Accounts receivable, net - Credit Quality Indicator and Age Analysis (Details) - USD ($) $ in Millions	Oct. 31, 2015	Jan. 31, 2015	Nov. 01, 2014
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 1,559.4	$ 1,666.0	$ 1,382.9
Valuation allowance	$ (122.2)	$ (113.1)	$ (102.6)
Gross	100.00%	100.00%	100.00%
Valuation allowance	7.80%	6.80%	7.40%
Performing Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	95.10%	96.20%	95.60%
Valuation allowance	3.10%	3.10%	3.10%
Performing Financing Receivable | Period One | 0 to 30 Days Aged Performing
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 1,212.2	$ 1,332.2	$ 1,087.9
Valuation allowance	(36.8)	(41.1)	(33.2)
Performing Financing Receivable | Period Two | 31 to 90 Days Aged Performing
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	271.2	271.1	233.8
Valuation allowance	$ (9.4)	$ (9.3)	$ (8.2)
Nonperforming Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	4.90%	3.80%	4.40%
Valuation allowance	100.00%	100.00%	100.00%
Nonperforming Financing Receivable | Period Two | More Than 90 Days Aged Non Performing
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 76.0	$ 62.7	$ 61.2
Valuation allowance	$ (76.0)	$ (62.7)	$ (61.2)