Arithmetic for ideals uses the standard symbols. Below are examples of the basic arithmetic functions for ideal.

For more information about quotient rings see quotient rings.

For more information see Ideal + Ideal, Ideal * Ideal, and Ideal ^ ZZ.

i1 : R = ZZ/101[a..d]/(b*c-a*d,c^2-b*d,b^2-a*c); |

i2 : I = ideal (a*b-c,d^3); o2 : Ideal of R |

i3 : J = ideal (a^3,b*c-d); o3 : Ideal of R |

i4 : I+J 3 3 o4 = ideal (a*b - c, d , a , a*d - d) o4 : Ideal of R |

i5 : I*J 4 3 2 3 3 4 4 o5 = ideal (a b - a c, a b*d - a*b*d - a*c*d + c*d, a d , a*d - d ) o5 : Ideal of R |

i6 : I^2 3 2 3 3 6 o6 = ideal (a c - 2a d + b*d, a*b*d - c*d , d ) o6 : Ideal of R |