Functions to work with the ODE structure

_reduce_mod_p(f, p)

Reduces a polynomial/rational function over Q modulo p

power_series_solution(ode, param_values, initial_conditions, input_values, prec)

Input:

• ode - an ode to solve
• param_values - parameter values, must be a dictionary mapping parameter to a value
• initial_conditions - initial conditions of ode, must be a dictionary mapping state variable to a value
• input_values - power series for the inputs presented as a dictionary variable => list of coefficients
• prec - the precision of solutions

Output:

• computes a power series solution with precision prec presented as a dictionary variable => corresponding coordinate of the solution

reduce_ode_mod_p(ode, p)

Input: ode is an ODE over QQ, p is a prime number Output: the reduction mod p, throws an exception if p divides one of the denominators

rename_variables(ode, transform)

Input: ode and a map from the old names to the new names Output: variables and parameters are renamed according to the correspondce given in the transform; if a variable is not given any new name, it keeps the name it had.

set_parameter_values(ode, param_values)

Input:

• ode - an ODE as above
• param_values - values for (possibly, some of) the parameters as dictionary parameter => value

Output:

• new ode with the parameters in param_values plugged with the given numbers

find_submodels(ode)

The function calculates and returns all valid submodels given a system of ODEs.

Input:

• ode - an ODEs system to be studied

Output:

• A list of submodels represented as ode objects

Example:

>ode = @ODEmodel(x1'(t) = x1(t)^2, 
                 x2'(t) = x1(t) * x2(t), 
                 y1(t) = x1(t), 
                 y2(t) = x2(t))
>find_submodels(ode)
    ODE{QQMPolyRingElem}[
        
        x1'(t) = a(t)*x2(t)^2 + x1(t)
        y1(t) = x1(t)
    ]