2(); matrix dropped dimensions
o Fixed: function eqmcc() for complete truth tables (thanks to R. Huang)
Version 0.5-0
o Function truthTable() now returns object of class "tt"
o New: internal functions is.tt() and print.tt()
o Improved: functions qmcc() and eqmcc() now accept truth tables or raw data
Version 0.4-9
o Improved: function factorize(); previous version did not detect some
combinations
o Changed: functions findPrimes() and findSubsets() now at user level
Version 0.4-8
o New: internal function findPrimes()
Version 0.4-7
o New: internal function findSubsets()
o Improved: function eqmcc()
o Improved: function truthTable()
o Fixed: function rowDominance2()
Version 0.4-6
o Improved: eqmcc() now at least twice as fast
o Changed: function rowDominance2()
o Renamed: function shortqca() to eqmcc()
Version 0.4-5
o New: experimental function shortqca(); many times faster than qmcc() for
large number of conditions (> 11) and very low memory consumption;
works with 16 or 17 conditions
Version 0.4-3
o Fixed: in function qmcc() matrix dropped dimensions upon subsetting
Version 0.4-2
o New: argument "use.letters" to function demoChart()
o Fixed: in function qmcc() data was subset incorrectly
o Fixed: in function qmcc() involving argument "show.cases"
o Fixed: function verify.truthTable()
Version 0.4-1
o New: namespace for "QCA" package
o New: argument "diffmat" to function qmcc(); users can now choose to
generate difference matrix or not: speed or low memory consumption
o Improved: function base3rows() now faster
o Improved: function createMatrix() now faster for same number of values in
each condition
Version 0.4-0
o New: function base3rows()
o Improved: function qmcc(); lower memory consumption;
now works with up to 15 conditions in 1GB RAM
o Fixed: function writeSolution()
Version 0.3-5
o Improved: function qmcc(); does no longer possess argument "tt";
now works with up to 13 conditions
o Changed: function truthTable()
Version 0.3-1
o New: function rowDominance() facilitates solving of large prime implicant
charts
Version 0.3-0
o New: function getRow() returns combination of levels for specific row numbers
o New: function createMatrix() now accepts multi-value sets
o Improved: function qmcc() now 20 times faster
o Changed: function createChart() redesigned and internalized
o Renamed: function createChart() to demoChart()
o Fixed: various problems caused by changes in version 0.2-6
Version 0.2-6
o New: "QCA" package does not depend on package "cluster" any more
Version 0.2-5
o New: "QCA" package no longer depends on package "combinat"
o New: function sortMatrix() in internal functions
o New: argument verifications now part of internal functions
o New: function readTosmana() for reading Tosmana type XML data files
o Improved: documentation for many functions
o Changed: function prettyTable()
o Changed: minor parts in function truthTable()
Version 0.2-2
o New: internal functions; function qmcc() now less cluttered
o New: user-level function solveChart(); pulled out of function qmcc()
o Improved: allExpressions() now faster
o Renamed: function allExpr() now allExpressions()
Version 0.2-1
o New: function createMatrix() creates base matrix for truth tables
o New: function base3rows()
o Fixed: in function writeSolution()
Version 0.2-0
o New: function factorize() finds all common factors in Boolean products