def _parseGroup(tup):
def Error(index, message):
return Left("system #" + str(index) + ": " + message)
(lines, index) = tup
one = lines[0].split()
two = lines[1].split()
line3 = lines[2].strip()
line4 = lines[3].strip()
if len(one) == 0 or len(two) == 0:
return Error(index, "lines 1 or 2 empty")
if not forall(one + two, isFraction):
return Error(index, "at least one token on line #1 or #2 is not a valid fractional number")
n = len(one)
np = len(two)
if np % n != 0:
return Error(index, "number of tokens on line #2 is not multiple of number of tokens on #1")
p = np / n
if line3 != noSolutionSymbol and line4 != noSolutionSymbol:
three = lines[2].split()
if not forall(three, isFraction):
return Error(index, "at least one token on line #3 is not a valid fractional number")
if len(three) != p:
return Error(index, "line #3 is the wrong size for being a particular solution")
pSol = map(fractionMaker, three)
if line4 == nullVecSpaceSymbol:
kerBase = []
else:
four = line4.split()
if not forall(four, isFraction):
return Error(index, "at least one token on line #4 is not a valid fractional number")
pq = len(four)
if pq % p != 0:
return Error(index, "number of tokens on line #4 is not multiple of number of token on #3")
kerBase = grouped(map(fractionMaker, four), p)
maybeSolution = Just((kerBase, pSol))
elif line3 == noSolutionSymbol and line4 == noSolutionSymbol:
maybeSolution = Nothing
else:
return Error(index, "lines #3 and #4 are invalid, somehow")
rightSide = map(fractionMaker, one)
leftSide = matrixFromList(map(fractionMaker, two), n, p)
system = (leftSide, rightSide)
out = (system, maybeSolution)
return Right(out)
def isValidLine(line):
if len(line) <= 1:
error(isValidLine,
"input list is too short to be part of a `System n`")
leftSide = line[:-1]
rightSide = line[-1]
if forall(leftSide, isZero):
return isZero(rightSide)
else:
return True
def _parseGroup(tup):
def Error(index, message):
return Left("system #" + str(index) + ": " + message)
(group, index) = tup
one = group[0].split()
two = group[1].split()
three = group[2].split()
four = group[3].split()
if len(one) != 1 or len(two) != 1 or len(three) == 0 or len(four) == 0:
return Error(index, "lines 1 or 2 too long, or lines 3 or 4 empty")
if not isNat(one[0]) or not isNat(two[0]):
return Error(index,
"line 1 or 2 does not contain a natural integer")
lineNumber = int(one[0])
varNumber = int(two[0])
if lineNumber == 0 or varNumber == 0:
return Error(
index,
"line 1 or 2 does not contain a non-zero natural integer")
if len(three) != lineNumber * varNumber or len(four) != lineNumber:
return Error(
index,
"length of line 3 or 4 don't match values of lines 1 and 2")
if not forall(three + four, isFraction):
return Error(
index,
"at least one token on line 3 or 4 is not a valid fraction")
leftSideMatrix = matrixFromList(map(fractionMaker, three), lineNumber,
varNumber)
rightSideVector = map(fractionMaker, four)
out = (leftSideMatrix, rightSideVector)
return Right(out)
def keepPivotalLines(system):
if not forall(system.nonPivotalLines, isNullVector):
error(
keepPivotalLines, "somehow after successfully echelonizing, " +
"one non pivotal line is not full of zeroes")
return system.pivotalLines
def maybeSystem(pivotalLines, nonPivotalLines):
if forall(pivotalLines + nonPivotalLines, isValidLine):
return Maybe(value=System(pivotalLines, nonPivotalLines))
else:
return Nothing