Let's see the actual form of the consistent system sys[1] after its integrability conditions are taken into account
Construct an inconsistent system departing from sys[1], by multiplying any two of its equations (both are equal to zero) and equating the result to 1
When the system is inconsistent and the option outputthesystem` is received, ConsistencyTest returns NULL and a related warning message is displayed
Warning: System is inconsistent
| |
An example involving mathematical functions (exp)
The output with three lists, typical of dpolyform, showing the consistent form of sys[3], involves an auxiliary function _F1 to represent in differential polynomial form the system originally containing exp
The output typical of casesplit for the same system does not contain auxiliary functions; to obtain it use the optional argument no_Fn
To compute a form of the system which does not involve auxiliary functions _Fn and also is entirely differential polynomial, so it does not involve mathematical functions, use dpolyform
Note however that, depending on the example, the elimination of the auxiliary functions as in the output above may be an expensive computational process.