bug in rawSelectByDegrees depending on internal degrees

[mahrud]

I have two multigraded free modules M = source mingens I and N = S^(- degrees M) of rank 86 with the same degrees (though the degree group has torsion) that exhibit bizarre behavior:

First, asking for their degrees takes very long:

ii110 : elapsedTime degrees N;
 -- .757907s elapsed

ii111 : elapsedTime degrees M;
 -- 1.68677s elapsed

Second, rawSelectByDegrees seems to behave differently for them:

ii104 : rawSelectByDegrees(raw M, d, d)

oo104 = {0}

ii105 : rawSelectByDegrees(raw N, d, d)

oo105 = {0, 3, 5, 12, 14, 42, 71, 73, 80, 83, 85}

I presume this is attributable to the internal degree object chosen for them, but I don't understand why:

oo102 = free(rank 86 degrees = {T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6})
        free(rank 86 degrees = {T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^4T_1T_2^3T_3^4T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^3T_2^3T_3^4T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^2T_2^6T_3^8T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1T_2^6T_3^8T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^6T_2^6T_3^8T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1^3T_2^4T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1^3T_2^4T_3T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1^4T_2^7T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^4T_1^4T_2^7T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^4T_1^3T_2^7T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^3T_1^3T_2^7T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^2T_1^6T_2^8T_3^2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0T_1^6T_2^8T_3^2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_1^6T_2^8T_3^2T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1^3T_2^5T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^4T_1^3T_2^5T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^4T_1^2T_2^5T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1^3T_2^8T_3^9T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^4T_1^5T_2^9T_3^6T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1^2T_2^3T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^3T_2^6T_3^9T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^2T_2^6T_3^9T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1^2T_2^6T_3^9T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1^5T_2^7T_3^6T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1^4T_2^7T_3^6T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^4T_1^4T_2^7T_3^6T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^5T_2^10T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1^5T_2^10T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1^4T_2^10T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1T_2T_3^5T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^9T_1^2T_2^4T_3^9T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^2T_2^4T_3^9T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1T_2^4T_3^9T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^3T_2^7T_3^13T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^11T_1^2T_2^7T_3^13T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^6T_1^4T_2^5T_3^6T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1^4T_2^5T_3^6T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1^3T_2^5T_3^6T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^9T_1^5T_2^8T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^5T_2^8T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^9T_1^4T_2^8T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^4T_2^8T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1^4T_2^8T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^3T_2^8T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1^3T_2^8T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^11T_1^5T_2^11T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^11T_1^4T_2^11T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^10T_1^4T_2^11T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^10T_1^3T_2^11T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^6T_1^6T_2^9T_3^7T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^5T_1^6T_2^9T_3^7T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^7T_2^12T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1^7T_2^12T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^6T_2^12T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^7T_1^6T_2^12T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^9T_1^4T_2^6T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^9T_1^3T_2^6T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^3T_2^6T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^4T_2^9T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^11T_1^4T_2^9T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^11T_1^3T_2^9T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^9T_1^6T_2^10T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^6T_2^10T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^8T_1^5T_2^10T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^11T_1^6T_2^13T_3^15T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^3T_2^7T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^9T_1^5T_2^8T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^6T_2^11T_3^15T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^5T_2^11T_3^15T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^11T_1^5T_2^11T_3^15T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^10T_1^2T_2^2T_3^10T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^13T_1^3T_2^5T_3^14T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^16T_1^4T_2^8T_3^18T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^10T_1^4T_2^6T_3^11T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^13T_1^5T_2^9T_3^15T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^5T_2^9T_3^15T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^4T_2^9T_3^15T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^15T_1^6T_2^12T_3^19T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^15T_1^5T_2^12T_3^19T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^10T_1^6T_2^10T_3^12T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^7T_2^13T_3^16T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^12T_1^6T_2^13T_3^16T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^14T_1^8T_2^16T_3^20T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^14T_1^7T_2^16T_3^20T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6, T_0^14T_1^6T_2^16T_3^20T_4^6T_5^6T_8^2T_10^6T_11^2T_12^2T_13^4T_18^6T_19^6T_20^6})

The order of their degrees is the same, so why are they represented differently in the engine? Presumably this has something to do with the ideal, in which case this seems to be a bug in rawSelectByDegrees.

cc: @mikestillman any ideas?

[mahrud]

I think this is related to torsion degrees, but I can't tell what is going wrong. Here is a minimal example:

debug Core
R = QQ[x, y, Degrees => map(ZZ^1 ++ ZZ^1/ideal 3, , id_(ZZ^2))]
C = res ((ideal vars R)^3);
degrees source C.dd_1 -- {{3, 0}, {2, 1}, {1, -1}, {0, 0}}
positions(degrees source C.dd_1, d -> d == {0,0})   -- gives {3}
rawSelectByDegrees(raw source C.dd_1, {0,0}, {0,0}) -- gives {}

Though this doesn't explain why degrees N and degrees M take so long in the example above.

Related: #1925

[mikestillman]

@mahrud Do you have a full example with the slowness you mention appearing?

[mahrud]

Sure, here it is:

debug needsPackage "NormalToricVarieties"
P = convexHull matrix transpose {
    {1,1,1,0,0,0}, {0,1,1,0,0,1},
    {1,1,0,1,0,0}, {0,1,0,1,1,0},
    {1,0,1,0,1,0}, {0,1,0,0,1,1},
    {1,0,0,1,0,1}, {0,0,1,1,1,0},
    {1,0,0,0,1,1}, {0,0,1,1,0,1}}
N = ZZ^5
P = affineImage(id_N | transpose matrix {{-1,-1,-1,-1,-1}}, P)
X' = normalToricVariety P
X = makeSimplicial X'
assert isComplete X -- if this fails, run the line above again

I = ideal X;
M = source mingens I;
elapsedTime degrees M; -- ~3s
N = (ring M)^(-degrees M);
elapsedTime degrees N; -- ~3s
elapsedTime degrees N; -- ~.00001s
M  == N
M === N -- fails

debug Core
d = first degrees M
rawSelectByDegrees(raw M, d, d)
rawSelectByDegrees(raw N, d, d)

It must have something to do with torsion degrees, but I can't figure out what.