We propose and implement an algorithm to calculate the norm and reduced density matrices (RDMs) of the antisymmetrized geminal power of any rank with polynomial cost. Our method scales quadratically per element of the RDMs. Numerical tests indicate that our method is very fast and capable of treating systems with a few thousand orbitals and hundreds of electrons reliably in double-precision. In addition, we present reconstruction formulas that allow one to decompose higher order RDMs in terms of linear combinations of lower order ones and geminal coefficients, thereby reducing the computational cost significantly.
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