Singular

D.2.6.1 modular

Usage:

modular(command, arguments[, primeTest, deleteUnluckyPrimes, pTest, finalTest, pmax), command string, arguments list, primeTest proc, deleteUnluckyPrimes proc, pTest proc, finalTest proc, pmax int

Return:

the result of command applied to arguments, computed using modular methods.

Note:

For the general algorithm and the role of the optional arguments primeTest, deleteUnluckyPrimes, pTest, and finalTest, see modStd and the reference given in modular_lib. The default for these arguments is that all tests succeed and that all primes are assumed to be lucky.
The type of the result when command is applied to arguments must be either bigint, ideal, module, or matrix.
The optional argument pmax is an upper bound for the prime numbers to be used for the modular computations. The default is 2147483647 (largest prime which can be represented as an int in Singular), or 536870909 (largest prime below 2^29} for baserings with parameters.

LIB "modular.lib";
ring R = 0, (x,y), dp;
ideal I = x9y2+x10, x2y7-y8;
modular("std", list(I));
==> _[1]=x2y7-y8
==> _[2]=x9y2+x10
==> _[3]=x12y+xy11
==> _[4]=x13-xy12
==> _[5]=y14+xy12
==> _[6]=xy13+y12