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I want to transform the lower triangular polynomial matrix into weak popov form, when I use the command <.weak_popov_form> in sage, something strange happened.

I construct a 100*100 lower triangular polynomial matrix A and B, the degree of elements in A( or B) are bounded 50(or 80).

[MS03] pointed out that the reduction of polynomial matrix is related to the dimension of the matrix and the exponent of its elements.According to the complexity formula, the running time of input A should less than that of input B.

But when I use the algorithm to transform A,B into weak popov form, the opposite result was obtained, Time A = 700+ sec is greater than Time B = 500+ sec !!

I experimented with several groups of random polynomial matrices and got similar results. Is my question too stupid? I hope I made a mistake.

I want to transform the lower triangular polynomial matrix into weak popov form, when I use the command <.weak_popov_form> .weak_popov_form in sage, something strange happened.

I construct a 100*100 lower triangular polynomial matrix A and B, the degree of elements in A( or B) are bounded 50(or 80).

[MS03] pointed out that the reduction of polynomial matrix is related to the dimension of the matrix and the exponent of its elements.According to the complexity formula, the running time of input A should less than that of input B.

But when I use the algorithm to transform A,B into weak popov form, the opposite result was obtained, Time A = 700+ sec is greater than Time B = 500+ sec !!

I experimented with several groups of random polynomial matrices and got similar results. Is my question too stupid? I hope I made a mistake.