Segment Information - Summary of Segment Information (Detail) - USD ($)	3 Months Ended		6 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2021	Mar. 31, 2020
Segment revenues:
Revenues	$ 331,361,000	$ 307,971,000	$ 643,775,000	$ 606,475,000
Segment operating expense	(230,162,000)	(232,245,000)	(447,855,000)	(478,867,000)
Operating income	101,199,000	75,726,000	195,920,000	127,608,000
Unallocated share-based compensation expense	(28,206,000)	(22,788,000)	(53,338,000)	(45,933,000)
Unallocated amortization expense	(945,000)	(1,202,000)	(1,882,000)	(2,998,000)
Unallocated gain on sale of product line assets	0	0	7,334,000	0
Unallocated restructuring and impairment charges	0	0	0	(3,104,000)
Unallocated interest expense	(9,943,000)	(11,254,000)	(19,584,000)	(21,022,000)
Unallocated other income, net	568,000	(2,008,000)	3,448,000	(2,227,000)
Income before income taxes	91,824,000	62,464,000	179,784,000	104,359,000
Depreciation expense	5,224,000	5,960,000	10,809,000	11,636,000
Operating Segments
Segment revenues:
Segment operating expense	(201,011,000)	(208,255,000)	(399,969,000)	(426,832,000)
Operating income	130,350,000	99,716,000	243,806,000	179,643,000
Unallocated Corporate Expenses
Segment revenues:
Segment operating expense	(33,392,000)	(33,785,000)	(63,645,000)	(67,995,000)
Operating income	(33,392,000)	(33,785,000)	(63,645,000)	(67,995,000)
Depreciation expense	45,000	108,000	78,000	333,000
Applications
Segment revenues:
Revenues	129,514,000	140,279,000	264,875,000	292,457,000
Applications | Operating Segments
Segment revenues:
Revenues	129,514,000	140,279,000	264,875,000	292,457,000
Segment operating expense	(102,142,000)	(111,456,000)	(202,001,000)	(227,466,000)
Operating income	27,372,000	28,823,000	62,874,000	64,991,000
Depreciation expense	4,110,000	4,553,000	8,484,000	8,902,000
Scores
Segment revenues:
Revenues	168,719,000	129,148,000	313,370,000	244,286,000
Scores | Operating Segments
Segment revenues:
Revenues	168,719,000	129,148,000	313,370,000	244,286,000
Segment operating expense	(22,177,000)	(15,660,000)	(43,803,000)	(33,372,000)
Operating income	146,542,000	113,488,000	269,567,000	210,914,000
Depreciation expense	167,000	141,000	361,000	257,000
Decision Management Software
Segment revenues:
Revenues	33,128,000	38,544,000	65,530,000	69,732,000
Decision Management Software | Operating Segments
Segment revenues:
Revenues	33,128,000	38,544,000	65,530,000	69,732,000
Segment operating expense	(43,300,000)	(47,354,000)	(90,520,000)	(97,999,000)
Operating income	(10,172,000)	(8,810,000)	(24,990,000)	(28,267,000)
Depreciation expense	902,000	1,158,000	1,886,000	2,144,000
Transactional and Maintenance
Segment revenues:
Revenues	280,919,000	240,702,000	533,069,000	461,076,000
Transactional and Maintenance | Applications | Operating Segments
Segment revenues:
Revenues	96,687,000	97,789,000	194,418,000	196,626,000
Transactional and Maintenance | Scores | Operating Segments
Segment revenues:
Revenues	167,212,000	127,610,000	305,802,000	235,056,000
Transactional and Maintenance | Decision Management Software | Operating Segments
Segment revenues:
Revenues	17,020,000	15,303,000	32,849,000	29,394,000
Technology Service
Segment revenues:
Revenues	37,794,000	47,905,000	79,219,000	91,930,000
Technology Service | Applications | Operating Segments
Segment revenues:
Revenues	27,627,000	35,134,000	58,232,000	69,157,000
Technology Service | Scores | Operating Segments
Segment revenues:
Revenues	703,000	819,000	820,000	1,083,000
Technology Service | Decision Management Software | Operating Segments
Segment revenues:
Revenues	9,464,000	11,952,000	20,167,000	21,690,000
License
Segment revenues:
Revenues	12,648,000	19,364,000	31,487,000	53,469,000
License | Applications | Operating Segments
Segment revenues:
Revenues	5,200,000	7,356,000	12,225,000	26,674,000
License | Scores | Operating Segments
Segment revenues:
Revenues	804,000	719,000	6,748,000	8,147,000
License | Decision Management Software | Operating Segments
Segment revenues:
Revenues	$ 6,644,000	$ 11,289,000	$ 12,514,000	$ 18,648,000