Documentation in rings does not tell the whole story

[sottile@…]

For version 4.2.0, the documentation declares that the possible prime characteristics are and "non-negative int_expression less or equal 2147483647".

The version 4.2.0 on my computer does not believe this. I am able to do some calculations in characteristic 1073741789 (=prime(2^{30)), but when I try to factorize a univariate polynomial in such a ring with the command: L= factorize(f,1);, I get the error message:}

? characteristic is too large(max is 2^{29) ? not implemented ? error occurred in or before STDIN line 50: L= factorize(f,1);}

-Frank Sottile

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Here is a session: sottile: Singular

SINGULAR /

A Computer Algebra System for Polynomial Computations / version 4.2.0

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by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Dec 2020

FB Mathematik der Universitaet, D-67653 Kaiserslautern \

ring r = 1073741789, (x), dp; poly f= (30+251*x)^{10; factorize(f,1);}

? characteristic is too large(max is 2^{29) ? not implemented ? error occurred in or before STDIN line 3: factorize(f,1);}

[hannes]

see Limitations (https://www.singular.uni-kl.de/Manual/4-2-0/sing_411.htm)

the characteristic of a prime field must be less than or equal to 2147483647 (2* *31) (the characteristic of a prime field in the factory routines must be less than 536870912 (2* *29)) (the characteristic of a prime field in the NTL routines must be less than NTL_SP_BOUND (2* *30) on 32bit machines - This is always the case since currently, only factory uses NTL.)

Thanks for the hint, I will add a pointer to this to the ring chapter.